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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.