A complete continuous adjoint formulation is presented here for the optimization of the turbulent flow entropy generation rate through a turbine cascade. The adjoint method allows one to have many design variables, but still afford to compute the objective function gradient. The new adjoint system can be applied to different structured and unstructured grids as well as mixed subsonic and supersonic flows. For turbulent flow simulation, the k-ω shear-stress transport turbulence model and Roe's flux function are used. To ensure all possible shape models, a mesh-point method is used for design parameters, and an implicit smoothing function is implemented to avoid the generation of non-smoothed blades. To analyse the capability of the presented algorithm, the shape of a turbine cascade blade is redesigned and a few physical observations are made on how the scheme improves the blade performance.
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.
In this paper, the effect of turbine stage efficiency on fuel consumption of both gas turbines and aerial engines is assessed quantitatively. At the beginning of the gas generator optimization to decrease the fuel consumption, it is necessary to analyze the sensitivity of fuel consumption to its main components efficiencies. This will guide us which component is more important to be optimized. Here a zero-dimensional analysis has been done to determine the effect of turbine stage efficiency on the fuel consumption. Results of this analysis are evaluated in the context of thermodynamic cycle of a gas turbine generator and an aerial engine. As an example, it is shown that if the efficiency of first stage of the turbine is increased from 82% to 84%, the fuel consumption of an aerial engine is computed to be decreased by 1%. The cycle analysis performed implies that the sensitivity of fuel consumption to turbine stage efficiency varies for different values of stage efficiency.
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