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Noise reduction in a small Francis turbine caused by vortex shedding at the trailing edge,

numerical analysis and field test.

Ruprecht, A., Kirschner, O., Lippold, F., Buntic, I.

Problem description

In a small old hydro power plant equipped with three Francis turbines one of the turbines is replaced by a new one. This new unit produces a low frequency noise. The noise level in the plant is not very high compared to other power plants. The problem in this plant, however, is that the low frequency noise emission carried over to the adjacent apartment of the operator and therefore can not be tolerated.

The disturbing noise depend on the point of operation of the turbine. At low head and consequently also at low discharge the noise level is reduced or even vanishes. Additionally the noise level depends on the guide vane opening. At guide vane opening lower than 40 % the noise appears but is not disturbing. With increasing opening the noise level increases at 70 % it reaches a maximum. Increasing the guide vane opening further to 100 % the noise level decreases slowly.

As mentioned above the noise level is not tolerable. Because of that the reason has to be detected. For that purpose noise measurements are carried out in order to evaluate the frequency. From that information the cause should be detected and cure measures should be detected to reduce the noise level or the shift the frequency.

Measurements

With the noise measurement equipment of the institute (type Brel & Kjaer) the noise level measurement level as well as a frequency spectrum are detected. In fig. 1 and 2 the measurement equipment in the power plant is shown.

The measurements are carried out at different of operation and at different locations in the power plant as well as in the apartment of the operator. In order to avoid any interaction with the other turbines only the new turbine is in operation.

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Fig. 1: Noise measurement in the power house

Fig. 2: Measuring equipment

The disturbing noise is, as mentioned earlier, at low frequency. It is detected that it has a frequency of approximately 166 Hz. The measured frequency spectrum is shown in fig. 3. In the power plant peaks at 31.5 Hz and at 160 Hz are clearly visible. In addition to that small peaks can be detected at 315 Hz, 500 Hz and 4000 Hz. In the apartment the frequencies up to 500 Hz are available with reduced intensity.

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Fig. 3: Measured frequency spectrum at different locations and for different points of operation

Estimated frequencies

In order to detect the source of the noise the characteristic frequencies of the turbine unit were estimated. They are summarized in tab. 1.

turbine speed 1.29 Hz speed of gear box 6.4 Hz generator speed 12.5 Hz

runner (13 blades) 16.8 Hz guide vanes (24 blades) 31 Hz

cog-wheels of gear box 1. level 115 Hz Karmn vortex street at runner trailing edge 170 Hz

cog-wheels of gear box 2. level 363 Hz Rotor-stator iteration 403 Hz

Tab. 1 Estimated characteristic frequencies

Comparing these frequencies with the measurements a coincidence is found at 31 Hz and at 170 Hz. Whereas the frequency of 31 Hz (caused by the guide vanes) was not disturbing, the problem-frequency is detected to be caused by vortex shedding at the trailing edge of the runner.

The turbine geometry is sketched in fig. 4. The shape of the trailing edge is shown in fig. 5.

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Fig. 4: Sketch of turbine

Fig. 5: Shape of leading and trailing edge

Later when the turbine was dismantled it was found that the structural eigenfrequency of the runner nearly coincides with the found frequency of 160 Hz.

Problem solution

In order to justify the estimated vortex shedding frequency and in order to investigate possible cure measures the flow behaviour at the trailing edge of the runner is studied by means of Computational Fluid Dynamics (CFD). The calculations are carried out in a two-dimensional meridional cut through the runner.

In fig. 6 the pressure distribution behind the bluff trailing edge is shown for a certain time step. Clearly visible are the vortices, shedded at the trailing edge. Because of the bluff shape a severe Karman vortex street occurs. In order to reduce the intensity and to shift the frequency of the vortex street the trailing edge has to be sharpened. For structural reasons however the trailing edge can not be thinner near the hub and near the shroud, because otherwise to high stresses would be obtained. Therefore the trailing edge is only modified in the middle part and kept constant at hub and shroud, see fig. 7.

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Fig. 6: Vortex shedding at the trailing edge of the runner

Fig. 7: Sketch of the modified trailing edge

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Fig. 8: Vortex shedding at the modified trailing edge of the runner

In fig. 8 the pressure distribution at the modified trailing edge is shown. Clearly visible is the reduces intensity of the vortices, compared to the original trailing edge, fig. 5. In fig. 9 the pressure fluctuation along the time at a spot point behind the trailing edge is shown for both geometries. For the modified shape the frequency is higher (because of the thinner edge) and the amplitude of the pressure fluctuations is smaller.

It is assumed that because of the frequency shift and the reduction of the amplitude of the pressure fluctuation the disturbing noise should be reduced. Therefore the trailing edge is changed. The obtained result are satisfactory. The noise is considerably reduced. It is not longer disturbing and therefore no final measurement were made.

Fig. 9: Pressure distribution behind the trailing edges (original and modified shape)

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Detailed numerical investigation

Reynolds averaged Navier-Stokes simulations The above shown investigation was carried out under a very tight time schedule, because the problem had to be solved very fast. During the simulation it was discovered, however, that the simulation results (especially the fluctuation amplitude) are quite sensitive to numerical and modelling parameters. For this reason a more detailed investigation of the numerical prediction of a vortex street has been carried out. The simulations are performed at a single air foil with bluff trailing edge.

In order to simulated the turbulent vortex shedding usually an unsteady simulation based on the Reynolds-averaged Navier-Stokes equations is applied. For unsteady flow phenomena, however, the choice of an appropriate turbulence model is essential for obtaining suitable results. Applying e. g. the standard k- model, which is widely used in industrial application leads to poor results. In fig. 10 the flow behind a buff trailing edge is shown. The unsteady simulation with the k- model leads to a steady state , symmetrical recirculation region behind the trailing edge.

Applying an extended k- model of Kim and Chen [1] the results are more accurate. A periodical vortex shedding is obtained. For details of the turbulence models and further applications the reader is referred to [2, 3].

Fig. 10: Comparison of different turbulence models

In the following the influence of the trailing edge shape is investigated. The results are obtained by applying the Kim&Chen k- turbulence model. The analysis is carried out at an airfoil. In fig. 11 the computational domain with the wing is shown. Different thickness of the trailing edge (2%, 4% and 6% of the cord length) are analysed.

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Fig. 11: Computational domain

In fig.12 the pressure distribution for the thickness of 6% is shown. Clearly visible are the vortices. The periodic vortex shedding results in a periodic force on the profile perpendicular to the flow direction.

Fig. 12: Pressure distribution

In fig. 13 the frequency of this force is given for the different thickness. With increasing thickness the frequency drops. The amplitude, however, increases with the size of the thickness. This is shown in fig. 14.

Fig. 13: Frequency of acting force depending on the trailing edge thickness

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Fig. 14: Amplitude of acting force depending on the trailing edge thickness

In fig. 15 the forces along the time are presented. As can be seen in fig.14 the amplitude increases with thickness and the frequency decreases, see also fig.13.

Fig. 15: Time series of the perpendicular force depending on the thickness of the trailing edge

For the investigations shown above the shape of the trailing edge was symmetrical, only the thickness varies. It is well known, however, that the intensity of vortex shedding can be reduced dramatically by an unsymmetrical trailing edge. As an example in fig. 16 the pressure distribution at an unsymmetrical trailing edge is shown. By the asymmetry the vortex shedding is suppressed nearly completely.

Fig. 16: Pressure distribution for an unsymmetrical trailing edge

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Very large eddy simulation

As mentioned above the simulation of the vortex shedding needs quite sophisticated turbulence models. When applying the wrong models the vortices are severely damped and the amplitudes of the forces are underpredicted. A better approach compared to Reynolds-averaged Navies-Stokes simulations is a Very Large Eddy Simulation (VLES), for details see [4,5].

Real Large Eddy Simulation (LES) from the turbulence research point of view require an enormous computational effort since all anisotropic turbulence structures have to be resolved in the computation and only the smallest isotropic scales are modeled. Consequently this method also can not be applied for industrial problems today.

Todays calculations of flows of practical relevance (characterized by complex geometry and high Reynolds number) are usually based on the Reynolds-averaged Navier-Stokes (RANS) equations. This means that the influence of the complete turbulence behavior is expressed by means of an appropriate turbulence model. To find a turbulence model, which is able to capture a wide range of complex flow effects quite accurate is impossible. Especially for unsteady flow behavior this method often leads to rather poor results. The RANS and LES approach can schematically be seen in fig. 17, where a typical turbulent spectrum and its division in resolved and modeled parts is shown.

Fig. 17: Modelling approach for RANS and LES.

The recently new established approach of Very Large Eddy Simulation can lead to quite promising results, especially for unsteady vortex motion. Contrary to URANS there is a requirement to the applied turbulence model, that it can distinguish between resolved unsteady motion and not resolved turbulent motion which must be included in the model. It is similar to LES, only that a minor part of the turbulence spectrum is resolved (schematically shown in Figure 18). VLES is also found in the literature under different other names:

- Semi-Deterministic Simulation (SDS), - Coherent Structure Capturing (CSC), - Detached Eddy Simulation (DES), - Hybrid RANS/LES, - Limited Numerical Scales (LNS).

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Fig. 18: Turbulence treatment in VLES.

For comparison the pressure distribution around the airfoil is shown for URANS(fig 19) and for VLES (fig. 20). It can be observed that the damping of the vortices in the far field of the trailing edge is reduced dramatically by the VLES approach. The forces on the airfoil, however, are nearly unchanged.

Fig. 19: Pressure distribution by URANS

Fig. 20: Pressure distribution by VLES

Conclusion

By noise measurement the frequency the source of noise has to be detected in a hydro power plant. By analysing the frequency spectrum and compare it with estimated characteristic frequencies the vortex shedding behind the bluff trailing edge has been detected as exciting source. This was confirmed by numerical simulations. By sharpening the trailing edge the

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frequency could be shifted and the amplitude could be reduced. The problem could be solved by this measure. Even when the quantitative numerical predictions of the fluctuation amplitudes is not highly accurate, the simulation is an appropriate tool to predict the phenomena and to investigate cure measures.

References

[1] Chen, Y. S., Kim, S. W. (1987): Computation of turbulent flows using an extended k- turbulence closure model, NASA CR-179204. [2] Ruprecht A. (2003): Numerische Strmungs-simulation am Beispiel hydraulischer Strmungsmaschinen. Habilitationsschrift, Universitt Stuttgart. [3] Ruprecht, A., "Unsteady flow simulation in hydraulic machinery", Invited lecture, Seminar CFD for turbomachinery applications, Gdansk, September 2001, erschienen in TASK QUATERLY, 6, No 1 (2002), 187-208. [4] Ruprecht, A., Helmrich, T., Buntic, I., Very large eddy simulation for the prediction of unsteady vortex motion, Conference on Modeling Fluid Flow, Budapest, 2003. [5] Helmrich, T., Buntic, I., Ruprecht, A., Very Large Eddy Simulation for flow in hydraulic turbo machinery, Classics and Fashion in Fluid Mechanics, Belgrade, 2002.