Proper Orthogonal Decomposition of Pressure Fields in a Draft Tube Cone of the Francis (Tokke) Turbine Model

D Stefan,P Rudolf

doi:10.1088/1742-6596/579/1/012002

Abstract

The simulations of high head Francis turbine model (Tokke) are performed for three operating conditions - Part Load, Best Efficiency Point (BEP) and Full Load using software Ansys Fluent R15 and alternatively OpenFOAM 2.2.2. For both solvers the simulations employ Realizable k-e turbulence model. The unsteady pressure pulsations of pressure signal from two monitoring points situated in the draft tube cone and one behind the guide vanes are evaluated for all three operating conditions in order to compare frequencies and amplitudes with the experimental results. The computed velocity fields are compared with the experimental ones using LDA measurements in two locations situated in the draft tube cone. The proper orthogonal decomposition (POD) is applied on a longitudinal slice through the draft tube cone. The unsteady static pressure fields are decomposed and a spatio-temporal behavior of modes is correlated with amplitude-frequency results obtained from the pressure signal in monitoring points. The main application of POD is to describe which modes are related to an interaction between rotor (turbine runner) and stator (spiral casing and guide vanes) and cause dynamic flow behavior in the draft tube. The numerically computed efficiency is correlated with the experimental one in order to verify the simulation accuracy.

Highlights

The numerical simulations of hydraulic turbines are recently common for industrial companies
In the industry there are not usually enough computational resources and time to deal with complex calculations to verify turbulence models, discretisation schemes and perform time-consuming post-processing on large computational grids
The Francis-99 test case is a good option to deal with the post-processing methods e.g. proper orthogonal decomposition (POD) and compare it with the experimental results of the model Francis turbine [1]

Summary

Introduction

The numerical simulations of hydraulic turbines are recently common for industrial companies. At BEP and High Load the largest discrepancies can be observed close to the draft tube axis, where especially in LDA-2 location the magnitude of numerically computed axial velocity is significantly underestimated.

Results

Conclusion