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INVESTIGATION OF THE CONTINUOUS AND DISCRETE ADJOINT IN THE CONTROL OF PLANE JETS

Daniel Marinc
Chair of Fluid Mechanics University of Siegen Paul-Bonatz-Strasse 9-11

Holger Foysi
Aerodynamic Institute RWTH Aachen; Fachgebiet Stromungsmechanik TU Munchen, Boltzmannstr. 15, D-85748 Garching, Germany; UC San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USA

Abstract

A comparison of the optimal control of two- and three-dimensional plane jets using the continuous and discrete adjoint of the instationary Navier-Stokes equations was performed. The control aim was to reduce the sound emission in the near far-field by using a heat source actuation within the transitioning jet shear layers. The fully compressible Navier-Stokes equations were solved using dispersion-relation preserving spatial discretization schemes and a low-dissipation- dispersion Runge-Kutta scheme. The Reynolds number based on the slot diameter was set to 2000 and the Mach number to 0.9. Direct numerical as well as large-eddy simulations in two and three dimensions where performed to estimate the influence of modelling and resolution on the results. The results show a slight advantage of using the discrete adjoint, especially when handling boundary conditions, since the calculation of the gradient of the cost functional is more accurate. It is interesting, too, that the control efficiency reduces with increasing resolution and therefore dimension of the control. Reducing it by applying a selected interpolation in the control area shows an increase in efficiency and sound reduction.