Computations for Unsteady Compressible Flows in a Multistage Steam Turbine With Steam Properties at Low Load Operations

Abstract

A computational technique for multistage steam turbines, which can allow for thermodynamic properties of steam, is presented. Conventional three-dimensional multistage calculations for unsteady flows have two main problems. One is the long computation time and the other is how to include the thermodynamic properties of steam. Ideal gas is assumed in most computational techniques for compressible flows. To shorten the computational time, a quasi-three-dimensional flow calculation technique is developed. In the analysis, conservation laws for compressible fluid in axisymmetric cylindrical coordinates are solved using a finite volume method based on an approximate Riemann solver. Blade forces are calculated from the camber and lean angles of blades with momentum equations. The axisymmetric assumption and the blade force model enable the effective calculation for multistage flows, even when the flow is strongly unsteady under off-design conditions. To take into account steam properties including effects of the gas-liquid phase change and two-phase flow, a flux-splitting procedure of compressible flow is generalized for real fluid. Density and internal energy per unit volume are selected as independent thermodynamic variables. Pressure and temperature in a superheated region or wetness mass fraction in a wet region are calculated by using a steam table. To improve computational efficiency, a discretized steam table matrix is made in which the density and specific internal energy are independent variables. For accuracy and continuity of steam properties, the second order Taylor expansion and linear interpolation are introduced. The computed results of the last four-stage low-pressure steam turbine at low load conditions show that there is a reverse flow near the hub region of the last stage bucket and the flow concentrates in the tip region due to the centrifugal force. At a very low load condition, the reverse flow region extends to the former stages and the unsteadiness of flow gets larger due to many vortices. Four-stage low-pressure steam turbine tests are also carried out at low load. The radial distributions of flow direction downstream from each stage are measured by traversing pneumatic probes. Additionally, pressure transducers are installed in the side wall to measure unsteady pressure. The regions of reverse flow are compared between computations and experiments at different load conditions, and their agreement is good. Further, the computation can follow the trends of standard deviation of unsteady pressure on the wall to volumetric flow rate of experiments.