The lack of established optimal design guidelines for turbomachinery operating in the nonideal flow regime (e.g., organic Rankine cycle turbines, CO₂ compressors, compressors for refrigeration systems) demands for effective and efficient automated design methods. Past research work focused on gradient-free methods applied to computational fluid-dynamic simulations. The application of the adjoint method is a cost-effective alternative as it enables gradient-based optimization irrespective of the number of design variables. This paper presents the application of a fully turbulent unsteady adjoint method for the automated design of multirow turbomachinery partly operating in the nonideal flow regime. The method therefore allows for the solution of constrained unsteady fluid-dynamic optimization problems, in which the thermodynamic properties of the working fluid need to be modeled by means of complex equations of state. The optimal designs computed with unsteady simulations obtained with the harmonic balance method are then compared with optimal design resulting from mixing-plane simulations. The method is applied to the optimization of 1) a two-dimensional turbine cascade subject to time-varying inlet conditions, and 2) a two-dimensional turbine stage of an organic Rankine cycle power system. The results demonstrate the importance of computing fluid properties using accurate thermodynamic models and of using unsteady simulations for shape optimization of these machines.

High temperature Organic Rankine Cycles power systems of low power capacity, i.e. 3-50 kW_e, are receiving recognition for distributed and mobile energy generation applications. For this type of power plants, it is customary to adopt a radial-turbine as prime mover, essentially for their ability to cope with very large volumetric flow ratio with limited fluid-dynamic penalty. To date, the design of such turbines is based on design guidelines and loss models developed mainly for turbo-chargers, subsequently adapted by means of non-validated computational fluid-dynamic calculations. In the attempt to provide data sets for CFD validation and calibration of loss models, a mini-ORC radial inflow turbine delivering 10kW of mechanical power will be realized and tested in the Propulsion and Power Laboratory of TU-Delft. The fluid dynamic design and characterization of the machine is detailed in this paper. According to available models, the results indicate that the optimal layout of mini-ORC turbines can substantially differ from that of radial-inflow turbines utilized in more traditional applications, strengthening the need of experimental campaigns to support the conception of new design practices.

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.