Unsteady simulation of quasi-periodic flows in Organic Rankine Cycle cascades using a Harmonic Balance method

Abstract

Currently, turbomachinery design optimization methodologies are mainly restricted to steady state approaches, due to the high computational cost associated with time-accurate shape optimization algorithms. However, the possibility to include unsteady effects in turbomachinery optimization can significantly increase the level of accuracy of the design predictions, leading to a more realistic representation of the actual performance and ultimately to a substantial increase in operating efficiency. Unsteady effects are particularly relevant in Organic Rankine Cycle turbines. A trade-off between high-fidelity time-accurate unsteady simulations of the flow solution and computational cost is therefore needed at design level. In this paper, a first application of the harmonic balance method to non-ideal compressible flows is presented. The methodology allows to solve the unsteady flow equations for a set of specified frequencies only, with significant computational time savings. An algorithm is proposed for non uniform time sampling in order to resolve frequencies that do not need to be integral multiple of one fundamental harmonic. This enables the solution of quasi-periodically forced non-linear flow problems, in combination with complex fluid models based on accurate equations of state. The method is applied to the unsteady analysis of a supersonic Organic Rankine Cycle stator with quasi-periodic inlet operating conditions, showing about one order magnitude lower computational cost compared to time-accurate simulations.