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1. 30P30N多段翼
增升装置对于提高现代大型运输类飞机性能十分重要。高效的增升装置可以增加载重和航程、减轻飞机重量等。高升力机翼构型一般由翼身、前缘缝翼和后缘襟翼组成。在高速条件下，多段翼流场中可能存在转捩、分离、激波/边界层干扰等复杂流动现象。本文以30P30N多段翼为测试算例，检验SU2对于二维复杂外形的模拟能力。
图1：30P30N多段翼外形
图2：多段翼流动特征
表130P30N多段翼网格参数
| 网格构型 | 网格单元数 |
| L1 | 63957 |
| L2 | 112474 |
| L3 | 260909 |
| L4 | 583226 |
| L5 | 1043636 |
网格采用JAXA提供的结构化网格(https://cfdws.chofu.jaxa. jp/apc/grids/3element_highlift_airfoil/30P30N_modified_slat_configF/plot3d/)。该网站提供了L1-L5等不同网格密度的五种结构化网格，这些网格具有相同的拓扑结构，都是由117块网格块构成，具体参数见表1。受计算资源限制，本文将对前4种网格进行网格无关性研究。该多段翼机翼弦长0.4572 m（18 inch），前缘逢翼和后缘襟翼均偏转30°。
图3：30P30N多段翼拓扑结构及网格
下面以马赫数为0.20、攻角为16°、湍流模型为SA的计算工况为例，介绍30P30N算例的cfg文件参数设置。
（1）问题定义
| % ------------- DIRECT, ADJOINT, AND LINEARIZED PROBLEM DEFINITION ------------% % % Physical governing equations (EULER, NAVIER_STOKES, % WAVE_EQUATION, HEAT_EQUATION, FEM_ELASTICITY, % POISSON_EQUATION) PHYSICAL_PROBLEM= NAVIER_STOKES % % Specify turbulent model (NONE, SA, SA_NEG, SST) KIND_TURB_MODEL= SST % % Mathematical problem (DIRECT, CONTINUOUS_ADJOINT) MATH_PROBLEM= DIRECT % % Restart solution (NO, YES) RESTART_SOL= NO |
（2）自由来流参数设置
| % -------------------- COMPRESSIBLE FREE-STREAM DEFINITION --------------------% % % Mach number (non-dimensional, based on the free-stream values) MACH_NUMBER= 0.2 % % Angle of attack (degrees, only for compressible flows) AOA= 16.0 % % Free-stream temperature (288.15 K by default) FREESTREAM_TEMPERATURE= 300 % % Reynolds number (non-dimensional, based on the free-stream values) REYNOLDS_NUMBER= 9.0E6 % % Reynolds length (1 m by default) REYNOLDS_LENGTH= 0.4572 |
（3）参考值设置
| % ---------------------- REFERENCE VALUE DEFINITION ---------------------------% % % Reference origin for moment computation REF_ORIGIN_MOMENT_X = 0.25 REF_ORIGIN_MOMENT_Y = 0.00 REF_ORIGIN_MOMENT_Z = 0.00 % % Reference length for pitching, rolling, and yawing non-dimensional moment REF_LENGTH= 1.0 % % Reference area for force coefficients (0 implies automatic calculation) REF_AREA= 0.4572 |
（4）边界条件设置
| % -------------------- BOUNDARY CONDITION DEFINITION --------------------------% % % Navier-Stokes wall boundary marker(s) (NONE = no marker) MARKER_HEATFLUX= ( slat, 0.0, main, 0.0, flap, 0.0 ) % % Farfield boundary marker(s) (NONE = no marker) MARKER_FAR= ( far ) % % Marker(s) of the surface to be plotted or designed MARKER_PLOTTING= ( slat, main, flap ) % % Marker(s) of the surface where the functional (Cd, Cl, etc.) will be evaluated MARKER_MONITORING= ( slat, main, flap ) |
（5）数值求解通用参数
| % ------------- COMMON PARAMETERS DEFINING THE NUMERICAL METHOD ---------------% % % Numerical method for spatial gradients (GREEN_GAUSS, WEIGHTED_LEAST_SQUARES) NUM_METHOD_GRAD= WEIGHTED_LEAST_SQUARES % % Courant-Friedrichs-Lewy condition of the finest grid CFL_NUMBER= 5 % % Adaptive CFL number (NO, YES) CFL_ADAPT= NO % % Parameters of the adaptive CFL number (factor down, factor up, CFL min value, % CFL max value ) CFL_ADAPT_PARAM= ( 1.5, 0.5, 1.0, 100.0 ) % % Number of total iterations EXT_ITER= 99999 % % Linear solver for the implicit formulation (BCGSTAB, FGMRES) LINEAR_SOLVER= BCGSTAB % % Min error of the linear solver for the implicit formulation LINEAR_SOLVER_ERROR= 1E-6 % % Max number of iterations of the linear solver for the implicit formulation LINEAR_SOLVER_ITER= 20 |
（6）多重网格参数
| % -------------------------- MULTIGRID PARAMETERS -----------------------------% % % Multi-Grid Levels (0 = no multi-grid) MGLEVEL= 0 % % Multi-grid cycle (V_CYCLE, W_CYCLE, FULLMG_CYCLE) MGCYCLE= W_CYCLE % % Multi-grid pre-smoothing level MG_PRE_SMOOTH= ( 1, 2, 3, 3 ) % % Multi-grid post-smoothing level MG_POST_SMOOTH= ( 0, 0, 0, 0 ) % % Jacobi implicit smoothing of the correction MG_CORRECTION_SMOOTH= ( 0, 0, 0, 0 ) % % Damping factor for the residual restriction MG_DAMP_RESTRICTION= 0.95 % % Damping factor for the correction prolongation MG_DAMP_PROLONGATION= 0.95 |
（7）流场计算数值格式
| % -------------------- FLOW NUMERICAL METHOD DEFINITION -----------------------% % % Convective numerical method (JST, LAX-FRIEDRICH, CUSP, ROE, AUSM, HLLC, % TURKEL_PREC, MSW) CONV_NUM_METHOD_FLOW= JST % % Monotonic Upwind Scheme for Conservation Laws (TVD) in the flow equations. % Required for 2nd order upwind schemes (NO, YES) MUSCL_FLOW= YES % % Slope limiter (VENKATAKRISHNAN, MINMOD) SLOPE_LIMITER_FLOW= VENKATAKRISHNAN % % Coefficient for the limiter (smooth regions) VENKAT_LIMITER_COEFF= 0.03 % % 2nd and 4th order artificial dissipation coefficients JST_SENSOR_COEFF= ( 0.5, 0.02 ) % % Time discretization (RUNGE-KUTTA_EXPLICIT, EULER_IMPLICIT, EULER_EXPLICIT) TIME_DISCRE_FLOW= EULER_IMPLICIT |
（8）湍流计算数值格式
| % -------------------- TURBULENT NUMERICAL METHOD DEFINITION ------------------% % % Convective numerical method (SCALAR_UPWIND) CONV_NUM_METHOD_TURB= SCALAR_UPWIND % % Monotonic Upwind Scheme for Conservation Laws (TVD) in the turbulence equations. % Required for 2nd order upwind schemes (NO, YES) MUSCL_TURB= NO % % Time discretization (EULER_IMPLICIT) TIME_DISCRE_TURB= EULER_IMPLICIT |
（9）收敛准则
| % --------------------------- CONVERGENCE PARAMETERS --------------------------% % % Convergence criteria (CAUCHY, RESIDUAL) % CONV_CRITERIA= RESIDUAL % % Residual reduction (order of magnitude with respect to the initial value) RESIDUAL_REDUCTION= 10 % % Min value of the residual (log10 of the residual) RESIDUAL_MINVAL= -8 % % Start convergence criteria at iteration number STARTCONV_ITER= 10 % % Number of elements to apply the criteria CAUCHY_ELEMS= 100 % % Epsilon to control the series convergence CAUCHY_EPS= 1E-6 % % Function to apply the criteria (LIFT, DRAG, NEARFIELD_PRESS, SENS_GEOMETRY, % SENS_MACH, DELTA_LIFT, DELTA_DRAG) CAUCHY_FUNC_FLOW= DRAG |
（10）输入输出设置
| % ------------------------- INPUT/OUTPUT INFORMATION --------------------------% % % Mesh input file MESH_FILENAME= L1-30P30N.su2 % % Mesh input file format (SU2, CGNS, NETCDF_ASCII) MESH_FORMAT= SU2 % % Mesh output file MESH_OUT_FILENAME= mesh_out.su2 % % Restart flow input file SOLUTION_FLOW_FILENAME= restart_flow.dat % % Restart adjoint input file SOLUTION_ADJ_FILENAME= solution_adj.dat % % Output file format (PARAVIEW, TECPLOT, STL) OUTPUT_FORMAT= TECPLOT % % Output file convergence history (w/o extension) CONV_FILENAME= history % % Output file restart flow RESTART_FLOW_FILENAME= restart_flow.dat % % Output file restart adjoint RESTART_ADJ_FILENAME= restart_adj.dat % % Output file flow (w/o extension) variables VOLUME_FLOW_FILENAME= flow % % Output file adjoint (w/o extension) variables VOLUME_ADJ_FILENAME= adjoint % % Output objective function gradient (using continuous adjoint) GRAD_OBJFUNC_FILENAME= of_grad.dat % % Output file surface flow coefficient (w/o extension) SURFACE_FLOW_FILENAME= surface_flow % % Output file surface adjoint coefficient (w/o extension) SURFACE_ADJ_FILENAME= surface_adjoint % % Writing solution file frequency WRT_SOL_FREQ= 250 % % Writing convergence history frequency WRT_CON_FREQ= 1 |
图4：30P30N多段翼压力分布SA和SST计算结果对比
图4展示了SU2求解器分别采用SA模型和SST模型计算的30P30N多段翼表面压力分布（Ma=0.20 AoA=16° Rec=9.0×106）。可以看到，SA、SST模型计算的压力分布在压力面（迎风面、正压区）与试验结果符合较好，而在吸力面（背风面、负压区）与试验结果存在一定差异。两种湍流模型相比，SA模型比SST模型更加接近试验结果。
图5：30P30N多段翼压力分布不同网格密度计算结果对比
图5展示了SU2求解器分别采用不同网格密度计算的30P30N多段翼表面压力分布，湍流模型为SA模型。可以看到，随着网格密度的增加，背风面负压峰值不断升高，也越来越接近试验结果。该计算结果表明，30P30N多段翼算例对计算网格的密度较为敏感。采用L4网格和SA湍流模型计算的30P30N多段翼压力分布与试验结果基本符合。
1）采用SU2求解器计算了30P30N多段翼流场（Ma=0.20 AoA=16°Rec=9.0×106），计算结果与试验结果基本符合，表明SU2能够较好地模拟30P30N等二维复杂外形流场。
2）计算结果表明，湍流模型和网格密度对30P30N算例计算结果都有一定的影响。采用高密度网格和SA模型能更好地模拟背风区流动，获得与试验更加接近的结果。
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