Adjoint shape optimization of a duct for a wall jet film cooling setup

Abstract

The paper presents the results of optimization of the geometric parameters of the simplified wall jet cooling system using a modified Adjoint Shape optimization method for algebraic systems of equations (Discrete Adjoint Optimization). The modification consists in using a linearized discrete system of equations with the replacement of derivatives by their finite-volume approximations. The jet flowed through a duct and out from a nozzle. The duct was inclined at an angle of 35 degrees to the cooled wall. The mean velocity ratio between the jet and the main flow was set to 2. The total heat flux on the cooled wall was taken as a cost function. The problem was considered in a two-dimensional stationary turbulent formulation (RANS). As a result of optimization, the shape of the duct changed significantly, affecting the flow inside it. The optimization led to the disappearance of the recirculation zone and reattaching of the jet to the cooled wall. As a result of the optimization performed, the heat flux at the wall increased by 20%.