Parallelized Coupled Solver (PCS) Model Refinements & Extensions

Transcription

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

2 Outline 2007 Parallelized Coupled Navier-Stokes/Vortex-Panel Solver - PCS Nacelle Model, Latest version 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 2

3 Coupling of NS Solver with Vortex Method Navier-Stokes Biot-Savart Law (discrete) v = δ Γ 4π + Boundary of Navier-Stokes Zone _ Γ 4π Vortex Method Vortex Filament l r 3 r Bound Vortex l r 3 r Converged for Γ( y ) = v. ds = ω. da Bound Vortex L Γ( y ) n+ 1 Γ( y ) n 10 A 5 Vortex Filament δγ = Γ( y 1) Γ( y ) Schmitz GE Wind - PCS 3

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. Latest Version : GEWIND-PCS_2_1.tar (avail. to GE) New version of asymptotics for influence coefficients [Chattot, 2007]. Schmitz GE Wind - PCS 4

5 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 Γ B concentrated at LL. => Effect of LL position unclear. Spread LL (respect. Γ B ) along sectional chord to receive Γ i,b with i= ixb 1 Γ B i, = Γ B Schmitz GE Wind - PCS 5

6 Extension of Lifting-Line (LL) to Lifting-Surface (LS) - PCS Implementation : Obtain Γ i,b from Γ 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 Bound Vortex ixb i= 1 Γ B i, = Γ B δγ Trailing Vortex ixb ixb T B B B B = Γi, 1 + Γi, = Γ Γ 1 i= 1 i= 1 Schmitz GE Wind - PCS 6

7 Quasi-Steady PCS Motivation : Current (steady) PCS limited to zero-yaw condition. - PCS-Q 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 7

8 Quasi-Steady PCS - PCS-Q CFX ψ=0deg Solve N blades Γ B, N Vortex Model Converged to steady-state ψ=ψ+ ψ BC u,v,w 1/N Revolutions completed. Schmitz GE Wind - PCS 8

9 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 9

10 Unsteady PCS - PCS-U CFX ψ=0deg Solve N blades Γ B, N Vortex Model Γ B, N t + U Wind Γ B, N x = 0 Converged or # subiterations Converged BC u,v,w ψ=ψ+ ψ # Revolutions until solution is periodic. Schmitz GE Wind - PCS 10

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