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

2

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

5

<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

6

• Normalized

radial vector;

no scaling

• r-component scaled by

radius

The inlet condition is combined with SRFVelocity to work with simpleSRFFoam.

7

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

12

• 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

13

(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°

14

The Computational DomainCAD created in SolidWorks®

Mesh generated in Pointwise®.

15

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

16

• 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.

17

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

18

The residuals can be tracked by constructing a gnuplot script.

19

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

20

The No-Runner ComputationFinding the right RPM.

21

The RPM is calculated through velocity triangles at the leading edge.

22

• 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

23

• 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.

26

Inlet flow direction

simpleFoamAnalysis of a non-rotating turbine.

27

The global convergence criterion indicates adequate convergence.

• The holding torque, (Mz) converges to

550 N-m

28

• Relative residuals decrease three orders of magnitude, but increase in latter iterations

The flow field passing through the runners develops a vortex core.

29

simpleSRFFoamUsing a single reference frame.

30

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

31

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

34

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

35

Comparing the residuals and the lateral forces alludes a pseudo-steady condition.

36

• F_x leads F_y by approximately 90°

The pressure contour on the Francis turbine shows the expected distribution.

37

• Pressure Side

• Suction Side

The formation of a vortex rope indicates the unsteady nature of the flow field.

38

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

39

Thank You.

Questions?

40

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.

41