Turbine Blade Aerodynamic Optimization on Unstructured Grids Using a Continuous Adjoint Method

Abstract

A gradient based optimization using the continuous adjoint method for inverse design of a turbine blade cascade is presented. The advantage of the adjoint method is that the objective function gradients can be evaluated by solving the adjoint equations with coefficients depending on the flow variables. This method is particularly suitable for aerodynamic design optimization for which the number of design variables is large. Bezier polynomials are used to parameterize suction side of the turbine blade. The numerical convective fluxes of both flow and adjoint equations are computed by using a Roe-type approximate Riemann solver. An approximate linearization is applied to simplify the calculation of the numerical flux of adjoint variables on the faces of computational cell. The problem examined is that of the inverse design of NASA C3X blade that reproduces a given pressure distributions over its surfaces. Adjoint results show a good agreement with those obtained by finite-difference method.

A review on aerodynamic optimization of turbomachinery using adjoint method

“…219 Using the continuous adjoint method, a wide range of inverse optimization has been performed. 127,128,183,[207][208][209] The adjoint method linearity may cause it to diverge due to large flow separation in the initial flow field. 92 This concern was investigated by Wang and Li.…”

“…The adjoint approach has been combined with either the inverse method 183,207–213 or the gradient-free optimization method 214–218 to provide new methods with enhanced capabilities and addressed limitations.…”

A coupled adjoint formulation for non-cooled and internally cooled turbine blade optimization

“…The adjoint convective fluxes are computed using a first order Roe-type approximate Riemann solver [18]. Details of the convective flux discretization can be found in [19]. The viscous terms of the adjoint equations are discretized using a second order central difference scheme.…”

Entropy minimization in turbine cascade using continuous adjoint formulation

“…The adjoint convective fluxes are computed using a first-order Roe-type approximate Riemann solver (Anderson and Venkatakrishnan 1999). Details of convective flux discretization can be found in Zeinalpour, Mazaheri and Irannejad (2012). The viscous terms of the adjoint equations are discretized using a second-order central difference scheme.…”

“…The unstructured triangular mesh used here is shown in Figure 2. More details are given in Zeinalpour, Mazaheri and Irannejad (2012).…”