Emre Özkaya

Single-step One-shot Aerodynamic Shape Optimization

In this paper we consider the shape optimization of a transonic airfoil whose aerodynamic properties are calculated by a structured Euler solver. The optimization strategy is based on a one-shot technique in which pseudo time-steps of the primal and the adjoint solver are iterated simultaneously with design corrections done on the airfoil geometry. The adjoint solver which calculates the necessary sensitivities is based on discrete adjoints and derived by using reverse mode of automatic differentiation. A new preconditioner which is derived by considering an augmented Lagrangian formulation of the optimization problem is employed in order to achieve bounded retardation of the overall optimization process. A design example of drag minimization for an RAE2822 airfoil under transonic flight conditions is included.

Automated Extension of Fixed Point PDE Solvers for Optimal Design with Bounded Retardation

We study PDE-constrained optimization problems where the state equation is solved by a pseudo-time stepping or fixed point iteration. We present a technique that improves primal, dual feasibility and optimality simultaneously in each iteration step, thus coupling state and adjoint iteration and control/design update. Our goal is to obtain bounded retardation of this coupled iteration compared to the original one for the state, since the latter in many cases has only a Q-factor close to one. For this purpose and based on a doubly augmented Lagrangian, which can be shown to be an exact penalty function, we discuss in detail the choice of an appropriate control or design space preconditioner, discuss implementation issues and present a convergence analysis. We show numerical examples, among them applications from shape design in fluid mechanics and parameter optimization in a climate model.

Optimal Control of Unsteady Flows Using a Discrete and a Continuous Adjoint Approach

While active flow control is an established method for controlling flow separation on vehicles and airfoils, the design of the actuation is often done by trial and error. In this paper, the development of a discrete and a continuous adjoint flow solver for the optimal control of unsteady turbulent flows governed by the incompressible Reynolds-averaged Navier-Stokes equations is presented. Both approaches are applied to testcases featuring active flow control of the blowing and suction type and are compared in terms of accuracy of the computed gradient.

Optimal Design with Bounded Retardation for Problems with Non-separable Adjoints

In the natural and enginiering sciences numerous sophisticated simulation models involving PDEs have been developed. In our research we focus on the transition from such simulation codes to optimization, where the design parameters are chosen in such a way that the underlying model is optimal with respect to some performance measure. In contrast to general non-linear programming we assume that the models are too large for the direct evaluation and factorization of the constraint Jacobian but that only a slowly convergent fixed-point iteration is available to compute a solution of the model for fixed parameters. Therefore, we pursue the so-called One-shot approach, where the forward simulation is complemented with an adjoint iteration, which can be obtained by handcoding, the use of Automatic Differentiation techniques, or a combination thereof. The resulting adjoint solver is then coupled with the primal fixed-point iteration and an optimization step for the design parameters to obtain an optimal solution of the problem. To guarantee the convergence of the method an appropriate sequencing of these three steps, which can be applied either in a parallel (Jacobi) or in a sequential (Seidel) way, and a suitable choice of the preconditioner for the design step are necessary. We present theoretical and experimental results for two choices, one based on the reduced Hessian and one on the Hessian of an augmented Lagrangian. Furthermore, we consider the extension of the One-shot approach to the infinite dimensional case and problems with unsteady PDE constraints.

Optimal Design of Active Flow Control for a Complex High-Lift Configuration

This paper presents the optimal design of an active flow control mechanism for an industry relevant complex high-lift configuration. To control the flow, a large number of synthetic jet actuators are placed on the wing and flap faces. The actuation parameters at these faces are considered as control variables. The optimal set of actuation parameters that yield maximum mean-lift is evaluated by combining an unsteady discrete adjoint RANS solver with a gradient based optimisation algorithm. The adjoint solver is developed by employing Algorithmic Differentiation (AD) techniques. Numerical results have shown that optimisation has resulted in reasonable improvement in the mean-lift compared to the initial actuated flow. This study demonstrates the robustness, accuracy and applicability of AD based unsteady adjoint solver for large scale industrial applications.

A Discrete Adjoint Approach for Unsteady Optimal Flow Control

In this paper, we present a discrete adjoint method for optimal flow control of unsteady incompressible viscous flows. The discrete adjoint solver is developed in an automatic fashion from the flow solver by applying the Automatic Differentiation technique in reverse mode. The unsteady adjoint method requires the storage of the entire flow solution during the forward-in-time integration, which is then used in solving the adjoint equations in reverse time. For large-scale practical applications, the memory requirements can become prohibitively expensive. To reduce the memory requirements, the binomial checkpointing algorithm is combined with the adjoint solver. Numerical results are presented for laminar and turbulent cases to validate the discrete adjoint solver.

An Efficient One-Shot Algorithm for Aerodynamic Shape Design

In this paper we consider the shape optimization of a transonic airfoil whose aerodynamic properties are calculated by a structured Euler solver. The optimization strategy is based on a one-shot technique in which pseudo time-steps of the primal and the adjoint solver are iterated simultaneously with design corrections done on the airfoil geometry. The adjoint solver which calculates the necessary sensitivities is based on discrete adjoints and derived by using reverse mode of automatic differentiation (AD). A design example of drag minimization for an RAE2822 airfoil under transonic flight conditions and lift constraints is included.

Quantifying Retardation in Simulation Based Optimization

In many applications one wishes to optimize designs on the basis of an established simulation tool. We consider the situation where “simulation” means solving a system of state equations by a fixed point iteration. “Optimization” may then be performed by appending an adjoint solver and an iteration step on the design variables. The main mathematical goal of this chapter is to quantify and estimate the retardation factor, i.e., the complexity of an optimization run compared to that of a single simulation, measured in terms of contraction rates. It is generally believed that the retardation factor should be bounded by a reasonably small number irrespective of discretization widths and other incidental quantities. We show that this is indeed the case for a simple elliptic control problem, when the state equations are solved by Jacobi or a multigrid V-cycle. Moreover, there is strong dependence on a regularization term. This is also shown to be true when the state equation is solved by Newton’s method and the projected Hessian is explicitly available

Discrete Adjoint Based Optimal Active Control of Separation on a Realistic High-Lift Configuration

This paper presents a framework for the optimal active separation control mechanism on a realistic high-lift configuration. To control the separation, synthetic jet actuation is applied on the pressure and suction side of a 3D wing with slats, flaps and flap track fairings. Flow control is realised by varying the parameters of actuation like amplitude, frequency, phase shift and blowing angles. An optimal set of actuation parameters that delay the separation and enhance the aerodynamic performance is found by combining a gradient based optimisation algorithm with a discrete adjoint Unsteady Reynolds-averaged Navier Stokes (URANS) solver. A detailed analysis of the sensitivities with respect to the actuation parameters is presented. Optimisation has yielded a noticeable increase in the lift compared to the initial actuated flow.

A TWO-LEVEL HYBRID APPROACH FOR OPTIMAL ACTIVE FLOW CONTROL ON A THREE-ELEMENT AIRFOIL

In this paper we present a two-level approach that combines an adjoint-based gradient search method with an evolutionary algorithm for optimal active flow control. The suggested method effectively combines the advantages of both approaches and achieves a good compromise between the computational effort and the degree of freedom used in optimization. In the first level, a global optimization is performed with few design parameters using an evolutionary algorithm. In the second level, the global optimal solution from the first level is taken as the initial setting for the adjoint based local optimization using a large number of design parameters. The unsteady discrete adjoint solver required for the second level is developed based on Algorithmic Differentiation techniques for the unsteady incompressible flowsgoverned by Unsteady Reynolds-Averaged Navier Stokes (URANS) equations. In this way, the discrete adjoint solver is robust and has exactly the same functionality with the underlying URANS flow solver. The applicability of the two-level method is demonstrated by finding the optimal parameters of the active flow control mechanism on a three element airfoil configuration at a Reynolds number of Re = 10 and an angle of attack of AoA = 6◦. Numerical results have shown that the hybrid approach completely suppressed the separation and very significantly increased the mean-lift coefficient by 67% compared to the un-actuated baseline flow.