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Research Papers: Flows in Complex Systems

# Pressure Fluctuation Prediction of a Model Kaplan Turbine by Unsteady Turbulent Flow Simulation

[+] Author and Article Information
Shuhong Liu, Yulin Wu

State Key Laboratory of Hydro Science and Hydraulic Engineering, Tsinghua University, Beijing 100084, China

Shengcai Li1

WIMRC, University of Warwick, Coventry CV4 AL, UKS.Li@warwick.ac.uk

The excitation frequency, which is equal to the rotation speed multiplied by the number of runner blades, is defined as the blade passing frequency. Owing to the interaction of the runner blades with the guide vanes, higher frequencies of up to $k$ folds of the blade passing frequency can be generated, with $k$ being typically between 1 and 2 for hydraulic turbines. For this turbine, it is equal to $f=126.8 Hz$, if $k=1$. The pressure fluctuation component, with the highest amplitude at the front-runner and in the downstream of the runner, has $k$ value of 4, which is the guide vane number $(Z0=24)$ divided by the runner blade number $(Z=6)$. The component is produced by the rotor-stator interaction.

The hydraulic impedance $Z(x)$ is a complex-valued function in a fluid system, which is defined as the ratio of the complex head $H(x)$ to the complex discharge $Q(x)$ at a particular point in the system $(Z(x)=H(x)/Q(x))$.

It is defined as $−∂Vvap/∂NPSE$, where $Vvap$ is the cavitation volume in the draft tube, and $NPSE$ is the net positive suction head of the turbine. $Vvap$ can be predicted using the cavity flow calculation in the flow passage of the turbine by using cavity two-phase flow (compressible flow) simulation.

It is defined as the ratio of the maximum amplitude in time history with 97% reliability to the effective head.

This is a common practice in most power stations.

1

Corresponding author.

J. Fluids Eng 131(10), 101102 (Sep 18, 2009) (9 pages) doi:10.1115/1.3184025 History: Received May 19, 2008; Revised April 14, 2009; Published September 18, 2009

## Abstract

While larger and larger turbines are being developed, hydraulic stability has become one of the key issues for their performance assessments. An accurate prediction of their pressure fluctuations is vital to the success of new model development. In this paper, we briefly introduced the method, i.e., the three-dimensional unsteady turbulent flow simulation of the complete flow passage, which we used for predicting the pressure fluctuations of a model Kaplan turbine. In order to verify the prediction, the model turbine was tested on the test rig at the Harbin Electric Machinery Co., Ltd. (HEC), China, which meets all the international standards. Our main findings from this numerical prediction of pressure fluctuations for a model Kaplan turbine are as follows. (1) The approach by using 3D unsteady turbulent flow including rotor-stator interaction for the whole flow passage is a feasible way for predicting model turbine hydraulic instability. The predicted values at different points along its flow passage all agree well with the test data in terms of their frequencies and amplitudes. (2) The low-frequency pressure fluctuation originating from the draft tube is maximal and influences the stability of the turbine operation mostly. The whole flow passage analysis shows that the swirling vortex rope in the draft tube is the major source generating the pressure fluctuations in this model turbine. (3) The second harmonic of the rotational frequency $2fn$ is more dominant than the blade passing frequency $Zfn$ in the draft tube. This prediction, including the turbulence model, computational methods, and the boundary conditions, is valid either for performance prediction at design stage and/or for operation optimization after commissioning.

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## Figures

Figure 1

Operation performances of the prototype turbine: (a) test, and (b) prediction by steady flow simulation (GVO-guide vane opening, BA-blade angle, η-efficiency, σa-cavitation number)

Figure 2

Flow passage of the Kaplan turbine

Figure 3

N and η versus mesh elements; (–◼–) calculated power, (– –) tested power, (--★--) calculated efficiency, and (——) tested efficiency

Figure 4

Calculated pressure fluctuations at the inlet of the draft tube (TS): (a) pressure variation with time, and (b) pressure fluctuation spectrum

Figure 5

Locations where the numerical and experimental sampling for the pressure fluctuations were taken: (a) plan view and (b) side view

Figure 6

Predicted pressure fluctuations at various sampling locations of the model turbine flow passage: (a) pressure variation with time, and (b) pressure fluctuation spectrum (FFT)

Figure 7

Predicted pressure variations with time at various locations of the model turbine: (a) t=0.4 s, and (b) t=0.5 s

Figure 8

The international standard test rig at HEC (courtesy of HEC)

## Errata

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