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Enhancements and Refinements of the Parallelized Coupled Solver (PCS) for Wind Turbine Applications

This report details the advancements and refinements made to the Parallelized Coupled Solver (PCS), focusing on its application in modeling wind turbine dynamics. Key developments include the extension from lifting-line (LL) to lifting-surface (LS) methods, improving the accuracy of blade surface modeling. It introduces 'Quasi-Steady' (PCS-Q) and 'Unsteady' (PCS-U) modeling methodologies to better handle yawed flow conditions and dynamic stall effects. The updated methodologies facilitate more efficient simulations for N-bladed turbines, delivering enhanced performance metrics for engineering applications.

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Enhancements and Refinements of the Parallelized Coupled Solver (PCS) for Wind Turbine Applications

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

  3. Navier-Stokes Biot-Savart Law (discrete) Boundary of Navier-Stokes Zone Vortex Method Bound Vortex Converged for … Vortex Filament Coupling of NS Solver with Vortex Method 2007 - PCS 2008 - PCS 2008 - PCS-Q 2008 - PCS-U GE Wind - PCS

  4. 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]. GE Wind - PCS

  5. 2007 - PCS2008 - 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 GE Wind - PCS

  6. 2007 - PCS2008 - 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 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’. GE Wind - PCS

  8. y=0deg CFX Solve N blades Vortex Model Converged to steady-state BC – u,v,w y=y+Dy 1/N Revolutions completed. 2007 - PCS 2008 - PCS 2008 - PCS-Q 2008 - PCS-U ‘Quasi-Steady’ PCS - PCS-Q 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. GE Wind - PCS

  10. y=0deg CFX Solve N blades Vortex Model Converged or # subiterations Converged BC – u,v,w y=y+Dy # Revolutions until solution is periodic. 2007 - PCS 2008 - PCS 2008 - PCS-Q 2008 - PCS-U ‘Unsteady’ PCS - PCS-U 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. GE Wind - PCS

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