Approximation of hub leakage flow in a high speed axial flow compressor rotor with adjoint method

This paper focuses the effect of hub leakage flow on the performance of a high speed transonic rotor. The rotor considered here is NASA rotor 37. General computational fluid dynamics of this rotor have been unable to predict a total pressure deficit from the hub wall to the mid span height observed in the experiments. In this study, computations have been performed on the rotor with the boundary condition assumed the leakage flow from the tip gap at the upstream of the rotor. In the computations, the velocity distribution is determined on the computational domain corresponding to the location of the tip gap. The swirl velocity at the boundary is calculated with the rotational speed and the radial length of the hub wall. The radial velocity is estimated based on the leakage mass flow. However, the mass flow is an uncertain quantity, and it has effect to the prediction of the total pressure deficit. Therefore, an adjoint method has been applied for the approximation to the uncertain quantity. The simulation results using the leakage flow boundary and the result without the boundary condition have been compared with the experiment. The comparisons have shown that the boundary condition and the approximation with the adjoint method have enabled to predict the total pressure deficit.