Anil Nemili

Optimal Control of Unsteady Flows Using Discrete Adjoints

We present the development of a discrete adjoint approach for the optimal control of viscous ows, governed by unsteady incompressible Reynolds Averaged Navier Stokes equations. The adjoint solver is developed by applying the automatic di erentiation (AD) techniques in reverse mode of di erentiation. The unsteady adjoints usually require the storage of complete ow history during the forward-in-time integration of the primal equations, which is then used while solving the adjoint equations in backward-in-time integration. For large scale applications, the memory requirements for storing the ow solutions can become prohibitively expensive. To reduce the excessive memory demands, the binomial checkpointing strategy has been employed. Numerical results are presented for the test cases of optimal active ow control around a rotating cylinder and a NACA4412 airfoil to validate the automatic di erentiation generated derivative codes. The sensitivities based on forward and adjoint mode AD codes are compared with the values obtained from nite di erences.

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.

Discrete Adjoint based Sensitivity Analysis for Optimal Flow Control of a 3D High-Lift Configuration

Active flow control techniques are used to delay or prevent the turbulent flow separation on the flap of a high-lift configuration. Effective separation control and thus lift enhancement can be achieved by finding the optimal set of actuation parameters, which may be in very large number. In this paper, a consistent unsteady discrete adjoint RANS solver in three-dimensions is developed towards the objective of finding the optimal set of actuation parameters. The adjoint code is applied to the sensitivity analysis of a practically relevant three-dimensional high-lift configuration. The sensitivities with respect to actuation parameters based on the consistent adjoint approach are compared with finite differences. The effect of frozen turbulence assumption on the accuracy of actuation sensitivities is studied.

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.

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.

Optimal Separation Control on the Flap of a 2D High-Lift Configuration

Flow separation on the flap of a high-lift device degrades the overall aerodynamic performance and hence results in a drop in the lift coefficient. However, by employing the active flow control techniques, separation can be delayed and thus the lift can be enhanced. In these methods, the flow is controlled by varying the parameters of actuation. In the present work, the optimal set of actuation parameters is found using the gradient-based optimisation algorithms combined with an accurate and robust discrete adjoint method for unsteady RANS. Numerical results are presented for the optimal separation control on the flap of a high-lift configuration over a large time interval.

Application of Automatic Differentiation to an Incompressible URANS Solver

This paper deals with the task of generating a discrete adjoint solver from a given primal Unsteady Reynolds Averaged Navier-Stokes (URANS) solver for incompressible flows. This adjoint solver is to be employed in active flow control problems to enhance the performance of aerodynamic configurations. We discuss on how the development of such a code can be eased through the use of the reverse mode of Automatic/Algorithmic Differentiation (AD). If AD is applied in a black-box fashion then the resulting adjoint URANS solver will have prohibitively expensive memory requirements. We present several strategies to circumvent the excessive memory demands. We also address the parallelization of the adjoint code and the adjoint counterparts of the MPI directives that are used in the primal solver. The adjoint code is validated by applying it to the standard test case of a rotating cylinder by active flow control. The sensitivities based on the adjoint code are compared with the values obtained from finite differences and forward mode AD code.