Research Papers: Power Engineering

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

[+] Author and Article Information
Shigeki Senoo

 Hitachi, Limited, Power Systems Company, Energy and Environmental Systems Laboratory, Hitachi, 319-1221, Ibaraki, Japanshigeki.senoo.dc@hitachi.com

Kiyoshi Segawa, Hisashi Hamatake

 Hitachi, Limited, Power Systems Company, Energy and Environmental Systems Laboratory, Hitachi, 319-1221, Ibaraki, Japan

Takeshi Kudo, Tateki Nakamura, Naoaki Shibashita

 Hitachi, Limited, Hitachi Works, Power Systems Company, Hitachi, Ibaraki, Japan

J. Eng. Gas Turbines Power 133(10), 103001 (May 03, 2011) (10 pages) doi:10.1115/1.4003069 History: Received August 04, 2010; Revised August 05, 2010; Published May 03, 2011; Online May 03, 2011

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.

Copyright © 2011 by American Society of Mechanical Engineers
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Figure 1

x−r−θ coordinate system and blades

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Figure 2

Interpolation of a thermodynamic property using a discrete steam table

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Figure 3

Photo of the four-stage LP test turbine

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Figure 4

Longitudinal section of the test turbine with the locations of the unsteady pressure sensors (black circles) and the traversing planes of the multihole total pressure and temperature probes

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Figure 5

Unsteady pressure sensors

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Figure 6

Multihole total pressure and temperature probes

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Figure 7

The definitions of flow angle and reverse flow region

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Figure 8

Total pressure distributions around 360 deg at tip and hub after the last stage (about 5% load)

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Figure 9

Computational grids, every two grids shown in axial direction

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Figure 10

Comparison of experimental and calculated total pressure distributions after each of the four stages

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Figure 11

Comparison of experimental and calculated flow angle distributions and reverse regions after each of the four stages: (a) 20% load, (b) 5% load, and (c) 0% load

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Figure 12

Path lines calculated by average flow field and comparison of reverse flow regions with experimental results (Thick red curves are the highest positions of the reverse flow calculated by the average flow field, filled red circles are calculated by the average flow direction, and vertical red lines are their standard deviations. White circles are the highest positions of the reverse flow measured experimentally by the total pressure probes.): (a) 20% load, (b) 5% load, and (c) 0% load.

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Figure 13

Comparison of experimental and calculated standard deviations of pressure on the inner and outer side walls




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