OpenFOAM®® and Turbomachinery: a Demonstration of a Simplified Francis Turbine Geometry
A. Wouden, B. Lewis, J. Cimbala, E. Paterson
The Pennsylvania State University
Funded by the US Department of Energy
http://psuhydroresearch.org
Contents
• Motivation
• Some preliminary bench-work
Cylindrical Inlet Velocity Patch
forFoam
• The Simplified Francis Turbine
• The Computational Domain
• The OpenFOAM® Setup
• The No-Runner Computation
• Results from potentialFoam, simpleFoam, simpleSRFFoam, MRFSimpleFoam
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Motivation
• The study of flow through a Francis turbine is complex
• An understanding of pre-processing methodology is useful
• A simplified Francis turbine demonstrates the methodology without the complex geometry
• The resulting OpenFOAM® case structure provides an archetype for other hydro turbine applications
3
Cylindrical Inlet Velocity PatchAdapted from OpenFOAM® 1.7.
4
The inlet velocity patch alters the variable list.
OpenFOAM® 1.7<name>
{
type cylindricalInletVelocity;
axis (0 0 1);
centre (0 0 0);
axialVelocity 30;
rpm 100;
radialVelocity -10;
}
Modification
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<name>
{
type cylindricalInletVelocity;
axis (0 0 1);
centre (0 0 0);
axialVelocity 30;
tangentVelocity 10;
radialVelocity -10;
}
• Given an inlet surface <name>, the velocity (0/U) can be specified in
cylindrical coordinates.
The modification corrects an error in OF1.7 version of cylindrical inlet velocity.
OpenFOAM® 1.7 Modification
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• Normalized
radial vector;
no scaling
• r-component scaled by
radius
The inlet condition is combined with SRFVelocity to work with simpleSRFFoam.
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SRFcylindricalInletVelocity
• SRFVelocity
“If relative, include the effects of the SRF” [1]
• cylindricalInletVelocity
Specify boundary in cylindrical coordinates
• SRFcylindricalInletVelocity
Specify boundary in cylindrical coordinates, and
“If relative, include the effects of the SRF”
<name>
{
type SRFcylindricalInletVelocity;
relative yes;
axis (0 0 1);
centre (0 0 0);
axialVelocity 30;
tangentVelocity 10;
radialVelocity -10;
}
SRFVelocity cylindricalInletVelocity
forFoam: Initial Condition UtilityCreated as a semi-automatic (user-interactive) OpenFOAM® utility.
8
A Fortran-based utility creates initial condition files.
• Motivation
Create run-ready initial condition files
Provide user interaction• Automate definite surface types
• Prompt ambiguous surface types (i.e. type patch)
• Remember user responses
9
kforFOAM
Up
ω
The Simplified Francis TurbineAdapted from GAMM Francis turbine geometry.
10
Disclaimer• The geometry of this turbine, though based on a the GAMM Francis
turbine, does not represent any actual turbine in operation; there are no experimental data available.
• Rather, the simpler geometry provides for a tutorial to turbomachinery analysis in OpenFOAM®
11
The turbine housing is identical to the GAMM geometry.
• Stator Ring
Outer Diameter: 692 mm
Inner Diameter: 334 mm
Altitude: 120 mm
• Band
Top Diameter: 422 mm
Bottom Diameter: 402 mm
Altitude: 99 mm
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• Crown
Outer Diameter: 334 mm
Inner Diameter: 44 mm
Altitude: 134 mm
• Diffuser
Min Diameter: 402 mm
Max Diameter: 490 mm
Altitude: 446 mm
The stay bolt, wicket gate, and runner blade have some geometric equivalence to GAMM.
• Stay Bolt
Reduced to circular cylinder
Diameter: 12 mm
• Wicket Gate
Reduced to rounded flat plate
Chord: 73 mm
Thickness: 9 mm
• Runner Blade
Reduced to rounded flat plate
Thickness: 6 mm
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(Not to scale)
d d
Lt
L
t
t
(Not to scale)
t
The computational domain includes the 360°profile.
• Stay Row
# of blades: 20
Periodicity: 18°
• Wicket Row
# of blades: 20
Periodicity: 18°
• Runner Passage
# of blades: 13
Periodicity: 27.69°
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The Computational DomainCAD created in SolidWorks®
Mesh generated in Pointwise®.
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The mesh consists of four independently built regions.
• Stay Vane Zone
502,080 cells
y+min=15.82
• Wicket Gate Zone
1,171,200 cells
y+min=20.14
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• Runner Blade Zone
1,117,090 cells
y+min=3.97
• Diffuser Zone
23,520 cells
y+min=90.20
ggi: C`
OutletSlip Wall
ggi: A`
ggi: B
Inlet
ggi: A
ggi: B`
ggi: C
The OpenFOAM® SetupUsing OpenFOAM® 1.6-ext.
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The Allrun script contains a step-by-step process of the OpenFOAM® operations.
• Consists of five steps1. Zoning
• identify nonOrthoFace zones
• create ggi zones
• define MRF zones
2. Initializing
• retrieve results from a previous solution
3. Decomposing
• divide mesh for parallel computing
4. Executing
• run the solver
5. Reconstructing
• recombine results for the converged time step
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The residuals can be tracked by constructing a gnuplot script.
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The OpenFOAM® setup is consistent between solvers.
• The simplified turbine OpenFOAM® case maintains
1. k-ω SST turbulence model
2. Steady-state, Gauss-linear finite volume schemes
3. GAMG solver on pressure
4. smoothSolver on velocity and turbulence parameters
5. small under-relaxation factors• p = 0.2
• U = 0.3
• k = 0.3
• ω = 0.3
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The No-Runner ComputationFinding the right RPM.
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The RPM is calculated through velocity triangles at the leading edge.
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• From textbook formulation [3],
• Solving for the angular speed:
• By convention,
• And converting into RPM:
The rpm is determined through processing the no-runner geometry.
• Processed using simpleFoam
• For the simplified turbine
rpm = 363.32
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• Velocity Waypoint
potentialFoamInitializing the flow field.
24
Preliminary processing in potentialFoam sets an initial velocity distribution.
• Convergence Criterion
Pressure residual decreases by three orders of magnitude
• Parameter Update
Velocity field data are updated to 0/U
Other field data are unaffected
25
Swirl component at the inlet seems to disappear inside the computational domain.
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Inlet flow direction
simpleFoamAnalysis of a non-rotating turbine.
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The global convergence criterion indicates adequate convergence.
• The holding torque, (Mz) converges to
550 N-m
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• Relative residuals decrease three orders of magnitude, but increase in latter iterations
The flow field passing through the runners develops a vortex core.
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simpleSRFFoamUsing a single reference frame.
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The convergence using simpleSRFFoam is only partially achieved.
• The p-residual hovers at a-less-than adequate level
• The head and efficiency converge to
15.9 m, 29.9%
respectively
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Coriolis terms in the internal flow field misrepresent the flow through the stator.
• Absolute velocity on inlet, stator ring, and turbine
• Relative velocity on inlet, stator ring, and turbine
• Streamlines progress around obstacles
The simpleSRFFoam solution is unreliable for this configuration
MRFSimpleFoamUsing multiple reference frames.
33
The RPM of the turbine is imposed on the runner Zone only.
Non-Rotating Zone Rotating Zone
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The convergence in the MRFSimpleFoam case exhibits distinctive behavior.
• Residuals “flat-line” on latter iterations.
• The head and efficiency converge to
2.8 m, 71.5%
respectively
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Comparing the residuals and the lateral forces alludes a pseudo-steady condition.
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• F_x leads F_y by approximately 90°
The pressure contour on the Francis turbine shows the expected distribution.
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• Pressure Side
• Suction Side
The formation of a vortex rope indicates the unsteady nature of the flow field.
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Summary
• The simplified turbine cases provide a template for more complex hydro turbines:
simpleFoam returns a steady state solution to the non-rotating rotor
simpleSRFFoam returns an unreliable solution for this configuration
MRFSimpleFoam returns a pseudo-steady solution at convergence
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Thank You.
Questions?
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References• [1] OpenFOAM®, /scr/finiteVolume/cfdTools/general/SRF
/derivedFvPatchFields/SRFVelocityFvPatchVectorField/ SRFVelocityFvPatchVectorField.C
• [2] Gshaider, Bernhard, pyFoam: Happy foaming with Python, 4th OpenFOAM® Workshop, 1-4 June 2009
• [3] Cengal and Cimbala. Fluid Mechanics: Fundamentals and Applications. McGraw Hill, 2006.
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