Aerodynamic/stealth design of S-duct inlet based on discrete adjoint method

It is a major challenge for the airframe-inlet design of modern combat aircrafts,as the flow and electromagnetic wave propagation in the inlet of stealth aircraft are very complex.In this study,an aerodynamic/stealth optimization design method for an S-duct inlet is proposed.The upwind scheme is introduced to the aerodynamic adjoint equation to resolve the shock wave and flow separation.The multilevel fast multipole algorithm(MLFMA)is utilized for the stealth adjoint equation.A dorsal S-duct inlet of flying wing layout is optimized to improve the aerodynamic and stealth characteristics.Both the aerodynamic and stealth characteristics of the inlet are effectively improved.Finally,the optimization results are analyzed,and it shows that the main contradiction between aerodynamic characteristics and stealth characteristics is the centerline and crosssectional area.The S-duct is smoothed,and the cross-sectional area is increased to improve the aerodynamic characteristics,while it is completely opposite for the stealth design.The radar cross section(RCS)is reduced by phase cancelation for low frequency conditions.The method is suitable for the aerodynamic/stealth design of the aircraft airframe-inlet system.

Effect of constant eddy viscosity assumption on optimization using a discrete adjoint method

This paper presents a thorough study of the effect of the Constant Eddy Viscosity(CEV)assumption on the optimization of a discrete adjoint-based design optimization system.First,the algorithms of the adjoint methods with and without the CEV assumption are presented,followed by a discussion of the two methods’solution stability.Second,the sensitivity accuracy,adjoint solution stability,and Root Mean Square(RMS)residual convergence rates at both design and offdesign operating points are compared between the CEV and full viscosity adjoint methods in detail.Finally,a multi-point steady aerodynamic and a multi-objective unsteady aerodynamic and aeroelastic coupled design optimizations are performed to study the impact of the CEV assumption on optimization.Two gradient-based optimizers,the Sequential Least-Square Quadratic Programming(SLSQP)method and Steepest Descent Method(SDM)are respectively used to draw a firm conclusion.The results from the transonic NASA Rotor 67 show that the CEV assumption can deteriorate RMS residual convergence rates and even lead to solution instability,especially at a near stall point.Compared with the steady cases,the effect of the CEV assumption on unsteady sensitivity accuracy is much stronger.Nevertheless,the CEV adjoint solver is still capable of achieving optimization goals to some extent,particularly if the flow under consideration is benign.

Automatic differentiation based discrete adjoint method for aerodynamic design optimization on unstructured meshes

A systematic methodology for formulating,implementing,solving and verifying discrete adjoint of the compressible Reynolds-averaged Navier-Stokes（RANS） equations for aerodynamic design optimization on unstructured meshes is proposed.First,a general adjoint formulation is constructed for the entire optimization problem,including parameterization,mesh deformation,flow solution and computation of the objective function,which is followed by detailed formulations of matrix-vector products arising in the adjoint model.According to this formulation,procedural components of implementing the required matrix-vector products are generated by means of automatic differentiation（AD） in a structured and modular manner.Furthermore,a duality-preserving iterative algorithm is employed to solve flow adjoint equations arising in the adjoint model,ensuring identical convergence rates for the tangent and the adjoint models.A three-step strategy is adopted to verify the adjoint computation.The proposed method has several remarkable features：the use of AD techniques avoids tedious and error-prone manual derivation and programming;duality is strictly preserved so that consistent and highly accurate discrete sensitivities can be obtained;and comparable efficiency to hand-coded implementation can be achieved.Upon the current discrete adjoint method,a gradient-based optimization framework has been developed and applied to a drag reduction problem.

Continuous and Discrete Adjoint Approach Based on Lattice Boltzmann Method in Aerodynamic Optimization Part I:Mathematical Derivation of Adjoint Lattice Boltzmann Equations

The significance of flow optimization utilizing the lattice Boltzmann(LB)method becomes obvious regarding its advantages as a novel flow field solution method compared to the other conventional computational fluid dynamics techniques.These unique characteristics of the LB method form the main idea of its application to optimization problems.In this research,for the first time,both continuous and discrete adjoint equations were extracted based on the LB method using a general procedure with low implementation cost.The proposed approach could be performed similarly for any optimization problem with the corresponding cost function and design variables vector.Moreover,this approach was not limited to flow fields and could be employed for steady as well as unsteady flows.Initially,the continuous and discrete adjoint LB equations and the cost function gradient vector were derived mathematically in detail using the continuous and discrete LB equations in space and time,respectively.Meanwhile,new adjoint concepts in lattice space were introduced.Finally,the analytical evaluation of the adjoint distribution functions and the cost function gradients was carried out.

On the Use of Adjoint-Based Sensitivity Estimates to Control Local Mesh Refinement

The goal of efficient and robust error control, through local mesh adaptationin the computational solution of partial differential equations, is predicated on theability to identify in an a posteriori way those localized regions whose refinement willlead to the most significant reductions in the error. The development of a posteriori errorestimation schemes and of a refinement infrastructure both facilitate this goal, howeverthey are incomplete in the sense that they do not provide an answer as to where themaximal impact of refinement may be gained or what type of refinement — elementalpartitioning (h-refinement) or polynomial enrichment (p-refinement) — will best leadto that gain. In essence, one also requires knowledge of the sensitivity of the error toboth the location and the type of refinement. In this communication we propose theuse of adjoint-based sensitivity analysis to discriminate both where and how to refine.We present both an adjoint-based and an algebraic perspective on defining and usingsensitivities, and then demonstrate through several one-dimensional model problemexperiments the feasibility and benefits of our approach.

Adjoint based state estimation of compressible flow in porous media

In this paper,we study the state estimation of compressible single phase flow in compressible porous media.The initial pressure distribution is estimated according to discrete adjoint approach based on the collected well pressure data.The first-order Tykhonov regularization method is used to obtain reasonable estimation.By analyzing the optimality condition of estimation problem,the discrete adjoint state equation and discrete adjoint gradient are derived based on the numerical scheme of the continuous equations.A quasi-Newton numerical optimization method related to adjoint gradient is proposed to solve the estimation problem.The estimation results with different regularization coefficients are compared and analyzed by numerical experiments.The deviation between the estimated pressure obtained without regularization and the real pressure is large.Estimation result with smaller deviation and higher smoothness can be obtained through appropriate regularization coefficient.When the observation error is large,the observed values generated by the estimated pressure fit well with the real pressure.