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

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

Coupling of NS Solver with Vortex Method 2007 - PCS 2008 - PCS 2008 - PCS-Q 2008 - 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

No feedback from GE so far. 2007 - PCS 2008 - PCS 2008 - PCS-Q 2008 - 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

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

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

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

‘Quasi-Steady’ PCS - PCS-Q 2007 - PCS 2008 - PCS 2008 - PCS-Q 2008 - 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

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

‘Unsteady’ PCS - PCS-U CFX y=0deg Solve N blades Vortex Model y=y+Dy 2007 - PCS 2008 - PCS 2008 - PCS-Q 2008 - 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

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