Angelo Carnarius

Adjoint Approaches For Optimal Flow Control

In many engineering applications, aerodynamic behaviour is significantly influenced by flow separation. A promising concept for improving the aerodynamic design is to manipulate the separated flow using active flow control. This is often realised by blowing and suction, whereby gradient-based optimisation methods can help to find an optimal set of excitation parameters. In the present paper, three methods for calculating the gradient are compared: Finite Differences, a continuous adjoint approach and a discrete adjoint method based on Automatic Differentiation (AD). The methods have been applied to the flow around a rotating cylinder at Reynolds numbers of Re = 100 and Re = 5000 to calculate the derivative of the drag coefficient with respect to the revolution rate of the cylinder. The results of these computations are used for a detailed comparison of the methods in terms of consistency, numerical efficiency and accuracy with special emphasis on the treatment of turbulence to demonstrate the superiority of the discrete adjoint approach.

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.

Numerical Study of the Optimization of Separation Control

The concept of active flow control is applied to the steady flow around a NACA4412 and to the unsteady flow around a generic high-lift configuration in order to delay separation. To the former steady suction upstream of the detachment position is applied. In a series of computations the suction angle β is varied and the main flow features are analyzed. A gradient descent method and an adjoint-based method are successfully used to optimize β. For the unsteady case periodic blowing and suction is employed to control the separation. Various calculations are conducted to obtain the dependency of the lift on the amplitude and frequency of the perturbation and the amplitude is optimized with the gradient descent method.

Numerical Investigation of Active Flow Control Applied to an Airfoil with a Camber Flap

This paper gives an overview of numerical flow control investigations for a high-lift airfoil. The flow around a real glider airfoil with a deflected camber flap at stall conditions was simulated with the Reynolds-averaged Navier-Stokes equations in combination with the LLR-k-ω turbulence model. For this configuration flow separation can be delayed by periodic excitation through a slot close to the leading edge of the camber flap. By simulating different excitation positions, modes, frequencies, intensities and blow-out directions, a set of control parameters suitable for delaying separation and enhancing the lift could be identified.

Simulation Study of the Robust Closed-Loop Control of a 2D High-Lift Configuration

The investigation focuses on the closed-loop separation control of a two dimensional high-lift configuration in a numerical simulation study. The lift is to be controlled by adjusting the non-dimensional intensity of the harmonic excitation near the leading edge of the single slotted flap. Since control laws based on a high-dimensional discretisation or low-dimensional description of the Navier-Stokes equations are not applicable in real-time, this investigation presents a fast and efficient controller synthesis methodology employing robust methods. This offers real-time capability for future experimental implementations. In spite of the nonlinear and infinite-dimensional Navier-Stokes equations, it is surprising to observe that the dynamic behaviour appears very simple. This input-output behaviour in the vicinity of set points can be empirically approximated by stable linear black-box models of second order. Based on these, a simple robust controller is synthesised that autonomously adjusts the excitation such that a desired lift is obtained.

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.

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.

Modeling Supersonic and Hypersonic Flow Transition over Three-Dimensional Bodies

In this study we propose a local-variable-based laminar-turbulence transition model that considers the effects of different instability modes existing in highspeed aerodynamic flows. This model is validated with a number of available experiments on transition including supersonic and hypersonic flows past straight/flared cones at small incidences and elliptic cones at zero incidences. Computed results are in good agreement with experimental data.