LES of wind turbine wakes - PDF Free Download

LES of wind turbine wakes... and an SD7003 Airfoil! Hamid Sarlak Fluid Mechanics Section, Department of Wind Energy, Technical University of Denmark, hsar@dtu.dk Wake Conference - 2017 Uppsala University Campus Cotland H. Sarlak (DTU Vindenergi) LES Characterisation: Wakes - Airfoils 1/1

Introduction Introduction SGS modeling in actuator-type models 1 SGS effects, Reynolds number effects, smearing function effects Presence of solid walls (?) Agenda: (1) Actuator line based simulations of two inline rotors (2) LES of SD7003 airfoil: Presence of solid walls (Very quickly!) 1 H Sarlak et al. Direct and Large-Eddy Simulation IX, 169-175, Sarlak et al, Renewable Energy 77, 386-399 H. Sarlak (DTU Vindenergi) LES Characterisation: Wakes - Airfoils 2 / 1

Part 1 - Wake simulations Part 2. SD7003 Airfoil Simulations H. Sarlak (DTU Vindenergi) LES Characterisation: Wakes - Airfoils 3 / 1

Role of SGS in WT Wakes H. Sarlak (DTU Vindenergi) LES Characterisation: Wakes - Airfoils 4 / 1

Governing Equations Filtered Navier-Stokes equations must be solved: v t + v v = p ρ + [(ν + ν sgs) v](+f b ), (1) where ν sgs = 0 ν sgs = c mo 1.5 q 0.25 ν sgs = c ms 1.5 q 0.25 ν sgs = c s 2 S ν sgs = c d 2 S ν sgs = c dmo 1+α d q ν sgs = c dmo 1+α d q c Ω 0.5 0.5 c S 1 α d 2 c 1 α d 2 c Ω α d S α d No model or implicit LES: NO Mix-ω: MO Mix-S: MS Smagorinsky: SM, Dynamic Smagorinsky: DS (GM) Dynamic MO: DMo Dynamic MS: DMs H. Sarlak (DTU Vindenergi) LES Characterisation: Wakes - Airfoils 5 / 1

Role of SGS in WT Wakes Tower modeled by body forces Wind Tunnel (L,W,H)= (12.7, 2.7, 2)m. D r = 894mm, U i = 10m/s. Dimensionless time step: dt = dt.u /R = 0.004 Omega = 127rad/s, Re r = 50, 000 and 500, 000 T I = 0.3% + uniform inflow 8.4 million FV cells, rotor resolution: 35 points along each blade Four SGS models tested: implicit LES (NO), Ta Phuoc s vorticity-based Mixed Scale (MO), Smagorisnly (SM), Dynamic Smagorinsly using Germano identity (GM), (plus selected cases (DMo) - (DMs)). FV solver, EllipSys3D, used for simulations. H. Sarlak (DTU Vindenergi) LES Characterisation: Wakes - Airfoils 6 / 1

Role of SGS in WT Wakes Figure: Vorticity snapshots for (a) NO, (b) MO, (c) DS, and (d) DMo models. H. Sarlak (DTU Vindenergi) LES Characterisation: Wakes - Airfoils 7 / 1

Role of SGS in WT Wakes Figure: Time averaged velocity contours H. Sarlak (DTU Vindenergi) LES Characterisation: Wakes - Airfoils 8 / 1

Role of SGS in WT Wakes Figure: Time averaged normal stress contours H. Sarlak (DTU Vindenergi) LES Characterisation: Wakes - Airfoils 9 / 1

Role of SGS in WT Wakes Renewable Energy 77, 386-399 Figure: Time averaged normalized eddy viscosity H. Sarlak (DTU Vindenergi) LES Characterisation: Wakes - Airfoils 10 / 1

Role of SGS in WT Wakes Renewable Energy 77, 386-399 H. Sarlak (DTU Vindenergi) LES Characterisation: Wakes - Airfoils 11 / 1

Role of SGS in WT Wakes Renewable Energy 77, 386-399 Figure: Kinetic energy ratios for MO and SM models H. Sarlak (DTU Vindenergi) LES Characterisation: Wakes - Airfoils 12 / 1

Role of SGS in WT Wakes SGS Effectiveness factor can be defined as: EF LES = k res k t = k sgs (+k num ) k res + k sgs + k num (2) k sgs = (ũ i u i ) 2 through explicit filtering k res = 0.5(u 2 rms) Two ways to calculate EF LES Linear least squares fit Ratio of accumulated values H. Sarlak (DTU Vindenergi) LES Characterisation: Wakes - Airfoils 13 / 1

Role of SGS in WT Wakes Renewable Energy 77, 386-399 MO, 35 ppb, EF bf = 2%, EF s = 6% DS, 35 ppb, EF bf = 1.6%, EF s = 4% MO, 26 ppb, EF bf = 1%, EF s = 14% H. Sarlak (DTU Vindenergi) LES Characterisation: Wakes - Airfoils 14 / 1

Summary - part 1 SGS models have a strong impact on the eddy viscosities, but not so much on the flow structure (esp. in the near wake), and no impact on Cp and Ct At Re = 10 6, different SGS models behave similarly [results not published] Higher SGS effects on coarser grids, yet decreasing grid resolution makes the predictions less accurate compared to measurements. Power and thrust coefficients predictions are identical for all models Question: Are the SGS models worth the extra computational time in this case? H. Sarlak (DTU Vindenergi) LES Characterisation: Wakes - Airfoils 15 / 1

Case 2. SGS effects on airfoil aerodynamics Part 2 - SD7003 simulations Part 2. SD7003 Airfoil Simulations H. Sarlak (DTU Vindenergi) LES Characterisation: Wakes - Airfoils 16 / 1

Case 2. SGS effects on airfoil aerodynamics Numerical setup - Results Dimensionless time step: dt = dt.u /R = 0.002 Simulations run for 80sec - averaging after 30sec NO, MO, MS and DS models chosen 1.2 1 0.8 0.6 -C p 0.4 0.2 0-0.2-0.4 NO MO MS DS NO MO MS DS Selig '96 R. Mikkelsen 2017-0.6-10 -5 0 5 10 15 20 x/c Figure: Lift polars for the SD7003 airfoil at Reynolds number 60,000. H. Sarlak (DTU Vindenergi) LES Characterisation: Wakes - Airfoils 17 / 1

Case 2. SGS effects on airfoil aerodynamics Figure: Effect of SGS modeling on the predicted streamwise turbulence intensity contours on the SD7003 airfoil for Reynolds number 10,000 obtained using various SGS models at α = 4 o. NO: implicit (no model) LES, MO: Mix-Ω, MS: Mix-S, DS: dynamic Smagorinsky, as in [?]. x-axis: x/c, y-axis: y/c. H. Sarlak (DTU Vindenergi) LES Characterisation: Wakes - Airfoils 18 / 1 SGS effects on turbulence intensities - Re = 10,000 NO MO MS DS

Case 2. SGS effects on airfoil aerodynamics Figure: Effect of SGS modeling on the predicted streamwise turbulence intensity contours on the SD7003 airfoil for Reynolds number 60,000 and angle of attack α = 4 o using various SGS models. NO: implicit (no model) LES, MO: Mix-Ω, MS: Mix-S, DS: dynamic Smagorinsky, as in [?]. x-axis: x/c, y-axis: y/c. H. Sarlak (DTU Vindenergi) LES Characterisation: Wakes - Airfoils 19 / 1 SGS effects on turbulence intensities - Re = 60,000 NO MO MS DS

Case 2. SGS effects on airfoil aerodynamics Effect of SGS modeling on pressure distribution over the airfoil 1.5 1 Implicit LES Mix-O Mix-S DynSmag Galbraith and Visbal 0.5 -C p 0-0.5-1 -1.5-0.2 0 0.2 0.4 0.6 0.8 1 x/c Figure: Pressure coefficient distribution over the SD7003 airfoil at Reynolds number 60,000 using α = 4 o. H. Sarlak (DTU Vindenergi) LES Characterisation: Wakes - Airfoils 20 / 1

Case 2. SGS effects on airfoil aerodynamics Comparison of SGS models for mean streamwise velocities 0.4 0.35 0.4 0.35 0.4 0.35 0.4 0.35 0.4 0.35 NO MO MS DS 0.3 0.3 0.3 0.3 0.3 0.25 0.25 0.25 0.25 0.25 y/c 0.2 y/c 0.2 y/c 0.2 y/c 0.2 y/c 0.2 0.15 0.15 0.15 0.15 0.15 0.1 0.1 0.1 0.1 0.1 0.05 0.05 0.05 0.05 0.05 0 0 0.5 1 x/c=0 (LE) 0-0.05 0 0.05 x/c=0.25 0-0.2 0 0.2 x/c=0.5 0-0.2 0 0.2 x/c=0.75 0-0.4-0.2 0 x/c=1 (TE) (a) H. Sarlak (DTU Vindenergi) LES Characterisation: Wakes - Airfoils 21 / 1

Case 2. SGS effects on airfoil aerodynamics Comparison of SGS models for mean TKEs 0.4 0.35 0.4 0.35 0.4 0.35 0.4 0.35 0.4 0.35 NO MO MS DS 0.3 0.3 0.3 0.3 0.3 0.25 0.25 0.25 0.25 0.25 y/c 0.2 y/c 0.2 y/c 0.2 y/c 0.2 y/c 0.2 0.15 0.15 0.15 0.15 0.15 0.1 0.1 0.1 0.1 0.1 0.05 0.05 0.05 0.05 0.05 0 0 2 4 x/c=0 (LE) 10-5 0 0 2 4 x/c=0.25 10-4 0 0 0.005 0.01 x/c=0.5 0 0 0.02 0.04 x/c=0.75 0 0 0.05 0.1 x/c=1 (TE) (b) H. Sarlak (DTU Vindenergi) LES Characterisation: Wakes - Airfoils 22 / 1

Conclusions Conclusions Increasing Reynolds number results in shorter separtion region - towards LE Unlike the ACL simulations, SGS does have significant impacts Increasing Reynolds number results in stronger SGS effects NO and MO models predict accurate results Generally DS model is found the least accurate. Yields large separation and over-prediction of lift All models - except DS - predict the lift (fairly) accurately Further analysis to be done H. Sarlak (DTU Vindenergi) LES Characterisation: Wakes - Airfoils 23 / 1

Conclusions Thank you for listening Hamid Sarlak hsar@dtu.dk And thanks to C. Meneveau (JHU), R. Mikkelsen (DTU), JN. Sørensen (DTU). H. Sarlak (DTU Vindenergi) LES Characterisation: Wakes - Airfoils 24 / 1