A Novel Hybrid Approach for Numerical Modeling of the Nucleating Flow in Laval Nozzle and Transonic Steam Turbine Blades

Abstract

In the present research, considering the importance of desirable steam turbine design, improvement of numerical modeling of steam two-phase flows in convergent and divergent channels and the blades of transonic steam turbines has been targeted. The first novelty of this research is the innovative use of combined Convective Upstream Pressure Splitting (CUSP) and scalar methods to update the flow properties at each calculation point. In other words, each property (density, temperature, pressure and velocity) at each calculation point can be computed from either the CUSP or scalar method, depending on the least deviation criterion. For this reason this innovative method is named “hybrid method”. The next novelty of this research is the use of an inverse method alongside the proposed hybrid method to find the amount of the important parameter z in the CUSP method, which is herein referred to as “CUSP’s convergence parameter”. Using a relatively simple computational grid, firstly, five cases with similar conditions to those of the main cases under study in this research with available experimental data were used to obtain the value of z by the Levenberg-Marquardt inverse method. With this innovation, first, an optimum value of z = 2.667 was obtained using the inverse method and then directly used for the main cases considered in the research. Given that the aim is to investigate the two-dimensional, steady state, inviscid and adiabatic modeling of steam nucleating flows in three different nozzle and turbine blade geometries, flow simulation was performed using a relatively simple mesh and the innovative proposed hybrid method (scalar + CUSP, with the desired value of z = 2.667 ). A comparison between the results of the hybrid modeling of the three main cases with experimental data showed a very good agreement, even within shock zones, including the condensation shock region, revealing the efficiency of this numerical modeling method innovation. The main factor in improving the aforementioned results was found to be a reduction of the numerical errors by up to 70% in comparison to conventional methods (scalar, Jameson original), so that the mass flow rate is well conserved, thereby proving better satisfaction of the conservation laws. It should be noted that by using this innovative hybrid method, one can take advantages of both central difference scheme and upstream scheme (scalar and CUSP, respectively) at the same time in simulating complex flows in any other finite volume scheme.