Gradient Based Aerodynamic Shape Optimization Design And Applications

Aerodynamic shape optimization design is a technique that uses computers to modify aircraft’s shape automatically in order to improve its performance.It has been increasingly applied in aircraft industries.The key techniques in aerodynamic shape optimization design include CFD flow solver,shape parameterization,grid warping,optimization algorithms,etc.Optimization algorithm is the top level framework,which determines the basic optimization strategy.Based on the requirement of gradient information,optimization algorithms could be classified into gradient-based approach and gradient-free approach.Gradient-free algorithms are often of slow convergence,in which the function evaluations scale quadratically or even more with the dimensionality of the problem,namely the number of the design variables.In real applications with large number of design variables,gradient-free methods are not feasible with limited computational resources.Gradient-based methods,however,often converge fast,and its function evaluations scale almost linearly with the dimensionality of the problem.Due to the advantages of gradient-based methods,studies on research of gradient-based aerodynamic shape optimization design approach have been conducted.An optimization design system has been established for large dimensional problems.The main work in this thesis are as following:1.Develop a Newton-Krylov based CFD solver for solving steady Reynolds-Averaged Navier-Stokes equations.A three-dimensional structured grid based CFD solver has been developed,with 2nd order JST central difference spatial discretlization scheme,Spalart-Allmaras one equation turbulence model.Explicit multi-stage Runge-Kutta scheme,semi-implicit DADI scheme and pure implicit Newton-Krylov scheme have been developed.Within the implicit scheme,GMRES method is used for solving large scale linear equations system,Additive Schwarz and Imcomplete LU factorization methods have been used to form the precondition matrix.A strategy for efficient solving steady flow problem has been proposed that using explit or semi-implicit scheme to start the solver until convergence to some degree,and then switching to implicit scheme to achieve tight convergence.2.Aiming at multi-component simultaneous shape design,the application of FFD method has been extended to accomplish multi-component integral parameterization.First,FFD geometry parameterizaton method has been studied and accomplished,with the Bernstein basis function being replaced by B-spline basis function in order to improve its local control.Besides,an hybrid direct-search-Newton method has been proposed for local parameters solving within the parameterization procedure.Then,with the application of multi-block face-matching FFD technique,multiple components bould be parameterized simultaneously and intergrally.The approach directly manipulates the surface mesh and could maintain the original geometrical property and topology.By integrately handling multiple FFD control blocks,horizontal-tail solid rotation could be achieved for trimming the aircraft while optimizing the wing shape.3.Automatic mesh warping scheme has been developed based on inverse distance weighting interpolation method,which is for automatically updating the mesh within optimization.By this method,both of the displacement and torsion of the mesh have been included,and the surface deformation would be transmited to space by interpolation scheme.Quaternions interpolation method is used for computing the torsional component.The test case shows that this scheme is of good robustness when large deformation exists.4.The discrete adjoint solver of RANS has been developed using automatic differentiation method and GMRES algorithm,which could compute the functional gradient with respect large number of design variables in optimization accurately and efficiently.First,the discrete adjoint equations have been deduced and formed.Then,GMRES has been applied in solving the discrete adjoint equations,which is a large scale and sparse linear system.Reverse mode automatic differentiation has been used to compute the transposed Jacobian matrix vector product efficiently,which avoids explicitly forming and storing the large matrix in order to reduce the memory expense.Based on the comparison with the results obtained by finite difference method,the accuracy of the derivatives by adjoint solver has been verified.5.An approach for efficient aerodynamic shape optimization design with large number of design variables has been proposed.Combined with RANS flow solver,FFD geometry parameterization,IDW mesh warpping,discrete adjoint solver and sequential quadratic programming,gradient-based aerodynamic shape optimization design system has been established.Based on this design system,study on shape design of the blended wing body aircraft and conventional wing-body-tail configuration has been conducted.The results have shown that the design system could achieve self-trimming by shaping the geometry of the BWB aircraft,together with reducing drag in multiple design point;in the shape optimization of wing-body-tail configuration,the design system could automatically rotate the tail to trim the aircraft,while optimizing the wing shape.6.In optimization of unconventional belended wing-body configuration,the influence of the trimming constraint to span-wise lift distribution and geometrical twist distribution has been studied.In optimization of conventional wing-body-tail configuration,the influence of the tail rotation based trimming constraint has been studied.The results from with/without trimming constraints and with/without tail shape design variables have been compared.An approach of computing trim drag penaly by surrogate model has been proposed,which could be used to consider trim penalty within the design of a configuration without an explicit horizontal-tail.