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Javier Sanz Rodrigo Daniel Cabezón Ignacio Martí (CENER) 19-03-2009

Parameterization of the atmospheric boundary layer for offshore wind resource assessment with a limited-length-scale k-ε model. Javier Sanz Rodrigo Daniel Cabezón Ignacio Martí (CENER) 19-03-2009. Introduction. Motivation. On ABL parameterization: mixing length vs k- ε modeling .

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Javier Sanz Rodrigo Daniel Cabezón Ignacio Martí (CENER) 19-03-2009

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  1. Parameterization of the atmospheric boundary layer for offshore wind resource assessment with a limited-length-scale k-ε model Javier Sanz Rodrigo Daniel Cabezón Ignacio Martí (CENER) 19-03-2009

  2. Introduction • Motivation. • On ABL parameterization: mixing length vs k-ε modeling. • Mixing length parameterizations. • Verification of ABL solver on the Leipzig wind profile. • Validation with FINO-1 test case. • Conclusions. • Outlook.

  3. Motivation • OFFSHORE wind resource assessment characterized by: • Lack of measurements. • Very low roughness  important influence of thermal effects in the structure of the ABL. • Surface similarity theory (log-laws) appear to be usable above the surface layer only in neutral and unstable conditions. • STABLE atmospheric conditions are very frequent in the offshore environment, producing: • Extreme wind speed and direction shear  non-uniform wind loading. • Very low turbulence  long lasting wind turbine wakes. • It is necessary to model the entire ABL to consider stable conditions: from surface to geostrophic wind levels.

  4. On ABL parameterization • Assumptions: • Horizontally homogeneous conditions: d/dx0, d/dy0 • Hydrostatic: • 1D Momentum and Energy equations: Coriolis parameter Geostrophic Wind: Kinematic momentum and heat fluxes

  5. On ABL parameterization • Closure problem: turbulent viscosity formulation • Two unknowns: turbulent kinetic energy (k) and mixing length (lm) • Transport equation for k: • k-lm: parameterization of mixing length from ABL scales (u*,L,etc) • k-ε: mixing length indirectly obtained from turbulent dissipation rate ε, assuming ld=lm ABL flows:

  6. Mixing Length Parameterizations (k-lm) • Prognostic equation for the mixing length based on ABL scales: • u*0, u*: Friction velocity (surface or local) • z0: Roughness length • L0, L: Monin-Obukhov (surface or local) • zi: Boundary layer depth • Blackadar (1997): • Apsley and Castro (1971): • Delage (1972): • Gryning (2007): • Mahrt and Vickers (2003): (Stable) (Stable)

  7. Mixing Length Parameterizations (k-lm) • Comparison: NEUTRAL ABL • Agreement with surface layer scaling only in the first 5% • Main differences in the upper part of the ABL • Blackadar=Apsley • Mahrt and Delage models agree • Gryning model produces the largest mixing length

  8. Mixing Length Parameterizations (k-lm) • Comparison: UNSTABLE ABL • Agreement with surface layer scaling up to the first 20-30% • Blackadar=Apsley=Delage (neutral formulation) • Mahrt model between ‘neutral’ and Gryning formulation • Gryning model produces the largest mixing length

  9. Mixing Length Parameterizations (k-lm) • Comparison: STABLE ABL • Agreement with surface layer scaling only in the first 3% • Blackadar with stability function • Apsley with local L has similar performance to Mahrt and Delage models • Gryning model produces the largest mixing length with deeper influence of lmax

  10. Two equation closure (k-ε) • Standard k-ε model: • Produces a mixing length proportional to the height above the ground, i.e it is only valid in the surface boundary layer. • Too deep boundary layer due to too much mixing (turbulent viscosity) in the upper part of the ABL • Modifications to ε production term: • Detering and Etling (1985): • Apsley and Castro (1997): • Weng and Taylor (2003):

  11. Verification of ABL solver: Leipzig profile • Leipzig wind profile: Neutral ABL (z0=0.3m, u*=0.65m, Ug=17.5m) • Standard k-ε model produces a very deep ABL • Mixing-length and limited-length-scale k-ε model perform well

  12. Validation: FINO-1 (North Sea)

  13. FINO-1: MeteorologicalInstrumentation

  14. Stability distribution • Very low roughness: z0~0.2mm • Predominant non-neutral conditions. • STABLE ABL at all relevant wind speeds.

  15. Data screening • Objective: Clustering of wind profiles for stability classification according to flux M-O length at 80m. • Filtering of registers: • Open sea • Without mast distortions: 190º-250º • Velocity > 3m/s • Stationary test

  16. Preliminary Results: k-ε (Apsley and Castro) • Fitting with u*,Ug,L and lmax. • Too deep boundary layers require very low lmax (<10m) to increase wind shear and reduce turbulence intensity  Local scaling?

  17. Mixing length parameterization • Mixing length Mahrt and Vickers (2003) parameterization. • Stability function depends on local M-O length. • Low dependency with height. • FINO1: best fitting with b=7

  18. Mixing length parameterization • Mixing length Mahrt and Vickers (2003) parameterization. • Measured mixing length • FINO1: best fitting with p=3.5

  19. Conclusions and Outlook • ABL modeling requires parameterization of mixing length. • Preliminary results in offshore conditions indicate the K-εmodel produces too deep boundary layers. • k-lm model with Mahrt and Vickers parameterization looks promising. • Outlook: • Benchmarking of mixing length parameterizations. • Meso-CFD coupling: Study mesoscale databases, where geostropic winds and boundary layer depth are readily available.

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