Matteo Pini

Preliminary Design of a Centrifugal Turbine for Organic Rankine Cycle Applications

Organic rankine cycles (ORC) are renowned to be attractive energy conversion systems for the thermal energy sources in the small-to-medium power range. A critical component in the ORC technology is the turbo-expander; the difficulties involved in the accurate thermodynamic modeling of organic fluids and, especially, the complex gasdynamic phenomena that are commonly found in ORC turbines may result in relatively low efficiency and in performance reduction at partial loads. In this perspective, a relevant path of development can be outlined in the evaluation of nonconventional turbine architectures, such as the radial-outward or centrifugal turbine. In the present work, a critical evaluation of the feasibility of multistage transonic centrifugal turbines for ORC systems is presented. To support this study, a two-step design procedure, specifically oriented to ORC turbines, was developed. The methodology includes a 1D mean-line code coupled to an external optimizer to perform a preliminary design of the machine. The selected configurations are then verified with a CFD (computational fluid dynamics)-based throughflow solver, able to deal with any flow regime and to treat fluids described by arbitrary equations of state. The overall procedure is applied to the design of two different turbines of the same target power of about 1 MW, the former representing a transonic six-stage turbine and the latter a supersonic three-stage turbine. The two machines are characterized by very different shape and comparable performances. The results are extensively discussed in terms of both overall data and detailed flow fields.

Adjoint Method for Shape Optimization in Real-Gas Flow Applications

An adjoint-based shape optimization approach for supersonic turbine cascades is proposed for application to organic Rankine cycle (ORC) turbines. The algorithm is based on an inviscid discrete adjoint method and encompasses a fast look-up table (LuT) approach to accurately deal with real-gas flows. The turbine geometry is defined by adopting state-of-the-art parameterization techniques (NURBS), enabling to handle both global and local control of the shape of interest. A preconditioned steepest descent method has been chosen as gradient-based optimization algorithm to efficiently search for the nearest minimum. The potential of the optimization approach is first verified by application on the redesign of an existing converging–diverging turbine nozzle operating in thermodynamic regions characterized by relevant real-gas effects. A significant efficiency improvement and a more uniform flow at the blade outlet section are achieved, with expected beneficial effects on the aerodynamics of the downstream rotor. The optimized configuration is also assessed by means of high-fidelity turbulent simulations, which point out the capability of the present inviscid approach in optimizing supersonic turbine cascades with very limited computational burdens. Finally, the newly developed real-gas adjoint method is compared against adjoints based on ideal equations of state on the same design problem. Results show that the performance gain obtained by a fully real-gas optimization strategy is by far higher than that achieved with simplified approaches in case of ORC turbines. This proves the relevance of including accurate thermodynamic models in all steps of ORC turbine design.

Extension of the SU2 open source CFD code to the simulation of turbulent flows of fuids modelled with complex thermophysical laws

This paper presents the extension of the open source SU2 software suite to perform turbulent Non-Ideal Compressible Fluid-Dynamics (NICFD) simulations. A new built-in thermodynamic library has been developed and tightly coupled with the existing structure of the code, properly re-organized for accommodating arbitrary thermophysical models. The library implements simple models and interfaces to an external software for a more accurate estimation of thermophysical properties of NICFD pure fluids and mixtures. Moreover, the Reynolds-averaged Navier-Stokes (RANS) equations are spatially discretized by resorting to suitably defined convective and viscous numerical schemes for general fluids. The capabilities of the code are finally verified on twoand three-dimensional inviscid and turbulent flow problems against solutions obtained with different NICFD solvers, and known analytical ones. The results prove that SU2 is comparatively accurate and computational efficient with respect to existing codes. Definitively, SU2 can be considered as a trustworthy tool for NICFD-based simulations and the future pillar of advanced automated design techniques involving complex fluid laws.

Fluid dynamic design of Organic Rankine Cycle turbines

Successful Organic Rankine Cycle (ORC) power systems demand highly efficient turbo-expanders. In order to meet this goal, a sound strategy for the fluid-dynamic design of the turbine is necessary. The key point of this strategy is the integration of preliminary design methods based on mean-line and throughflow models with the most advanced shape optimization techniques exploiting Computational Fluid-Dynamics (CFD). After an overview on present-day ORC turbine architectures, this chapter discusses the rational connection amongst the various steps of the fluid-dynamic design process, supplementing the dissertation with several applicable examples. Specific design remarks for ORC turbines are highlighted throughout the discussion, and emerging and future trends in the ORC framework are considered.

Fully turbulent discrete adjoint solver for non-ideal compressible flow applications

Non-Ideal Compressible Fluid-Dynamics (NICFD) has recently been established as a sector of fluid mechanics dealing with the flows of dense vapors, supercritical fluids, and two-phase fluids, whose properties significantly depart from those of the ideal gas. The flow through an Organic Rankine Cycle (ORC) turbine is an exemplary application, as stators often operate in the supersonic and transonic regime, and are affected by NICFD effects. Other applications are turbomachinery using supercritical CO2 as working fluid or other fluids typical of the oil and gas industry, and components of air conditioning and refrigeration systems. Due to the comparably lower level of experience in the design of this fluid machinery, and the lack of experimental information on NICFD flows, the design of the main components of these processes (i.e., turbomachinery and nozzles) may benefit from adjoint-based automated fluid-dynamic shape optimization. Hence, this work is related to the development and testing of a fully-turbulent adjoint method capable of treating NICFD flows. The method was implemented within the SU2 open-source software infrastructure. The adjoint solver was obtained by linearizing the discretized flow equations and the fluid thermodynamic models by means of advanced Automatic Differentiation (AD) techniques. The new adjoint solver was tested on exemplary turbomachinery cases. Results demonstrate the method effectiveness in improving simulated fluid-dynamic performance, and underline the importance of accurately modeling non-ideal thermodynamic and viscous effects when optimizing internal flows influenced by NICFD phenomena.

NUMERICAL INVESTIGATION OF METASTABLE CONDENSING FLOWS WITH AN IMPLICIT UPWIND METHOD

This work proposes and assesses two numerical models for solving high-speed condensing flows in metastable conditions. Each model involves a set of governing equations (mass, momentum, and energy) for the mixture or the continuum phase, i.e. the vapor, and two additional transport equations to characterize the dispersed phase. Such relations are formulated through the so-called method of moments that allows to represent the wetness fraction and the number of droplets of the liquid. The transport relations are discretized in space by means of a new coupled up-wind scheme. A segregated implicit time integration strategy is exploited to hasten the convergence of the full system to steady-state. The performance and accuracy of both models are thoroughly investigated on a reference quasi-1D problem and confronted against experimental data and more advanced two-phase flow models. Results show that experimental observations are adequately predicted, especially concerning the droplets dimension. It is additionally inferred that the new upwind flux is beneficial to improve robustness of the underlying numerical methods. Finally, it is demonstrated that the continuum phase model outperforms the mixture one in terms of numerical stability and computational cost, thereby making it very promising for the extension to multi-dimensional problems.

Active subspaces for the preliminary fluid dynamic design of unconventional turbomachinery

The fluid dynamic preliminary design of unconventional turbomachinery is customary done with meanline design procedures coupled with gradient-free optimizers. This method features various drawbacks, since it might become computationally expensive, and it does not provide design insights or guidelines to the designer. This work proposes a strategy to abate this disadvantages, namely, the construction of a reduced-order model by means of active sub-spaces, and the use of the surrogate combined with a gradient-based optimizer. The case study is the design optimization of a Organic Rankine Cycle radial inflow turbine. The results show that active subspaces exist for this application, and that it is possible to construct a surrogate with an approximate error of ±1% for the total-to-static efficiency. Additionally, the optimization using the surrogate leads to accurate results and a computational cost at least four times faster. Furthermore, the results reveal that the models for unconventional turbomachinery feature multiple regions containing constrained optima. Active subspace methods thus prove to be a promising alternative for optimization of unconventional turbomachinery.

A look-up table method based on unstructured grids and its application to non-ideal compressible fluid dynamic simulations

Fast and accurate computation of thermo-physical properties is essential in computationally expensive simulations involving fluid flows that significantly depart from the ideal gas or ideal liquid behavior. A look-up table algorithm based on unstructured grids is proposed and applied to non-ideal compressible fluid dynamics simulations. The algorithm grants the possibility of a fully automated generation of the tabulated thermodynamic region for any boundary and to use mesh refinement. Results show that the proposed algorithm leads to a computational cost reduction up to one order of magnitude, while retaining the same accuracy level compared to simulations based on more complex equation of state. Furthermore, a comparison of the LuT algorithm with a uniformly spaced quadrilateral tabulation method resulted in similar performance and accuracy.