Parallelized Coupled Solver (PCS) Model Refinements & Extensions
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Transcript of Parallelized Coupled Solver (PCS) Model Refinements & Extensions
Schmitz GE Wind - PCS 1
Parallelized Coupled Solver (PCS)Parallelized Coupled Solver (PCS)Model Refinements & ExtensionsModel Refinements & Extensions
Sven Schmitz
University of California, DavisGE Wind November 29th, 2007 Greenville, SC
Schmitz GE Wind - PCS 2
OutlineOutline2007Parallelized Coupled Navier-Stokes/Vortex-Panel Solver - PCS
Nacelle Model, Latest version.
2008Extension of Lifting-Line (LL) to Lifting-Surface (LS) - PCS
Vortex-Lattice type method on the blade surface.
‘Quasi-Steady’ PCS - PCS-QQuasi-Steady RANS/Vortex Model, Solution methodology for N blades.
‘Unsteady’ PCS - PCS-UTime-accurate RANS/Vortex Model, Solution methodology for N blades.
Schmitz GE Wind - PCS 3
Navier-Stokes
Vortex Method
)()( 1 jjj yy Vortex Filament
Biot-Savart Law (discrete)
j
Bound
Vortex
j
j
Vortex
Filament
j
r
rl
r
rlv
3
_
3
4
4
Boundary of Navier-Stokes Zone
Converged for …
51 10)()(
njnj yy
j jL Aj dAdsvy ..)( Bound Vortex
Coupling of NS Solver with Vortex MethodCoupling of NS Solver with Vortex Method2007 - PCS 2008 - PCS 2008 - PCS-Q 2008 - PCS-U
Schmitz GE Wind - PCS 4
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.
2007 - PCS 2008 - PCS 2008 - PCS-Q 2008 - PCS-U
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 jB concentrated at LL. => Effect of LL position unclear.
• Spread LL (respect. jB ) along sectional chord to receive …
i,jB with
ixb
i
Bj
Bji
1,
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 i,jB from j
B 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 …
ixb
i
Bj
Bji
1,
Bj
Bj
ixb
i
Bji
ixb
i
Bji
Tj 1
1,
11,
Bound Vortex Trailing 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
2007 - PCS 2008 - PCS 2008 - PCS-Q 2008 - PCS-U
‘Quasi-Steady’ PCS - PCS-Q
=0deg
Solve N blades
Vortex Model
NBj
,
BC – u,v,w
Converged to steady-state
=+
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
2007 - PCS 2008 - PCS 2008 - PCS-Q 2008 - PCS-U
‘Unsteady’ PCS - PCS-U
=0deg
Solve N blades
Vortex Model
NBj
,
BC – u,v,w
Converged or # subiterations
=+
# Revolutions until solution is periodic.
CFX
0,,
xU
t
NBj
Wind
NBj
Converged
Schmitz GE Wind - PCS 11
Research Proposal 2008Research Proposal 2008
Extension of Lifting-Line (LL) to Lifting-Surface (LS) - PCSUseful extension of steady PCS.
‘Quasi-Steady’ PCS - PCS-Q1st Step towards fully unsteady PCS, yet limited in capability.
‘Unsteady’ PCS - PCS-UTime-accurate extension of PCS-Q.
PCS-Q/PCS-U require extended implementation/validation time. Detailed model specifications are to be discussed.