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.