7 宇宙航空研究開発機構特別資料 JAXA-SP-7- Background APC-I, II Lift curve slope obtained by CFD did not agree with * test despite taking wing deformation into accou

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1 Third Aerodynamics Prediction Challenge (APC-Ⅲ) 75 3 rd Aerodynamic Prediction Challenge. Jun. National Olympics Memorial Youth Center, Tokyo Cflow による NASA-CRM の JAXA 及び 風試条件での解析 CFD Result of NASA-CRM using Cflow with Wind Tunnel Test Conditions at JAXA and Hidemasa Yasuda, Akio Ochi Kawasaki Heavy Industries, Ltd. Introduction of Cflow Kawasaki original CFD tool Cflow = Grid Generator + Flow Solver Cartesian based AMR +layered grid highly complicated unsteady large-scale Cflow has been validated in various workshops. - BANC I-IV DPW 7 HiLift-PW3 5- APC-I, II

2 7 宇宙航空研究開発機構特別資料 JAXA-SP-7- Background APC-I, II Lift curve slope obtained by CFD did not agree with * test despite taking wing deformation into account Lift curve (APC-I, II) CFD(deformed) APC-III (Sub.) M=.7, Re=.mln WIC* applied SIC* applied (CFD based) CFD No tunnel wall No sting support * WIC : Wall Interference Correction * SIC : Sting Interference Correction Results of * test and CFD are compared here. * : JAXA Transonic Wind Tunnel * : European Transonic Wind tunnel 3 Wind Tunnel Test Conditions APC-I, II Wind Tunnel * Re (x ). 5 3 Mach.7.5 This presentation P[kPa] 9 33 Q[kPa] Model Size (b/) [mm] 3.35 (% of model) 793. Case No test conditions are different from test. Reynolds number Dynamic Pressure (Q) Model Size Reynolds number effect The same Re number was applied to CFD. Wing deformation effect Deformed wing geometries were not available for arbitrary AoA. * test data :

3 Third Aerodynamics Prediction Challenge (APC-Ⅲ) 77 CFD Validation Procedure Validation methods Deformed wing geometry for test case was not available for arbitrary angles of attack. CFD was conducted with non-deformed geometry. Lift curve for deformed wing was estimated by following steps. () Estimate displacement at wing tip (wtip) in the test using test results. () Estimate ( deformed non-deformed ) using relationship of.vs. wtip obtained by CFD under the test condition. (3) Lift curve for deformed wing was estimated by correcting wing deformation effect using the values calculated above. CFD results were compared with test under the same condition (deformed wing, w/o sting). 5 Estimation Method of Wing Tip Displacement Wing tip displacement was estimated by Bernoulli-Euler beam theory assuming uniform load. Scaled by total at wind tunnel test C L * q w tip EI Scaled by dynamic pressure at wind tunnel test. Bending stiffness (EI) is scaled by th power of model span. Young s modulus (E) was assumed to be the same in all models. Second moment of area (I) has dimension of th power of length. I x A y d A wtip/(b/) wtip.vs. () y =.9x +. Re=.mln. Linear approximation.5.5 (WTT) wtip measurement position Wing tip displacement (wtip) is proportional to total. * WTT : Wind Tunnel Test pres * local chord.. α=.5 α=.9 α=.39 α=-. Load distribution (CFD) η distribution on the wing (APC-II, deformed wing, Re=.mln, Cflow)

4 7 宇宙航空研究開発機構特別資料 JAXA-SP-7- () Estimation of Wing Tip Displacement Graph below shows (wind tunnel test) versus wing tip displacement (wtip). () Estimate wtip Wing tip displacement (wtip) () Estimate C L f. Wtip values for test were. estimated using test result. Next page... deformed *. nondeformed.5.5 (WTT) non w tip wtip/(b/).5..3 (Re=.mln) Measured (3) Calculate deformed deformed = non-deformed + wtip b b q * q wtip * b each AoA 7 () Estimation of Wing Tip Displacement Graph below shows (wind tunnel test) versus wing tip displacement (wtip)..5 (Re=3mln) Estimated () Estimate wtip. (Re=.mln) Measured Wing tip displacement (wtip) () Estimate C L f deformed *. nondeformed.5.5 (WTT) non w tip wtip/(b/) (Re=5mln) Estimated.3.. (Re=5mln) Measured (AIAA--33) (3) Calculate deformed deformed = non-deformed + Bending stiffness (EI) was scaled by.9 for model as to estimated wtip agreed with measured wtip in Re=5mln case..

5 Third Aerodynamics Prediction Challenge (APC-Ⅲ) 79 () Estimation of Method of estimating (= deformed non-deformed ) for CFD results with the test conditions. () Estimate wtip Wing tip displacement (wtip) () Estimate Lift curve slope at Δ.5.5 Estimated was well estimated in test case. Re=5mln (Estimated) (Estimated) each AoA in CFD. CFD for (Calculated).5 nondeformed C L f w tip * nondeformed.5 Linear function. Linear approximation Re=3mln (Estimated) Averaged lift curve slope for the data. at linear region in nondeformed.75 CFD. (3) Calculate deformed wtip/(b/) deformed = non-deformed + 9 (3) Calculation of deformed Method of estimating (= deformed non-deformed ) for CFD results with the test conditions. () Estimate wtip Wing tip displacement (wtip) () Estimate C L f non w tip * deformed nondeformed..... Estimated Lift Curve CFD non-deformed CFD deformed (estimated) M=.5, Re=3mln (3) Calculate deformed Both effects of wing twist and bending were included deformed = non-deformed + in the because was obtained from CFD results with deformed* and non-deformed geometry. * Wing twist and bending were reflected to the deformed geometry.

6 宇宙航空研究開発機構特別資料 JAXA-SP-7- Intruduction Validation Procedure Wing Deformation Effect Correction Computational Methods Result Summary Computational Methods Cflow solver methods are summarized in the table below. The same methods were employed in APC-I and II. Solver methods Gverning Equations Spatial Discretization RANS (Reynolds Averaged Navier-Stokes) equations Cell-centerd finite volume method with nd-order accurate reconstruction based on MUS Inviscid Flux SLAU (Simple Low dissipation AUSM) scheme Viscous Flux nd-order accurate central difference Time Integration MFGS (Matrix Free Gauss Seidel) implicit method with local time stepping Turbulence Model SA-noft (fully turbulent) Intruduction Validation Procedure Wing Deformation Effect Correction Computational Methods Result Summary Computational Grid Cflow Grid Cartesian based AMR layered grid NCell 9M y+< (Initial wall spacing was different depending on Reynolds number.) Section E Spatial Grid Section E Wing Upper Surface

7 Third Aerodynamics Prediction Challenge (APC-Ⅲ) Result Lift Curve , Re=.mln CFD(non-deformed) CFD(deformed), Re=5mln CFD(non-deformed) CFD(estimated) APC-I, II M=.7 Lift curve slope estimated by CFD agreed well with test results. M= Data Correction WIC applied SIC applied (CFD based) WIC applied SIC applied CFD No tunnel wall No sting support, Re=3mln CFD(non-deformed) CFD(estimated) in CFD was lower than WTT result by about. ~.[deg] M=.5 in all cases. 3 Lift Curve Slope Graph below shows lift curve slope versus Reynolds number. Wing deformation effect was eliminated in all data. (w/o sting) - WIC applied, SIC applied 9 Lift curve slope of result seemed higher than and CFD results when considering the wing deformation effect and Reynolds number effect. α[/rad].5 CFD(w/o Sting) (w/o sting) - WIC applied, SIC applied CFD result agreed well with test results. Lift curve slope averaged at -.75 o α.7 o 7.5 WIC : Wall Interference Correction, SIC : Sting support Interference Correction. (α=.[/rad].7 [/deg]) Re (x^)

8 宇宙航空研究開発機構特別資料 JAXA-SP-7- Summary Lift curves were compared in CFD and results. Wing deformation effect on the lift curve was corrected using CFD result with the test condition. Lift curve slope obtained by CFD agreed well with test results when wing deformation effect was corrected, while not agreed with test. Lift curve slope obtained in test seemed higher than test result when considering the effects of wing deformation and Reynolds number. Effect of porous ratio of the wind tunnel wall? obtained by CFD was lower than WTT by about. -.[deg] in all cases. Turbulence model effect? 5 Appendix Results of Discussion with JAXA after APC-III Abstract KHI and JAXA discussed the wing deformation correction results of lift curve and its slope. At first, wing deformation effect correction results of KHI and JAXA were compared. JAXA results were quoted from []. After that, lift curve slope was calculated using JAXA corrected data. As a result, KHI results and JAXA results were well agreed. [] K. Yasue, M. Ueno, Model Deformation Corrections of NASA Common Research Model Using Computational Fluid Dynamics, Journal of Aircraft, Vol. 53, No., ().

9 Third Aerodynamics Prediction Challenge APC-Ⅲ WTT Result w/o WDC* 3 * Wing Deformation effect Correction WTT results employed by KHI and JAXA[] are different run. So WTT results without wing deformation effect are compared before discussing WDC. Re=.mln Re=5mln Re.mln Run (KHI). Re5mln Run53 (KHI). WTT results employed by. KHI and JAXA were well matched Run Run JAXA data : [] Fig. a) JAXA data : [] Fig. a) 7 WTT results w/ WDC (KHI.vs. JAXA method) WTT results corrected by KHI and JAXA are compared. JAXA correction used CFD to obtain between deformed and non-deformed configuration. Re=.mln.7.. JAXA correction KHI correction.5 KHI correction KHI corrected lift curve and JAXA corrected result are well agreed in both Re=.mln and 5mln cases.. JAXA correction Re=5mln.7-3 JAXA data : [] Fig. b) JAXA data : [] Fig. b) 5

10 宇宙航空研究開発機構特別資料 JAXA-SP-7- Lift Curve Slope of JAXA Corrected WTT Results Graph below shows lift curve ([] Fig. b)) and local lift curve slope calculated from the lift curve. Local lift curve slope of case seems higher than Re5M case in α<[deg] JAXA corrected WTT results ( [] Fig. b), replot) 3 5 Lift curve slope Re.M DefCorr Re5M DefCorr NTF Re5M DefCorr α[/rad] Local lift curve slope Averaged lift curve slope (next page) was calculated using data in this region. Re.M DefCorr Re5M DefCorr NTF Re5M DefCorr 3 5 Local lift curve slope i i i i i 9 Lift Curve Slope Lift curve slope calculated by least-squares method using JAXA corrected WTT results. 9 Lift curve slope calculated using KHI corrected WTT results (, ) and JAXA corrected ( ) have similar tendency. result seemed to have higher slope than result. JAXA correction α[/rad].5 KHI correction. (α=.[/rad].7 [/deg]) 7.5 Re (x^)

11 Third Aerodynamics Prediction Challenge (APC-Ⅲ) 5 Acknowledgement Authors would like to show special thanks to JAXA who had discussions together after APC-III and provided us the digital data of the paper for comparing the wing deformation effect correction on the lift curve. There may be some issues both in CFD and wind tunnel test. Discussing such issues in the future APC will contribute to improve CFD and wind tunnel test technology. Thank you for your attention.