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A Numerical Model for the 3D-Simulation of Flow
through the Intake of Water Power Stations
Gerd Demny, Katja Rettemeier, Christian
Forkel, JÜrgen KÖngeter
Institute of Hydraulic Engineering and Water Resources Management, Aachen University of Technology
Mies-van-der-Rohe-Str. 1, 52056 Aachen, Germany; Phone: +49 / 241 / 80-5265, Fax: +49 / 241 / 8888-348, E-Mail: demny@iww.rwth-aachen.de
Abstract
Especially the intakes of run-of-the-river power plants are very complex engineering buildings. The application of a finite element code, which calculates the three-dimensional, transient, and turbulent flow, arise the possibility to investigate all flow phenomena in the intake area in detail. After numerous verification examples, the intake of the run-of-river power plant Wintrich at the river Moselle was selected for the validation as a real hydraulic engineering problem. The three dimensional finite element grid of the intake cove contains one third of the weir, the separation pier and the bulb turbine power plant with four intake chambers. The grid counts 40.105 nodes and 34.584 elements. Even though the numerical grid is fairly rough, a Large Eddy turbulence approach is applied with a Smagorinsky subgrid scale model for the medium scale eddies. The smallest scales are accounted for with a constant background eddy-viscosity. The dimension of the grid allows reasonable calculation time while all significant current structures can be modelled. An accustic-doppler-current-profiler (ADCP) and a hydrometric-current-meter were used to obtain verification data. The measurements were taken in various places within the weir and the intake cove. The ADCP measurements and the current meter data provides high quality data for a detailed validation of the model. The comparison between simulated and measured velocity vectors in different investigated spots shows very good results. The simulations show, that the geometry of the intake building has an important influence on the quality of the inflow. The presented results indicate a distinct vortex shedding at the separation pier. The extension of the separation zone is non-steady and fully three-dimensional. A large dead water zone in front of the weir causes a pulsing flow around the separation pier and an oblique inflow into the turbines.
Keywords: Numerical Modelling, Large-Eddy Simulation, Finite-Element Method, 3D-Velocity measurements, ADCP, Validation, Hydraulic Structures, Run-of-River Power Plant
Introduction
The computation of the flow in complex
geometries like the intake cove of a run-of-river power plant requires a
three-dimensional, transient and turbulent model. A finite element code on the
base of a 'Large-Eddy' model is used for the efficient and realistic
calculation of the complex flow behavior. The numerical model was applied and
validated for the low head power plant Wintrich at the river Moselle. The weir
Wintrich with integrated low head power plant is one of ten weirs at the
Moselle in Germany. The weir and the power station are set in one axis while
the power station is located in a bay. Weir and power station are separated by
a pier with a buffle in front of it. The design flow of the hydropower plant,
which contains four bulb turbines, is 400 m³/s with a rated power release of 20
MW. The maximum piezometric head is 7,70 m. The numerical model, and the
discretization of the intake cove will be presented in the following chapters.
Afterwards, the validation of the model and a selection of simulation results
will be discussed.
Numerical Model
The flow phenomena in large-scale geometry are very complex and in most cases fully three-dimensional. This is due to the very irregular boundaries inducing high velocity gradients and a large spectrum of turbulent flow. Therefore the model must be capable of representing the whole eddy spectrum and simulating three-dimensional flow in the irregular boundaries. A three-dimensional 'Large-Eddy' approach, which is based on the Finite-Element method, fulfills these requirements.
Numerical
Method
The numerical model PASTIS-3D, which was developed at the Institute of Hydraulic Engineering and Water Resources Management at the University of Technology in Aachen, contains the three-dimensional 'Large-Eddy' approach in combination with the finite element method. All sub-grid stresses are modeled with a SMAGORINSKY (1963) turbulence model. A constant background eddy viscosity is introduced for the smallest turbulence scales. This background eddy viscosity is set to the molecular viscosity enlarged by factor 200. Finite hexahedron elements with arbitrary shape are used for the spatial discretization. Therefor all integrations on the element level are obtained by full 2x2x2 Gauss point integration. The approximation functions are tri-linear for the velocities and constant for the pressure respectively (Forkel et al., 1995 and Forkel, 1995). For the time discretization the semi-implicit LEISMANN-FRIND (1989) scheme is used and time-accurate solutions are obtained by applying the very efficient 'projection 2' algorithm which was developed and analyzed by Gresho (1990) and Gresho and Chan (1990). For more details of the numerical approach and its verification see Forkel (1995).
Discretization
The three
dimensional finite element grid of the intake cove contains one third of the
weir, the separation pier and the four intake chambers of the power plant
including the machine casing of the generator. The discretization ends in front
of the wicket gates. The
spatial resolution of the grid must be adapted to the structure of the expected
solution of the flow field. Regions with high velocity gradients require small
element sizes. Therefore, the discretization nearby and inside the intake
chambers is finer than in the upstream water bay and in front of the weir.
However, a high geometric resolution leads to high node and element numbers.
Because of limited computer capacities, it is necessary to develop a compromise
between spatial resolution and computational efficiency. This optimization
process leads to a grid, which counts 40105 nodes and 34584 elements
(RETTEMEIER, 1997). Figure 1 shows an inside view of the grid. The flow
direction is towards the intake bellmouth (right hand side). The separation
pier with the buffle in front of it is located in the background.
Figure 1: Outline of the discretization
(insight)
A porous media approach is used to consider the
influence of the trashrack on the flow field. Simulation results published by
Demny et. al. (1998) show, that the porous media approach is a very useful tool
to model the effects of the trashrack for three-dimensional simulations. The
approach indicates no instabilities even for high energy head losses, which is
an important advantage over more simple approaches like constant eddy viscosity
models.
Validation of the Model
The numerical model is validated on the basis of 3D natural measurements, which were taken at the intake of the run-of-river power plant Wintrich. The validation is performed under low (140 m³/s) and high (460 m³/s) flow conditions.
Measurements
Several measurements have been taken in various
places within the weir and the intake cove (RETTEMEIER, 1997 and RÜSSMANN,
1997). The measurements of the velocity profiles have been carried out at a
high number of points on different cross-sections with different measuring
instruments. The model and all cross-sections are indicated in figure 2. In the
sketch, the first section of the weir is located above and the power station
can be recognized below. Those points at the cross-sections, which are used for
comparison in this paper, are marked.
Figure 2: Sketch of the run-of-the-river power
plant Wintrich (above: first weir section, below: power station) and measurement
cross sections.
An accustic-doppler-current-profiler (ADCP) and
a hydrometric-current-meter (HCM) have been used to obtain velocity profiles.
The ADCP provides fully three-dimensional data and also detailed time history
plots of the turbulent fluctuations. Although, the HCM measures the total
velocity correctly, it splits up only the horizontal components of the velocity
and gives no information about the vertical component. Both instruments have a
limited range. They cannot track the velocity close to the bottom and the ADCP
cannot track the velocity at water level. Only the HCM can provide data near
the surface.
Comparison
between Measured and Calculated Velocities
Out of the high number of verification data
(RÜSSMANN, 1997 and HOFFMANN, 1998) only a few results can be presented here.
In this paper, the velocity profiles for the points A, B, and C, indicated in figure
2, are represented. The results are considered to be representative for all
measured points.
Figure 3: Profiles of absolute velocities at
points A (left) and C (right)
Figure 3 (left) presents the comparison of the
HCM measurements and the simulation results for point A, which is located in
front of turbine 3. The flow rate is 140 m³/s. The shown profile is the
absolute value averaged over 5 min for the HCM and over 2.5 min for the
simulation. The general pattern of the velocity vector is the same but the
values differ. The reason for the difference is the slight variation of the
total flow rate and the inflow rates into the different turbines during the
measurements. Figure 3 (right) shows the comparison of the modeled absolute
velocities with ADCP measurements averaged over 2 min at point C for a flow
rate of 460 m³/s. The presented examples show, that the simulation results for
both flow rates are in very high accordance with the measurements.
Figure 4: Profiles of the velocity components
at point B
The ADCP gives the possibility to consider the
different velocity components for the validation. Figure 4 presents the
comparison of the ADCP-measurements at point B with the computed velocities.
This velocity profile is typical for the current inside the intake cove. The
flow rate is 140 m³/s. Measurement and simulation are both averaged over 2.5
min. The y- and z-velocities show a very good agreement both for the vector and
the value. The x-velocities match only in profile while the values differ.
Accordingly, the same can be recognized for the absolute value and is due to
the slight variation of flow rate mentioned above. In conclusion, all the simulation
results at different locations and different flow rates show very good
similarities with the measured velocities. As a result, the model is validated
and can be used for detailed flow investigations.
Flow Investigations
The design of the separation pier should be
carried out very carefully. An inappropriate shape can lead to disturbances of
turbine inflow. Figure 5 shows two snapshots of the flow around the separation
pier for two different time steps.
Figure
5: Velocity vectors at
the separation pier 2 m below the water level, left:
t = 510 s, right: t = 570 s
Obviously, the vortex shedding is not
steady-state. The extension of the vortex depends on the turbulent fluctuations
in front of the weir section. At t = 510 s (Figure 5, left) the extension of
the vortex is almost one third of the intake width. After additional 60
seconds, a second vortex downstream of the baffle appears, and the extension of
the separation zone is nearly doubled (Figure 5, right). This pulsing
separation zone is not uniform in space, as Figure 6 illustrates.
Figure 6: Velocity vectors in a vertical
cross-section at the separation pier and the first intake chamber at t = 510 s.
The vertical cross-section, placed in the
center of the separation zone, shows, that the eddy is pulled through the trash
rack into the turbine chamber. In addition, different vortex structures can be
observed in front of the separation pier. They are affected by the unsteady
jet, running from the area in front of the weir across the steeply sloping
bottom into the turbine intakes (Figure 7).
Figure 7: Velocity field in front of the separation pier and the turbine intakes at
t = 510 s
The accelerated flow around the separation pier along the steeply sloping plane affects the slow main flow of the intake. The resulting rolls and cross-flows continue themselves up to the trash-rack and lead to an oblique inflow into the turbines.
Figure 8: Average iso-velocities in front of
the turbines.
The quality of the inflow conditions can be
assessed by analyzing an iso-velocity plot. In Figure 8, the average velocities
over a period of 10 s in the cross-section of the trashrack are plotted. The
mean velocity is about 1 m/s. Except for the domain in front of turbine 1, a
regular shape of the iso-velocities can be observed. The strong spatial variety
of velocities close to the separation pier indicates the existing eddy
structures. The fast flow around the separating pier and the blocking eddies
lead to high flow velocities of more than 1.50 m/s in front of the bellmouth of
turbine 1.
Conclusion
The flow analysis of the complex flow in the intake
of a run-of-river power plant requires a non-steady and three-dimensional
computational method. A three-dimensional, Large-Eddy simulation method is
applied to a German run-of-river power plant. A large number of measurements
have been carried out in the intake cove with different measuring instruments
and different flow rates. The simulation results show very good similarities
with the measured velocities. In conclusion, the model for flow calculation in
the intake cove of the run-of-river power plant Wintrich is validated. The simulated
flow shows a distinct vortex shedding at the separation pier. The extension of
the separation zone is non-steady and fully three-dimensional. A large dead
water zone in front of the weir causes a pulsing flow around the separation
pier and an oblique inflow into the turbines. The detail precise discretization
of the geometry and the use of a 'Large Eddy' model in combination with the
three-dimensional, transient, finite element model PASTIS-3D provides an
efficient instrument for flow computation in intake coves of run-of-river power
plants.
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