simulation of vortex rope in a turbine … · proceedings of the hydraulic machinery and systems...

Proceedings of the Hydraulic Machinery and Systems 21st IAHR Symposium September 9-12, 2002, Lausanne

SIMULATION OF VORTEX ROPE IN A TURBINE DRAFT TUBE

Albert RUPRECHT, Institute of Fluid Mechanics and Hydraulic Machinery / University of Stuttgart, Stuttgart, Germany

Thomas HELMRICH, Institute of Fluid Mechanics and Hydraulic Machinery / University of Stuttgart, Stuttgart, Germany

Thomas ASCHENBRENNER, Voith Siemens Hydro Power Generation, Heidenheim, Germany

Thomas SCHERER, Voith Siemens Hydro Power Generation, Heidenheim, Germany

ABSTRACT

The flow in a draft tube is investigated under part load conditions. The existing vortex rope is predicted and the resulting pressure pulsations are compared with measurement. The calculated results, amplitudes and frequencies agree quite well with the experimental data from the model tests. However, the vortex rope is damped too much and therefore its intensity is underpredicted further downstream. This is caused by the used turbulence model. Therefore improved turbulence models are discussed and their performances evaluated. Additionally it is taken into account the response of the power plant water passage to the exciting pressure oscillation caused by the vortex rope.

RÉSUMÉ

Le flot dans l’aspirateur est testé dans des conditions partiel charge . Le tourbillon en roulée réel est prédit et les changements de pulsation de la pression résultant sont comparées avec les mesures. Les résultat calculés (amplitudes et fréquences) montre une cohérence avec les données expérimentales des modèles testés. Toutefois le tourbillon en roulée décroît de façon excessive et son intensité est imprévisible dans le coude. Cela est du au modèle de turbulence utilisé. En conséquence, des modèles de turbulence améliorés sont étudiés et leurs performances évaluées. De plus la réponse du conduite de l’eau de la centrale à perturbation de la pression due au tourbillon en roulée et pris en compte.

INTRODUCTION

One of the major difficulties in hydraulic machinery is the operation under part load conditions. Especially severe pressure oscillations can occur for Francis turbine units in part load. They are generated by an unsteady vortex behaviour in the draft tube, the so-called vortex rope. It rotates with 30-50% of the runner speed causing rotating pressure pulsations in the draft tube. Beside the rotating fluctuations a synchronous pressure oscillations can occur in elbow draft tubes. This means a fluctuation of the complete pressure level at the draft tube inlet. This synchronous part works as an excitation to the entire power plant, especially if the exciting frequency is close to an eigenfrequency of the penstock. As a consequence the restriction of the range of operation can be necessary.


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The goal of this paper is to present a numerical prediction of the vortex rope as well as an investigation of its influence on the power plant water passage. Therefore the flow in a draft tube is simulated by means of CFD. As these simulatione require an accurate turbulence model - the standard k-ε model is not able to predict this phenomenon - different models are discussed.

NUMERICAL METHODS

For the simulation the computer code FENFLOSS, developed at University of Stuttgart is used. It is based on the Reynolds averaged Navier-Stokes equations with various models of turbulence. For details on the algorithm the reader is referred to Ruprecht (Ref. 1) or Maihöfer (Ref. 2).

TURBULENCE MODELLING

The simulation of unsteady vortex movement requires a more sophisticated model of turbulence than for steady state simulations. Otherwise the vortex motion is severely damped or the predicted flow even becomes steady state. For example the use of the standard k-ε model, which is frequently applied in steady state calculations, causes a severe damping and no vortex rope appears. Better results are obtained by the extended k-ε model of Kim & Chen (Ref. 3). This two-scale model takes additionally into account the dissipation rate of the large vortices, resulting in an additional production term in the ε-equation. The modified ε-equation reads

�� termAdditional

kk

3

2

2k1j

t

jjj P

k

Pc

kcP

kc

xxxU

t⋅��

+ε−ε+��

��∂

ε∂��

σν

+ν∂∂=

∂ε∂+

∂ε∂

εεεε

Using this model better results can be obtained compared to the standard k-ε model. In fig. 1. the flow simulation in a straight diffuser is shown. At the inlet a swirling velocity profile is prescribed, which is obtained from a runner simulation in part load. Whereas the standard k-ε model leads to a steady state flow with recirculation in the centre the extended model of Kim & Chen predicts an unsteady rotating vortex rope.

VORTEX ROPE IN AN ELBOW DRAFT TUBE

The draft tubes in hydraulic machinery are usually elbow type. The investigated draft tube consists of three outflow channels with two piers between. At the inlet, the computational domain is enlarged up to the runner hub. The area between runner hub and inlet of the draft tube is simplified with a straight tube. The computational grid and the inlet boundary conditions are shown in fig 2. The grid consists of about 250 000 nodes. A circumferential averaged velocity profile, obtained from a 3-dimensional steady state runner calculation under part load conditions, is taken as inlet condition for calculation domain. At the outlet of the draft tube, a constant pressure value is assumed. The calculations are carried out using the extended model of Kim & Chen.


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Fig. 2 Prediction of swirling flow in a straight diffuser by Standard k-ε model and by the extended model of Kim & Chen

Fig. 3 Computational mesh and inlet boundary conditions of the elbow draft tube

The results show a strongly unsteady flow behaviour in the draft tube. Fig. 4 presents the vortex rope as an iso-surface of the pressure for two different time steps. It can be seen that the vortex rope has the shape of a rotating cork-screw. The changing size of the vortex rope indicates strong pressure surges, which means a synchronous, non-rotating pressure fluctuation. This synchronous part usually causes the problems in the power plant.


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Fig 4: Vortex rope in the draft tube for two time steps

In order to compare the unsteady flow simulation with measurements, the pressure values are taken in each time step at the same position, where the pressure transducers are located in the experiment. (Fig. 5). As an example the measured and calculated pressure over time are shown in fig. 6 for the position 1 and 2.

Fig. 5 Measurement positions

Fig. 6 Pressure distribution for measurement and calculation

It can be clearly seen, that the simulated pressure at position 1 corresponds quite well with the measured value. The amplitude of the pressure oscillation is predicted a slightly smaller. The frequency, however, agrees extremely well.

For position 2 the frequency of the measured and calculated pressure also agrees quite well. The amplitudes, however, show a greater discrepancy. As expected, the amplitude of the calculation in position 2 is much more damped compared to the measurement. Possible


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reasons are the fixed discharge in calculation, caused by the steady inlet condition at the draft tube, and the damping effects of the turbulence model on the swirl.

A Fast Fourier Transformation is carried out for the measured and calculated signals at position 1 and 2. The relative amplitude of the signal is shown over the frequency in fig. 7. In both cases one can detect the dominating frequency of 7 Hz, which is the frequency of the vortex rope. It is 33% of the runner speed.

Fig. 7 Fourier transformed pressure signals

RESPONSE OF WATER PASSAGE

As mentioned above the synchronous part of the pressure fluctuations causes oscillations in the power plant water passage, leading to a discharge variation. However, this can not be considered by applying fixed velocity boundary conditions at the draft tube inlet. Therefore the dynamic behaviour of the water passage is taken into account for a simple power plant consisting of upper basin, penstock, turbine, draft tube and lower basin. The dynamic behaviour of the penstock is calculated by the one-dimensional Method of Characteristics (MoC), the turbine is represented by its linearized steady state hill chart and the draft tube is simulated by CFD.

From the CFD results the pressure at the draft tube inlet is averaged in each time step and is given as a boundary condition to the MoC. From the MoC a new discharge is obtained, which is introduced into the CFD simulation as a new velocity boundary condition by stretching the profile of the axial velocity and keeping the flow angles constant.

This coupled simulation leads to a synchronous pressure oscillation of approximately 3% and a resulting discharge variation of approximately 1%. The distributions are shown in fig. 9. The considered power plant has been chosen arbitrarily. It was considered that the penstock is not in resonance with the draft tube surge. Otherwise much severer pressure and discharge oscillations will occur.


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Fig. 9 Coupled simulation of the vortex rope and the dynamic behaviour of the water passage

Fig. 10 Pressure and discharge variations for the coupled simulation

ENHANCED TURBULENCE MODELING

The results shown above indicate that the vortex rope is too much damped by the applied turbulence model. Consequently an improvement of the model is necessary and therefore the development of an “unsteady” model is performed. As large eddies are enclosed in the unsteady simulation, they have not to be considered by the turbulence modelling. This approach is called Very Large Eddy Simulation (VLES) or Coherent Structure Capturing (CSC), Ref. 4. Applying Large Eddy Simulation (LES) a huge part of the turbulent spectrum (the anisotropic vortices) has to be resolved by the computation. This is impossible for high Reynolds numbers. Contrary to the LES, in VLES only the dominant main frequencies are included in the simulation and most of the turbulent spectrum is modelled. This is schematically shown in fig. 11.

Fig. 11 Schematic procedure for VLES


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For VLES or CSC the classical turbulence models are not suitable as they do not distinguish between resolved and unresolved scales. An “unsteady” or adaptive model (Ref. 5) contains a filtering according to the resolved time scale and length scale. This means, these parts of the spectrum, which are included in the computation are no longer included in the turbulence model. The resolved length scale and time scale are defined by

��

�

�

��

�

�∆=∆ t;

u

hmaxt max

t , ( )maxh;tumaxL ∆⋅=∆ ,

where hmax is the maximum cell length, u is the local velocity and ∆t the time step of the simulation.

The model applied is based on the two-scale model of Hanjalic et al. (Ref. 6) , where two sets of k-ε equations are solved, one for large scales and one for small scales. This model has been adapted to the fact, that the turbulent kinetic energy of the large scales is included in the simulation and consequently this equation has not to be solved. On the other hand the dissipation rate of the small scales is simplified by the Kolmogorov relation. As a result the model contains two transport equation, one for the dissipation rate of the large scales and one for the turbulent kinetic energy of the small scales. Thus it requires nearly the same computational effort than the standard k-ε model.

An application of the model to a bluff trailing edge is shown in fig. 11, where the pressure distribution at a certain time step is presented. Much stronger vortices are clearly visible using the unsteady model compared to the model of Kim & Chen.

Fig. 11 Vortex shedding behind a bluff trailing edge, pressure distribution comparison of Kim & Chen model(left) and “ unsteady” model (right)

The flow in a straight diffuser is shown in fig. 12. The simulation results using the Kim & Chen model is presented on the left hand side and the results applying the “unsteady” model are given on the right hand side. Looking at the vortex length - both models predict a vortex rope - it can be seen, that the vortex is longer using the unsteady model. This means that this model contains less damping effects.

It seems that the results of the new model are quite promising, however it has to be tested further. Detailed comparison with measurements are necessary. At present specific measurements (by PIV and LDA) are carried out for different vortex flows for getting accurate validation data.


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Fig. 12 Vortex rope in a straight diffuser, comparison of Kim & Chen model(left) and “ unsteady” model (right)

CONCLUSION

The unsteady flow in a draft tube has been calculated under part load conditions. The simulation requires an accurate turbulence model. Using the standard k-ε model the predicted flows become stationary, whereas in the experiment a vortex rope occur. Applying the extended model of Kim & Chen the prediction is improved and a vortex rope is obtained in the simulation. The calculated frequencies of the vortex rope agree quite well with measurements on the test rig. However the pressure amplitudes and the vortex behaviour indicate, that the swirl is damped to fast downstream in the draft tube. Improved results are expected by applying a Very Large Eddy Simulation (or Coherent Structure Capturing) with an enhanced model of turbulence, which distinguishes between resolved und modelled scales.

REFERENCES

Ref. 1 Ruprecht, A., 2002, „Numerische Strömungssimulation am Beispiel hydraulischer Strömungs-maschinen“, Habilitationsschrift, Universität Stuttgart.

Ref. 2 Maihöfer, M. (2002), „Effiziente Verfahren zur Berechnung dreidimensionaler Strömungen mit nicht-passenden Gittern, Dissertation, Universität Stuttgart.

Ref. 3 Kim, S.-W., Chen, C.-P., 1989, “A multiple-time-scale turbulence model based on variable partitioning of the turbulent kinetic energy spectrum”, Numerical Heat Transfer 16(B).

Ref. 4 Sagaut, P., 2001, Large Eddy Simulation for Incompressible Flows, Springer-Verlag.

Ref. 5 Magnato, F., Gabi, M., 2000, “A new adaptive turbulence model for unsteady flow fields in rotating machinery” , ISROMAC 8.

Ref. 6 Hanjalic, K., Launder B. E., Schiestel, R. (1980): Multiple-time-scale concepts in turbulent transport modeling, Turbulent Shear Flows, Springer-Verlag.

simulation of vortex rope in a turbine … · proceedings of the hydraulic machinery and systems...

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