An adjoint method for the calculation of remote sensitivities in supersonic flow

Jameson, Antony; Alonso, J.R.; Nadarajah, Siva

doi:10.2514/6.2002-261

Cited by 14 publications

(1 citation statement)

References 17 publications

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“…In addition to difficulties involved in the prediction of complex flow physics, multi-element airfoils provide an additional challenge to the adjoint method: The effect of the changes in the shape of one element must be felt by the other elements in the system. Whereas preliminary studies of the adjoint method in such a situation have already been carried out, 19,33,34 this research is designed to validate the adjoint method for complex applications of this type. Emphasis is placed on the validation and not on the creation of realistic designs, which is beyond the scope of this work.…”

Section: Introductionmentioning

confidence: 99%

Multi-Element High-Lift Configuration Design Optimization Using Viscous Continuous Adjoint Method

Kim

Alonso

Jameson

2004

Journal of Aircraft

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An adjoint-based Navier-Stokes design and optimization method for two-dimensional multi-element high-lift configurations is derived and presented. The compressible Reynolds-averaged Navier-Stokes equations are used as a flow model together with the Spalart-Allmaras turbulence model to account for high Reynolds number effects. When a viscous continuous adjoint formulation is used, the necessary aerodynamic gradient information is obtained with large computational savings over traditional finite difference methods. The high-lift configuration parallel design method uses a point-to-point matched multiblock grid system and the message passing interface standard for communication in both the flow and adjoint calculations. Airfoil shape, element positioning, and angle of attack are used as design variables. The prediction of high-lift flows around a baseline three-element airfoil configuration, denoted as 30P30N, is validated by comparison with available experimental data. Finally, several design results that verify the potential of the method for high-lift system design and optimization are presented. The design examples include a multi-element inverse design problem and the following optimization problems: lift coefficient maximization, lift-to-drag ratio maximization, and the maximum lift coefficient maximization problem for both the RAE2822 single-element airfoil and the 30P30N multi-element airfoil. NomenclatureC d , C l = airfoil coefficients of drag and lift C lmax = maximum lift coefficientboundary shape G G = gradient vector H = total enthalpy I = cost function L = lift M ∞ = freestream Mach number p = static pressure p d = desired target static pressure R = governing equations or residual Re = Reynolds number S = surface area t/c = thickness-to-chord ratio w = conservative flow variables in Cartesian coordinates x,y = Cartesian coordinates y + = dimensionless wall distance α = angle of attack α cl max = stall angle of attack δ = first variation λ = step size in steepest descent method ψ = Lagrange multiplier, costate or adjoint variables

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Section: Introductionmentioning

confidence: 99%

Multi-Element High-Lift Configuration Design Optimization Using Viscous Continuous Adjoint Method

Kim

Alonso

Jameson

2004

Journal of Aircraft

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Direct, adjoint and mixed approaches for the computation of Hessian in airfoil design problems

Papadimitriou

Giannakoglou

2007

Numerical Methods in Fluids

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SUMMARYIn this paper, four approaches to compute the Hessian matrix of an objective function used often in aerodynamic inverse design problems are presented. The computationally less expensive among them is selected and applied to the reconstruction of cascade airfoils that reproduce a prescribed pressure distribution over their walls, under inviscid and viscous flow considerations. The selected approach is based on the direct sensitivity analysis method for the computation of first derivatives, followed by the discrete adjoint method for the computation of the Hessian matrix. The applications presented in this paper show that the Newton method, based on exact Hessian matrices, outperforms other gradient-based algorithms such as steepest descent or BFGS algorithm.

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Numerical control of two‐dimensional shock waves in dual solution domain by instant temperature disturbances

Alekseev

Navon

2012

Numerical Methods in Fluids

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Abstract. The search for the temperature disturbance causing transition between regular and Mach reflections in a dual solution domain is addressed in an optimization statement. The gradient of the discrepancy between the current and target flow fields was calculated using the adjoint equations. The control was determined by a gradient based optimization. The flowfield simulation is verified via a posteriori error estimates using the solution of an additional adjoint problem.Key words: flow control, adjoint equations, Euler equations, initial temperature disturbances, a posteriori error estimation IntroductionBoth the numerical simulation of high speed flows with an interaction of shock waves and the control of such flows are of significant current theoretical and practical interest. There are many techniques for the aerodynamic flow control at high speeds based on different ways of energy deposition [1][2][3]. The flow parameter domains where the solution is not unique are of the special interest from the viewpoint of control efficiency. The coexistence of two stable flow modes under the same conditions provides attractive prospects for controls since the support of selected mode past transition is not necessary. We consider, herein, one of the well known bistable flow patterns. At the intersection of two symmetric shock waves, there exists a range of Mach numbers and shock slopes where both the regular and the Mach reflections exist, see for example, [4,5]. Several works [6][7][8][9][10] consider triggering in the dual solution domain using various disturbances of the flow parameters. The transition from a regular reflection to a Mach mode was obtained in [6] and investigated from the perspective of minimal control energy. Shock waves caused by the energy deposition at the edge surface were studied. The transition from the Mach to regular reflection was achieved in [7] by the numerical simulation of the injection of cold gas jet that occupies the total Mach stem zone. The paper [8] considers both experimentally and computationally the influence of impulse laser heat deposition on the flowfield near shock crossing. The influence of energy impulse was imitated in computations by an initial temperature variation. The computations provided the transition from Mach to regular modes, while the experiments demonstrated some reduction of the Mach stem height with its consequent recovery to the original magnitude. Similar results are reported by Yan et al [9]. The paper [10] states the impossibility of transition from the Mach to regular mode under any energy deposition control.The search for controls on a base of qualitative and intuitive assumptions is the common feature of approaches described in refs. [6][7][8][9][10]. It seems to be expedient to enrich these methods by some quantitative technique. The present paper addresses the search for triggering disturbances using an Inverse Problem in the framework of an optimization statement. We address the control of transition from the Mach to regular mode and vice versa...

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An adjoint method for the calculation of remote sensitivities in supersonic flow

Cited by 14 publications

References 17 publications

Multi-Element High-Lift Configuration Design Optimization Using Viscous Continuous Adjoint Method

Multi-Element High-Lift Configuration Design Optimization Using Viscous Continuous Adjoint Method

Direct, adjoint and mixed approaches for the computation of Hessian in airfoil design problems

Numerical control of two‐dimensional shock waves in dual solution domain by instant temperature disturbances

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