﻿ 伴随压力分布反设计方法在大型客机气动优化中的初步探索
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1. 中国航空工业西安航空计算技术研究所, 西安 710065;
2. 中国商飞上海飞机设计研究院, 上海 201210

Aerodynamic optimization design of large civil aircraft using pressure distribution inverse design method based on discrete adjoint
LIU Fengbo1, JIANG Cheng1, MA Tuliang2, LIANG Yihua1
1. AVIC Aeronautics Computing Technique Research Institute, Xi'an 710065, China;
2. COMAC Shanghai Aircraft Design and Research Institute, Shanghai 201210, China
Abstract: From the engineering application point of view, the application of the discrete adjoint companion pressure distribution inverse design optimization method in the design of wide-body civil aircraft wing is studied. The optimization design idea of three-dimensional configuration combined with pressure distribution inverse design and adjoint optimization is proposed, which promotes the engineering of discrete adjoint aerodynamic optimization design method. Firstly, the three-dimensional pressure distribution inverse design is carried out for the CRM wing configuration, which verifies the accuracy and efficiency of the discrete adjoint pressure distribution inverse design in the three-dimensional problem. Secondly, based on the new optimization design idea proposed by the application, the pressure distribution inverse design constraint method is introduced on the basis of a wide-body full-body two-point aerodynamic optimization result, and the wing pressure distribution and the resistance creep increase characteristic of the low Mach number are improved. And achieved good drag reduction and resistance divergence characteristics to improve the engineering applicability of the optimized configuration.
Keywords: aerodynamic optimization design    discrete adjoint method    multipoint optimization    inverse design    supercritical wing

1 离散伴随方程和敏感性导数

 $\begin{array}{l} L\left( {\mathit{\boldsymbol{D}}, \mathit{\boldsymbol{Q}}, \mathit{\boldsymbol{X}}, {\mathit{\boldsymbol{ \boldsymbol{\varLambda} }}_f}, {\mathit{\boldsymbol{ \boldsymbol{\varLambda} }}_{\rm{g}}}} \right) = f(\mathit{\boldsymbol{D}}, \mathit{\boldsymbol{Q}}, \mathit{\boldsymbol{X}}) + \\ \mathit{\boldsymbol{ \boldsymbol{\varLambda} }}_f^{\rm{T}}\mathit{\boldsymbol{R}}(\mathit{\boldsymbol{D}}, \mathit{\boldsymbol{Q}}, \mathit{\boldsymbol{X}}) + \mathit{\boldsymbol{ \boldsymbol{\varLambda} }}_8^{\rm{T}}\mathit{\boldsymbol{G}}(\mathit{\boldsymbol{D}}, \mathit{\boldsymbol{X}}) \end{array}$ （1）

 $\begin{array}{l} \frac{{{\rm{d}}L}}{{{\rm{d}}\mathit{\boldsymbol{D}}}} = \left( {\frac{{\partial f}}{{\partial \mathit{\boldsymbol{D}}}} + \mathit{\boldsymbol{ \boldsymbol{\varLambda} }}_f^{\rm{T}}\frac{{\partial \mathit{\boldsymbol{R}}}}{{\partial \mathit{\boldsymbol{D}}}} + \mathit{\boldsymbol{ \boldsymbol{\varLambda} }}_{\rm{g}}^{\rm{T}}\frac{{\partial \mathit{\boldsymbol{G}}}}{{\partial \mathit{\boldsymbol{D}}}}} \right) + \left( {\frac{{\partial f}}{{\partial \mathit{\boldsymbol{Q}}}} + \mathit{\boldsymbol{ \boldsymbol{\varLambda} }}_f^{\rm{T}}\frac{{\partial \mathit{\boldsymbol{R}}}}{{\partial \mathit{\boldsymbol{Q}}}}} \right)\frac{{\partial \mathit{\boldsymbol{Q}}}}{{\partial \mathit{\boldsymbol{D}}}} + \\ \;\;\;\;\;\;\;\;\;\left( {\frac{{\partial f}}{{\partial \mathit{\boldsymbol{X}}}} + \mathit{\boldsymbol{ \boldsymbol{\varLambda} }}_f^{\rm{T}}\frac{{\partial \mathit{\boldsymbol{R}}}}{{\partial \mathit{\boldsymbol{X}}}} + \mathit{\boldsymbol{ \boldsymbol{\varLambda} }}_{\rm{g}}^{\rm{T}}\frac{{\partial \mathit{\boldsymbol{G}}}}{{\partial \mathit{\boldsymbol{X}}}}} \right)\frac{{\partial \mathit{\boldsymbol{X}}}}{{\partial \mathit{\boldsymbol{D}}}} \end{array}$ （2）

 $\left\{ {\begin{array}{*{20}{l}} {\frac{{\partial f}}{{\partial \mathit{\boldsymbol{Q}}}} + \mathit{\boldsymbol{ \boldsymbol{\varLambda} }}_f^{\rm{T}}\frac{{\partial \mathit{\boldsymbol{R}}}}{{\partial \mathit{\boldsymbol{Q}}}} = 0}\\ {\frac{{\partial f}}{{\partial \mathit{\boldsymbol{X}}}} + \mathit{\boldsymbol{ \boldsymbol{\varLambda} }}_f^{\rm{T}}\frac{{\partial \mathit{\boldsymbol{R}}}}{{\partial \mathit{\boldsymbol{X}}}} + \mathit{\boldsymbol{ \boldsymbol{\varLambda} }}_{\rm{g}}^{\rm{T}}\frac{{\partial \mathit{\boldsymbol{G}}}}{{\partial \mathit{\boldsymbol{X}}}} = 0} \end{array}} \right.$ （3）

 $\frac{{d\mathit{\boldsymbol{L}}}}{{d\mathit{\boldsymbol{D}}}} = \frac{{\partial f}}{{\partial \mathit{\boldsymbol{D}}}} + \mathit{\boldsymbol{ \boldsymbol{\varLambda} }}_f^{\rm{T}}\frac{{\partial \mathit{\boldsymbol{R}}}}{{\partial \mathit{\boldsymbol{D}}}} + \mathit{\boldsymbol{ \boldsymbol{\varLambda} }}_g^{\rm{T}}\frac{{\partial \mathit{\boldsymbol{G}}}}{{\partial \mathit{\boldsymbol{D}}}}$ （4）

 $F_{j}=\sum\limits_{i=1}^{N}\left(C_{p i}-C_{p i}^{*}\right)^{2}$ （5）

 图 1 压力分布插值 Fig. 1 Pressure distribution interpolation

 $\left\{ {\begin{array}{*{20}{l}} {{F_{{\rm{total }}}} = \sum\limits_{j = 1}^k {{\omega _j}} {F_j}}\\ {{\rm{ s}}{\rm{. t}}{\rm{. }}\quad \sum\limits_{j = 1}^k {{\omega _j}} = 1} \end{array}} \right.$ （6）
2 翼面压力分布约束控制方法

1) 确定机翼展向控制剖面站位信息(展向Y值坐标)。

2) 对各剖面的压力分布进行上下翼面分割，分开上下翼面压力分布，确定分割信息。

3) 分别给出上下翼面目标/约束压力分布信息(可分段给出XCp信息)。

 图 2 压力分布约束 Fig. 2 Pressure distribution constraints

1) X1~X2段用于控制吸力平台区域。

2) X2~X3段用于控制激波位置及强度。

3) X3~X4段用于控制波后加速区。

4) X4~X5段用于控制压力恢复区。

3 面向工程应用的伴随优化及压力反设计

 图 3 考虑压力分布约束的气动外形优化设计流程 Fig. 3 Framework of aerodynamic optimization design with pressure distribution constraints
4 超临界机翼气动压力反设计算例

 算例定义 初始构型 优化目标 Case 1 随意扰动后的CRM机翼 CRM机翼原始构型多个站位压力分布 Case 2 CRM机翼原始构型 CRM机翼多点优化多个站位压力分布
4.1 Case 1压力分布反设计优化

 图 4 CRM机翼表面网格 Fig. 4 Surface grid of CRM wing

 图 5 CRM机翼FFD控制体 Fig. 5 FFD control box of CRM wing

 ${F_{{\rm{obj}}}} = \sum\limits_{i = 1}^8 {\sum\limits_{j = 1}^n {{{\left( {{C_{p, ij}} - C_{p, ij}^*} \right)}^2}} }$

 图 6 Case 1目标函数收敛历程 Fig. 6 Convergence history of objective function for Case 1 study

 Type α/(°) CL CD Cmy Baseline 2.327 5 0.471 0.023 625 -0.154 42 Target 2.327 5 0.500 0.020 513 -0.173 22 Inverse design 2.327 5 0.499 0.020 539 -0.172 61

 图 7 Case 1反设计机翼的表面压力云图及典型站位压力分布 Fig. 7 Pressure contour and pressure distribution of typical span-wise stations of inverse design wing in Case 1 study
 图 8 Case 1初始构型、目标构型与反设计构型6个典型站位翼型形状对比 Fig. 8 Comparision of sectional airfoil shapes for baseline, target and inverse design configuration at 6 span-wise positions in Case 1 study
4.2 Case 2压力分布反设计优化

 图 9 Case 2目标函数收敛历程 Fig. 9 Convergence history of objective function for Case 2 study

 Type α/(°) CL CD Cmy Baseline 2.327 5 0.500 0.020 513 -0.173 22 Target 2.451 1 0.500 0.019 774 -0.169 24 Inverse design 2.427 5 0.499 0.019 685 -0.165 82

 图 10 Case 2反设计机翼的表面压力云图及典型站位压力分布 Fig. 10 Pressure contour and pressure distribution of typical span-wise stations of inverse design wing in Case 2 study
 图 11 Case 2初始构型、目标构型与反设计构型在6个典型站位翼型形状对比 Fig. 11 Comparision of sectional airfoil shapes for baseline, target and inverse design configuration at 6 span-wise positions in Case 2 study
5 宽体客机压力分布修正优化设计

5.1 Design 1不考虑压力分布约束的两点优化

 Type Function/variable Description Quantity Minimize CD(Ma=0.85)CD(Ma=0.87) Drag coefficient 2 Design variables Zα FFD control pointz-coordinates Angle of attack 140+1 Aerodynamical constraints CL=CL_targetCmx≤Cmx_baseCmy≥Cmy_base Lift coefficient Bending moment Pitching moment 3×2 Geometryic constraints T > 0.98T0 Spar thickness Max thickness 3×10
 图 12 宽体客机FFD控制体分布及约束分布 Fig. 12 Constraints location and FFD control box of wide-body aircraft

 图 13 宽体客机机翼第1轮优化后表面压力云图及典型站位压力分布 Fig. 13 Pressure contour and pressure distribution of typical span-wise stations of optimal wing in the first round optimization design
5.2 Design 2考虑压力分布约束的优化

1) 展向直等压线分布控制

 $F_{\mathrm{cons}}=\sum\limits_{i=1}^{10}\left(C_{p, i, 55 \%}-C_{p, i, 55 \%}^{*}\right)^{2}$

2) 吸力平台压力波动修正

 $\hat{C}_{p, j j}^{*}=k x_{i j}+b$

 $F_{\mathrm{cons}}=\sum\limits_{i=1}^{10} \sum\limits_{j=1}^{n}\left(C_{p, i j}-\hat{C}_{p, i j}^{*}\right)^{2}$

3) 激波后二次加速区修正

 $F_{\text {cons }}=\sum\limits_{i=1}^{10} \sum\limits_{j=1}^{n}\left(C_{p, i j}-C_{p, i, 60 \%}^{*}\right)^{2}$

 图 14 宽体客机机翼第2轮优化后表面压力云图及典型站位压力分布 Fig. 14 Pressure contour and pressure distribution of typical span-wise stations of optimal wing in the second round optimization design
 图 15 阻力发散曲线对比 Fig. 15 Comparison of drag divergence curves

6 结论

1) 采用目标点邻域线性插值的方法解决了目标压力分布在非结构混合网格剖面上的装配难题。

2) 直接对三维CRM机翼进行压力分布反设计，验证本文的伴随压力分布反设计方法能有效的对宽体客机机翼进行反设计优化，反设计效果明显，效率高，结果可靠。

3) 利用伴随压力分布反设计方法直接对三维机翼进行反设计，相比于传统翼型反设计再装配方案，具有更高的效率和精度。

4) 在宽体全机构型离散伴随两点气动优化结果的基础上，引入压力分布反设计约束方法，改进了展向直等压线分布和吸力平台区压力分布波动等问题，使优化构型更加接近工程实用性。

5) 对于宽体客机超临界机翼设计，采用考虑压力分布约束的伴随多点优化是很有必要的。这种方法将数值优化与人工经验结合，可以促进伴随气动优化方法在工程应用中的实用性。

http://dx.doi.org/10.7527/S1000-6893.2019.23372

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#### 文章信息

LIU Fengbo, JIANG Cheng, MA Tuliang, LIANG Yihua

Aerodynamic optimization design of large civil aircraft using pressure distribution inverse design method based on discrete adjoint

Acta Aeronautica et Astronautica Sinica, 2020, 41(5): 623372.
http://dx.doi.org/10.7527/S1000-6893.2019.23372