1. Parallelized Coupled Solver (PCS) Model Refinements & Extensions
Sven Schmitz
University of California, Davis
GE Wind
November 29th, 2007
Greenville, SC
Schmitz
GE Wind - PCS

2. Outline
2007
Parallelized Coupled Navier-Stokes/Vortex-Panel Solver - PCS
Nacelle Model, Latest version.
2008
Extension of Lifting-Line (LL) to Lifting-Surface (LS) - PCS
Vortex-Lattice type method on the blade surface.
‘Quasi-Steady’ PCS PCS-Q
Quasi-Steady RANS/Vortex Model, Solution methodology for N blades.
‘Unsteady’ PCS PCS-U
Time-accurate RANS/Vortex Model, Solution methodology for N blades.
Schmitz
GE Wind - PCS

3. Coupling of NS Solver with Vortex Method
PCS PCS PCS-Q PCS-U
Navier-Stokes
Vortex Method
Vortex Filament
Biot-Savart Law (discrete)
Boundary of
Navier-Stokes Zone
Converged for …
Bound Vortex
Schmitz
GE Wind - PCS

4. No feedback from GE so far.
PCS PCS PCS-Q PCS-U
Nacelle Model : GEWIND-PCS_2_0.tar (avail. to GE)
Nacelle is approximated as a non-rotating ‘Rankine Body’.
User Input : Height, Width, Axial Location (dimens. by R)
Model finds position/strength of Source/Sink pair.
Influence coefficients are added to each point in RANS boundary.
=> … acts as a perturbation to the incoming wind speed Uwind.
May reduce need for complex blade/nacelle grid topology.
No feedback from GE so far.
Latest Version : GEWIND-PCS_2_1.tar (avail. to GE)
New version of asymptotics for influence coefficients [Chattot, 2007].
Schmitz
GE Wind - PCS

5. 2007 - PCS 2008 - PCS 2008 - PCS-Q 2008 - PCS-U
Extension of Lifting-Line (LL) to Lifting-Surface (LS) - PCS
Motivation :
Current PCS limited to LL at blade ¼ chord, vortex filaments emanating from trailing edge (TE).
Bound Vorticity GjB concentrated at LL. => Effect of LL position unclear.
Spread LL (respect. GjB ) along sectional chord to receive …
Gi,jB with
Schmitz
GE Wind - PCS

6. 2007 - PCS 2008 - PCS 2008 - PCS-Q 2008 - PCS-U
Extension of Lifting-Line (LL) to Lifting-Surface (LS) - PCS
Implementation :
Obtain Gi,jB from GjB using …
‘Parabolic Plate’ vorticity distribution on RANS mesh.
Treat each blade surface element in RANS zone as an ‘Elemental Horseshoe Vortex’ located on the blade’s sectional camber line.
Determine influence coefficients for the Lifting-Surface (LS).
(… at small computational expense)
Satisfy the following conditions …
Trailing Vortex
Bound Vortex
Schmitz
GE Wind - PCS

7. 2007 - PCS 2008 - PCS 2008 - PCS-Q 2008 - PCS-U
‘Quasi-Steady’ PCS PCS-Q
Motivation :
Current (steady) PCS limited to zero-yaw condition.
Extension of PCS as an efficient hybrid method for wind turbine blade analysis under yawed flow conditions.
Implementation :
Extend vortex model to account for yaw in vortex structure. Neglect ‘shed’ vorticity.
Solution methodology of a N-bladed wind turbine in yawed flow.
Converge to steady-state at each azimuth angle.
PCS-Q is suitable for small yaw angles (<15deg), yet not capable of handling ‘dynamic stall’ and/or ‘blunt trailing edge airfoils’.
Schmitz
GE Wind - PCS

8. ‘Quasi-Steady’ PCS - PCS-Q
PCS PCS PCS-Q PCS-U
‘Quasi-Steady’ PCS PCS-Q
y=0deg
Solve N blades
Vortex Model
BC – u,v,w
Converged to steady-state
y=y+Dy
1/N Revolutions completed.
CFX
Schmitz
GE Wind - PCS

9. 2007 - PCS 2008 - PCS 2008 - PCS-Q 2008 - PCS-U
‘Unsteady’ PCS PCS-U
Motivation :
PCS-Q limited to small yaw angles.
Extension of PCS-Q to a fully ‘unsteady’ hybrid method.
Implementation :
Extend vortex model of PCS-Q to account for ‘shed’ vorticity in vortex structure. (Perform subiterations on convection equation along helicoidal sheet)
Solution methodology of a N-bladed wind turbine in yawed flow.
Time-accurate solution of RANS/Vortex Model.
PCS-U is capable of handling ‘dynamic stall’ and/or ‘blunt trailing edge airfoils’ through a fully unsteady solution methodology.
Schmitz
GE Wind - PCS

10. ‘Unsteady’ PCS - PCS-U CFX y=0deg Solve N blades Vortex Model y=y+Dy
PCS PCS PCS-Q PCS-U
‘Unsteady’ PCS PCS-U
y=0deg
Solve N blades
Vortex Model
BC – u,v,w
Converged or # subiterations
y=y+Dy
# Revolutions until solution is periodic.
CFX
Converged
Schmitz
GE Wind - PCS

11. Research Proposal 2008
Extension of Lifting-Line (LL) to Lifting-Surface (LS) - PCS
Useful extension of steady PCS.
‘Quasi-Steady’ PCS PCS-Q
1st Step towards fully unsteady PCS, yet limited in capability.
‘Unsteady’ PCS PCS-U
Time-accurate extension of PCS-Q.
PCS-Q/PCS-U require extended implementation/validation time. Detailed model specifications are to be discussed.
Schmitz
GE Wind - PCS