Optimization of an ORC Radial Turbine Nozzle

Organic Rankine Cycle (ORC) turbogenerators usually operate in thermodynamic regions characterized by high pressure ratios and strong real-gas effects in the flow expansion, requiring therefore a non-standard turbomachinery design. An effective approach can be based on the intensive use of Computational Fluid Dynamics (CFD) and optimization procedures to investigate a wide range of possible configurations.


ORC Radial Turbine Nozzle

Figure 1 – ORC Radial Turbine Nozzle

Expansions through impulse stages of ORC turbines are commonly characterized by large pressure ratios and a low speed of sound of the working-fluid is generally observed. As a consequence, the flow can easily reach sonic conditions. In this context, non-standard geometries, such as blade shapes with a converging-diverging channel, are therefore required to accelerate the flow to supersonic conditions. In order to have an advanced local control of the blade shape, NURBS curves and surfaces with arbitrary order and number of control points have been implemented into a fully automated parametric geometry generator. The design parameters required to correctly define the geometry are directly driven by Nexus.

In this work a global optimization methodology is coupled with a state-of-the-art CFD solver in order to assist the design of ORC turbines. In particular, the optimization strategy is based on the coupling of a Genetic Algorithm and Surrogate Models, i.e., Feed-Forward Neural Network

Radial blade shape parameterization based on the definition of NURBS curves and surfaces.

Figure 2 – Radial blade shape parameterization

(FFNN) and Kriging (KRG). The initial population has been initialized using a Latin hypercube sampling strategy. The capability of this procedure is demonstrated by improving the design of an existing one-stage impulse radial turbine. The goal of the optimization is to minimize the total pressure losses and to obtain a uniform annular stream at the stator discharge section, in both terms of velocity magnitude and direction of the flow.

Advantages in using Nexus

Main advantages of using Nexus to guide the optimisation:

  • Easy integration of external FEM and CFD solvers among which Nastran, Abaqus, Radioss, Adams, Star-CCM+, Ansys Fluent and CFX;
  • Parallel and concurrent evaluations to exploit your hardware and software resources in the best possible way. A scalable architecture that you can tune application by application;
  • Easy scripting capabilities and nested execution of the program in batch mode;
  • Advanced Design of Experiment (DoE) and statistical tools to explore and analyse results;
  • State-of-the-art libraries for single- and multi-objective optimisations, DoE and Response Surfaces modelling.


Comparison of the flow angle (a), Mach number (b) and total pressure (c) distributions along the stator discharge bound.

Figure 3 – Comparison of the flow angle (a), Mach number (b) and total pressure (c) distributions.

Due to the surrogate model assisted approach, the genetic algorithm required only about 100 geometry evaluations to reach the optimum design with a reduction of about 10 times the number of evaluation required by a standard genetic algorithm. The optimized blade produces a shock-free expansion, obtaining a more uniform flow and therefore reducing significantly the total pressure losses. The optimal geometry shows an increase of about 10% of the stage efficiency. Moreover, the optimization system, which has been developed in Nexus, offers a remarkable potential in a wide range of applications aiming to design high-efficiency turbomachineries. In figure is shown, on left side, the convergence rate comparison between standard Genetic Algorithm (GA) and GA assisted by Kriging (KRG) and Feed-Forward Neural Network (FFNN), on the right side instead, the comparison of the flow angle distributions along the stator discharge bound between the baseline (red) and the optimized geometry (blue)

Convergence Rate

Figure 4 – Convergence rate and flow angle distribution

(*) Presented at the First International Seminary on ORC Power Systems 2011 and published on the Journal of Engineering for Gas Turbines and Power: D.Pasquale, A.Ghidoni, S.Rebay “Shape Optimization of an ORC Radial Turbine Nozzle”