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ERROR: type should be string, got "https://doi.org/10.5194/acp-2021-147\nPreprint. Discussion started: 7 April 2021\nc⃝Author(s) 2021. CC BY 4.0 License. Roles of the Inner Eyewall Structure in the Secondary Eyewall Formation of Simulated \n1 \nTropical Cyclones \n2 \nNannan Qin1,2, Liguang Wu1,4, Qingyuan Liu3 \n3 \n1Department of Atmospheric and Oceanic Sciences and Institute of Atmospheric Sciences, Fudan \n4 \nUniversity, Shanghai, 200438, China \n5 \n2State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, \n6 \nBeijing, 100081, China \n7 \n3Nanjing Joint Institute for Atmospheric Sciences, Nanjing, China \n8 \n4Innovation Center of Ocean and Atmosphere System, Zhuhai Fudan Innovation Research \n9 \nInstitute，Zhuhai, 518057, China \n10 \n \n13 \n \n14 \n \n15 \n \n16 \n \n17 \nCorrespondence to: Dr. Liguang Wu (liguangwu@fudan.edu.cn) \n18 \n \n19 \n \n20 \n11 \n \n12 Roles of the Inner Eyewall Structure in the Secondary Eyewall Formation of Simulated \n1 \nTropical Cyclones \n2 \nNannan Qin1,2, Liguang Wu1,4, Qingyuan Liu3 \n3 \n1Department of Atmospheric and Oceanic Sciences and Institute of Atmospheric Sciences, Fudan \n4 \nUniversity, Shanghai, 200438, China \n5 \n2State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, \n6 \nBeijing, 100081, China \n7 \n3Nanjing Joint Institute for Atmospheric Sciences, Nanjing, China \n8 \n4Innovation Center of Ocean and Atmosphere System, Zhuhai Fudan Innovation Research \n9 \nInstitute，Zhuhai, 518057, China \n10 https://doi.org/10.5194/acp-2021-147\nPreprint. Discussion started: 7 April 2021\nc⃝Author(s) 2021. CC BY 4.0 License. Abstract. It has been suggested that the inner eyewall structure may play an important role in the \n21 \nsecondary eyewall formation (SEF) of tropical cyclones (TCs). This study is to further examine \n22 \nthe role of the inner eyewall structure by comparing two numerical experiments, which were \n23 \nconducted with the same large-scale environment and initial and boundary conditions but different \n24 \ngrid sizes. The SEF was simulated in the experiment with the finer grid spacing, but not in the \n25 \nother. 26 Abstract. It has been suggested that the inner eyewall structure may play an important role in the \n21 \nsecondary eyewall formation (SEF) of tropical cyclones (TCs). This study is to further examine \n22 \nthe role of the inner eyewall structure by comparing two numerical experiments, which were \n23 \nconducted with the same large-scale environment and initial and boundary conditions but different \n24 \ngrid sizes. The SEF was simulated in the experiment with the finer grid spacing, but not in the \n25 \nother. 1 Introduction \n39 Many intense tropical cyclones (TCs) usually undergo the secondary eyewall formation (SEF) \n40 \n(Fortner, 1958; Willoughby, 1982). Observational study shows that about 80% of intense TCs \n41 \n(maximum surface wind > 62 m s-1) in the western North Pacific, 70% in the Atlantic, and 50% in \n42 \nthe eastern Pacific possessed concentric eyewalls at least once (Hawkins and Helveston, 2008). 43 \nThe eyewall replacement circle is one of the most important issues remaining in understanding \n44 \nand predicting the change of TC intensity due to the resulting dramatic intensity fluctuations \n45 \n(Samsury and Zipser, 1995; Terwey and Montgomery, 2008; Bell et al., 2012). Although much \n46 \neffort has been made to understand the mechanisms of the SEF, a consensus has not been reached \n47 \nso far. 48 Many intense tropical cyclones (TCs) usually undergo the secondary eyewall formation (SEF) \n40 \n(Fortner, 1958; Willoughby, 1982). Observational study shows that about 80% of intense TCs \n41 \n(maximum surface wind > 62 m s-1) in the western North Pacific, 70% in the Atlantic, and 50% in \n42 \nthe eastern Pacific possessed concentric eyewalls at least once (Hawkins and Helveston, 2008). 43 \nThe eyewall replacement circle is one of the most important issues remaining in understanding \n44 \nand predicting the change of TC intensity due to the resulting dramatic intensity fluctuations \n45 \n(Samsury and Zipser, 1995; Terwey and Montgomery, 2008; Bell et al., 2012). Although much \n46 \neffort has been made to understand the mechanisms of the SEF, a consensus has not been reached \n47 \nso far. 48 Previous studies have pointed out the dynamic importance of the vortex circulation in the \n49 \nSEF (Montgomery and Kallenbach, 1997; Chen and Yau, 2001; Qiu et al., 2010). Given a negative \n50 \nradial gradient of vorticity outside the primary eyewall, vortex Rossby waves (VRWs) propagate \n51 \noutward and stop at a stagnation radius, where the mean flow strengthens through the interaction \n52 \nof eddies with the azimuthal-mean vortex (Montgomery and Kallenbach, 1997; Qiu et al., 2010; \n53 \nChen and Yau, 2001; Hogsett and Zhang, 2009; Dai et al., 2021). With the strengthening mean \n54 \nflow, the outer convection occurs and evolves into an outer eyewall through the wind-induced \n55 \nsurface heat exchange (Emanuel, 1986). Terwey and Montgomery (2008) proposed that cumulus \n56 \nconvection forms and maintains in a far-field region with a weak negative radial gradient of \n57 \nvorticity (the β –skirt) and moderate stretching time. 26 Comparing the eyewall structure in the simulated TCs with and without the SEF indicates \n27 \nthat the eyewall structure can play an important role in the SEF. For the simulated TC with the \n28 \nSEF, the eyewall is more upright with stronger updrafts, accompanied by a wide eyewall anvil at \n29 \na higher altitude. Compared to the simulated TC without the SEF, diagnostic analysis reveals that \n30 \nthe cooling outside the inner eyewall is induced by the sublimation, melting and evaporation of \n31 \nhydrometeors falling from the eyewall anvil. The cooling also induces upper-level dry, cool inflow \n32 \nbelow the anvil, prompting the subsidence and moat formation between the inner eyewall and the \n33 \nspiral rainband. In the simulated TC without the SEF, the cooling induced by the falling \n34 \nhydrometeors is significantly reduced and offset by the diabatic warming. There is no upper-level \n35 \ndry inflow below the anvil and no moat formation between the inner eyewall and the spiral \n36 \nrainband. This study suggests that a realistic simulation of the intense eyewall convection is \n37 \nimportant to the prediction of the SEF in the numerical forecasting model. 38 Comparing the eyewall structure in the simulated TCs with and without the SEF indicates \n27 \nthat the eyewall structure can play an important role in the SEF. For the simulated TC with the \n28 \nSEF, the eyewall is more upright with stronger updrafts, accompanied by a wide eyewall anvil at \n29 \na higher altitude. Compared to the simulated TC without the SEF, diagnostic analysis reveals that \n30 \nthe cooling outside the inner eyewall is induced by the sublimation, melting and evaporation of \n31 \nhydrometeors falling from the eyewall anvil. The cooling also induces upper-level dry, cool inflow \n32 \nbelow the anvil, prompting the subsidence and moat formation between the inner eyewall and the \n33 \nspiral rainband. In the simulated TC without the SEF, the cooling induced by the falling \n34 \nhydrometeors is significantly reduced and offset by the diabatic warming. There is no upper-level \n35 \ndry inflow below the anvil and no moat formation between the inner eyewall and the spiral \n36 \nrainband. This study suggests that a realistic simulation of the intense eyewall convection is \n37 \nimportant to the prediction of the SEF in the numerical forecasting model. 38 2 https://doi.org/10.5194/acp-2021-147\nPreprint. Discussion started: 7 April 2021\nc⃝Author(s) 2021. CC BY 4.0 License. 1 Introduction \n39 \nMany intense tropical cyclones (TCs) usually undergo the secondary eyewall formation (SEF) \n40 \n(Fortner, 1958; Willoughby, 1982). Observational study shows that about 80% of intense TCs \n41 \n(maximum surface wind > 62 m s-1) in the western North Pacific, 70% in the Atlantic, and 50% in \n42 \nthe eastern Pacific possessed concentric eyewalls at least once (Hawkins and Helveston, 2008). 43 \nThe eyewall replacement circle is one of the most important issues remaining in understanding \n44 \nand predicting the change of TC intensity due to the resulting dramatic intensity fluctuations \n45 \n(Samsury and Zipser, 1995; Terwey and Montgomery, 2008; Bell et al., 2012). Although much \n46 \neffort has been made to understand the mechanisms of the SEF, a consensus has not been reached \n47 \nso far. 48 \nPrevious studies have pointed out the dynamic importance of the vortex circulation in the \n49 \nSEF (Montgomery and Kallenbach, 1997; Chen and Yau, 2001; Qiu et al., 2010). Given a negative \n50 \nradial gradient of vorticity outside the primary eyewall, vortex Rossby waves (VRWs) propagate \n51 \noutward and stop at a stagnation radius, where the mean flow strengthens through the interaction \n52 \nof eddies with the azimuthal-mean vortex (Montgomery and Kallenbach, 1997; Qiu et al., 2010; \n53 \nChen and Yau, 2001; Hogsett and Zhang, 2009; Dai et al., 2021). With the strengthening mean \n54 \nflow, the outer convection occurs and evolves into an outer eyewall through the wind-induced \n55 \nsurface heat exchange (Emanuel, 1986). Terwey and Montgomery (2008) proposed that cumulus \n56 \nconvection forms and maintains in a far-field region with a weak negative radial gradient of \n57 \nvorticity (the β –skirt) and moderate stretching time. A secondary eyewall forms through the \n58 \nupscale cascade and axisymmetrization of eddy vorticities in the sustained convection. It has been \n59 \nfound that the secondary eyewall can be simulated in a barotropic model when the preexisting \n60 \nouter convection is stretched into a closed vorticity band by the rotation of the inner vortex (Kuo \n61 1 Introduction \n39 A secondary eyewall forms through the \n58 \nupscale cascade and axisymmetrization of eddy vorticities in the sustained convection. It has been \n59 \nfound that the secondary eyewall can be simulated in a barotropic model when the preexisting \n60 \nouter convection is stretched into a closed vorticity band by the rotation of the inner vortex (Kuo \n61 3 3 https://doi.org/10.5194/acp-2021-147\nPreprint. Discussion started: 7 April 2021\nc⃝Author(s) 2021. CC BY 4.0 License. et al., 2004, 2008). Based on a nonlinear boundary layer model, Kepert (2013) proposed that the \n62 \nsecondary eyewall can form through a positive feedback among the local enhancement of the radial \n63 \nvorticity gradient, the frictional updraft. Those studies highlight the positive feedback of the eddy \n64 \nkinetic energy to the storm-scale flow through the dynamics of the VRW, vorticity interaction, and \n65 \nthe Ekman pumping. However, the convective activity related to the generation of the eddy kinetic \n66 \nenergy is not fully addressed. 67 Some studies focused on spiral rainbands because the SEF generally starts from convective \n68 \nrainbands (Houze, 2007; Zhao et al., 2008, 2016; Kossin and Sitkowski, 2009). When the rainband \n69 \noutside the eyewall is enhanced by adding a large diabatic heating rate to the rainband in a \n70 \nnumerical simulation, the TC can experience the SEF (Wang, 2009). Zhu and Zhu (2014) \n71 \nemphasized that a critical strength of the rainbands is needed for the formation of a secondary wind \n72 \nmaximum through diabatic heating. Idealized numerical simulations indicated that the sustained \n73 \nconvection in the SEF region was enhanced by the interaction between the unbalanced boundary \n74 \nlayer process and the asymmetric inflows induced by the outside rainbands that propagated inward \n75 \n(Qiu and Tan, 2013; Wang and Tan, 2020). Recent studies revealed that, for SEF cases, the \n76 \ndescending inflow in the downwind portion of the spiral rainbands transfers high angular \n77 \nmomentum inward, leading to the outward expansion of the wind field (Didlake et al., 2018; \n78 \nWunsch and Didlake, 2018; Wang et al., 2019; Yu et al., 2020). A radial expansion of storm wind \n79 \nprecedes the SEF through the boundary layer processes and coupled convective dynamics (Rozoff \n80 \net al., 2012; Huang et al., 2012; Abarca and Montgomery, 2013; Sun et al., 2013). However, not \n81 \nall the spiral rainbands outside of the TC eyewall can evolve into a closed outer eyewall. 1 Introduction \n39 82 Many numerical studies have also shown the importance of various microphysical processes \n83 \nin the SEF since the inner-core structure and intensity of TCs are sensitive to the microphysical \n84 Many numerical studies have also shown the importance of various microphysical processes \n83 \nin the SEF since the inner-core structure and intensity of TCs are sensitive to the microphysical \n84 https://doi.org/10.5194/acp-2021-147\nPreprint. Discussion started: 7 April 2021\nc⃝Author(s) 2021. CC BY 4.0 License. processes (Wang, 2002; Zhu and Zhang, 2006). Zhu and Zhang (2006) proposed that varying cloud \n85 \nmicrophysics processes affect the timing of the spinup of the secondary eyewall since the \n86 \ndifferences in the inner eyewall convection and the rainband structure of the simulated TCs. 87 \nNumerical simulations showed that changing the terminal velocity of snow led to changes in the \n88 \nmagnitude and distribution of the diabatic heating of inner-core convection at outer radii, which is \n89 \nimportant for the SEF (Zhu and Zhu, 2015). Influenced by the evaporative cooling from the fallout \n90 \nof hydrometeors, the penetrative downdrafts can promote the local convection outside the primary \n91 \neyewall, where the SEF occurs (Tyner et al., 2018). Moreover, microphysical processes are also \n92 \nimportant to the occurrence of the moat, by which the spiral rainband is separated from the inner \n93 \neyewall with a chance to become a secondary eyewall. Willoughby et al. (1982) considered the \n94 \nmoat generated with subsidence as the evaporative cooling of precipitation falling from the \n95 \ncumulus anvil. In our previous study based on a numerical modeling simulation (Qin et al., 2021), \n96 \nwe demonstrated that the moat subsidence is mainly caused by the negative buoyancy resulting \n97 \nfrom the cooling from sublimation, melting and evaporation processes of hydrometeors from the \n98 \ncumulus eyewall and the related well-developed anvil, and the moat subsidence is further enhanced \n99 \nby the compensating upper-level dry-air inflows. 100 processes (Wang, 2002; Zhu and Zhang, 2006). Zhu and Zhang (2006) proposed that varying cloud \n85 \nmicrophysics processes affect the timing of the spinup of the secondary eyewall since the \n86 \ndifferences in the inner eyewall convection and the rainband structure of the simulated TCs. 87 \nNumerical simulations showed that changing the terminal velocity of snow led to changes in the \n88 \nmagnitude and distribution of the diabatic heating of inner-core convection at outer radii, which is \n89 \nimportant for the SEF (Zhu and Zhu, 2015). 1 Introduction \n39 Influenced by the evaporative cooling from the fallout \n90 \nof hydrometeors, the penetrative downdrafts can promote the local convection outside the primary \n91 \neyewall, where the SEF occurs (Tyner et al., 2018). Moreover, microphysical processes are also \n92 \nimportant to the occurrence of the moat, by which the spiral rainband is separated from the inner \n93 \neyewall with a chance to become a secondary eyewall. Willoughby et al. (1982) considered the \n94 \nmoat generated with subsidence as the evaporative cooling of precipitation falling from the \n95 \ncumulus anvil. In our previous study based on a numerical modeling simulation (Qin et al., 2021), \n96 \nwe demonstrated that the moat subsidence is mainly caused by the negative buoyancy resulting \n97 \nfrom the cooling from sublimation, melting and evaporation processes of hydrometeors from the \n98 \ncumulus eyewall and the related well-developed anvil, and the moat subsidence is further enhanced \n99 \nby the compensating upper-level dry-air inflows. 100 The objective of this study is to further examine the roles of the inner eyewall structure and \n101 \nthe associated cooling in the formation of the moat between the inner eyewall and the spiral \n102 \nrainband that later becomes the outer eyewall. Our examination was based on two numerical \n103 \nexperiments with the same large-scale environment and initial and boundary conditions, but \n104 \ndifferent grid sizes since the strength and distribution of the inner-core convection of TCs are \n105 \nsensitive to the horizontal resolutions (Zhang et al., 2015; Qin and Zhang, 2018; Wu et al., 2018, \n106 \n2019). This paper is organized as follows. Section 2 briefly summarizes the experimental design. 107 5 https://doi.org/10.5194/acp-2021-147\nPreprint. Discussion started: 7 April 2021\nc⃝Author(s) 2021. CC BY 4.0 License. Section 3 describes the simulated TCs with different horizontal spacings. In Section 4, different \n108 \neyewall structures are identified, followed by Section 5, in which how the differences in the \n109 \neyewall structure affect the SEF is investigated. A summary and concluding remarks are given in \n110 \nthe final section. 111 Section 3 describes the simulated TCs with different horizontal spacings. In Section 4, different \n108 \neyewall structures are identified, followed by Section 5, in which how the differences in the \n109 \neyewall structure affect the SEF is investigated. A summary and concluding remarks are given in \n110 \nthe final section. 111 Section 3 describes the simulated TCs with different horizontal spacings. 1 Introduction \n39 In Section 4, different \n108 \neyewall structures are identified, followed by Section 5, in which how the differences in the \n109 \neyewall structure affect the SEF is investigated. A summary and concluding remarks are given in \n110 \nthe final section. 111 2 Experimental design \n112 In our previous study, a 72-h simulation (CTL) was conducted using the Weather Research \n113 \nand Forecasting model (WRF, version 3.2.1) with quintuply nested domains (27/9/3/1/0.3 km), in \n114 \nwhich the simulated TC experienced the SEF (Qin et al., 2021). In order to understand the \n115 \ninfluence of structural changes of the eyewall on the SEF, a sensitivity experiment (NSEF) was \n116 \nfurther designed by removing the innermost domain used in CTL. The two experiments were \n117 \nconducted over the open ocean for 72 hours. The sea surface temperature is fixed at 29 ℃. The \n118 \noutermost domain is centered at 30 °N, 132.5 °E. The domains with the grid spacing of 3 km and \n119 \nless moved with the TC center. There are 75 vertical levels with the model top at 50 hPa. The \n120 \nNational Centers for Environmental Prediction (NCEP) Final Operational Global Analysis data (1°\n121 \n×1°) is utilized for the initial and lateral boundary conditions. The simulations begin with a TC-\n122 \nlike vortex. 123 Model physics options are the same as those used in Chen and Wu (2016) and Qin et al. 124 \n(2021). The major model physics options include the single-moment 3-class microphysics scheme \n125 \nfor the outermost domain, the single-moment 6-class microphysics scheme for the rest of the \n126 \ndomains, the Yonsei University planetary boundary layer (PBL) scheme (Noh et al., 2003), the \n127 \nlongwave radiation scheme of the Rapid Radiative Transfer Model (RRTM, Mlawer et al., 1997), \n128 \nthe shortwave radiation scheme of the Dudhia (Dudhia, 1989). The Kain-Fritsch cumulus \n129 \nparameterization scheme (Kain and Fritsch, 1993) is applied only in the outermost domain. 130 Model physics options are the same as those used in Chen and Wu (2016) and Qin et al. 124 \n(2021). The major model physics options include the single-moment 3-class microphysics scheme \n125 \nfor the outermost domain, the single-moment 6-class microphysics scheme for the rest of the \n126 \ndomains, the Yonsei University planetary boundary layer (PBL) scheme (Noh et al., 2003), the \n127 \nlongwave radiation scheme of the Rapid Radiative Transfer Model (RRTM, Mlawer et al., 1997), \n128 \nthe shortwave radiation scheme of the Dudhia (Dudhia, 1989). The Kain-Fritsch cumulus \n129 \nparameterization scheme (Kain and Fritsch, 1993) is applied only in the outermost domain. 130 6 https://doi.org/10.5194/acp-2021-147\nPreprint. Discussion started: 7 April 2021\nc⃝Author(s) 2021. CC BY 4.0 License. 3 Evolution of the simulated TCs \n131 There is little difference in the track of the simulated storms largely because the large-scale \n132 \nenvironmental conditions are the same in the two experiments (figure not shown). Despite the \n133 \nsame large-scale environment and initial and boundary conditions, the intensity evolution is \n134 \ndifferent in the two simulations (Fig. 1). In NSEF, after an 18-h spin-up, the near-surface maximum \n135 \nwind speed (VMAX) experiences a persistent increase and reaches its peak intensity of 62.5 m s-1 at \n136 \n57 h, then the VMAX decreases. In CTL, the storm experiences a weakening stage from 32 h to 48 \n137 \nh and a reintensification from 48 h to 63 h due to the SEF. There are pronounced fluctuations in \n138 \nthe VMAX in CTL, suggesting the influence of the small-scale structures simulated with the finer \n139 \ngrid size in the innermost domain. 140 The different eyewall structures between the two experiments can be seen from the evolution \n141 \nof the azimuthal-mean tangential wind. Figure 2 compares the time-radius cross-sections of the \n142 \nazimuthal-mean tangential wind and the vertical motion at 0.5 km between the two simulations. In \n143 \nNSEF, a single maximum wind core maintains and the tangential wind expands radially outward \n144 \nduring the intensification. It is indicated that no SEF occurs in this experiment. In CTL, the \n145 \nsimulated TC experiences the SEF, as discussed in Qin et al. (2021). The formation of the \n146 \nsecondary eyewall begins around 32 h with a secondary maximum tangential wind of over 35 m \n147 \ns-1 at the radius of 85 km. After the SEF, the outer eyewall contracts and intensifies with its strength \n148 \ncatching up with the primary eyewall at t = 40 h (Fig. 2b). A few hours later, the primary eyewall \n149 \nweakens and is replaced by the new eyewall around 46 h. 150 The different eyewall structures between the two experiments can be seen from the evolution \n141 \nof the azimuthal-mean tangential wind. Figure 2 compares the time-radius cross-sections of the \n142 \nazimuthal-mean tangential wind and the vertical motion at 0.5 km between the two simulations. In \n143 \nNSEF, a single maximum wind core maintains and the tangential wind expands radially outward \n144 \nduring the intensification. It is indicated that no SEF occurs in this experiment. In CTL, the \n145 \nsimulated TC experiences the SEF, as discussed in Qin et al. (2021). 3 Evolution of the simulated TCs \n131 Figure 3 \n159 \nshows the horizontal distributions of the 5-km radar reflectivity at the selected times. In NSEF, the \n160 \nbroad and active rainband is evident in the downshear quadrant of the storm, while the rainband in \n161 \nthe upshear quadrant is weak with sporadic convection located around the radii of 100-150 km at \n162 \n28 h. Afterward, the rainbands contract and merge with the inner eyewall, leading to an expansion \n163 \nof the wind field and a broad single eyewall without the formation of a moat. In CTL, the rainbands \n164 \nshow a pattern similar to that in NSEF by 28 h (Fig. 3d), but the rainbands are elongated \n165 \nazimuthally and became a closed ring outside the primary eyewall by 32 h. A clear moat region \n166 \nforms at 50-60 km radii between the primary and the outer eyewalls. After a weakening stage, the \n167 \nprimary eyewall almost dissipates by 44 h (Fig. 3f), followed by an inward contraction of the outer \n168 \neyewall. 169 Moreover, the simulated inner rainbands evolve differently in the two experiments. Figure 3 \n159 \nshows the horizontal distributions of the 5-km radar reflectivity at the selected times. In NSEF, the \n160 \nbroad and active rainband is evident in the downshear quadrant of the storm, while the rainband in \n161 \nthe upshear quadrant is weak with sporadic convection located around the radii of 100-150 km at \n162 \n28 h. Afterward, the rainbands contract and merge with the inner eyewall, leading to an expansion \n163 \nof the wind field and a broad single eyewall without the formation of a moat. In CTL, the rainbands \n164 \nshow a pattern similar to that in NSEF by 28 h (Fig. 3d), but the rainbands are elongated \n165 \nazimuthally and became a closed ring outside the primary eyewall by 32 h. A clear moat region \n166 \nforms at 50-60 km radii between the primary and the outer eyewalls. After a weakening stage, the \n167 \nprimary eyewall almost dissipates by 44 h (Fig. 3f), followed by an inward contraction of the outer \n168 \neyewall. 169 3 Evolution of the simulated TCs \n131 The formation of the \n146 \nsecondary eyewall begins around 32 h with a secondary maximum tangential wind of over 35 m \n147 \ns-1 at the radius of 85 km. After the SEF, the outer eyewall contracts and intensifies with its strength \n148 \ncatching up with the primary eyewall at t = 40 h (Fig. 2b). A few hours later, the primary eyewall \n149 \nweakens and is replaced by the new eyewall around 46 h. 150 The different inner-core structures can also be seen in the evolution of the azimuthal-mean \n151 \nvertical motion (Figs. 2c and 2d). In NSEF, the strong upward motion in the single eyewall is \n152 \nmaintained during the 72-h simulation. The vertical motion in the eyewall with a speed larger than \n153 The different inner-core structures can also be seen in the evolution of the azimuthal-mean \n151 \nvertical motion (Figs. 2c and 2d). In NSEF, the strong upward motion in the single eyewall is \n152 \nmaintained during the 72-h simulation. The vertical motion in the eyewall with a speed larger than \n153 7 https://doi.org/10.5194/acp-2021-147\nPreprint. Discussion started: 7 April 2021\nc⃝Author(s) 2021. CC BY 4.0 License. 0.2 m s-1 extends about 20-30 km at 0.5-km height. In CTL, prior to the SEF, the primary eyewall \n154 \ncontracts inward and the width of the eyewall with the upward motion over 0.2 m s-1 is reduced. 155 \nAround 34 h, a secondary maximum upward motion occurs at a radius of around 60 km. After the \n156 \nSEF, the weakening and dissipation of the primary eyewall can also be seen from the upward \n157 \nmotion shown in Fig. 2d. It is seen that the double eyewall structure exists for 14 h. 158 0.2 m s-1 extends about 20-30 km at 0.5-km height. In CTL, prior to the SEF, the primary eyewall \n154 \ncontracts inward and the width of the eyewall with the upward motion over 0.2 m s-1 is reduced. 155 \nAround 34 h, a secondary maximum upward motion occurs at a radius of around 60 km. After the \n156 \nSEF, the weakening and dissipation of the primary eyewall can also be seen from the upward \n157 \nmotion shown in Fig. 2d. It is seen that the double eyewall structure exists for 14 h. 158 Moreover, the simulated inner rainbands evolve differently in the two experiments. 4 Differences in the vertical structures of the eyewall \n170 One of the major differences in the eyewall between NSEF and CTL is the magnitude and the \n171 \nvertical distribution of the vertical motion, which can be examined with the azimuthally averaged \n172 \nvertical motion within the radius of 100 km (Fig. 4) and the contoured frequency by altitude \n173 \ndiagram (CFAD) of the vertical motion (Fig. 5a). The CFAD illustrates the frequency distribution \n174 \nof the vertical motion of the indicated values at each altitude in the region of the 10-km radially \n175 \ninside and outside of the radius of the maximum tangential wind (RMW) for two simulations. The \n176 8 https://doi.org/10.5194/acp-2021-147\nPreprint. Discussion started: 7 April 2021\nc⃝Author(s) 2021. CC BY 4.0 License. azimuthal-mean upward motion in the eyewall is stronger in CTL than that in NSEF (Fig. 4). 177 \nSpecifically, the upward motion in the eyewall in NSEF is maximized at 10- and 12-km height \n178 \nwith peaks of 11 and 13 m s-1 for the 0.1 % and 0.05% percentiles (Fig. 5a), respectively. The weak \n179 \nupward motion between 45- to 75-km radii is associated with the broad rainbands (Figs. 4a and \n180 \n4b). In contrast, the maximum upward motion in CTL is 12 and 14 m s-1 for the 0.1 % and 0.05% \n181 \npercentiles (Fig. 5a). The stronger upward motion in CTL indicates that a higher resolution in the \n182 \nmodel simulation can resolve more intense eyewall updrafts (Yau et al., 2004). Moreover, the \n183 \neyewall with strong updrafts in CTL is more upright in the vertical direction. 184 azimuthal-mean upward motion in the eyewall is stronger in CTL than that in NSEF (Fig. 4). 177 \nSpecifically, the upward motion in the eyewall in NSEF is maximized at 10- and 12-km height \n178 \nwith peaks of 11 and 13 m s-1 for the 0.1 % and 0.05% percentiles (Fig. 5a), respectively. The weak \n179 \nupward motion between 45- to 75-km radii is associated with the broad rainbands (Figs. 4a and \n180 \n4b). In contrast, the maximum upward motion in CTL is 12 and 14 m s-1 for the 0.1 % and 0.05% \n181 \npercentiles (Fig. 5a). The stronger upward motion in CTL indicates that a higher resolution in the \n182 \nmodel simulation can resolve more intense eyewall updrafts (Yau et al., 2004). Moreover, the \n183 \neyewall with strong updrafts in CTL is more upright in the vertical direction. 4 Differences in the vertical structures of the eyewall \n170 184 Another important difference in the eyewall between NSEF and CTL is the feature of the \n185 \nupper-level outflow layer. Figure 5b compares the upper-level outflow in the two simulations by \n186 \nshowing the 0.1% and 0.05% contoured frequency of the radial wind in the region of a radial \n187 \ndistance of 60 km starting from the radius of 10-km outside the eyewall. In NSEF, the upper-level \n188 \noutflow peaks around the 11-km height with maxima of 28 and 26 m s-1 for the 0.05% and 0.1% \n189 \npercentages, respectively. The outflow layer is deep with a magnitude of over 15 m s-1 extending \n190 \ndownward to 8 km. In CTL, the maximum outflow with values of over 29 m s-1 is located around \n191 \nthe 14-km height. The outflow layer at the higher altitude in CTL is associated with the strong \n192 \nupward motion in the eyewall that can lift the hydrometeors much higher. 193 Another important difference in the eyewall between NSEF and CTL is the feature of the \n185 \nupper-level outflow layer. Figure 5b compares the upper-level outflow in the two simulations by \n186 \nshowing the 0.1% and 0.05% contoured frequency of the radial wind in the region of a radial \n187 \ndistance of 60 km starting from the radius of 10-km outside the eyewall. In NSEF, the upper-level \n188 \noutflow peaks around the 11-km height with maxima of 28 and 26 m s-1 for the 0.05% and 0.1% \n189 \npercentages, respectively. The outflow layer is deep with a magnitude of over 15 m s-1 extending \n190 \ndownward to 8 km. In CTL, the maximum outflow with values of over 29 m s-1 is located around \n191 \nthe 14-km height. The outflow layer at the higher altitude in CTL is associated with the strong \n192 \nupward motion in the eyewall that can lift the hydrometeors much higher. 193 The different eyewall structures can also be seen in the horizontal distribution of the cloud-\n194 \ntop temperature (Fig. 6). In NSEF, the eyewall is wider and possesses relatively weaker convection \n195 \nas indicated by the cloud-top temperature of above -750C (Fig. 6a). In CTL, the cloud associated \n196 \nwith the eyewall is deeper since the coldest cloud-top temperature is below -75 0C (Fig. 6b). The \n197 \ncoldest cloud-top temperature is located at the downshear- and upshear-right region due to the \n198 \ninfluence of the southeastward VWS. 4 Differences in the vertical structures of the eyewall \n170 The strong eyewall convection is accompanied by the strong \n199 The different eyewall structures can also be seen in the horizontal distribution of the cloud-\n194 \ntop temperature (Fig. 6). In NSEF, the eyewall is wider and possesses relatively weaker convection \n195 \nas indicated by the cloud-top temperature of above -750C (Fig. 6a). In CTL, the cloud associated \n196 \nwith the eyewall is deeper since the coldest cloud-top temperature is below -75 0C (Fig. 6b). The \n197 \ncoldest cloud-top temperature is located at the downshear- and upshear-right region due to the \n198 \ninfluence of the southeastward VWS. The strong eyewall convection is accompanied by the strong \n199 9 https://doi.org/10.5194/acp-2021-147\nPreprint. Discussion started: 7 April 2021\nc⃝Author(s) 2021. CC BY 4.0 License. and high-altitude outflow compared to that in NSEF. 200 \n5 Influence of the eyewall structure on the moat formation \n201 \n5.1 Buoyancy effects \n202 \nAs discussed above, the rainbands can encircle into a closed outer eyewall instead of merging \n203 \nwith the inner eyewall in CTL due to the formation of the moat. First, we investigate the \n204 \nrelationship between the distribution of buoyancy and the occurrence of the moat subsidence. 205 \nMany studies indicated that buoyance, which is determined by temperature perturbation, affects \n206 \nthe vertical motion tendency (e.g., Zhang et al., 2000; Braun, 2002; Miller et al., 2015). It is \n207 \nintended to examine how the buoyancy changes when the SEF fails in NSEF with a different \n208 \neyewall structure. Following the method used by Braun (2002), the perturbation associated with \n209 \nthe buoyance calculation is defined as 𝐴𝐴′(𝜆𝜆, 𝑟𝑟, 𝑧𝑧) = 𝐴𝐴(𝜆𝜆, 𝑟𝑟, 𝑧𝑧) −𝐴𝐴0(𝑧𝑧) −𝐴𝐴0,1(𝜆𝜆, 𝑟𝑟, 𝑧𝑧) , where A \n210 \nrepresents any variable in a cylindrical coordinate (𝜆𝜆, 𝑟𝑟, 𝑧𝑧), 𝜆𝜆, r, z are the azimuthal angle, the \n211 \nradius from the TC center, and the vertical height axis, respectively, 𝐴𝐴0 is averaged over the whole \n212 \narea of the 1-km domain, 𝐴𝐴0,1 are the wavenumber-0 and -1 components of the perturbation field \n213 \nfrom 𝐴𝐴0. 𝐴𝐴0 + 𝐴𝐴0,1 denotes the reference state for the buoyance analysis. Following Houze (1993) \n214 \nand Braun (2002), buoyancy (B) is defined as: \n215 \n𝐵𝐵\n𝑔𝑔൤\n𝜃𝜃𝑣𝑣′𝜃𝑣𝜃𝑣\n+ (𝜅𝜅\n1)\n𝑝𝑝′𝑝𝑝\n𝑞𝑞′൨\n(1)\n216 As discussed above, the rainbands can encircle into a closed outer eyewall instead of merging \n203 \nwith the inner eyewall in CTL due to the formation of the moat. 4 Differences in the vertical structures of the eyewall \n170 First, we investigate the \n204 \nrelationship between the distribution of buoyancy and the occurrence of the moat subsidence. 205 \nMany studies indicated that buoyance, which is determined by temperature perturbation, affects \n206 \nthe vertical motion tendency (e.g., Zhang et al., 2000; Braun, 2002; Miller et al., 2015). It is \n207 \nintended to examine how the buoyancy changes when the SEF fails in NSEF with a different \n208 \neyewall structure. Following the method used by Braun (2002), the perturbation associated with \n209 \nthe buoyance calculation is defined as 𝐴𝐴′(𝜆𝜆, 𝑟𝑟, 𝑧𝑧) = 𝐴𝐴(𝜆𝜆, 𝑟𝑟, 𝑧𝑧) −𝐴𝐴0(𝑧𝑧) −𝐴𝐴0,1(𝜆𝜆, 𝑟𝑟, 𝑧𝑧) , where A \n210 \nrepresents any variable in a cylindrical coordinate (𝜆𝜆, 𝑟𝑟, 𝑧𝑧), 𝜆𝜆, r, z are the azimuthal angle, the \n211 \nradius from the TC center, and the vertical height axis, respectively, 𝐴𝐴0 is averaged over the whole \n212 \narea of the 1-km domain, 𝐴𝐴0,1 are the wavenumber-0 and -1 components of the perturbation field \n213 \nfrom 𝐴𝐴0. 𝐴𝐴0 + 𝐴𝐴0,1 denotes the reference state for the buoyance analysis. Following Houze (1993) \n214 \nand Braun (2002), buoyancy (B) is defined as: \n215 𝐵𝑔𝜃𝑣𝜅𝑝𝑞 𝐵𝐵= 𝑔𝑔൤\n𝜃𝜃𝑣𝑣′\n𝜃𝜃𝑣𝑣0+𝜃𝜃𝑣𝑣\n0,1 + (𝜅𝜅−1)\n𝑝𝑝′\n𝑝𝑝0+𝑝𝑝0,1 −𝑞𝑞′൨, (1) \n216 𝜃𝑣𝜅 𝐵𝐵= 𝑔𝑔൤\n𝜃𝜃𝑣𝑣′\n𝜃𝜃𝑣𝑣0+𝜃𝜃𝑣𝑣\n0,1 + (𝜅𝜅−1)\n𝑝𝑝′\n𝑝𝑝0+𝑝𝑝0,1 −𝑞𝑞′൨, (1) \n216 𝜃𝑣𝜅 (1) 10𝐵𝑔𝜃𝑣𝜃𝑣𝜅𝑝𝑝𝑞\nwhere g is the gravitational acceleration, 𝜃𝜃𝑣𝑣 is the virtual potential temperature, 𝜅𝜅= 0.286, p is \n217 \nthe pressure, and q is the hydrometeor mixing ratio, including the mixing ratio of the cloud water \n218 \n(qc), rain water (qr), graupel (qg), snow (qs), and ice (qi). Terms on the right-hand side of Eq. (1) \n219 \nare the thermal buoyancy, the dynamic buoyancy, and the hydrometeor loading, respectively. 220 \nConsidering that the rainband distributes asymmetrically prior to the SEF, it is appropriate to use \n221 \nquarter-mean variables, i.e. the upshear-right quadrant, to analyze the moat and outer eyewall \n222 10 https://doi.org/10.5194/acp-2021-147\nPreprint. Discussion started: 7 April 2021\nc⃝Author(s) 2021. CC BY 4.0 License. formation in our following discussions. 223 \nFor the convenience of the following buoyancy analysis, Fig. 7 shows the radius-height cross \n224 \nsections of the perturbation virtual potential temperature (𝜃𝜃𝑣𝑣\n′). Consistent with the broad eyewall \n225 \nconvection in NSEF, positive 𝜃𝜃𝑣𝑣\n′ appears under the eyewall anvil, which may force the air parcel \n226 \nupward since the local 𝜃𝜃𝑣𝑣 exceeds the ambient environmental value. 4 Differences in the vertical structures of the eyewall \n170 On the contrary, the 𝜃𝜃𝑣𝑣\n′ is \n227 \nnegative outside and underneath the inner eyewall in CTL (Fig. 7e), which will suppress the \n228 \nupward motion there. 229 𝜃𝑣 Given the different distribution of 𝜃𝜃𝑣𝑣\n′, we next examine the related thermal buoyancy, as well \n230 \nas the dynamic buoyancy and the hydrometeor loading (Fig. 8). In NSEF, we note that the positive \n231 \nbuoyancy coinciding with the positive 𝜃𝜃𝑣𝑣\n′ appears outside the inner eyewall since the buoyancy is \n232 \nlargely determined by the thermal buoyancy and the dynamical buoyancy and the water loading \n233 \neffects are relatively small (Figs. 8a-8d). The positive buoyancy forces upward motion, leading to \n234 \nthe widespread upward motion in NSEF (Fig. 8b). There is no moat formation without the \n235 \nconsiderable subsidence, and the spiral rainband merges with the primary eyewall and no SEF \n236 \noccurs. In CTL, the emergence of the moat subsidence is largely caused by the negative buoyancy, \n237 \nespecially the negative thermal buoyancy in response to the negative 𝜃𝜃𝑣𝑣\n′ outside the inner eyewall. 238 \nMoreover, the dynamic buoyancy and the water loading effect both contribute to the enhancement \n239 \nof the moat subsidence. Note that the negative buoyancy also occurs in the inner eyewall below 6-\n240 \nkm height (Fig. 8e), which is consistent with the weakening of the primary eyewall when the outer \n241 \neyewall intensifies. These results indicate that the negative buoyancy beneath the high-altitude \n242 \neyewall anvil from the inner eyewall is crucial for the subsidence generation and the moat \n243 \nemergence. The moat plays an important role in the SEF by separating the preexisting spiral \n244 \nrainbands from the inner eyewall. 245 Given the different distribution of 𝜃𝜃𝑣𝑣\n′, we next examine the related thermal buoyancy, as well \n230 \nas the dynamic buoyancy and the hydrometeor loading (Fig. 8). In NSEF, we note that the positive \n231 \nbuoyancy coinciding with the positive 𝜃𝜃𝑣𝑣\n′ appears outside the inner eyewall since the buoyancy is \n232 \nlargely determined by the thermal buoyancy and the dynamical buoyancy and the water loading \n233 \neffects are relatively small (Figs. 8a-8d). The positive buoyancy forces upward motion, leading to \n234 \nthe widespread upward motion in NSEF (Fig. 8b). There is no moat formation without the \n235 \nconsiderable subsidence, and the spiral rainband merges with the primary eyewall and no SEF \n236 \noccurs. 4 Differences in the vertical structures of the eyewall \n170 In CTL, the emergence of the moat subsidence is largely caused by the negative buoyancy, \n237 \nespecially the negative thermal buoyancy in response to the negative 𝜃𝜃𝑣𝑣\n′ outside the inner eyewall. 238 \nMoreover, the dynamic buoyancy and the water loading effect both contribute to the enhancement \n239 \nof the moat subsidence. Note that the negative buoyancy also occurs in the inner eyewall below 6-\n240 \nkm height (Fig. 8e), which is consistent with the weakening of the primary eyewall when the outer \n241 \neyewall intensifies. These results indicate that the negative buoyancy beneath the high-altitude \n242 \neyewall anvil from the inner eyewall is crucial for the subsidence generation and the moat \n243 \nemergence. The moat plays an important role in the SEF by separating the preexisting spiral \n244 \nrainbands from the inner eyewall. 245 11 11 https://doi.org/10.5194/acp-2021-147\nPreprint. Discussion started: 7 April 2021\nc⃝Author(s) 2021. CC BY 4.0 License. To further demonstrate the tendency of the vertical motion, the perturbation vertical pressure \n246 \ngradient force and the net force among the buoyancy and the perturbation vertical pressure gradient \n247 \nforce are shown in Fig. 9. Even though the perturbation vertical pressure gradient force exhibits \n248 \noppositely to the buoyancy in the two simulated TCs, the net force contributes to the upward \n249 \nacceleration of updrafts in NSEF (Fig. 9c) but the downward acceleration of the subsidence outside \n250 \nthe primary eyewall in CTL (Fig. 9f). As a result, the subsidence outside the inner eyewall in CTL \n251 \ncontributes to the formation of the moat, followed by the SEF, while no SEF occurs in NSEF \n252 \nwithout the emergence of the moat. 253 To further demonstrate the tendency of the vertical motion, the perturbation vertical pressure \n246 \ngradient force and the net force among the buoyancy and the perturbation vertical pressure gradient \n247 \nforce are shown in Fig. 9. Even though the perturbation vertical pressure gradient force exhibits \n248 \noppositely to the buoyancy in the two simulated TCs, the net force contributes to the upward \n249 \nacceleration of updrafts in NSEF (Fig. 9c) but the downward acceleration of the subsidence outside \n250 \nthe primary eyewall in CTL (Fig. 9f). As a result, the subsidence outside the inner eyewall in CTL \n251 \ncontributes to the formation of the moat, followed by the SEF, while no SEF occurs in NSEF \n252 \nwithout the emergence of the moat. 253 5.2 Diabatic heating \n254 279 The evolution of subsidence in the moat area is largely controlled by the distribution of the \n269 \ndiabatic cooling. The azimuthal extension of the diabatic cooling and the related moat subsidence \n270 \nand their differences in CTL and NSEF at upper levels are further examined in Fig. 11. Before 24 \n271 \nh, both the diabatic cooling and the related subsidence in NSEF and CTL are characterized by a \n272 \nhighly asymmetric structure with intense subsidence/cooling located in the upshear-left quadrant \n273 \n(see Figs. 11a, 11b, and Fig. 3). After 24 h, the evolution of the diabatic cooling and subsidence \n274 \ndiffers in the two simulations. The asymmetric structure of the intense diabatic cooling and \n275 \nsubsidence maintains in NSEF, while the diabatic cooling and subsidence extend cyclonically from \n276 \nthe upshear-left quadrant to the downshear-right quadrant, ending with a quasi-symmetric structure \n277 \nfrom 24 h to 32 h (Fig. 11b), which is also confirmed by showing the differences in the diabatic \n278 \ncooling and moat subsidence between NSEF and CTL in Fig. 11c. 279 5.3 Subsidence in response to the diabatic cooing \n280 5.2 Diabatic heating \n254 Since the negative buoyancy is associated with the negative temperature disturbance, the \n255 \ndiabatic heating is examined. Figure 10 shows the radius-height distributions of the diabatic \n256 \nheating and diabatic cooling induced by the sublimation, melting, and evaporation of hydrometeors. 257 \nIn NSEF, the diabatic warming dominates the region within the radius of 100 km, except for the \n258 \neye and a local area around 40-km radius from 1- to 6-km heights (Fig. 10a). This broad warming \n259 \nis caused by the wider eyewall convection as shown in Fig. 3 and Fig 4a. Although the diabatic \n260 \ncooling related to the sublimation, melting and evaporation processes always exist in the storm \n261 \n(Figs. 10b-10d), the low- to middle-level convection outside the inner eyewall produces much \n262 \ndiabatic warming than cooling, leading to net diabatic warming appearing outside the primary \n263 \neyewall in NSEF. In contrast, instead of diabatic warming, the net diabatic cooling appears with \n264 \nthe absence of convection outside of the inner eyewall in CTL (Fig. 10e). This cooling is \n265 \nmaximized at 6- to 10-km height, which is largely induced by the sublimation of hydrometeors \n266 \nbeneath the eyewall anvil (Figs. 10f-10h), while the cooling located below 6-km height is caused \n267 \nby the melting and evaporative processes. 268 12 12 https://doi.org/10.5194/acp-2021-147\nPreprint. Discussion started: 7 April 2021\nc⃝Author(s) 2021. CC BY 4.0 License. The evolution of subsidence in the moat area is largely controlled by the distribution of the \n269 \ndiabatic cooling. The azimuthal extension of the diabatic cooling and the related moat subsidence \n270 \nand their differences in CTL and NSEF at upper levels are further examined in Fig. 11. Before 24 \n271 \nh, both the diabatic cooling and the related subsidence in NSEF and CTL are characterized by a \n272 \nhighly asymmetric structure with intense subsidence/cooling located in the upshear-left quadrant \n273 \n(see Figs. 11a, 11b, and Fig. 3). After 24 h, the evolution of the diabatic cooling and subsidence \n274 \ndiffers in the two simulations. The asymmetric structure of the intense diabatic cooling and \n275 \nsubsidence maintains in NSEF, while the diabatic cooling and subsidence extend cyclonically from \n276 \nthe upshear-left quadrant to the downshear-right quadrant, ending with a quasi-symmetric structure \n277 \nfrom 24 h to 32 h (Fig. 11b), which is also confirmed by showing the differences in the diabatic \n278 \ncooling and moat subsidence between NSEF and CTL in Fig. 11c. 5.3 Subsidence in response to the diabatic cooing \n280 13\nThe Sawyer-Eliassen equation (SEE) is used to better understand how the diabatic heating \n281 \nwith the different eyewall structures affects the evolution of the moat and outer eyewall without \n282 \nconsidering the momentum forcing. The SEE is a useful analytical tool for diagnosing the response \n283 \nof the transverse circulation to diabatic heating (Smith et al., 2005; Bui et al., 2009; Zhu and Zhu, \n284 \n2014; Qin et al., 2021). According to Qin et al. (2021), the SEE used in this study is \n285 \n𝜕𝜕 \n𝜕𝜕𝜕𝜕ቂ\n𝜒𝜒\n𝜌𝜌𝜌𝜌\n𝜕𝜕𝜕𝜕\n𝜕𝜕𝜕𝜕\n𝜕𝜕𝜕𝜕\n𝜕𝜕𝜕𝜕−\n𝜒𝜒\n𝜌𝜌𝜌𝜌\n𝜕𝜕𝜕𝜕\n𝜕𝜕𝜕𝜕\n𝜕𝜕𝜕𝜕\n𝜕𝜕𝜕𝜕 ቃ+\n𝜕𝜕 \n𝜕𝜕𝜕𝜕ቂቀ𝜒𝜒𝜒𝜒𝜁𝜁𝑎𝑎−\n𝐶𝐶𝜒𝜒\n𝑔𝑔\n𝜕𝜕𝜕𝜕\n𝜕𝜕𝜕𝜕ቁ\n1\n𝜌𝜌𝜌𝜌\n𝜕𝜕𝜕𝜕\n𝜕𝜕𝜕𝜕−\n𝜒𝜒\n𝜌𝜌𝜌𝜌\n𝜕𝜕𝜕𝜕 \n𝜕𝜕𝜕𝜕\n𝜕𝜕𝜕𝜕\n𝜕𝜕𝜕𝜕ቃ= 𝑔𝑔\n𝜕𝜕𝜒𝜒2𝑄𝑄 \n𝜕𝜕𝜕𝜕\n+\n𝜕𝜕𝐶𝐶𝐶𝐶2𝑄𝑄 \n𝜕𝜕𝜕𝜕\n , (2) \n286 \nwhere 𝜒𝜒= 1/𝜃𝜃 and 𝜃𝜃 is the potential temperature, 𝜌𝜌 is the density, b is the buoyancy term, 𝜓𝜓 is a \n287 \nstream function, 𝜉𝜉= 2𝑣𝑣/𝑟𝑟+ 𝑓𝑓 is the local Coriolis parameter and f is the Coriolis parameter, 𝜁𝜁𝑎𝑎 \n288 \nis the vertical component of the absolute vorticity, 𝐶𝐶= 𝑣𝑣2/𝑟𝑟+ 𝑓𝑓𝑓𝑓 is the sum of the centrifugal \n289 \nforce and Coriolis force where v is the tangential wind, g is the gravitational acceleration, r and z \n290 \nare the radial and vertical coordinate, and 𝑄𝑄 is the diabatic heating rate (heating forcing). Note that, \n291 The Sawyer-Eliassen equation (SEE) is used to better understand how the diabatic heating \n281 \nwith the different eyewall structures affects the evolution of the moat and outer eyewall without \n282 \nconsidering the momentum forcing. The SEE is a useful analytical tool for diagnosing the response \n283 \nof the transverse circulation to diabatic heating (Smith et al., 2005; Bui et al., 2009; Zhu and Zhu, \n284 \n2014; Qin et al., 2021). According to Qin et al. 5.3 Subsidence in response to the diabatic cooing \n280 These results suggest that the formation of the moat is \n303 \nsensitive to the diabatic heating, especially the diabatic cooling beneath the eyewall anvil. 304 Figure 12 shows the radius-height cross sections of the SEE-diagnosed vertical and radial \n296 \nwind forced by the diabatic heating, diabatic cooling, and cooling induced by the sublimation, \n297 \nmelting and evaporation of hydrometeors, respectively. Significantly, in NSEF, the diabatic heating \n298 \nreleased by the wider eyewall convection induces the upward motion and deep-layer outflows \n299 \noutside the inner eyewall, and a compensated downdraft in the eye (Fig. 12a). In CTL, intense \n300 \ndiabatic cooling forces subsidence of over -0.3 m s-1 outside the inner eyewall, which contributes \n301 \nto the formation of the moat. Meanwhile, the diabatic cooling also induces the upper-level inflow \n302 \nbelow the strong outflow layer (Fig. 12e). These results suggest that the formation of the moat is \n303 \nsensitive to the diabatic heating, especially the diabatic cooling beneath the eyewall anvil. 304 Although the diabatic cooling caused by phase changes usually occurs in TCs, the magnitude \n305 \nof the diabatic cooling, especially the cooling due to the sublimation of ice particles, matters much \n306 \nin the formation of the moat (Figs. 12c and 12g). The cooling due to the sublimation process is \n307 \nmuch less outside the primary eyewall in NSEF compared to that in CTL (cf. Figs. 12c and 12g). 308 \nIn NSEF, the diabatic warming released by the low- to middle-level convection outside the primary \n309 \neyewall exceeds the cooling, resulting in net diabatic warming (Fig. 12a). Thus, a wider eyewall \n310 \nwith warming-forced upward motion prevails due to the positive feedback among the diabatic \n311 \nheating and the convection (Fig. 12a). In addition, the warming-forced upward motion is \n312 \naccompanied by the deep-layer outflow (Fig. 13a), under which the low-level inflow appears \n313 \nbelow the 8-km height (Fig. 13a), which brings moist air enhancing the convection in NSEF. In \n314 Although the diabatic cooling caused by phase changes usually occurs in TCs, the magnitude \n305 \nof the diabatic cooling, especially the cooling due to the sublimation of ice particles, matters much \n306 \nin the formation of the moat (Figs. 12c and 12g). The cooling due to the sublimation process is \n307 \nmuch less outside the primary eyewall in NSEF compared to that in CTL (cf. Figs. 12c and 12g). 5.3 Subsidence in response to the diabatic cooing \n280 (2021), the SEE used in this study is \n285 𝜕𝜒𝜕𝜕𝜕𝜕𝜒𝜕𝜕𝜕𝜕𝜕𝜒𝜒𝜁𝐶𝜒𝜕𝜕𝜕𝜕𝜒𝜕𝜕𝜕𝜕𝑔𝜕𝜒𝑄𝜕𝐶𝐶𝑄 𝜕𝜕 \n𝜕𝜕𝜕𝜕ቂ\n𝜒𝜒\n𝜌𝜌𝜌𝜌\n𝜕𝜕𝜕𝜕\n𝜕𝜕𝜕𝜕\n𝜕𝜕𝜕𝜕\n𝜕𝜕𝜕𝜕−\n𝜒𝜒\n𝜌𝜌𝜌𝜌\n𝜕𝜕𝜕𝜕\n𝜕𝜕𝜕𝜕\n𝜕𝜕𝜕𝜕\n𝜕𝜕𝜕𝜕 ቃ+\n𝜕𝜕 \n𝜕𝜕𝜕𝜕ቂቀ𝜒𝜒𝜒𝜒𝜁𝜁𝑎𝑎−\n𝐶𝐶𝜒𝜒\n𝑔𝑔\n𝜕𝜕𝜕𝜕\n𝜕𝜕𝜕𝜕ቁ\n1\n𝜌𝜌𝜌𝜌\n𝜕𝜕𝜕𝜕\n𝜕𝜕𝜕𝜕−\n𝜒𝜒\n𝜌𝜌𝜌𝜌\n𝜕𝜕𝜕𝜕 \n𝜕𝜕𝜕𝜕\n𝜕𝜕𝜕𝜕\n𝜕𝜕𝜕𝜕ቃ= 𝑔𝑔\n𝜕𝜕𝜒𝜒2𝑄𝑄 \n𝜕𝜕𝜕𝜕\n+\n𝜕𝜕𝐶𝐶𝐶𝐶2𝑄𝑄 \n𝜕𝜕𝜕𝜕\n , (2) \n286 𝜒𝜃𝜃𝜌𝜓 (2) 𝜓 where 𝜒𝜒= 1/𝜃𝜃 and 𝜃𝜃 is the potential temperature, 𝜌𝜌 is the density, b is the buoyancy term, 𝜓𝜓 is a \n287 \nstream function, 𝜉𝜉= 2𝑣𝑣/𝑟𝑟+ 𝑓𝑓 is the local Coriolis parameter and f is the Coriolis parameter, 𝜁𝜁𝑎𝑎 \n288 \nis the vertical component of the absolute vorticity, 𝐶𝐶= 𝑣𝑣2/𝑟𝑟+ 𝑓𝑓𝑓𝑓 is the sum of the centrifugal \n289 \nforce and Coriolis force where v is the tangential wind, g is the gravitational acceleration, r and z \n290 \nare the radial and vertical coordinate, and 𝑄𝑄 is the diabatic heating rate (heating forcing). Note that, \n291 13 𝑄 https://doi.org/10.5194/acp-2021-147\nPreprint. Discussion started: 7 April 2021\nc⃝Author(s) 2021. CC BY 4.0 License. in the absence of the momentum forcing, the diagnosed radial inflow within the boundary layer is \n292 \nlargely underestimated, while the diagnosed secondary circulation above the boundary is \n293 \ncomparable to the simulated results, which is also found in other studies (Bui et al., 2009; Zhu and \n294 \nZhu, 2014; Qin et al., 2021). 295 in the absence of the momentum forcing, the diagnosed radial inflow within the boundary layer is \n292 \nlargely underestimated, while the diagnosed secondary circulation above the boundary is \n293 \ncomparable to the simulated results, which is also found in other studies (Bui et al., 2009; Zhu and \n294 \nZhu, 2014; Qin et al., 2021). 295 Figure 12 shows the radius-height cross sections of the SEE-diagnosed vertical and radial \n296 \nwind forced by the diabatic heating, diabatic cooling, and cooling induced by the sublimation, \n297 \nmelting and evaporation of hydrometeors, respectively. Significantly, in NSEF, the diabatic heating \n298 \nreleased by the wider eyewall convection induces the upward motion and deep-layer outflows \n299 \noutside the inner eyewall, and a compensated downdraft in the eye (Fig. 12a). In CTL, intense \n300 \ndiabatic cooling forces subsidence of over -0.3 m s-1 outside the inner eyewall, which contributes \n301 \nto the formation of the moat. Meanwhile, the diabatic cooling also induces the upper-level inflow \n302 \nbelow the strong outflow layer (Fig. 12e). 5.3 Subsidence in response to the diabatic cooing \n280 308 \nIn NSEF, the diabatic warming released by the low- to middle-level convection outside the primary \n309 \neyewall exceeds the cooling, resulting in net diabatic warming (Fig. 12a). Thus, a wider eyewall \n310 \nwith warming-forced upward motion prevails due to the positive feedback among the diabatic \n311 \nheating and the convection (Fig. 12a). In addition, the warming-forced upward motion is \n312 \naccompanied by the deep-layer outflow (Fig. 13a), under which the low-level inflow appears \n313 \nbelow the 8-km height (Fig. 13a), which brings moist air enhancing the convection in NSEF. In \n314 14 https://doi.org/10.5194/acp-2021-147\nPreprint. Discussion started: 7 April 2021\nc⃝Author(s) 2021. CC BY 4.0 License. CTL, with the considerable cooling forced by the sublimation outside of the inner eyewall (Fig. 315 \n12g), the subsidence is induced outside the primary eyewall. Of importance is that the cooling-\n316 \nforced inflow is located at a higher level, which send dry air inward (Fig. 13b). The penetration of \n317 \ndry air through the upper-level inflow plays an important role in increasing the diabatic cooling \n318 \nthat promotes the subsidence. The cooling-induced subsidence contributes significantly to the \n319 \nformation of the moat. Subsequently, the spiral rainband evolves into the separated outer eyewall \n320 \nin CTL with the formation of the moat. 321 CTL, with the considerable cooling forced by the sublimation outside of the inner eyewall (Fig. 315 \n12g), the subsidence is induced outside the primary eyewall. Of importance is that the cooling-\n316 \nforced inflow is located at a higher level, which send dry air inward (Fig. 13b). The penetration of \n317 \ndry air through the upper-level inflow plays an important role in increasing the diabatic cooling \n318 \nthat promotes the subsidence. The cooling-induced subsidence contributes significantly to the \n319 \nformation of the moat. Subsequently, the spiral rainband evolves into the separated outer eyewall \n320 \nin CTL with the formation of the moat. 321 The differences in the azimuthal distributions of the subsidence and the related upper-level \n322 \nradial inflow between NSEF and CTL are shown in Fig. 14. In NSEF, a highly asymmetric \n323 \nstructure with strong subsidence located in the upshear-left quadrant persists during 18-32 hours \n324 \n(Fig. 14a). Although there is upper-level inflow appearing in the upshear-right region (Fig. 14a), \n325 \nit is largely offset by the strong upper-level outflow, leading to net outflow at upper levels as seen \n326 \nin Fig. 13a. 5.3 Subsidence in response to the diabatic cooing \n280 In contrast, the subsidence in CTL extends azimuthally, ending with a quasi-symmetric \n327 \nstructure from 18 h to 32 h (Fig. 14b). The azimuthal extension of the subsidence follows the \n328 \nappearance of the upper-level inflow, which advects dry air inward to enhance the cooling \n329 \nprocesses. Therefore, without the penetration of dry air by the upper-level descending inflow, the \n330 \ndiabatic cooling and the cooling-forced subsidence beneath the eyewall anvil are limited, which \n331 \nare unfavorable for the moat formation outside the inner eyewall. 332 In this study, two numerical experiments are conducted with the same large-scale \n334 \nenvironment and initial and boundary conditions. The simulated inner eyewall structures are \n335 \ndifferent due to different grid spacings used in the two experiments. The SEF occurs in CTL with \n336 \na fine resolution of 333 m, while no SEF occurs in the other with a coarse resolution of 1 km. 337 15 https://doi.org/10.5194/acp-2021-147\nPreprint. Discussion started: 7 April 2021\nc⃝Author(s) 2021. CC BY 4.0 License. There are two major differences in the eyewall structure by comparing the simulated TCs \n338 \nwith and without the SEF. For the simulated TC with the SEF, the eyewall updrafts are stronger \n339 \nand the eyewall is more upright. The eyewall anvil is located at a higher altitude together with the \n340 \ndeep eyewall convection. As illustrated in Fig. 15, the upper-level dry-air inflow beneath the high-\n341 \naltitude anvil from the inner eyewall is important to the formation of the moat. Diagnostic analysis \n342 \nindicates that the dry inflow below the eyewall anvil is induced by the diabatic cooling released \n343 \nby the sublimation, melting and evaporation of hydrometeors falling from the eyewall anvil. With \n344 \nthe penetration of dry air by the upper-level inflow, subsidence occurs, promoting the formation \n345 \nof the moat between the inner eyewall and the spiral rainband. Afterward, the SEF occurs by \n346 \nshowing the double eyewall structure and the moat with subsidence. In the TC without the SEF, \n347 \nthe eyewall updrafts are weak and tilt much outward, showing an eyewall anvil at the lower altitude. 348 \nThe cooling induced by the falling hydrometeors beneath the low-altitude eyewall anvil is \n349 \nsignificantly reduced and offset by the diabatic warming. As a result, no upper-level dry-air inflow \n350 \noccurs below the eyewall anvil, and no moat forms between the inner eyewall and the spiral \n351 \nrainband. 5.3 Subsidence in response to the diabatic cooing \n280 In addition to the mesoscale descending inflow at \n362 \nmiddle levels, the upper-level dry inflow also contributes to the SEF by forcing the moat formation. 363 \nIn this sense, both the inner-eyewall and the rainband structures are important to the SEF. In \n364 \naddition, our study suggests that a realistic simulation of the eyewall convection is important to \n365 \nthe prediction of the SEF in the numerical forecasting model. 366 trigger new convective updrafts that are important to the subsequent SEF (Didlake et al., 2018; \n361 \nWunsch and Didlake, 2018; Yu et al., 2020). In addition to the mesoscale descending inflow at \n362 \nmiddle levels, the upper-level dry inflow also contributes to the SEF by forcing the moat formation. 363 \nIn this sense, both the inner-eyewall and the rainband structures are important to the SEF. In \n364 \naddition, our study suggests that a realistic simulation of the eyewall convection is important to \n365 \nthe prediction of the SEF in the numerical forecasting model. 366 Data availability. The simulation data is archived at the High-Performance Computing Center of \n368 \nNanjing University of Information Science and Technology and is available upon request. 369 Data availability. The simulation data is archived at the High-Performance Computing Center of \n368 \nNanjing University of Information Science and Technology and is available upon request. 369 Data availability. The simulation data is archived at the High-Performance Computing Center of \n368 \nNanjing University of Information Science and Technology and is available upon request. 369 Author contributions. LW designed research; NQ conceptualized the analysis and wrote the \n371 \nmanuscript; LW provided scientific suggestions for the manuscript. QL carried out the simulations \n372 \nand modified the model code. All authors were involved in helpful discussions and contributions \n373 \nto the manuscript. 374 Author contributions. LW designed research; NQ conceptualized the analysis and wrote the \n371 \nmanuscript; LW provided scientific suggestions for the manuscript. QL carried out the simulations \n372 \nand modified the model code. All authors were involved in helpful discussions and contributions \n373 \nto the manuscript. 374 Author contributions. LW designed research; NQ conceptualized the analysis and wrote the \n371 \nmanuscript; LW provided scientific suggestions for the manuscript. QL carried out the simulations \n372 \nand modified the model code. All authors were involved in helpful discussions and contributions \n373 \nto the manuscript. 374 Competing interests. The authors declare that they have no conflict of interest. 375 Acknowledgments. 5.3 Subsidence in response to the diabatic cooing \n280 352 There are two major differences in the eyewall structure by comparing the simulated TCs \n338 \nwith and without the SEF. For the simulated TC with the SEF, the eyewall updrafts are stronger \n339 \nand the eyewall is more upright. The eyewall anvil is located at a higher altitude together with the \n340 \ndeep eyewall convection. As illustrated in Fig. 15, the upper-level dry-air inflow beneath the high-\n341 \naltitude anvil from the inner eyewall is important to the formation of the moat. Diagnostic analysis \n342 \nindicates that the dry inflow below the eyewall anvil is induced by the diabatic cooling released \n343 \nby the sublimation, melting and evaporation of hydrometeors falling from the eyewall anvil. With \n344 \nthe penetration of dry air by the upper-level inflow, subsidence occurs, promoting the formation \n345 \nof the moat between the inner eyewall and the spiral rainband. Afterward, the SEF occurs by \n346 \nshowing the double eyewall structure and the moat with subsidence. In the TC without the SEF, \n347 \nthe eyewall updrafts are weak and tilt much outward, showing an eyewall anvil at the lower altitude. 348 \nThe cooling induced by the falling hydrometeors beneath the low-altitude eyewall anvil is \n349 \nsignificantly reduced and offset by the diabatic warming. As a result, no upper-level dry-air inflow \n350 \noccurs below the eyewall anvil, and no moat forms between the inner eyewall and the spiral \n351 \nrainband. 352 Our study highlights the importance of the inner eyewall structure in the moat formation \n353 \nthrough the cooling-induced upper-level inflow and subsidence beneath the eyewall anvil. While \n354 \nthe subsidence induced by the evaporative cooling from the precipitation at the outer radii from \n355 \nthe anvil is revealed by Tyner et al. (2018), who emphasized the role of the penetrative downdraft \n356 \nin promoting the local rainband convection and the subsequent outer eyewall formation, the \n357 \ncooling-induced upper-level dry-air inflow and its important role in the moat formation are not \n358 \nmentioned in their study. Recent studies indicated that a mesoscale descending inflow driven by \n359 \nthe middle-level melting and evaporative cooling in the downwind portion of the rainband can \n360 16 https://doi.org/10.5194/acp-2021-147\nPreprint. Discussion started: 7 April 2021\nc⃝Author(s) 2021. CC BY 4.0 License. trigger new convective updrafts that are important to the subsequent SEF (Didlake et al., 2018; \n361 \nWunsch and Didlake, 2018; Yu et al., 2020). 5.3 Subsidence in response to the diabatic cooing \n280 This study was jointly supported by the National Natural Science Foundation \n376 \nof China (41730961, 41675009, 42075072, 41905001), the Postdoctoral Science Foundation of \n377 \nChina (2019M661342), the Natural Science Foundation of Jiangsu Province (BK20201505), and \n378 \nthe Open Research Program of the State Key Laboratory of Severe Weather (2019LASW-A02). 379 \nWe would like to acknowledge the use of computational resources for conducting the simulations \n380 \nat the High-Performance Computing Center of Nanjing University of Information Science and \n381 \nTechnology. 382 17 17 https://doi.org/10.5194/acp-2021-147\nPreprint. Discussion started: 7 April 2021\nc⃝Author(s) 2021. CC BY 4.0 License. References 383 Abarca, S. F. and Montgomery, M. 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Rev., \n143, \n914-932, \ndoi: \n516 \nhttps://doi.org/10.1175/MWR-D-14-00102.1, 2015. 517 \nZhao, K., Lee, W.-C., and Jou, B. J.-D.: Single Doppler radar observation of the concentric eyewall \n518 \nin Typhoon Saomai, 2006, near landfall. Geophys. Res. Lett., 35, L07807, doi: \n519 \nhttps://doi.org/10.1029/2007GL032773, 2008. 520 \nZhao, K., Lin, Q., Lee, W-C., Sun, Y., and Zhang, F.: Doppler radar analysis of triple eyewalls in \n521 \nTyphoon \nUsagi \n(2013). Bull. Amer. Meteor. Soc., \n97, \n25-30, \ndoi: \n522 \nhttps://doi.org/10.1175/BAMS-D-15-00029.1, 2016. 523 \nZhu, T., and Zhang, D.-L.: Numerical simulation of Hurricane Bonnie (1998). Part II: Sensitivity \n524 \nto varying cloud microphysical processes, J. Atmos. Sci., 63, 109-126, doi: \n525 \nhttps://doi.org/10.1175/JAS3599.1, 2006. 526 \nZhu, Z., and Zhu, P.: The role of outer rainband convection in governing the eyewall replacement \n527 \ncycle in numerical simulations of tropical cyclones, J. Geophys. Res. 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Soc., \n97, \n25-30, \ndoi: \n522 \nhttps://doi.org/10.1175/BAMS-D-15-00029.1, 2016. doi: 523 Zhao, K., Lin, Q., Lee, W-C., Sun, Y., and Zhang, F.: Doppler radar analysis of triple\n521 Zhu, T., and Zhang, D.-L.: Numerical simulation of Hurricane Bonnie (1998). Part II: Sensitivity \n524 \nto varying cloud microphysical processes, J. Atmos. Sci., 63, 109-126, doi: \n525 \nhttps://doi.org/10.1175/JAS3599.1, 2006. 526 to varying cloud microphysical processes, J. Atmos. Sci., 63, 109-126, doi: \n525 \nhttps://doi.org/10.1175/JAS3599.1, 2006. 526 Zhu, Z., and Zhu, P.: The role of outer rainband convection in governing the eyewall replacement \n527 \ncycle in numerical simulations of tropical cyclones, J. Geophys. Res. Atmos., 119, 8049-8072, \n528 \ndoi: 10.1002/2014JD021899, 2014. 529 Zhu Z., and Zhu, P.: Sensitivities of eyewall replacement cycle to model physics, vortex structure, \n530 \nand background winds in numerical simulations of tropical cyclones, J. Geophys. Res. Atmos., \n531 \n120, 590-622, doi: 10.1002/2014JD022056, 2015. 532 24 534 \nFigure 1. Time series of intensity changes for the maximum azimuthal-mean near-surface wind \n535 \n(VMAX, m s-1) during the 72-h sensitivity (NSEF, black) and control run (CTL, red). The gray \n536 \nshading denotes the period of the eyewall replacement circle. 537 \nhttps://doi.org/10.5194/acp-2021-147\nPreprint. Discussion started: 7 April 2021\nc⃝Author(s) 2021. CC BY 4.0 License. https://doi.org/10.5194/acp-2021-147\nPreprint. Discussion started: 7 April 2021\nc⃝Author(s) 2021. CC BY 4.0 License. 534 \nFigure 1. Time series of intensity changes for the maximum azimuthal-mean near-surface wind\n535\nPreprint. Discussion started: 7 April 2021\nc⃝Author(s) 2021. CC BY 4.0 License. 534 \nFigure 1. Time series of intensity changes for the maximum azimuthal-mean near-surface wind \n535 \n(VMAX, m s-1) during the 72-h sensitivity (NSEF, black) and control run (CTL, red). The gray \n536 \nshading denotes the period of the eyewall replacement circle. 537 534 Figure 1. Time series of intensity changes for the maximum azimuthal-mean near-surface wind \n535 \n(VMAX, m s-1) during the 72-h sensitivity (NSEF, black) and control run (CTL, red). The gray \n536 \nshading denotes the period of the eyewall replacement circle. 537 25 https://doi.org/10.5194/acp-2021-147\nPreprint. Discussion started: 7 April 2021\nc⃝Author(s) 2021. CC BY 4.0 License. 538 \nFigure 2. Time-radius cross-sections of the azimuthal-mean (a, b) tangential wind (m s-1) and (c\n539 \nd) vertical motion (m s-1) at 0.5-km height for (a, c) NSEF and (b, d) CTL. The solid lines\n540 \nindicate the radius of the maximum tangential wind (RMW). doi: The black dashed lines indicate\n541 \nthe SEF, while the blue dashed lines denote the time when the secondary maximum wind is\n542 \nequal to the primary maximum wind. 543 538 538 \nFigure 2. Time-radius cross-sections of the azimuthal-mean (a, b) tangential wind (m s-1) and (c, \n539 \nd) vertical motion (m s-1) at 0.5-km height for (a, c) NSEF and (b, d) CTL. The solid lines \n540 \nindicate the radius of the maximum tangential wind (RMW). The black dashed lines indicate \n541 \nthe SEF, while the blue dashed lines denote the time when the secondary maximum wind is \n542 \nequal to the primary maximum wind. 543 26 https://doi.org/10.5194/acp-2021-147\nPreprint. Discussion started: 7 April 2021\nc⃝Author(s) 2021. CC BY 4.0 License. 544 \nFigure 3. Horizontal distributions of the radar reflectivity at 5-km height at (a, d) 28, (b, e) 32, and \n545 \n(c, f) 44 h for (a-c) NSEF and (d-f) CTL. Vectors are the large-scale vertical wind shear (VWS, \n546 \nVspeed (200 hPa) -Vspeed (850 hPa)). 547 Figure 3. Horizontal distributions of the radar reflectivity at 5-km height at (a, d) 28, (b, e) 32, and \n545 \n(c, f) 44 h for (a-c) NSEF and (d-f) CTL. Vectors are the large-scale vertical wind shear (VWS, \n546 \nVspeed (200 hPa) -Vspeed (850 hPa)). 547 27 548 \nFigure 4. Radius-height cross-sections of the azimuthal-mean vertical motion (shaded, m s-1), in-\n549 \nplain flow (vector, m s-1) and radial inflows of -1 and -3 m s-1 (white contours) at (a, c) 30 h \n550 \nand (b, d) 32 h for (a, b) NSEF and (c, d) CTL. The white dashed arrows denote the eyewall. 551 \n \n \n552 \nhttps://doi.org/10.5194/acp-2021-147\nPreprint. Discussion started: 7 April 2021\nc⃝Author(s) 2021. CC BY 4.0 License. https://doi.org/10.5194/acp-2021-147\nPreprint. Discussion started: 7 April 2021\nc⃝Author(s) 2021. CC BY 4.0 License. 548 \nFigure 4 Radius-height cross-sections of the azimuthal-mean vertical motion (shaded m s-1) in-\n549 548 \nFigure 4. Radius-height cross-sections of the azimuthal-mean vertical motion (shaded, m s-1), in-\n549 \nplain flow (vector, m s-1) and radial inflows of -1 and -3 m s-1 (white contours) at (a, c) 30 h \n550 \nand (b, d) 32 h for (a, b) NSEF and (c, d) CTL. The white dashed arrows denote the eyewall. 551 \n \n \n552 Figure 4. doi: Radius-height cross-sections of the azimuthal-mean vertical motion (shaded, m s-1), in-\n549 \nplain flow (vector, m s-1) and radial inflows of -1 and -3 m s-1 (white contours) at (a, c) 30 h \n550 \nand (b, d) 32 h for (a, b) NSEF and (c, d) CTL. The white dashed arrows denote the eyewall. 551 \n552 28 https://doi.org/10.5194/acp-2021-147\nPreprint. Discussion started: 7 April 2021\nc⃝Author(s) 2021. CC BY 4.0 License. https://doi.org/10.5194/acp-2021-147\nPreprint. Discussion started: 7 April 2021\nc⃝Author(s) 2021. CC BY 4.0 License. 553 \n554 553 \n \n554 \nFigure 5. The contoured frequency by altitude diagram (CFAD, %) of (a) the vertical motion for \n555 \nthe 10-km radially inside and outside of the RMW and (b) the radial wind within a radial \n556 \ndistance of 60 km starting from the radius of 10-km outside the eyewall (RMW+10 km to \n557 \nRMW+70 km) for CTL (dashed lines) and NSEF (solid lines) at 30 h. The red and blue lines \n558 \nare the 0.1, and 0.05 percentile. 559 553 \n554 Figure 5. The contoured frequency by altitude diagram (CFAD, %) of (a) the vertical motion for \n555 \nthe 10-km radially inside and outside of the RMW and (b) the radial wind within a radial \n556 \ndistance of 60 km starting from the radius of 10-km outside the eyewall (RMW+10 km to \n557 \nRMW+70 km) for CTL (dashed lines) and NSEF (solid lines) at 30 h. The red and blue lines \n558 \nare the 0.1, and 0.05 percentile. 559 29 https://doi.org/10.5194/acp-2021-147\nPreprint. Discussion started: 7 April 2021\nc⃝Author(s) 2021. CC BY 4.0 License. https://doi.org/10.5194/acp-2021-147\nPreprint. Discussion started: 7 April 2021\nc⃝Author(s) 2021. CC BY 4.0 License. 560 560 \nFigure 6. Horizontal distribution of the cloud-top temperature (CTT, shaded, Co) superimposed \n561 \nwith the 15-km horizontal wind field (vector, m s-1) and RMW (white circle) at 30 h for (a) \n562 \nNSEF and (b) CTL. The black circle indicates the radius of 100 km relative to the TC center. 563 560 560 Figure 6. Horizontal distribution of the cloud-top temperature (CTT, shaded, Co) superimposed \n561 \nwith the 15-km horizontal wind field (vector, m s-1) and RMW (white circle) at 30 h for (a) \n562 \nNSEF and (b) CTL. The black circle indicates the radius of 100 km relative to the TC center. 563 30 564 \nFigure 7. doi: Radius-height cross-sections of the upshear-right quadrant-mean perturbation virtual \n565 \npotential temperature (shaded, K) at 30 h for (a) NSEF and (b) CTL. Contours are the vertical \n566 \n1\nhttps://doi.org/10.5194/acp-2021-147\nPreprint. Discussion started: 7 April 2021\nc⃝Author(s) 2021. CC BY 4.0 License. https://doi.org/10.5194/acp-2021-147\nPreprint. Discussion started: 7 April 2021\nc⃝Author(s) 2021. CC BY 4.0 License. 564 \nFigure 7. Radius-height cross-sections of the upshear-right quadrant-mean perturbation virtual \n565 \npotential temperature (shaded, K) at 30 h for (a) NSEF and (b) CTL. Contours are the vertical \n566 \nmotion (updraft, black solid contours: 0.5 m s-1; downdrafts, black dashed contours: 0.05 m \n567 \ns-1). The black dashed arrows denote the eyewall. 568 564 \nFigure 7. Radius-height cross-sections of the upshear-right quadrant-mean perturbation virtual \n565 \npotential temperature (shaded, K) at 30 h for (a) NSEF and (b) CTL. Contours are the vertical \n566 \nmotion (updraft, black solid contours: 0.5 m s-1; downdrafts, black dashed contours: 0.05 m \n567 \ns-1). The black dashed arrows denote the eyewall. 568 Figure 7. Radius-height cross-sections of the upshear-right quadrant-mean perturbation virtual \n565 \npotential temperature (shaded, K) at 30 h for (a) NSEF and (b) CTL. Contours are the vertical \n566 \nmotion (updraft, black solid contours: 0.5 m s-1; downdrafts, black dashed contours: 0.05 m \n567 \ns-1). The black dashed arrows denote the eyewall. 568 31 https://doi.org/10.5194/acp-2021-147\nPreprint. Discussion started: 7 April 2021\nc⃝Author(s) 2021. CC BY 4.0 License. 569 \nFigure 8. Radius-height cross-sections of the upshear-right quadrant-mean (a, e) buoyance force \n570 \n(shaded, 10-3 m s-2), (b, f) the thermal buoyancy (shaded, 10-3 m s-2), (c, g) the dynamic \n571 \nbuoyancy (shaded, 10-3 m s-2), and (d, h) the hydrometeor loading (shaded, 10-3 m s-2) \n572 \nsuperimposed with the vertical motion (updraft, black solid contours: 0.5 m s-1; downdrafts, \n573 \nblack dashed contours: 0.05 m s-1) at 30 h for (a-d) NSEF and (e-h) CTL. The black dashed \n574 \narrows denote the eyewall. 575 Figure 8. Radius-height cross-sections of the upshear-right quadrant-mean (a, e) buoyance force \n570 \n(shaded, 10-3 m s-2), (b, f) the thermal buoyancy (shaded, 10-3 m s-2), (c, g) the dynamic \n571 \nbuoyancy (shaded, 10-3 m s-2), and (d, h) the hydrometeor loading (shaded, 10-3 m s-2) \n572 \nsuperimposed with the vertical motion (updraft, black solid contours: 0.5 m s-1; downdrafts, \n573 \nblack dashed contours: 0.05 m s-1) at 30 h for (a-d) NSEF and (e-h) CTL. The black dashed \n574 \narrows denote the eyewall. doi: 575 Figure 8. Radius-height cross-sections of the upshear-right quadrant-mean (a, e) buoyance force \n570 \n(shaded, 10-3 m s-2), (b, f) the thermal buoyancy (shaded, 10-3 m s-2), (c, g) the dynamic \n571 \nbuoyancy (shaded, 10-3 m s-2), and (d, h) the hydrometeor loading (shaded, 10-3 m s-2) \n572 \nsuperimposed with the vertical motion (updraft, black solid contours: 0.5 m s-1; downdrafts, \n573 \nblack dashed contours: 0.05 m s-1) at 30 h for (a-d) NSEF and (e-h) CTL. The black dashed \n574 \narrows denote the eyewall. 575 32 576 \nFigure 9. Radius-height cross-sections of the upshear-right quadrant-mean (a, b) vertical pressure \n577 \ngradient force (shaded, 10-3 m s-2) and (c, d) the sum of buoyancy and vertical pressure \n578 \ngradient force (shaded, 10-3 m s-2), superimposed with the vertical motion (updraft, black solid \n579 \ncontours: 0.5 m s-1; downdrafts, black dashed contours: 0.05 m s-1) at 30 h for (a, c) NSEF \n580 \nand (b, d) CTL. The black dashed arrows denote the eyewall. 581 \nhttps://doi.org/10.5194/acp-2021-147\nPreprint. Discussion started: 7 April 2021\nc⃝Author(s) 2021. CC BY 4.0 License. https://doi.org/10.5194/acp-2021-147\nPreprint. Discussion started: 7 April 2021\nc⃝Author(s) 2021. CC BY 4.0 License. 576 \nFigure 9. Radius-height cross-sections of the upshear-right quadrant-mean (a, b) vertical pressure \n577 \ngradient force (shaded, 10-3 m s-2) and (c, d) the sum of buoyancy and vertical pressure \n578 \ngradient force (shaded, 10-3 m s-2), superimposed with the vertical motion (updraft, black solid \n579 \ncontours: 0.5 m s-1; downdrafts, black dashed contours: 0.05 m s-1) at 30 h for (a, c) NSEF \n580 \nand (b, d) CTL. The black dashed arrows denote the eyewall. 581 576 \nFi\n9 R di\nh i ht\nti\nf th\nh\ni ht\nd\nt\n(\nb)\nti\nl\n577 Figure 9. Radius-height cross-sections of the upshear-right quadrant-mean (a, b) vertical pressure \n577 \ngradient force (shaded, 10-3 m s-2) and (c, d) the sum of buoyancy and vertical pressure \n578 \ngradient force (shaded, 10-3 m s-2), superimposed with the vertical motion (updraft, black solid \n579 \ncontours: 0.5 m s-1; downdrafts, black dashed contours: 0.05 m s-1) at 30 h for (a, c) NSEF \n580 \nand (b, d) CTL. The black dashed arrows denote the eyewall. 581 33 https://doi.org/10.5194/acp-2021-147\nPreprint. Discussion started: 7 April 2021\nc⃝Author(s) 2021. CC BY 4.0 License. 582 \nFigure 10. doi: Radius-height cross-sections of the upshear-right quadrant-mean (a, e) diabatic heating\n583 \nrate (shaded, 10-3 K s-1), (b, f) cooling rate including evaporation, melting and sublimation\n584 \nprocesses (shaded, 10-3 K s-1), (c, g) sublimation cooling rate, and (d, h) melting and\n585 \nevaporation cooling rates superimposed with the vertical motion (updraft, solid lines of 0.5\n586 \nm s-1; downdrafts, dashed lines of -0.05 and -0.3 m s-1) at 30 h for (a-d) NSEF and (e-h) CTL\n587 \nThe black dashed arrows denote the eyewall. 588 582 \nFigure 10. Radius-height cross-sections of the upshear-right quadrant-mean (a, e) diabatic heating \n583 \nrate (shaded, 10-3 K s-1), (b, f) cooling rate including evaporation, melting and sublimation \n584 \nprocesses (shaded, 10-3 K s-1), (c, g) sublimation cooling rate, and (d, h) melting and \n585 \nevaporation cooling rates superimposed with the vertical motion (updraft, solid lines of 0.5 \n586 \nm s-1; downdrafts, dashed lines of -0.05 and -0.3 m s-1) at 30 h for (a-d) NSEF and (e-h) CTL. 587 \nThe black dashed arrows denote the eyewall. 588 582 \nFigure 10. Radius-height cross-sections of the upshear-right quadrant-mean (a, e) diabatic heating \n583 \nrate (shaded, 10-3 K s-1), (b, f) cooling rate including evaporation, melting and sublimation \n584 \nprocesses (shaded, 10-3 K s-1), (c, g) sublimation cooling rate, and (d, h) melting and \n585 \nevaporation cooling rates superimposed with the vertical motion (updraft, solid lines of 0.5 \n586 \nm s-1; downdrafts, dashed lines of -0.05 and -0.3 m s-1) at 30 h for (a-d) NSEF and (e-h) CTL. 587 \nThe black dashed arrows denote the eyewall. 588 34 https://doi.org/10.5194/acp-2021-147\nPreprint. Discussion started: 7 April 2021\nc⃝Author(s) 2021. CC BY 4.0 License. https://doi.org/10.5194/acp-2021-147\nPreprint. Discussion started: 7 April 2021\nc⃝Author(s) 2021. CC BY 4.0 License. Figure 11. Azimuthal-time cross-sections of the layer-mean (11.5-12.5 km) diabatic cooling \n(shaded, 10-3 K s-1) and subsidence (contour, m s-1) averaged within a radial distance of 25 \nkm starting from the radius of 5-km outside the eyewall (RMW+5 km to RMW+30 km) of \n(a) NSEF, (b) CTL, and (c) differences between CTL and NSEF. The black contours are -0.8 \nm s-1 in (a, b) and -0.4 m s-1 in (c). Figure 11. doi: Azimuthal-time cross-sections of the layer-mean (11.5-12.5 km) diabatic cooling \n590 \n(shaded, 10-3 K s-1) and subsidence (contour, m s-1) averaged within a radial distance of 25 \n591 \nkm starting from the radius of 5-km outside the eyewall (RMW+5 km to RMW+30 km) of \n592 \n(a) NSEF, (b) CTL, and (c) differences between CTL and NSEF. The black contours are -0.8 \n593 \nm s-1 in (a, b) and -0.4 m s-1 in (c). 594 35 https://doi.org/10.5194/acp-2021-147\nPreprint. Discussion started: 7 April 2021\nc⃝Author(s) 2021. CC BY 4.0 License. 595 \nFigure 12. Radius-height cross-sections of the upshear-right quadrant-mean vertical (shaded\n596 \n1) and radial motion (contours, m s-1) forced by the (a, e) diabatic heating, (b, f) hydrome\n597 \ncooling, (c, g) sublimation cooling, (d, h) melting and evaporation cooling at 30 h for \n598 \nNSEF and (c-h) CTL. Note that the radial wind is at 2 m s-1 intervals in (a) and (e), and\n599 \ns-1 intervals in others. The white dashed lines with 0.5 m s-1 vertical motion indicat\n600 \neyewall convection region. The black dashed arrows denote the eyewall. 601 Figure 12. Radius-height cross-sections of the upshear-right quadrant-mean vertical (shaded, m s-\n596 \n1) and radial motion (contours, m s-1) forced by the (a, e) diabatic heating, (b, f) hydrometeors \n597 \ncooling, (c, g) sublimation cooling, (d, h) melting and evaporation cooling at 30 h for (a-d) \n598 \nNSEF and (c-h) CTL. Note that the radial wind is at 2 m s-1 intervals in (a) and (e), and 1 m \n599 \ns-1 intervals in others. The white dashed lines with 0.5 m s-1 vertical motion indicate the \n600 \neyewall convection region. The black dashed arrows denote the eyewall. 601 36 https://doi.org/10.5194/acp-2021-147\nPreprint. Discussion started: 7 April 2021\nc⃝Author(s) 2021. CC BY 4.0 License. https://doi.org/10.5194/acp-2021-147\nPreprint. Discussion started: 7 April 2021\nc⃝Author(s) 2021. CC BY 4.0 License. https://doi.org/10.5194/acp-2021-147\nPreprint. Discussion started: 7 April 2021\nc⃝Author(s) 2021. CC BY 4.0 License. 602 \nFigure 13. Radius-height cross-sections of the the upshear-right quadrant-mean relative humidity \n603 602 \nFigure 13. Radius-height cross-sections of the the upshear-right quadrant-mean relative humidity \n603 \n(shaded, %) and in-plain flows (vector, m s-1) at t = 30 h for (a) NSEF and (b) CTL. The black \n604 \nand purple lines are radial inflows of 0 01 and 1 m s-1 respectively The red dashed arrow\n605 Figure 13. doi: Radius-height cross-sections of the the upshear-right quadrant-mean relative humidity \n603 \n(shaded, %) and in-plain flows (vector, m s-1) at t = 30 h for (a) NSEF and (b) CTL. The black \n604 \nand purple lines are radial inflows of -0.01 and -1 m s-1, respectively. The red dashed arrow \n605 \nindicates the upper-level dry inflows. 606 37 https://doi.org/10.5194/acp-2021-147\nPreprint. Discussion started: 7 April 2021\nc⃝Author(s) 2021. CC BY 4.0 License. https://doi.org/10.5194/acp-2021-147\nPreprint. Discussion started: 7 April 2021\nc⃝Author(s) 2021. CC BY 4.0 License. 607 \nFigure 14. Same as in Fig. 11 but for subsidence (shaded, m s-1) and radial inflows (contour, m s-\n608 \n1) of (a) NSEF, (b) CTL, and (c) differences between CTL and NSEF. 609 \n \n \n610 607 \nFigure 14. Same as in Fig. 11 but for subsidence (shaded, m s-1) and radial inflows (contour, m s-\n608 \n1) of (a) NSEF, (b) CTL, and (c) differences between CTL and NSEF. 609 \n610 607 \nFigure 14. Same as in Fig. 11 but for subsidence (shaded, m s-1) and radial inflows (contour, m s-\n608 \n1) of (a) NSEF, (b) CTL, and (c) differences between CTL and NSEF. 609 \n610 38 38 https://doi.org/10.5194/acp-2021-147\nPreprint. Discussion started: 7 April 2021\nc⃝Author(s) 2021. CC BY 4.0 License. https://doi.org/10.5194/acp-2021-147\nPreprint. Discussion started: 7 April 2021\nc⃝Author(s) 2021. CC BY 4.0 License. 611 611 \n \n612 \nFigure 15. The inner-core structures of a hurricane undergoing the eyewall replacement circle, \n613 \nincluding the eye, the primary eyewall, the moat, and the rainband of evolving into the \n614 \nsecondary eyewall. The black solid arrows denote the air motion relative to the TC. The black \n615 \ndashed arrows show the upper-level descending inflows beneath the cumulus anvil from the \n616 \ninner eyewall. The light blue shading indicates the cooling induced by the sublimation, \n617 \nmelting, and evaporation of hydrometeors (ice, snow, graupel, and raindrops) associated with \n618 \nthe moat subsidence. The gray dashed lines indicate the precipitation below the clouds. The \n619 \nred solid line denotes the 0 oC temperature of the melting level. 620 611 \n612 Figure 15. The inner-core structures of a hurricane undergoing the eyewall replacement circle, \n613 \nincluding the eye, the primary eyewall, the moat, and the rainband of evolving into the \n614 \nsecondary eyewall. The black solid arrows denote the air motion relative to the TC. doi: The black \n615 \ndashed arrows show the upper-level descending inflows beneath the cumulus anvil from the \n616 \ninner eyewall. The light blue shading indicates the cooling induced by the sublimation, \n617 \nmelting, and evaporation of hydrometeors (ice, snow, graupel, and raindrops) associated with \n618 \nthe moat subsidence. The gray dashed lines indicate the precipitation below the clouds. The \n619 \nred solid line denotes the 0 oC temperature of the melting level. 620 39"

ERROR: type should be string, got "https://doi.org/10.5194/wes-2021-24\nPreprint. Discussion started: 29 April 2021\nc Author(s) 2021. CC BY 4.0 License.\n\nValidation of a modelling methodology for wind turbine rotor blades\nbased on a full scale blade test\nPablo Noever-Castelos1 , Bernd Haller2 , and Claudio Balzani1\n1\n2\n\nLeibniz University Hannover, Institute for Wind Energy Systems, Appelstr. 9A, Hanover, 30167, Germany\nFraunhofer Institute for Wind Energy Systems IWES, Am Seedeich 45, 27572 Bremerhaven, Germany\n\nCorrespondence: Pablo Noever-Castelos (research@iwes.uni-hannover.de)\nAbstract. Detailed 3D finite element simulations are state of the art for structural analyses of wind turbine rotor blades. It is\nof utmost importance to validate the underlying modelling methodology in order to obtain reliable results. Validation of the\nglobal response can ideally be done by comparing simulations with full scale blade tests. However, there is a lack of test results\nfor which the blade data are completely available.\nThe aim of this paper is to validate one particular blade modelling methodology that is implemented in an in-house model\n\n5\n\ngenerator, and to provide respective test results to the public. A hybrid 3D shell/solid element model is created including the\nrespective boundary conditions. The problem is solved via a commercially available finite element code. A full scale blade\ntest is performed as the validation reference, for which all relevant data are available. Some data have been measured prior to\nor after the test in order to account for manufacturing deviations. The tests comprise classical bending tests in flap-wise and\n10\n\nlead-lag direction as well as torsion tests.\nFor the validation of the modelling methodology, global blade characteristics from measurements and simulation are compared. These include the overall mass and centre of gravity as well as their distributions along the blade, deflections, strain\nlevels, and natural frequencies and modes. Overall, good agreement is obtained, though some improvements might be required\nfor the response in torsion. As a conclusion, the modelling strategy can be rated as validated.\n\n15\n\n1\n\nIntroduction\n\nRotor blades are major components of wind turbines. They are susceptible to damages, which, in case they need repair, can\nresult in severe turbine downtimes (Reder et al., 2016). It is thus crucial to develop a blade design that withstands all designated\nloads without damage. Though a blade prototype is always tested at the full blade scale in the certification process (International\nEletrotechnical Comission, 2014), such tests are very costly and time-consuming, especially for growing blade dimensions (Ha\n20\n\net al., 2020). For this reason, full scale blade tests are executed one time only for the final validation of design assumptions.\nHence, a reliable and fast virtual blade design procedure is required. Full 3D finite element (FE) analysis is accurate but\ncomputationally expensive. A widely used approach for wind turbine blade design is to carry out two-dimensional crosssectional analyses that offer a reduced level of complexity but are a fast and efficient alternative for rotor blade pre-designs\n(Chen et al., 2010). Tools like VABS (Yu et al., 2002) or BECAS (DTU Wind Energy) compute cross-sectional properties based\n\n1\n\n\fhttps://doi.org/10.5194/wes-2021-24\nPreprint. Discussion started: 29 April 2021\nc Author(s) 2021. CC BY 4.0 License.\n\n25\n\non a 2D-FE-analysis, which are necessary to feed the aero-elastic models in order to recalculate the design loads on the turbine\nblades and close the design iteration loop. Nevertheless, at a final stage 3D FE analyses have to be performed in order to obtain\na reliable blade design and double check structural details such as adhesive joints, geometric discontinuities, ply drops, etc.\nAutomated model creation is state of the art and a key to enhance the design process significantly by reducing time consumption, increasing the possible number of design loops and avoiding modelling errors. Among a vast selection of common\n\n30\n\nsoftware tools originated from the scientific community, QBlade (D. Marten et al., 2013) for example focuses on the aerodynamic blade design, neglecting details on structural information. Sandia’s NuMAD (Jonathan C. Berg and Brian R. Resor,\n2012) additionally contains a more sophisticated structural description taking into account a proper composite definition for the\nblades’ subcomponents. Same holds for the software package FOCUS developed by WMC Laboratories which is now part of\nLM Wind Power (N. P. Duineveld, 2008), which is a state of the art tool used for blade design in many engineering offices. In\n\n35\n\nFOCUS the user discretizes a few stations in span-wise direction with all necessary geometrical information of these particular\ncross-section and in between the tool interpolates linearly all missing data. Hence a high discretization of stations along the\nblade span is necessary to correctly reproduce non-linear changing geometrical or material information in span-wise direction.\nAnother more advanced tool is the optimization framework CP-Max, see Bottasso et al. (2014). The parametrization is based\non mathematical functions for the blade design description in span-wise direction. This method has the advantage of reducing\n\n40\n\nthe number of stations along the blade without loosing information in between, while enabling the framework to efficiently\nmanipulate the parameters during optimization. The focus of the optimization framework is to find a solution at minimum\ncosts. A similar blade parametrization is used within the FUSED-Wind Framework (Zahle et al., 2020), which contains spline\ndescriptions for each parameter as shown in the prominent example of the DTU 10MW reference blade design (C. Bak et al.,\n2013). An interface to the framework was later incorporated into the python-tool FEPROC and the correct modelling process\n\n45\n\nwas verified against the DTU 10MW reference blade (Rosemeier, 2018). Another blade modelling tool developed at Ghent\nUniversity also relies on function-based descriptions of the blade parameters and focuses on a modular principle of Finite\nElement (FE) constellations for modelling the different blade components and joints in the structure (Peeters et al., 2018). The\nlatter algorithm and CP-Max are able of generating solid element models, while the others rely on more common shell element\nrepresentations.\n\n50\n\nThough some of these model creation frameworks may work with functions or splines describing the blade’s geometrical or\nlayup information, most of them work with a reasonably high number of airfoils/stations that in addition to the blade’s geometry\nyield the outer blade shape by a global linear or higher order interpolation between the airfoils. Similar to Rosemeier (2018),\nwho uses Parametric Geometry Library (PGL, Zahle (2020)) to interpolate additional airfoils, the presented algorithm in this\nwork generates airfoils independent from the other parameters and uses the relative thickness distribution to position these\n\n55\n\nalong the span. Additionally a more detailed adaption of blade and material parameters is implemented to consider changes\nalong the span for all characteristics of the blade’s structure.\nA lot of scientific contributions deal with FE modelling and focus on structural details like trailing edge adhesive joints. Eder\nand Bitsche (2015) for instance use a local model with fracture analysis to deduce the debonding between shell and adhesive\ndue to buckling and validate the behaviour against experimental results. Ji and Han (2014) also apply fracture mechanics and\n2\n\n\fhttps://doi.org/10.5194/wes-2021-24\nPreprint. Discussion started: 29 April 2021\nc Author(s) 2021. CC BY 4.0 License.\n\n60\n\nuse a detailed model at the shear web adhesive joint to analyse crack propagation in the bond line. Most of these locally detailed\nmodels are used within a global-local modelling approach like in Chen et al. (2014) to reduce the global model complexity\nwhile keeping a high level of detail at local spots. However, this paper focuses on the global elastic response of wind turbine\nblades, so there is no need for local sub-models.\nDifferent FE modelling procedures can result in different deformation and stress solutions, though based on the same model\n\n65\n\nparameters, see (Lekou et al., 2015). Hence, it is important to validate modelling strategies by comparing simulations with full\nblade tests, which is the aim of this paper. A quasi-static full scale blade test is performed, including not only bending tests in\nflap and lead-lag direction – as are usually executed in the context of blade certification (International Eletrotechnical Comission, 2014) – but also torsion tests. This allows for an exceptionally detailed and thorough validation. Unlike other blade tests\nreported in literature (?), (Chen et al., 2017), (Jensen et al., 2006), (Overgaard and Lund, 2010), (Overgaard et al., 2010), the\n\n70\n\naim of the tests in this work is not the validation of failure models. Hence, the blade is not loaded up to failure. The aim rather\nis to measure the global blade behaviour expressed in terms of deflections, strains, mass distribution, and modal characteristics\nand to validate our own blade modelling technique. The blade under investigation is the SmartBlades DemoBlade (REFERENCE TO COME), a 20 m blade including pre-bend and pre-sweep towards the trailing edge. The blade is modelled with our\nin-house blade model creation tool MoCA (Model Creation and Analysis Tool for Wind Turbine Rotor Blades), taking into\n\n75\n\naccount some major manufacturing-related deviations. The test setup and the load introduction are approximated via a combination of suitable boundary conditions and multiple point constraints. The simulation results are thoroughly compared with\nthe test measurements. Generally good agreement is observed, especially for the bending loads. However, some improvements\nmay be required for accurately modelling the torsional behaviour of the blade.\nThe modelling strategy is addressed in section 2 and section 3. The test setup is described in section 4. The blade was cut into\n\n80\n\nsegments after the tests in order to accurately measure the mass distribution and the locations of the centres of gravity along\nthe blade. These measurements are also described in section 4. The simulation versus test comparison is reported in section 5,\nfollowed by the conclusions in section 6.\n2\n\nModel Creation Framework\n\nA framework to automatically generate fully parameterized 3D FE models of wind turbine rotor blades from a set of parameters\n85\n\nwas developed at the Institute for Wind Energy Systems at Leibniz University Hannover. The purpose of this tool called MoCA\n(Model Creation and Analysis Tool for Wind Turbine Rotor Blades) is to enable users to investigate and analyse different\nblade designs or design parameter variations in an efficient way, including structural details such as e. g. adhesive joints. The\nfollowing section presents a brief description of the framework.\nMoCA is based on a set of input parameters categorised in Geometry, Plybook, Structure, and Material. In general all\n\n90\n\nparameters that describe a distribution along the blade are stored as splines over the blade’s arc length, but even material\nparameters may be varied over the blade arc if necessary by using a spline. The parameter set Geometry contains all information\non the outer geometry of the blade, i. e. the airfoils used and their positions along the blade as well as the distributions of the\n\n3\n\n\fhttps://doi.org/10.5194/wes-2021-24\nPreprint. Discussion started: 29 April 2021\nc Author(s) 2021. CC BY 4.0 License.\n\nrelative thickness, chord length, twist angle, threading point location, prebend and presweep. The Structure set is associated\nwith the structural description of the blade. This includes the specification of shear webs, adhesive joints and additional masses\n95\n\nas well as cross-sectional division points that are mainly used to subdivide cross-sections into different regions of interest.\nThe Plybook parameters contain the stacking information of different composite layups used in the blade. The parameter set\nMaterial comprises all material properties assigned for the different materials. These can either be isotropic or anisotropic on\nthe macroscopic scale. The user can also specify a composite material based on microscopic characteristics of the fibre and\nmatrix constituents, which are then transformed to a laminate via the well-known rule of mixtures.\n\n100\n\nThe flowchart in figure 1 depicts the structure of the finite element creation procedure implemented in MoCA on the basis\nof the parameter sets described above. First, the blade segmentation, i. e. the discretization in span-wise direction, is defined.\nFor each blade segment edge, a cross-section of the blade is calculated by evaluating the Geometry data. Then a finite element\ndiscretization of the cross-sections is executed using the information of the Structure, Material, and Plybook parameter blocks.\n\n105\n\nAt this stage, an interface to the BECAS (DTU Wind Energy) software can be utilized to calculate the full 6 × 6 stiffness\n\nand mass matrices of a beam model. However, since our aim is to create a 3D blade model, we continue with the finite\n\nelement discretization in span-wise direction utilising a hybrid shell element/solid element strategy. Therein, we use shell\nelements to model the composite laminates and solid elements for the adhesives. The 3D FE mesh includes the node-toelement connectivity and elemental material assignments. The boundary conditions are added and the FE model is translated to\nan input file for the finite element solver of choice, which in our case is ANSYS Mechanical (ANSYS Inc.). In the following,\n110\n\nwe describe in more detail the different steps of this overall procedure.\n\nStructure\n\nPlanform\n\nLength discretization\n\neval. CS geometry\n\nCSShape\n\nMaterial\n\nPlybook\n\n2D meshing\n\nBECAS interface\n\n3D conectivity\n\n2D 2- & 4-Node Elems\n\nHybrid Shell & Solid 3D Mesh\n\nANSYS interface\n\nFigure 1. Flowchart of the finite element model creation procedure in MoCA.\n\nFigure 2 visualises the process of cross-section geometry calculation. After the blade segmentation, the Geometry data\nsplines are evaluated for the particular blade arc positions of the segment edges. Based on the spline-based interpolation of the\nrelative thickness trel , an airfoil AF is linearly interpolated between the basic input airfoils with the next higher and lower\nrelative thickness. In contrast to a global blade shape interpolation, the use of a blade independent airfoil interpolation enables\n115\n\nthe user to implement an own sub-function and replacing the former. The interpolated airfoils are then scaled by the chord\n4\n\n\fhttps://doi.org/10.5194/wes-2021-24\nPreprint. Discussion started: 29 April 2021\nc Author(s) 2021. CC BY 4.0 License.\n\nlength c∗ calculated via the respective spline, shifted along the chord to the correct threading point by the coordinate tp∗ , and\ntwisted by the twist angle θ∗ .\n\nArc Position\n\nrel. Thickness Spl trel\n\nTwist Angle Spl θ\n\nChord Length Spl c\n\nPrebend Spl pb\n\nThreading Point Spl tp\n\nPresweep Spl ps\n\neval. spline\n\nAirfoils AF *\n\ntrel *\n\nc*\n\ntp*\n\nθ*\n\npb*\n\ninterp. AF\n\nscale. AF\n\nthread. AF\n\ntwist. AF\n\n3D pos. AF\n\nps*\n\nCross Sectional Shape CSShape\n\nFigure 2. Flowchart of the calculation of the cross-sectional shapes CSShape .\n\nUntil here, all transformations are performed in a 2D chord coordinate system with its final origin in the threading point. The\ncross-sections are now shifted to the correct 3D position, locating the 2D cross-sectional threading centre on the prebended\n120\n\nand preswept global blade axis. By doing so, the 2D chord coordinate system is still parallel to the blade root plane. Hence, the\ncross-sections are rotated by the slope angles of the prebend and presweep spline functions so that the they are perpendicular\nto the threading axis. These shifted and rotated cross-sections are the final cross-sectional shapes denoted by CSShape .\nAccording to figure 1, the next step is the 2D cross-sectional meshing, which is executed using the cross-sectional shapes\nCSShape and the parameter sets Structure, Material, and Plybook. This process is presented in figure 3. As before, all data is\n\n125\n\nevaluated for the particular arc positions at the blade segment edges. The division points are generated on the cross-sectional\nshapes. They serve to subdivide the cross-sections into regions of different material layups. They are also used to define the\npositions of the shear webs. Then the shapes of the shear web/spar cap and/or trailing edge adhesive joints are computed. The\ncomputation of the blade’s outer geometry and its structural topology is now finished. After inclusion of the Material and\nPlybook information, the FE discretization on 2D cross-section level can be conducted. This yields either a two-dimensional\n\n130\n\nmesh with 4-noded plane elements for the BECAS (DTU Wind Energy) interface or a cross-sectional node map representing a\nhybrid 2D mesh with 2-noded elements for the composite laminates and 4-noded elements for the adhesives.\n\n5\n\n\fhttps://doi.org/10.5194/wes-2021-24\nPreprint. Discussion started: 29 April 2021\nc Author(s) 2021. CC BY 4.0 License.\n\nDivision Points dp\n\nArc Position\n\nAdhesive Information adh\n\nWeb Informaiton web\n\nMaterial Information mat\nPlybook Information plyb\n\neval. spline\n\nCSShape\n\ndp*\n\nweb*\n\nadh*\n\nset division points\n\npos. webs on CSShape\n\ndef. adhesive shape\n\ndiscretize shapes\n\nmat*\n\nplyb*\n\n2D 4-Node Elems\n\nBECAS interface\ndef. section layup\n\n2D 2- & 4-Node Elems\n\nFigure 3. Flowchart of the 2D cross-sectional meshing routine in MoCA.\n\nThe last step in the creation of a 3D finite element model is to connect the 2D cross-sectional models, see figure 1. The 2D\nline elements on the cross-sectional level yield 4-noded shell elements on 3D level after the 3D extension, and the 4-noded\nplane elements on cross-sectional level become 3D solid elements, respectively.\n135\n\nAn additional module called TestRig is included in MoCA to model the boundary conditions similar to a full scale blade\ntest. Full clamping of the blade root represents the geometrical boundary conditions, i. e. all degrees of freedom are fixed at\nthe blade root. Figure 4 shows the process of the TestRig module for the introduction of force-like boundary conditions. In the\nreal blade test, a number of load frames introduces loads that approximate the target bending moment distribution (or torsional\nmoment distribution, respectively). The TestRig module approximates the load frames by means of appropriate multiple point\n\n140\n\nconstraints MPC and additional masses. For each load frame, the position along the blade (arc position), the load frame width,\nthe centre of gravity (CoG) and the resulting mass are specified as well as the load and sensor points.\nIn the range where the load frame is located, MoCA searches all elements of the blade shell and defines 2D slave elements\nthat share their nodes. An additional cross-section is created at the desired load frame position according to the procedure\ndepicted in figure 2. In this additional cross-section, the position of the load introduction (load point), the sensor points, and\n\n145\n\nthe centre of gravity of the load frame are given in the blade coordinate system. These points are defined as master nodes.\n\n6\n\n\fhttps://doi.org/10.5194/wes-2021-24\nPreprint. Discussion started: 29 April 2021\nc Author(s) 2021. CC BY 4.0 License.\n\nArc Position\n\nLoad Points LP\nSensor Points SP\nCentre of Gravity CoG\n\nLoad Frame Width\n\nShell 3D Model\n\neval. CS geometry\n\nPlanform\n\ncollect Shell Elements\n\nCSShape\n\neval. Point Locations\n\ncreat Slave Nodes\n\ncreat MPC\n\ncreate Master Nodes\n\nLoad\n\nMass\n\nLoad Frame\n\nTest Rig\n\nFigure 4. Flowchart of the procedure to model the boundary conditions in the TestRig module.\n\nMPCs are included that connect the degrees of freedom of the master nodes and the slave nodes by means of a rigid connection,\ni. e. there are no relative displacements between the master and the slave nodes. The additional mass of the load frame is applied\nto the CoG node, while the load is applied to the position where the load is introduced in the real test (load point). In this way,\nwe model solid and quasi-rigid load frames and their effects on the blade response without adding detailed models of the load\n150\n\nframes themselves, which is beneficial in the context of computational costs.\nThe 3D finite element model including the mesh and the boundary conditions is translated to an input file for the finite\nelement solver of choice via an integrated interface.\n3\n\nModelling of the Test Blade\n\nThis section briefly describes the blade under consideration, which is the SmartBlades-DemoBlade, a 20m long blade with\n155\n\nprebend and presweep. It was designed and manufactured in the coordinated research projects Smart Blades (Teßmer et al.,\n2016) and SmartBlades2 (SmartBlades2, 2016-2020). The blade is abbreviated by DemoBlade in the following.\nThe DemoBlade was designed to investigate bend-twist coupling effects in wind turbine rotor blades. Therefore a presweep\nof 1 m towards the trailing edge at the tip is intended to introduce a torsional twist into the blade. The offset between the\naerodynamic centres of the swept airfoils and the pitch axis introduces a torsional moment and thus a torsional deformation, i. e.\n\n7\n\n\fhttps://doi.org/10.5194/wes-2021-24\nPreprint. Discussion started: 29 April 2021\nc Author(s) 2021. CC BY 4.0 License.\n\n160\n\na twist in the outer part of the blade. The twist reduces the angle of attack of the respective airfoils and hence the aerodynamic\ncoefficients. In this way the aerodynamic loads can be reduced.\nThe full blade design of the DemoBlade as designed and the manufacturing documentation is available to the authors. In\norder to allow precise modelling of the DemoBlade as built laser scanning of the blade mould was carried out in order to determine the geometry deviations. The derived chord length and absolute thickness distributions for the DemoBlade as designed\n\n165\n\nand as built can be found in Noever-Castelos et al. (2021). Though the manufacturing deviations in the outer geometry are\nnegligibly small, they will be considered in the modelling process.\nAfter the full scale blade tests, the DemoBlade was cut into segments. The masses and the centres of gravity were determined\nfor all blade segments. The respective procedure will be addressed later in this paper, see sections 4.4 and 5.5. Besides the\n\n170\n\nweighing, the geometry was measured thoroughly in each cut cross-section in order to guarantee the correct positioning of the\nshear webs in the FE model and to determine deviations from the design due to manufacturing errors. Especially the dimensions\nof the shear web/spar cap adhesive joints on the pressure side of the blade showed significant deviations to the blade design and\nhad to be adjusted in the FE model. Figure 5 shows the cut at a radial position of 5.2 m. On the suction side we see a nice, thin,\nand over-laminated shear web/spar cap bonding. However, on the pressure side the shear web/spar cap adhesive joint (which\n\n175\n\nwas the blind bond) is much thicker than specified in the design. Moerover, there is a lack of adhesive in large portions of the\nblade, so that the shear web flanges were not covered entirely by adhesive material. Noever-Castelos et al. (2021) contains the\nactual dimensions of the pressure side web adhesive.\nIn the FE model, we apply concentrated and line-distributed additional masses to cover any type of add-ons installed on the\nblade such as the lightning protection cable or reflectors of an optical sensor system. Noever-Castelos et al. (2021) includes\n\n180\n\na table wit all additional masses and the respective modelling methods. MoCA furthermore predefines node positions in the\nblade that correspond to strain gauges installed on the blade. These are documented in Haller and Noever-Castelos (2021).\nThey allow for accurate and easy extraction of strain results at the correct positions.\nIn advance a mesh convergence study based on strain results at different positions was performed to ensure a qualitatively\nsatisfying mesh density. The resulting base model of the DemoBlade consists of 77,693 elements and 71,781 nodes. A total\n\n185\n\nof 71,016 4-noded shell elements (SHELL181 elements in ANSYS) with offset nodes on the outer blade surface represent\nthe composite components and 6,260 8-noded solid elements (SOLID185 elements in ANSYS) the adhesive joints. All other\nelements are used to model additional masses in the blade. The only boundary conditions of the base model are the geometric\nboundary conditions at the blade root (full clamping as described above).\n4\n\n190\n\nTest Description and Virtual Modelling\n\nSeveral test configurations of the full scale blade test were performed to characterize the blade behaviour under different load\nconditions and to prove that the blade design meets all requirements of the certification guidelines(International Eletrotechnical\nComission, 2014). These configurations are than replicated in the virtual test setup and are described in this section.\n\n8\n\n\fhttps://doi.org/10.5194/wes-2021-24\nPreprint. Discussion started: 29 April 2021\nc Author(s) 2021. CC BY 4.0 License.\n\nFigure 5. Cut cross-section at a radial position of 5.2 m with a erroneous shear web/spar cap adhesive joint on the pressure side of the blade.\n\n4.1 Mass and Centre of Gravity\nThe first structural characterization considers the blade’s mass and centre of gravity (CoG). An indoor crane equipped with\n195\n\nload cells at every hook lifted two points on each root and tip transport structure as shown in Figure 6. As the blade remained\nstill and horizontally suspended the measurements and radial position of each suspension point was recorded. After weighing\nthe transport structures, loading chains and shackles individually, the weight was subtracted from the total recorded load at the\nmeasurement devices to obtain the total blade mass. Additionally, the weight of the blade bolts was subtracted from the total\nmass.\n\n200\n\nThe CoG is obtained by calculating the moment equilibrium with the measured loads with respect to a pivot point, in this\ncase the blade root centre. This procedure was performed for the z-direction (along the span) and y-direction (along the chord).\nThe mass and CoG of the FE model is calculated during every analysis by default and can be extracted directly from the\nANSYS log-file.\n9\n\n\fhttps://doi.org/10.5194/wes-2021-24\nPreprint. Discussion started: 29 April 2021\nc Author(s) 2021. CC BY 4.0 License.\n\nFigure 6. Setup for mass and centre of gravity measurements.\n\n4.2 Modal Analysis\n205\n\nThe experimental modal characterization was carried out by the German Aerospace Center (DLR) for different boundary\nconditions. The methodology is described briefly in the following. For details please refer to Gundlach and Govers (2019).\nFree-free boundary conditions were applied after the blade manufacturing by means of elastic suspensions connected to\nlifting straps. The blade was excited using an impact hammer with soft tip at a total of 8 excitation points. Sensors distributed\nalong the blade recorded the deformations, and the mode frequencies and shapes were extracted from the measurements.\n\n210\n\nThe blade was then transported to Fraunhofer IWES and mounted on the test rig. The aim was a second modal characterization with the boundary conditions of the full scale blade test. Electrodynamic long stroke shakers were employed for the\nexcitation of the blade, and sensor outputs were evaluated for the calculation of the mode frequencies and shapes.\nDuring the FE modal analysis, the boundary conditions are adapted to the different characterization tests. In the free-free\nconfiguration, no boundary conditions are applied at all, partially resulting in zero eigenvalues related to rigid body motions.\n\n215\n\nThese are not considered in the validation process. For the test rig configuration, the blade root is fully clamped, i. e. all 6\ndegrees of freedom of the shell elements are fixed, for the sake of simplicity. Note that we neglect flexibilities of the bolts and\nthe test rig in this way, which we have to keep in mind when evaluating the simulation results.\n\n10\n\n\fhttps://doi.org/10.5194/wes-2021-24\nPreprint. Discussion started: 29 April 2021\nc Author(s) 2021. CC BY 4.0 License.\n\n4.3 Static Bending and Torsion Test Configuration\nThe SmartBlades2 DemoBlade was loaded with extreme loads in 4 directions before and after the fatigue test. These four load\n220\n\ncases correspond to maximum and minimum edge-wise loading (MXMAX and MXMIN) as well as maximum and minimum\nflap-wise loading (MYMAX and MYMIN). Furthermore, three static torsion tests were conducted before the fatigue tests,\nin which a torsion moment was applied only at one load frame at a time. The tests are referred to as MZLF2, MZLF3 and\nMZLF4, where LFX indicates the particular load frame, in which the torsion moment was introduced. The static tests provide\nthe necessary information on the structural blade behaviour required to validate the virtual model and test setup.\n\n225\n\nThe tests were performed in the facilities of Fraunhofer IWES, where the blade was mounted almost horizontally on a\ntest rig. The experimental quasi-static loading of the blade is accomplished with a series of horizontally mounted hydraulic\ncylinders. These are connected to the load cells via cables which are attached to the load frames mounted on the rotor blade.\nEach cable runs through pulleys that are mounted on the floor and redirect the forces from a horizontal to a vertical orientation.\nBy attaching the load cells to the load frames (load point), the actual load applied to the rotor blade is measured and friction as\nwell as weight of the loading cables do not affect the measurements. The general test setup is shown in Figure 7.\n\nFigure 7. Photo of a static blade test configuration in flapwise direction.\n230\n\n11\n\n\fhttps://doi.org/10.5194/wes-2021-24\nPreprint. Discussion started: 29 April 2021\nc Author(s) 2021. CC BY 4.0 License.\n\nIn the following, some general information is given that is valid for all test setups. The test block angle (cone angle) is 7.5°\nupwards. The coordinate system referred to in this paper has its origin in the centre of the blade root. The y-axis is vertical,\nthe z-axis points horizontally from the origin towards the blade tip (parallel to the floor, not to the pitch axis), and the x-axis\nfollows from the right-hand rule (pointing left watching towards the tip). After turning the blade to the correct position and\n235\n\nwaiting for a static state, the signals of the load cells and the strain gauges are reset to zero. In the virtual test this is achieved\nby activating gravity, extracting the deformed nodal coordinates and taking these as the undeformed and stress-free state for\nthe load tests. Gravity is thus not applied in the further analysis and the nodal displacements are virtually reset to zero so that\nit is easier to postprocess the results. Preliminary verifications showed that the corresponding error is less than 0.5%.\nIn the tests, four steel load frames with wooden inlays that follow the blade shape at the respective span-wise positions are\n\n240\n\nused to introduce the loads, see Haller and Noever-Castelos (2021). In the following, we refer to the load frames (LF) as LF1\n(@ r = 6.7m), LF2 (@ r = 9.7m), LF3 (@ r = 14.0m), and LF4 (@ r = 17.7m), where r denotes the span-wise position along\nthe blade. Depending on the test setup, not all load frames are installed. Please refer to Noever-Castelos et al. (2021) to find an\noverview of all test setups. Each load frame is equipped with two eye-bolts to attach the load cables. These bolts are roughly\npositioned at the shear centre position in the blade’s cross-section to avoid unintended torsion loads. Detailed information on\n\n245\n\nthe load frames, such as mass, centre of gravity, and the corresponding shear centre position in the blade’s cross-section are\ngiven in Haller and Noever-Castelos (2021) .\nThe test setup is equipped with two different kinds of displacement measurements, an optical displacement measurement\nsystem and draw-wire-sensors (DWS). For the model validation in this paper, the DWS signals are considered. Using LINK11Elements in ANSYS provides a simple and exact model of the draw-wires by defining the attachment points only. The defor-\n\n250\n\nmation measured by the DWS is then modeled by the element-length variations of the link elements.\nAll necessary sensor positions (SP) and load introduction points (LP) on the load frames for the different test setups can\nbe found in Haller and Noever-Castelos (2021). At each load frame position, either with or without installed load frame, two\nDWS are attached. One is connected to a point most to the front bottom corner, i. e. negative y-direction and one at the rear\nbottom corner, i. e. positive y-direction, of the load frames or blade shells in case no load frame is installed. These two DWS\n\n255\n\nwill be referred to as front and rear DWS in the following. At the blade tip, one DWS is attached referred to as Tip DWS. Note\nthat during several load cases, one or the other load frame is not applied due to the setup design, thus the respective DWS have\nto be attached directly to the blade shell.\nThe angle between the loading cable and the blade axis can be adjusted in the experiment by changing the pulley block\nlocation within a discrete set of fixing points on the floor. Prior to the test setup, the optimal position for each pulley was\n\n260\n\ndetermined based on the predicted blade deformation and the desired loading cable angle. The applied loads should be aligned\nto the load frame planes in the deformed configuration. The DWS floor attachment and pulley block positions are specified for\neach test setup individually.\nAdditional to the DWS and the optical measurement system, several cross-sections along the blade are equipped with strain\ngauges, see Haller and Noever-Castelos (2021). The cross-sections at r = 5 m and r = 8 m are instrumented with strain gauge\n\n265\n\nrosettes (bi-axial strain gauges) with 0°/90° and ±45° orientations. The angles 0° and 90° denote the span-wise and the cross12\n\n\fhttps://doi.org/10.5194/wes-2021-24\nPreprint. Discussion started: 29 April 2021\nc Author(s) 2021. CC BY 4.0 License.\n\nsection-wise direction, wheres ±45° is defined accordingly. The 0°/90° rosettes are positioned every approx. 250-300 mm\n\nalong the shell circumference. The ±45° rosettes are located at each web position as well as the leading and trailing edges.\nDetails on strain gauge positions can be found in Haller and Noever-Castelos (2021).\n\nAll load cases have the same basic experimental procedure. They were designed to ensure that the actual test matches the\n270\n\nspecification requirements as closely as possible. Prior to each load case, the rotor blade is rotated to the desired position and\nmounted to the test stand (with the aforementioned 7.5° cone angle). The load cable pulley blocks are fixed to the appropriate\nfixation points on the floor. The load cells are installed between the load frames and the loading cables and are then connected\nto the data acquisition system. Each of the DWS is attached to the blade. The DWS base is positioned so that the wires run\nperpendicular to the floor. Finally, the loading cables are connected to the hydraulic cylinders.\n\n275\n\nThe tests are then executed in the following order:\n1. Functionality check of load cells and displacement sensors.\n2. Compensation of load cell and strain gauge measurements (reset to zero).\n3. Start data acquisition.\n4. Ramp up loads until 100% of the target load, pausing at 40%, 60% and 80% partial loads for 10s each.\n\n280\n\n5. Ramp down loads, pausing at same load fractions as at ramp up.\n6. Stop data acquisition and save measurement data to log file.\nThe process is similar in the simulation. Starting from the base model, which does not have a cone angle and the blade is\npositioned with the trailing edge pointing upwards, the steps are as follows:\n1. Install necessary load frames.\n\n285\n\n2. Rotate blade around z-axis to desired position.\n3. Include cone angle of test rig (incline the blade by 7.5° upwards around x-axis).\n4. Apply gravity and extract new nodal coordinates.\n5. Replace old nodal coordinates by the extracted new nodal coordinates (equal to resetting sensors to zero).\n6. Apply and ramp up loads onto the LINK11 elements acting as loading cables.\n\n290\n\n7. Extract element length variation of the LINK11 elements acting as DWS for 40%, 60%, 80% and 100% of the target\nload.\nAll individual setups for the simulation with modifications to the base model, all necessary load frames, load points, sensor\npositions, and forces as well as the corresponding ground positions of the pulley blocks and the DWS attachments are summarized in Haller and Noever-Castelos (2021). The ground position coordinates are given in the blade coordinate system of the\n\n295\n\nbase model (no cone angle, or rotation) described above at the beginning of this subsection.\nIn contrast to the bending tests, the torsion tests have a pair of forces pulling vertically upwards and downwards as shown in\nfigure 8. Because the blade is still mounted at a block angle of 7.5° the torsional moment is not parallel to the pitch axis. The\nload cable oriented upwards was attached to a ceiling crane and to the load frame at approximately the shear centre position.\nAs the ceiling crane location is hard to record, but the load rope is perpendicular to the ground it was assumed that the location\n13\n\n\fhttps://doi.org/10.5194/wes-2021-24\nPreprint. Discussion started: 29 April 2021\nc Author(s) 2021. CC BY 4.0 License.\n\n300\n\nis 30m above (y-direction) the corresponding load point. The force facing downwards was applied onto the load frame corner\non the trailing edge side in order to introduce a torsional moment in that load frame location.\n\nFigure 8. Configuration example of a static torsional loading on the blade with marked up and downwards facing forces.\n\n4.4 Blade Segment Measurement\nAfter finishing the full blade tests, the blade was cut into 17 segments for further characterization. Figure 5 shows a cut surface\nof the 7th segment at a span-wise position of r = 5.2 m. To determine the 3D centre of gravity (CoG), the segment was suspended\n305\n\nat one point with a flexible rope, so that the CoG settled exactly underneath this point (like a pendulum). Hence, the vector in\ndirection of the suspension rope defines an axis on which the CoG must be located (CoG axis). This procedure was repeated\nwith different suspension points at least 2 times. The CoG was then found in the intersection point of the different CoG axes.\nThe measurement setup can be seen in Figure 9 as well as a digital representation of the intersection of different CoG axes.\nTo measure the vectors and analyse the data an optical measurement system (photogrammetry) was used. Every segment\n\n310\n\nwas equipped with several coded and uncoded reflecting marks to obtain the shape of the segment, the suspension points and\na plummet that was used to get the CoG axes. All the point clouds were analysed in Autodesk Inventor and Siemens NX. All\nsegments were aligned in CAD and the CoG was extracted for each segment with regard to the blade coordinate system. In this\nway we obtained the distribution of the segment CoGs along the blade.\n\n14\n\n\fhttps://doi.org/10.5194/wes-2021-24\nPreprint. Discussion started: 29 April 2021\nc Author(s) 2021. CC BY 4.0 License.\n\nFigure 9. Measurement setup (left) and extracted vectors in CAD with intersection point defining the centre of gravity (right).\n\nConsidering the model validation, MoCA is able to generate the respective segments at their correct positions in the blade,\n315\n\nso the segment masses and CoGs are a natural output of ANSYS.\n5\n\nComparison of Experimental and Simulation Results\n\nIn this section, we compare the experimental results with the simulations. The observation scale will continuously decrease\nfrom a global to a more local scale. We start with the global blade characteristics such as eigenfrequencies, total mass, and total\ncentre of gravity. These give a rough estimate of the modeling correctness. Then the blade deformations by means of bending\n320\n\nand twist distributions during the static extreme load tests will be analysed. Finally the strain levels in two cross-sections during\nthe extreme load tests and the masses and centres of gravity of the cut blade segments are compared, which give a more detailed\nview on a local scale.\n5.1 Blade Mass, Centre of Gravity, and Eigenfrequencies\nTable 1 lists the total blade mass and the location of the centre of gravity in longitudinal (z) and chord direction (y) as well as\n\n325\n\nthe measurement uncertainties and the deviation of the numerical model. We see that the model from MoCA is 115.5 kg lighter\nthan the real blade, which corresponds to 6.44% relative difference related to the measurement. In contrast the measurement\nuncertainty is 45 kg. The mass difference is likely due to manufacturing deviations and/or additional masses (e.g. sensor wires\nand installations) that have not been considered in the numerical model. The location of the CoG matches perfectly in the\n\n15\n\n\fhttps://doi.org/10.5194/wes-2021-24\nPreprint. Discussion started: 29 April 2021\nc Author(s) 2021. CC BY 4.0 License.\n\nchord direction. There is only little deviation of 230 mm in the span-wise direction, which is almost within the measurement\n330\n\nuncertainty range of ± 200 mm.\nTable 1. Comparison of the total mass and the centre of gravity (CoG).\nExperiment\n\nUncertainty\n\nMoCA\n\nDifference\n\n(in kg)\n\n(in kg)\n\n(in kg)\n\n(in kg)\n\nMass\n\n1793\n\n45\n\n1673.5\n\n-115.5\n\nCoG\n\nExperiment\n\nUncertainty\n\nMoCA\n\nDifference\n\n(in m)\n\n(in m)\n\n(in m)\n\n(in m)\n\ny\n\n0.10\n\n0.04\n\n0.10\n\n0.00\n\nz\n\n6.58\n\n0.20\n\n6.35\n\n0.23\n\nThe results of the modal analysis, both experimental and numerical, are listed in Table 2. The experimental results are\ntaken from Gundlach and Govers (2019). The flapwise frequencies are in acceptable agreement with deviations of less than\n8%. The largest deviation in flapwise modes is found for the 2nd edgewise mode in the test rig configuration (7.94%, which\ncorresponds to an absolute deviation of 0.54 Hz). The smallest deviation can be observed for the 1st flapwise mode in the\n335\n\nfree-free configuration, which is 5.83% or 0.28 Hz, respectively. In edgewise direction, the approximation is even better. The\nlargest relative deviation is seen for the 1st edgewise mode in the test rig configuration, which is 4.84% (or 0.15 Hz in absolute\nnumbers). The 2nd edgewise mode is only 0.83% (or 0.09 Hz in absolute numbers) smaller in the simulation compared to\nthe experiment in the test rig configuration, which is an excellent agreement. The largest absolute deviation is present in the\nfree-free configuration, where the 1st edgewise mode is 0.36 Hz lower than the measured value. Anyways, the deviation of the\n\n340\n\nedgewise modes is less than 5% in all cases, which is a very good agreement. The 1st torsion mode is quite well approximated\nin the free-free configuration, where the simulation is 5.62% lower than the experiment. However, in the test rig configuration\nthe deviation is -11.76% (more than 2 Hz less compared to the test), which is relatively high. In general, the simulations\nagree better with the test results in the free-free configuration than in the test rig configuration. This is likely due to the rigid\nrepresentation of the test rig and the connection bolts, as already mentioned in section 4.2. Especially in torsion, the flexibility\n\n345\n\nof the test rig may not be negligible.\n5.2 Static Bending Tests\nThe results of the static bending tests will be illustrated by means of deflection lines. For each test setup, two lines exist, one\nfor the front and one for the rear DWS. The deflections in the front DWS are plotted in Figures 10 for each pausing load during\nramp-up (40 %, 60 %, 80 % and 100 % of the target load as described in section 4.3). The plots for the rear DWS are added in\n\n350\n\nappendix A. A table is added in each of the figures that show the differences between the simulations and the tests (in absolute\n16\n\n\fhttps://doi.org/10.5194/wes-2021-24\nPreprint. Discussion started: 29 April 2021\nc Author(s) 2021. CC BY 4.0 License.\n\nTable 2. Comparison of the modal analyses for the free-free (top) and the test rig (bottom) configuration. Experimental results are taken from\n(Gundlach and Govers, 2019).\n\nMode\n\nExperiment\n\nMoCA\n\n(in Hz)\n\n(in Hz)\n\n1st Flap-wise\n\n4.8\n\n5.08\n\n0.28\n\n5.83%\n\n1st Edge-wise\n\n10.1\n\n9.74\n\n-0.36\n\n-3.56%\n\n1st Torsion\n\n16.9\n\n15.95\n\n-0.95\n\n-5.62%\n\nMode\n\nExperiment\n\nMoCA\n\ntest rig\n\n(in Hz)\n\n(in Hz)\n\n(in Hz)\n\n(in %)\n\n1st Flap-wise\n\n2.2\n\n2.37\n\n0.17\n\n7.73%\n\n2nd Flap-wise\n\n6.8\n\n7.34\n\n0.54\n\n7.94%\n\nst\n\n3.1\n\n3.25\n\n0.15\n\n4.84%\n\nnd\n\n10.9\n\n10.81\n\n-0.09\n\n-0.83%\n\nst\n\n18.7\n\n16.50\n\n-2.20\n\n-11.76%\n\nfree-free\n\n1 Edge-wise\n2 Edge-wise\n1 Torsion\n\nDifference\n(in Hz)\n\n(in %)\n\nDifference\n\nand relative numbers). The tip DWS values are the same for the rear and the front DWS, as only one DWS is installed at the\nblade tip.\nFigure 10 (a) shows the result of the front DWS during the MXMAX load case. For this scenario a maximum deflection of\n180 mm at the blade tip is reached. The simulation shows excellent agreement for the front DWS sensors, with a maximum\n355\n\nabsolute difference of -2.3 mm at the tip for 100 % load and a maximum relative difference of -4.0 % at LF1, whereas the\ndeviations in all other positions are well below 2.0 %. The rear DWS results shown in figure A1 (a) in appendix A have slightly\nhigher errors with a maximum of -5.5 % at LF1 for full load.\nFor load case MXMIN, Figure 10 (b) illustrates the front DWS results. Except for LF1 the results are in very good agreement\nwith a maximum deflection error of -1.6 % at LF2 at full load. However, the results in LF1 return maximum errors of 3.8 % at\n\n360\n\n40 % load, which decreases to 1.8 % at full load. Similar behaviour is found for the rear DWS (Figure A1 (b)); excluding LF1\nthe maximum error is 1.7 % in LF3 and the tip during 40 % load.\nThe results of the front DWS during the maximum flap-wise setup (MYMAX, Figure 10 (c)) are in very good agreement,\nwhen excluding the LF1 data. The LF1 results tend to show the highest errors. This might probably be due to the smallest\nabsolute deflection values, as a systematic sensor/measurement inaccuracy will have a higher impact on relative errors. Con-\n\n365\n\ncerning the other load frames the maximum error is found to be -2.6 % for the LF4 DWS at full load, which corresponds to\n-22.4 mm deflection error at a maximum deflection of 875 mm in the experiment. All other values range between -0.9 % and\n-2.4 %. The excluded LF1 results show higher errors of up to 9.0 % for 60 % load. For the rear DWS (Figure A1 (c)) though\n\n17\n\n\fhttps://doi.org/10.5194/wes-2021-24\nPreprint. Discussion started: 29 April 2021\nc Author(s) 2021. CC BY 4.0 License.\n\n40\n0\n\nMXMIN-Front\n160\n\nDifference\n\n120\n80\n40\n0\n\n800\n600\n400\n200\n0\n\n600\n400\n200\n0\n0\n\n6\n\n8\n\n10\n\n12\n\n14\n\n16\n\n18\n\nabsolute\nabsolute\n\nCase Load\n40%\n60%\n80%\n100%\n40%\n60%\n80%\n100%\n\nMYMIN-Front\n800\n\nDifference\n\n(d)\n\nDisplacement [mm]\n\n1000\n\nabsolute\n\nCase Load\n40%\n60%\n80%\n100%\n40%\n60%\n80%\n100%\n\nMYMAX-Front\n\n1000\n\nDifference\n\nDisplacement [mm]\n\n1200\n\n(c)\n\nUnit LF1 LF2 LF3 LF4 Tip\nmm\n0.4 0.0 0.2 0.2 1.2\nmm\n0.4 -0.4 -0.2 -0.3 0.6\nmm\n0.5 -0.3 0.3 0.6 2.0\n0.4 -0.8 -0.2 -0.1 1.5\nmm\n%\n3.8 -0.1 0.5 0.3 1.7\n2.7 -1.4 -0.4 -0.3 0.5\n%\n%\n2.6 -0.8 0.4 0.5 1.3\n1.8 -1.6 -0.2 -0.1 0.8\n%\n\nrelative\n\nDisplacement [mm]\n\n200\n\n(b)\n\nCase Load\n40%\n60%\n80%\n100%\n40%\n60%\n80%\n100%\n\nDifference\n\n80\n\nrelative\n\n120\n\nUnit\nmm\nmm\nmm\nmm\n%\n%\n%\n%\n\nabsolute\n\n160\n\nCase Load\n40%\n60%\n80%\n100%\n40%\n60%\n80%\n100%\n\nrelative\n\nMXMAX-Front\n\nrelative\n\n(a)\n\nDisplacement [mm]\n\n200\n\nUnit\nmm\nmm\nmm\nmm\n%\n%\n%\n%\n\nUnit\nmm\nmm\nmm\nmm\n%\n%\n%\n%\n\nLF1\n-0.1\n-0.4\n-0.7\n-0.9\n-1.5\n-2.8\n-3.5\n-4.0\n\nLF1\n-2.2\n-3.5\n-4.5\n-5.6\n-8.8\n-9.0\n-8.8\n-8.7\n\nLF1\n-0.9\n-1.6\n-2.7\n-3.7\n-4.6\n-5.5\n-6.8\n-7.3\n\nLF2\n0.4\n0.0\n-0.1\n-0.2\n2.5\n0.2\n-0.2\n-0.5\n\nLF2\n-1.4\n-2.3\n-3.2\n-4.0\n-2.2\n-2.3\n-2.4\n-2.4\n\nLF3\n0.5\n-0.1\n-0.4\n-0.5\n1.3\n-0.2\n-0.5\n-0.5\n\nLF3\n-2.4\n-3.7\n-5.7\n-7.3\n-1.3\n-1.4\n-1.6\n-1.6\n\nLF4\n0.1\n-1.1\n-1.5\n-1.9\n0.1\n-1.2\n-1.2\n-1.3\n\nTip\n0.5\n-0.7\n-1.4\n-2.3\n0.7\n-0.7\n-1.0\n-1.2\n\nLF4 Tip\n-6.9 -4.3\n-11.7 -8.4\n-16.9 -14.5\n-22.4 -19.8\n-2.0 -0.9\n-2.2 -1.2\n-2.4 -1.6\n-2.6 -1.7\n\nLF2 LF3 LF4 Tip\n-0.3 2.3 4.4 -1.8\n-0.8 3.5 7.1 -1.6\n-1.9 2.6 6.0 -5.8\n-2.8 2.6 6.3 -8.3\n-0.6 1.6 1.7 -0.5\n-1.0 1.6 1.8 -0.3\n-1.8 0.9 1.1 -0.8\n-2.2 0.7 1.0 -1.0\n\n20\n\nRadial Position [m]\nExp: 40% L.\n\nExp: 60% L.\n\nExp: 80% L.\n\nExp: 100% L.\n\nSim: 40% L.\n\nSim: 60% L.\n\nSim: 80% L.\n\nSim: 100% L.\n\nFigure 10. Bending lines extracted from the front draw wire sensor for the (a) MXMAX; (b) MXMIN; (c) MYMAX; (d) MYMIN experiment\nand simulation. Results are shown for 40%, 60%, 80% and 100% of the target load. The table on the right shows the differences between the\nsimulation and the test.\n\n18\n\n\fhttps://doi.org/10.5194/wes-2021-24\nPreprint. Discussion started: 29 April 2021\nc Author(s) 2021. CC BY 4.0 License.\n\nexcluding LF1 (max. error -17.6 %) the LF2 results show errors above 6.7 % with the highest reaching -8.8 % during full load.\nFor the other two load frames the errors are low again and are between -0.9 % and -2.4 %. If taking a closer look at the LF2\n370\n\nfull load deflection d in the test and experiment the front DWS shows dExp,f = 165 mm and dSim,f = 161 mm, whereas the\nrear DWS returns dExp,r = 175 mm and dSim,r = 160 mm. That means the overall deflection of the simulation is less than in\nthe experiment but the difference between rear and front is ∆dExp = dExp,r − dExp,f = 10 mm and ∆dSim = −1 mm, i. e.\n\nthe simulation shows a positive twist while the experiment returns a much higher negative twist. The twist angle Θ can be\n\ncalculated by the relationship\n\u0012\n\u0013\n∆d\n375 Θ = arcsin\n,\nlSP\n\n(1)\n\nwhere lSP is the distance of both front and rear DWS attachment points on the load frame. The twist angles becomes\nΘExp,LF 2 = −0.268° in the experiment and ΘSim,LF 2 = 0.042° in the simulation. Assuming the pivot point is at the shear\n\ncentre (SC), a correction could be calculated to see if the bad results of the rear DWS at LF2 is due to the wrong twist. All\nnecessary geometric data can be found in Haller and Noever-Castelos (2021). Following Equation (1) and using the distance\n380\n\nof the front or rear DWS attachment to the shear centre, the front absolute difference is increased to -7.87 mm which results\nin an error of -4.8 % and the rear deflection is reduced to -7.7 mm, respective -4.4 % during 100 % loading. By this correction\ndue to a wrong predicted twist angle the rear DWS approximation improves by 4 %, while the accuracy of the front sensor\ndecreases by only 2.4 %. This correction is introduced to evaluate the accuracy for the bending prediction and only holds for\nthe LF2 position, as the other positions have different twist angle deviations. Additionally the major influence on the flap-wise\n\n385\n\nloading has to be noted as the DWS attachment distances to the shear centre are much higher than for the edge-wise loading,\ni.e. the influence from twist angle deviations is amplified significantly.\nFigure 10 (d) shows the front DWS results comparison during the minimum flap-wise loading scenario (MYMIN). All load\nframes are installed so can be evaluated and the results show a very good agreement with errors below 2.2 % for all DWS\nexcept LF1. At this first load frame again the results have significantly higher errors of up to -7.3 % at full load. Figure A1 (d)\n\n390\n\ncontains the rear DWS result of the MYMIN load case and lists throughout higher deviations of up to -13 % for the LF1 sensor.\nHere again, by analysing the twist behaviour of the blade all load frames show significant twist differences and after estimating\na correction, e.g. the accuracy of the LF1 front sensor would decrease to a deviation of -11 %, while that of the rear sensor\nincreases to -10.4 %. This is the worst approximation of the simulation for the static extreme load bending setups. Anyways,\nthe other load frames are in very good agreement.\n\n395\n\n5.3 Static Torsion Tests\nFull scale blade tests in pure torsion are usually not included in certification processes according to (International Eletrotechnical Comission, 2014) and are thus rarely available. As described in section 4.3 the blade is twisted during three different setups\nsuccessively at the load frames LF2, LF3 and LF4. The results of the tests and the simulations are plotted in Figure 11. The\nstructural behaviour behind the actual loaded frame position to the tip will not be addressed in this paper and is highlighted as\n\n400\n\ngrey-coloured areas, as the areas loaded in torsion are located between the root and the respective load frame. Though the raw\n19\n\n\fhttps://doi.org/10.5194/wes-2021-24\nPreprint. Discussion started: 29 April 2021\nc Author(s) 2021. CC BY 4.0 License.\n\nresults similar to the static bending experiments are the DWS length variation, for these torsional experiments the more relevant\ntwist angles are calculated and plotted according to Equation 1. Figure 11 (a) shows the first torsional test loaded at LF2. The\nabsolute angle deviation from experiment to simulation are in between -0.06° and -0.15° but yields high relative deviation up\nto 30 % due to the small twist angles of -0.55° at LF1 and -1.72° at LF2 during 100 % load.\n\nUnit\ndeg\ndeg\ndeg\ndeg\n%\n%\n%\n%\n\nLF1\n-0.06\n-0.07\n-0.08\n-0.09\n44.0\n32.9\n27.0\n24.9\n\nLF2\n-0.16\n-0.20\n-0.24\n-0.28\n44.8\n35.6\n32.0\n30.0\n\nLF3\n-0.53\n-0.60\n-0.59\n-0.50\n35.4\n25.0\n17.7\n11.7\n\nLF4\n-0.75\n-1.01\n-1.25\n-1.46\n59.3\n51.5\n47.1\n43.7\n\n−3\n−4\n\nMZLF3\n\n0\n−2\n\nCase Load\n40%\n60%\n80%\n100%\n40%\n60%\n80%\n100%\n\nUnit\ndeg\ndeg\ndeg\ndeg\n%\n%\n%\n%\n\nLF1 LF2\n-0.04 -0.03\n-0.04 -0.01\n-0.05 0.01\n-0.05 0.03\n36.1\n9.4\n24.1\n2.0\n19.4 -1.5\n15.8 -3.7\n\nLF3\n-0.18\n-0.14\n-0.10\n-0.05\n17.0\n9.1\n4.7\n1.8\n\nLF4\n-1.26\n-1.50\n-1.63\n-1.68\n45.5\n34.7\n27.9\n22.8\n\nDifference\n\n−4\n−6\n−8\n\nMZLF4\n0\n\n6\n\n8\n\n10\n\n12\n\n14\n\n16\n\n18\n\nabsolute\n\nCase Load\n40%\n60%\n80%\n100%\n40%\n60%\n80%\n100%\n\nDifference\n\nLF4\n-0.03\n-0.14\n-0.21\n-0.30\n3.9\n15.0\n16.4\n19.4\n\nDifference\n\nDisplacement [mm]\n\n−2\n\n−5\n\nDisplacement [mm]\n\nLF3\n-0.23\n-0.32\n-0.41\n-0.51\n43.8\n41.4\n39.0\n38.7\n\nrelative\n\nMZLF2\n\n−1\n\n−10\n\nLF2\n-0.12\n-0.15\n-0.13\n-0.11\n20.2\n15.6\n9.8\n6.6\n\nabsolut\n\n−1.5\n\n0\n\n(c)\n\nLF1\n-0.06\n-0.08\n-0.10\n-0.13\n30.5\n26.1\n22.9\n22.7\n\nrelative\n\n−1\n\n−2\n\n(b)\n\nUnit\ndeg\ndeg\ndeg\ndeg\n%\n%\n%\n%\n\nabsolut\n\n−0.5\n\nCase Load\n40%\n60%\n80%\n100%\n40%\n60%\n80%\n100%\n\nrelative\n\n(a)\n\nDisplacement [mm]\n\n0\n\n20\n\nRadial Position [m]\nExp: 40% L.\n\nExp: 60% L.\n\nExp: 80% L.\n\nExp: 100% L.\n\nSim: 40% L.\n\nSim: 60% L.\n\nSim: 80% L.\n\nSim: 100% L.\n\nLF Position\n\nexcluded Region\n\nFigure 11. Twist angles calculated from the draw wire sensors results for the (a) LF2; (b) LF3; (c) LF4 torsional loading experiment and\nsimulation. Results are shown for 40%, 60%, 80% and 100% of the target load. The table on the right shows the differences between the\nsimulation and the test.\n405\n\nMoving the load application to LF3 (Figure 11 (b)) does not change the situation. At the load application position the\nabsolute error is high with up to -0.6° at a maximum twisting of -4.3°. All errors exceed -10 % dramatically. However, the\n20\n\n\fhttps://doi.org/10.5194/wes-2021-24\nPreprint. Discussion started: 29 April 2021\nc Author(s) 2021. CC BY 4.0 License.\n\nexperiment with torsional loading on LF4, see Figure 11 (c), shows reasonably good results for the twist angle at LF2 and LF3\nwith angle deviations of 3.7 % and 1.8 %, respectively. The results at LF4, where the load is applied and which shows the\nhighest twist angle keeps high deviations of about 20 % for full load. Such high errors during torsional loading may base on the\n410\n\nshell element with a node offset to the exterior surface used for this model. Pardo and Branner (2005) and especially Laird et al.\n(2005) already stressed the high inaccuracy of shell elements with node offsets to predict the structural behaviour of hollow\nstructures subjected to torsional loading. However, the twisting is generally overestimated throughout the three torsional tests,\nwhich is inline with the aforementioned references.\n5.4 Local Strain Comparison\n\n415\n\nAs stated in section 4.3 the highly instrumented cross-sections at r = 5 m and r = 8 m offer a more detailed view on the local\nstrain levels in the rotor blade. The strain results are used to compare the simulations with the tests and to verify that local\neffects are correctly reproduced. We have selected a few representative load cases in this section. The remaining load cases can\nbe found in appendix B.\nIn Figure 12 (a) the strain in 0° (span-wise direction, in blue) and 90° (cross-wise, in yellow) directions for the MXMIN\n\n420\n\nsimulation (solid lines) and experiment (circles) are plotted over the normalized airfoil circumference (denoted by S) for\nthe 5 m cross-section, starting at the suction side trailing edge (S = 0), moving along the suction side to the leading edge\n(S ≈ 0.5), and then along the pressure side to the pressure side trailing edge (S = 1). This cross-section shows some general\ncharacteristics in all load cases, which are:\n\n– In the simulation at S = 0, there is a strain peak in the 90° direction, because the sandwich core material vanishes towards\n425\n\nthe trailing edge.\n– In the simulation at S = 0 − 0.25, there is an excessive or wrong curvature in the 90° strain curve, for which we do not\nhave a feasible explanation.\n\n– In the simulation at S = 0.25 − 0.35, there is a stepped dip or raise of the 90° strain, because the sandwich core material\nis substituted by core and UD layers and then completely by the UD spar cap and vice versa.\n\n430\n\n– In the simulation at S = 0.5, there is a strain peak in the 90° direction, because the sandwich core material vanishes\naround the leading edge.\n– In the experiment at S = 0.5 − 0.65, there is a strain dip in the 0° direction, for which we do not have a feasible explanation. The structure should be symmetric next to the leading edge.\n\n– In the simulation at S = 1, there is a strain peak in the 90° direction, because the sandwich core material vanishes towards\n435\n\nthe trailing edge.\nApart from the unclear dip around the suction side leading edge panel (S = 0.5 − 0.65), the longitudinal strain (in 0° direction)\n\ndiffers along the circumference only about ± 150 µm/m. This is about 15 % related to the maximum ± 1000 µm/m at the\nleading or trailing edge. However, the cross-wise strains (in 90° direction) reach deviations of up to ± 200 µm/m, which\n\ncorresponds to about 50 % related to its maximum. The MXMAX results (Figure C1 (a)) are very similar concerning maximum\n440\n\nvalues and strain errors.\n21\n\n\f(c)\n\nµ-Strains [µm/m]\n\n(b)\n\nµ-Strains [µm/m]\n\n(a)\n\nµ-Strains [µm/m]\n\nhttps://doi.org/10.5194/wes-2021-24\nPreprint. Discussion started: 29 April 2021\nc Author(s) 2021. CC BY 4.0 License.\n\n1000\nMXMIN\n500\n0\n−500\n−1000\n2000\nMYMAX\n1000\n0\n−1000\n−2000\n400\nMZLF3\n\n200\n0\n−200\n−400\n\n0\n\n0.1\n\n0.2\n\n0.3\n\n0.4\n\n0.5\n\n0.6\n\n0.7\n\n0.8\n\n0.9\n\n1\n\nNormalized Profile Circumference [-]\nExp: 0◦\n\nExp: 90◦\n\nSim: 0◦\n\nSim: 90◦\n\nFigure 12. Span-wise and cross-wise strains of the simulation and the test, plotted against the normalized profile circumference of the\ncross-section at r = 5 m for the (a) MXMIN; (b) MYMAX; (c) MZLF3 load case.\n\nFigure 12 (b) shows the MYMAX load case. Unlike the edge-wise case a wrong calibration or malfunction of the strain\ngauge at S = 0.3 was recorded in the experiment. The flap-wise bending of the blade in general is more excessive compared\nto the edge-wise bending and provokes the highest longitudinal strains in the spar cap positions reaching maximum values of\n445\n\nup to ± 2000 µm/m in the outer shell layer. Consequently the cross-wise strain also increases with maxima of ± 500 µm/m,\n\nboth approximately twice as much as in the edge-wise load case. All other aforementioned issues are also present here, some\nmore and some less pronounced. The same conclusion also holds for the MYMIN case in figure C1 (b), though the maximum\nvalues are slightly lower, due to smaller load sets.\nTaking a look at the torsion tests, in particular for the MZLF3 load case plotted in Figure 12 (c), the longitudinal strain shows\n\n450\n\na relatively good agreement with the test, except for S = 0.5 − 0.65 and at the pressure side trailing edge panel (S = 0.85 − 1).\n\nThe cross-wise strain shows partially good agreement with the experiments, except for the aforementioned characteristics\nwhich are more dominant than in the bending tests. E. g. the peaks at the trailing edge is more pronounced. As for the longitudinal strain, the cross-wise strain shows a disagreement between simulation and experimental results, which is even stronger\ndue to a shifted curvature in the plot. These can also be seen during the remaining two torsion tests. The MZLF4 load case in\n\n22\n\n\fhttps://doi.org/10.5194/wes-2021-24\nPreprint. Discussion started: 29 April 2021\nc Author(s) 2021. CC BY 4.0 License.\n\nFigure C1 (d) is very similar to the MZLF3 load case, whereas the MZLF2 load case (Figure C1 (c)) shows all of the stated\n455\n\ncharacteristics in a more pronounced manner as the load introduction is shifted closer to the evaluated section at r = 5 m.\nThe next highly equipped cross-section is at r = 8 m. While the previous cross-section was located at maximum chord,\nthis one is already in a region where geometric curvatures are smoother. For direct comparison the same three load cases were\nselected for this cross-section. As depicted in Figure 13 (a) the longitudinal as well as the cross-wise strains during the MXMIN\ntest follow very well the experimental results, both qualitatively and quantitatively. Strain levels are similar to the cross-section\n\n460\n\nat r = 5 m, but the strain errors of the simulation compared to the experiments are much lower (between ± 75 µm/m). Same\n\nholds for the MXMAX loading, see Figure D1 (a), where the strain error is even between ± 50 µm/m most of the time. Though\nthese are not very pronounced, the peaks at the trailing and leading edges as well as the stepped dips or raises can be identified\n\n(c)\n\nµ-Strains [µm/m]\n\n(b)\n\nµ-Strains [µm/m]\n\n(a)\n\nµ-Strains [µm/m]\n\nas consistent characteristics throughout all test.\n1000\n\nMXMIN @ r=8 m\n\n500\n0\n−500\n\n−1000\n−1500\n2500\n\nMYMAX @ r=8 m\n\n1250\n0\n−1250\n−2500\n200\n\nMZLF3 @ r=8 m\n\n100\n0\n−100\n−200\n\n0\n\n0.1\n\n0.2\n\n0.3\n\n0.4\n\n0.5\n\n0.6\n\n0.7\n\n0.8\n\n0.9\n\n1\n\nNormalized Profile Circumference [-]\nExp: 0◦\n\nExp: 90◦\n\nSim: 0◦\n\nSim: 90◦\n\nFigure 13. Span-wise and cross-wise strains of the simulation and the test, plotted against the normalized profile circumference of the\ncross-section at r = 8 m for the (a) MXMIN; (b) MYMAX; (c) MZLF3 load case.\n\nComparing the results of the MYMAX test depicted in Figure 13 (b), the good agreement between the simulation and the\n465\n\ntest are evident. Even the stepped raise at the two spar caps (S = 0.3 and S = 0.67) exist in the experimental results. The strain\nerror range is approximately between ± 100 µm/m, which is less than for the other cross-section, while having slightly higher\n\nstrain levels. This excellent agreement is also found in figure D1 (b) for the MYMIN load case.\n23\n\n\fhttps://doi.org/10.5194/wes-2021-24\nPreprint. Discussion started: 29 April 2021\nc Author(s) 2021. CC BY 4.0 License.\n\nHowever, the results from the torsional tests do not agree. As seen in figure D1 (c) the simulation results of the longitudinal\nstrain during the MZLF3 test may follow some correct trend of the experiments, but has significant variations. The same applies\n470\n\nto the cross-wise strains. Though the strain errors are in the same range as the bending test results, compared to the absolute\nstrain levels these have the same magnitude as the error. The remaining torsional test results (Figure D1 (c) and (d)) show\nsimilar problems.\n5.5 Segment mass and CoG comparison\nIn this subsection, we compare the experimental mass and CoG measurement of each segment with the respective simulation\n\n475\n\nresults. Table 3 contains the segment numbers, the segment locations along the blade defined by the span-wise positions of the\nleft and the right cutting sections r1 and r2 , respectively, and the differences of the segment masses and the CoG locations (in\nabsolute and relative numbers).\nTable 3. Segment mass and centre of gravity (CoG) differences between experiment and simulation. The relative distances of the CoG are\ngiven with respect to their corresponding geometrical cross-section parameter, i. e. absolute thickness (X), chord length (Y), and span-wise\nsegment length (Z).\n\nr2\n\n(in m)\n\n(in m)\n\n(in kg)\n\n1\n\n0.0\n\n0.9\n\nSection No.\n\nCentre of Gravity\n\nMass\n\nr1\n\nX\n\nY\n\nZ\n\nX\n\nY\n\nZ\n\n(in %)\n\n(in m)\n\n(in m)\n\n(in m)\n\n(in %)\n\n(in %)\n\n(in %)\n\n34.6\n\n9.8%\n\n-0.030\n\n0.000\n\n0.003\n\n-2%\n\n0%\n\n0%\n\n2\n\n0.9\n\n2.0\n\n-7.36\n\n-5.1%\n\n-0.003\n\n0.009\n\n0.035\n\n0%\n\n1%\n\n3%\n\n3\n\n2.0\n\n3.0\n\n-10.96\n\n-9.3%\n\n-0.031\n\n-0.004\n\n0.065\n\n-3%\n\n0%\n\n6%\n\n4\n\n3.0\n\n3.5\n\n-4.74\n\n-8.0%\n\n-0.066\n\n0.000\n\n-0.007\n\n-6%\n\n0%\n\n-1%\n\n5\n\n3.5\n\n4.0\n\n-3.419\n\n-6.1%\n\n-0.076\n\n-0.005\n\n0.021\n\n-8%\n\n0%\n\n4%\n\n6\n\n4.0\n\n5.2\n\n-7.39\n\n-5.9%\n\n-0.094\n\n-0.060\n\n0.055\n\n-10%\n\n-3%\n\n5%\n\n7\n\n5.2\n\n6.5\n\n-6.07\n\n-4.9%\n\n-0.102\n\n-0.036\n\n0.054\n\n-13%\n\n-2%\n\n4%\n\n8\n\n6.5\n\n8.5\n\n-9.81\n\n-5.8%\n\n-0.074\n\n-0.008\n\n0.071\n\n-12%\n\n0%\n\n4%\n\n9\n\n8.5\n\n9.5\n\n-3.572\n\n-4.8%\n\n-0.050\n\n0.007\n\n0.040\n\n-10%\n\n0%\n\n4%\n\n10\n\n9.5\n\n10.5\n\n-5.236\n\n-7.3%\n\n-0.049\n\n0.004\n\n0.132\n\n-11%\n\n0%\n\n13%\n\n11\n\n10.5\n\n11.5\n\n-3.685\n\n-5.4%\n\n-0.041\n\n-0.005\n\n0.108\n\n-10%\n\n0%\n\n11%\n\n12\n\n11.5\n\n12.5\n\n-4.087\n\n-6.6%\n\n-0.031\n\n0.003\n\n0.090\n\n-9%\n\n0%\n\n9%\n\n13\n\n12.5\n\n16.0\n\n-18.59\n\n-9.9%\n\n-0.036\n\n0.007\n\n0.091\n\n-13%\n\n1%\n\n3%\n\n14\n\n16.0\n\n16.5\n\n4.007\n\n16.3%\n\n-0.003\n\n-0.048\n\n0.128\n\n-1%\n\n-4%\n\n26%\n\n15\n\n16.5\n\n17.5\n\n16\n\n17.5\n\n19.0\n\n-4.405\n\n-9.1%\n\n-0.025\n\n0.094\n\n0.195\n\n-15%\n\n11%\n\n13%\n\n17\n\n19.0\n\n20.0\n\n1.104\n\n9.5%\n\n0.010\n\n0.023\n\n0.041\n\n10%\n\n4%\n\n4%\n\nThe relative difference of the mass is related to the measured segment mass and the CoG positions are with respect to the\ncorresponding geometrical mid cross-sectional dimensions, i. e. absolute thickness (X), chord length (Y) and radial segment\n480\n\nlength(Z). It was not possible to measure segment 15. The mass differs from -4.8 % to -9.9 % except for segment 1,14, and 17,\n24\n\n\fhttps://doi.org/10.5194/wes-2021-24\nPreprint. Discussion started: 29 April 2021\nc Author(s) 2021. CC BY 4.0 License.\n\nwhere the mass was overestimated. Unfortunately it was not possible to calculate an overall blade mass as one segment result\nwas missing. Concerning the CoG differences, the coordinate in cross-section thickness direction (X) varied up to -15 % but\nwas most of the time predicted closer to the suction side. The CoG location in chord direction (Y) agreed very well with the\n485\n\nmeasurement, except for segment 16, the variation were below ±4 %. The radial locations match well for most of the segments\n\n(≤ 6 %). However, the sections 10, 11, 12, 14, and 16 resulted in higher variations, predicting the CoG position closer to the\ntip by more than 10 % of the segment length.\n6\n\nConclusions\n\nThe aim of this paper was the validation of a parametrization and modelling methodology for wind turbine rotor blades. This\nmethodology was implemented in the in-house 3D finite element model generator MoCA (Model creation and analysis tool),\n490\n\nwhich creates hybrid shell/solid finite element models.\nFull-scale blade tests were performed on the SmartBlades DemoBlade as an experimental reference. The blade has a length\nof 20 m and is designed with pre-bend and pre-sweep. The following magnitudes were determined experimentally: The total\nmass and the centre of gravity of the full blade, the mass and centre of gravity distributions along the blade by weighing of blade\nsegments, the natural frequencies in a free-free and a clamped cantilever configuration, the deflection curves along the blade\n\n495\n\nfor both flap-wise and edge-wise bending as well as torsion, and the strains in the cross-sectional and longitudinal direction\nclose to the maximum chord position. The governing parameters such as geometry, material layup, manufacturing deviations,\nadditional sensor and load frame masses were extracted from the blade and test documentations. These were fed into MoCA.\nFinite element models for all test setups were created and the simulations were executed in the commercially available finite\nelement code ANSYS. Then, the simulations were compared with the experimental results.\n\n500\n\nThe mass and centre of gravity of the full blade compared very well (error of -6%). The masses and centres of gravity of the\nblade segments, i. e. the mass and centre of gravity distributions along the blade, were also in good agreement (error of 5-10%).\nModal analysis concluded for th natural frequencies with free-free boundary conditions also well (error <6%) matching results,\nthose for the clamped cantilever configuration matched reasonably well (error <8% for bending, 11.7% for torsion).\nThe deflections for bending in edge-wise direction was in excellent agreement (error <4%). While the deflection curve for\n\n505\n\nbending in flap-wise direction showed a comparably large deviation of 13% at the root, which decreased substantially towards\nthe tip (error at the tip <4%). A reason for that was an elastic twist during the test that was not replicated in the simulations.\nDuring torsion, the authors identified quite large deviations in the elastic twist distributions along the blade, because shell\nmodels cannot properly replicate torsional behaviour, as is also reported in literature.\nFor both flap-wise and edge-wise bending the strains in span-wise direction were in very good agreement. Strain gauges\n\n510\n\nwere distributed along the circumference of the cross-sections at span-wise positions of 5 m and 8 m, respectively, in order\nto measure the cross-sectional deformations. There, the authors observed good agreement between the simulations and the\nexperiments, especially at a span of 8 m. However, some local effects close to the spar-caps could not be resolved in the\n\n25\n\n\fhttps://doi.org/10.5194/wes-2021-24\nPreprint. Discussion started: 29 April 2021\nc Author(s) 2021. CC BY 4.0 License.\n\nsimulations. In the torsion test, the strains showed quite large deviations. Though, the longitudinal strains agreed sufficiently\nwell, at least qualitatively.\n515\n\nGenerally speaking, the authors observed good agreement between the simulations and the experiments in almost all situations. The parametrization and modelling methodology can thus be rated as validated. However, there were significant deviations in torsion, which need to be investigated further. The authors currently work on evaluating blade modelling by means of\nsolid elements and/or solid shell elements. In this way, the performance in torsion might be improved significantly.\n\nCode and data availability. The code of MoCA is not publicly available, but may be made available on request at conditions that need to be\n520\n\nagreed upon. All experimental and simulation data that support the results of this research as well as the baseline finite element model of the\nblade as an ANSYS mechanical input file are uploaded in Noever-Castelos et al. (2021)\n\n26\n\n\fhttps://doi.org/10.5194/wes-2021-24\nPreprint. Discussion started: 29 April 2021\nc Author(s) 2021. CC BY 4.0 License.\n\nAppendix A: Static bending test results\n\n40\n\nMXMIN-Rear\n160\n\n800\n600\n400\n200\n0\n\nMYMIN-Rear\n800\n600\n400\n200\n0\n0\n\n6\n\n8\n\n10\n\n12\n\n14\n\n16\n\n18\n\nLF2\n-0.2\n-0.7\n-1.1\n-1.3\n-1.0\n-2.8\n-3.2\n-3.1\n\nLF3\n-0.3\n-1.2\n-2.0\n-2.6\n-0.8\n-2.3\n-2.8\n-3.0\n\nLF4\n-0.5\n-2.1\n-3.0\n-3.9\n-0.8\n-2.4\n-2.6\n-2.7\n\nTip\n0.5\n-0.7\n-1.4\n-2.3\n0.7\n-0.7\n-1.0\n-1.2\n\nUnit\nmm\nmm\nmm\nmm\n%\n%\n%\n%\n\nLF1 LF2 LF3 LF4 Tip\n-4.1 -4.6 -2.7 -0.7 -4.3\n-6.6 -7.9 -4.7 -3.0 -8.4\n-9.3 -11.6 -8.5 -6.7 -14.5\n-12.2 -15.4 -12.2 -10.9 -19.8\n-15.1 -6.7 -1.4 -0.2 -0.9\n-16.0 -7.5 -1.7 -0.6 -1.2\n-16.9 -8.3 -2.3 -0.9 -1.6\n-17.6 -8.8 -2.6 -1.2 -1.7\n\nCase Load\n40%\n60%\n80%\n100%\n40%\n60%\n80%\n100%\n\nUnit\nmm\nmm\nmm\nmm\n%\n%\n%\n%\n\nLF1\n-2.2\n-3.6\n-5.1\n-6.8\n-10.7\n-11.8\n-12.4\n-13.0\n\nDifference\n\nDisplacement [mm]\n\n1000\n\nLF1\n-0.3\n-0.7\n-0.9\n-1.2\n-3.7\n-5.2\n-5.4\n-5.5\n\nCase Load\n40%\n60%\n80%\n100%\n40%\n60%\n80%\n100%\n\nDifference\n\nDisplacement [mm]\n\nMYMAX-Rear\n\n1000\n\nabsolute\n\n40\n\nrelative\n\n80\n\n1200\n\n(d)\n\nabsolute\n\nDifference\n\n120\n\n0\n\n(c)\n\nUnit LF1 LF2 LF3 LF4 Tip\nmm\n0.9 0.3 0.7 0.9 1.2\n1.1 0.1 0.4 0.5 0.6\nmm\nmm\n1.6 0.5 1.1 1.8 2.0\nmm\n1.8 0.3 0.6 1.3 1.5\n%\n8.5 1.3 1.7 1.4 1.7\n7.2 0.4 0.6 0.5 0.5\n%\n%\n7.8 1.3 1.3 1.5 1.3\n%\n6.9 0.6 0.6 0.8 0.8\n\nabsolute\n\nDisplacement [mm]\n\n200\n\nrelative\n\n80\n\n0\n\n(b)\n\nCase Load\n40%\n60%\n80%\n100%\n40%\n60%\n80%\n100%\n\nDifference\n\n120\n\nUnit\nmm\nmm\nmm\nmm\n%\n%\n%\n%\n\nabsolute\n\n160\n\nCase Load\n40%\n60%\n80%\n100%\n40%\n60%\n80%\n100%\n\nrelative\n\nMXMAX-Rear\n\nrelative\n\n(a)\n\nDisplacement [mm]\n\n200\n\nLF2 LF3 LF4\n-2.8 -3.2 -6.5\n-4.4 -5.2 -9.2\n-6.8 -8.9 -15.4\n-9.2 -12.3 -20.3\n-5.3 -2.2 -2.5\n-5.7 -2.5 -2.4\n-6.5 -3.2 -2.9\n-7.0 -3.5 -3.1\n\nTip\n-1.8\n-1.6\n-5.8\n-8.3\n-0.5\n-0.3\n-0.8\n-1.0\n\n20\n\nRadial Position [m]\nExp: 40% L.\n\nExp: 60% L.\n\nExp: 80% L.\n\nExp: 100% L.\n\nSim: 40% L.\n\nSim: 60% L.\n\nSim: 80% L.\n\nSim: 100% L.\n\nFigure A1. Bending lines extracted from the rear draw wire sensor for the (a) MXMAX; (b) MXMIN; (c) MYMAX; (d) MYMIN experiment\nand simulation. Results are shown for 40%, 60%, 80% and 100% of the target load. The table on the right shows the differences between the\nsimulation and the test.\n\n27\n\n\fhttps://doi.org/10.5194/wes-2021-24\nPreprint. Discussion started: 29 April 2021\nc Author(s) 2021. CC BY 4.0 License.\n\n(c)\n\n(d)\n\nµ-Strains [µm/m]\nµ-Strains [µm/m]\n\n(b)\n\nµ-Strains [µm/m]\n\n(a)\n\nµ-Strains [µm/m]\n\nAppendix B: Local strain comparison\n\n1000\n500\n0\n−500\n\nMXMAX @ r=5 m\n\n−1000\n2000\n1000\n0\n−1000\n\nMYMIN @ r=5 m\n\n−2000\n400\n\nMZLF2 @ r=5 m\n\n200\n0\n−200\n−400\n400\n\nMZLF4 @ r=5 m\n\n200\n0\n−200\n−400\n\n0\n\n0.1\n\n0.2\n\n0.3\n\n0.4\n\n0.5\n\n0.6\n\n0.7\n\n0.8\n\n0.9\n\n1\n\nNormalized Profile Circumference [-]\nExp: 0◦\n\nExp: 90◦\n\nSim: 0◦\n\nSim: 90◦\n\nFigure C1. Span-wise and cross-wise strains of the simulation and the test, plotted against the normalized profile circumference of the\ncross-section at r = 5 m for the (a) MXMAX; (b) MYMIN; (c) MZLF2; (d) MZLF4 load case.\n\n28\n\n\f(c)\n\n(d)\n\nµ-Strains [µm/m]\nµ-Strains [µm/m]\n\n(b)\n\nµ-Strains [µm/m]\n\n(a)\n\nµ-Strains [µm/m]\n\nhttps://doi.org/10.5194/wes-2021-24\nPreprint. Discussion started: 29 April 2021\nc Author(s) 2021. CC BY 4.0 License.\n\n1000\n500\n0\n−500\n\nMXMAX @ r=8 m\n\n−1000\n2000\n1000\n0\n−1000\n\nMYMIN @ r=8 m\n\n−2000\n300\n\nMZLF2 @ r=8 m\n\n150\n0\n−150\n−300\n200\n\nMZLF4 @ r=8 m\n\n100\n0\n−100\n−200\n\n0\n\n0.1\n\n0.2\n\n0.3\n\n0.4\n\n0.5\n\n0.6\n\n0.7\n\n0.8\n\n0.9\n\n1\n\nNormalized Profile Circumference [-]\nExp: 0◦\n\nExp: 90◦\n\nSim: 0◦\n\nSim: 90◦\n\nFigure D1. Span-wise and cross-wise strains of the simulation and the test, plotted against the normalized profile circumference of the\ncross-section at r = 8 m for the (a) MXMAX; (b) MYMIN; (c) MZLF2; (d) MZLF4 load case.\nAuthor contributions. Pablo Noever-Castelos implemented the parametrization and modeling methodology in MoCA, conducted the numer525\n\nical simulations, compared the simulations with the tests, and wrote the paper. Bernd Haller planned, executed, and documented the tests.\nClaudio Balzani is the supervisor and guided Pablo Noever-Castelos in the conception of the ideas and participated in the specification of\nstrain gauge positions as well as in writing, structuring, and reviewing the paper.\n\nCompeting interests. The authors declare that they do not have any conflicts of interests.\n\n29\n\n\fhttps://doi.org/10.5194/wes-2021-24\nPreprint. Discussion started: 29 April 2021\nc Author(s) 2021. CC BY 4.0 License.\n\nDisclaimer. The information in this paper is provided as is and no guarantee or warranty is given that the information is fit for any particular\n530\n\npurpose. The user thereof uses the information at its sole risk and liability.\n\nAcknowledgements. The authors acknowledge the financial support by the Federal Ministry for Economic Affairs and Energy of Germany in\nthe project SmartBlades2 (project numbers 0324032B/C). The authors further acknowledge the coordination effort of the German Aerospace\nCenter (DLR), the very good cooperation with the project partners and the fruitful discussions within the project consortium.\n\n30\n\n\fhttps://doi.org/10.5194/wes-2021-24\nPreprint. Discussion started: 29 April 2021\nc Author(s) 2021. CC BY 4.0 License.\n\nReferences\n535\n\nANSYS Inc.: Ansysr Academic Research Mechanical, Release 19.2.\nBottasso, C. L., Campagnolo, F., Croce, A., Dilli, S., Gualdoni, F., and Nielsen, M. 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