Sin ttulo de diapositiva

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SENSITIVITY ANALYSIS ON TURBULENCE MODELS FOR THE
ABL IN COMPLEX TERRAIN
Daniel Cabezón CENER, National Renewable Energy
Centre (Spain) Wind Energy Department
dcabezon_at_cener.com
Javier Sanz, Jeroen Van Beeck Von Karman
Institute for Fluid Dynamics (Belgium) Environment
al and Applied Fluid Dynamics sanz_at_vki.ac.be,
vanbeeck_at_vki.ac.be
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INDEX

• Introduction
• Turbulence modelling of the ABL
• 2.1 Standard k-e model (Default / modified)
• 2.2 RNG k-e model
• 2.3 Realizable k-e model
• Alaiz test site
• 3.1 General description
• 3.2 Data for validation
• Simulation features
• 4.1 Computational domain. Set up
• 4.2 Wall functions
• Results
• 5.1 Mean flow
• 5.2 Turbulent characteristics
• Conclusions

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1. INTRODUCTION

• Target IEC classification of wind turbine
  locations on wind speed and turbulence intensity
  on complex terrain
• Linear software uncertainty increase in power
  production and fatigue loading at those sites
• Development, adaptation and assessment of CFD
  codes for solving the Atmospheric Boundary Layer
  (ABL)
• Key issue Selection of the appropiate
  turbulence closure scheme
• We need
• Solve ABL for rugged complex terrain sites
• Microscale resolution (10m-20m)
• Reasonable computing time
• Robust and efficient model

ISOTROPIC K-e MODEL
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1. INTRODUCTION

• Important attempt to adapt k-e model to moderate
  terrain sites
• ASKERVEIN hill test case extensively
  instrumented site
• It allows modellers to analyze parameters when
  simulating the ABL
• Accurate fit upstream, some discrepancies at the
  hilltop and downstream
• No similar experiments has been made on highly
  complex terrain
• This analysis
• Revises some Askervein strategies (2 equations
  k-e closure) for non-complex terrain
• Checks how they work in a more complex terrain
  site
• Configuration universal or site dependent?

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2. TURBULENCE MODELLING OF THE ABL
2.1 Standard k-e model

• Original model. Launder Spalding (1972)
• Reasonable accuracy in the freestream
• Approximation of wall functions for the near
  wall region

Turbulent kinetic energy K
Turbulent dissipation rate e
Production of turbulence
DEFAULT constants (Launder Spalding)
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2. TURBULENCE MODELLING OF THE ABL

• Modified constants I.

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2. TURBULENCE MODELLING OF THE ABL

• 2.2 RNG k-e model
• Renormalization group theory (RNG)
• Additional term in e equation related to rapidly
  strained flows at areas of strong curvature

Turbulent dissipation rate e
If decreases, the production of e
increases locally to counteract the
over-production of k (Gk)
If the mean strain tensor Sij increases in areas
of strong curvature, RNG decreases
Inverse effective Prandtl number
for high-Reynolds numbers
RNG constants
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2. TURBULENCE MODELLING OF THE ABL

• 2.3 Realizable k-e model
• New formulation for the turbulent viscosity
  ratio involving a variable C?

where

• A new transport equation for the turbulent
  dissipation rate e

Upper value of (associated to the
generation of e) limited by the mean strain tensor
Realizable constants
where
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3. ALAIZ TEST SITE

• 3.1 General Description
• 4 kilometers long, complex terrain hill site
  (north RIX 16)
• Prevailing wind direction north
• Roughness description
• Clear terrain outside the hill z00.03
• Forest inside the hill z00.4

• 3.2 Wind data for validation
• 3 meteorological masts Alaiz_2 (20/40m),
  Alaiz_3 (30/40/55m), Alaiz_6 (20/40m)
• 10 min-average periods, 3 sec sampling rate
• Wind speed
• Wind direction
• Standard deviation of wind speed
• Measurement campaign 1 year
• Only considering data from north (20º sector)

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4. SIMULATION FEATURES

• 4.1 COMPUTATIONAL DOMAIN
• Structured mesh, 3.65 Million Hexas
• Dimensions 9x9 km2
• Horizontal resolution 20x20 m on site
• First cell height 0.5 m

• Set up
• Incompressible air, steady-state, RANS
• Thermal effects neglected
• Discretization 2nd order upwind
• Boundary conditions
• North inflow boundary Velocity inlet
• Southern outflow boundary Pressure outlet
• Eastern/western/top Symmetry
• Terrain surface Wall

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4. SIMULATION FEATURES

• 4.2 Wall functions Link between the first cell
  in the vertical direction and the wall ?
  Roughness modeling
• Fluent Law-of-the-wall modified for roughness

Smooth wall
Roughness
Blocken et al. (2007)
ks Roughness Reynolds Number (Dimensionless
roughness height)
Fluent roughness parameters Cs, ks
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4. SIMULATION FEATURES

• Compatibility with ABL log-law

Fluent roughness parameters Cs, ks ks Physical
roughness height Cs Roughness constant (0ltCslt1,
Cs0.5) z0 Aerodynamics roughness length z1
Height of first cell
Compatibility between ABL log-law and wall
function if
Blocken et al. (2007)

• z00.03m ? ks0.6m
• z00.4m ? ks7.8m

Requirement z1gtks
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4. SIMULATION FEATURES

• Inlet conditions ABL log-law has to be
  compatible with the wall conditions, defined by
  ks and Cs parameters. Otherwise a roughness
  change will be introduced and the inlet
  conditions progressively lost

Contours of vertical velocity
Internal boundary layer
Inlet
Outlet

• Simulation in an empty domain
• The outlet roughness depends on the height of the
  wall-adjacent cell (z1) and the roughness
  constant Cs.

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5. RESULTS
Horizontal evolution LINE A
NO DATA AVAILABLE
LINE A Topographical profile (N-S) 40m a.g.l.
aligned to Alaiz3
Fractional Speed Ratio

• Mean flow

Vertical evolution
DATA AVAILABLE
Z (a.s.l.)
Speed-up Ratio
HORIZONTAL DISTANCE
Horizontal evolution LINE A
NO DATA AVAILABLE
Normalized turbulent kinetic energy K
Turbulent characteristics
Vertical evolution
DATA AVAILABLE
Turbulent intensity
Numerical cross-validation in wind speed /
turbulence intensity
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5. RESULTS

• 5.1 Mean flow. Horizontal evolution of FSR - LINE
  A

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5. RESULTS
5.1 Mean flow. Vertical evolution of speed-up
ratios

• Vertical profiles in the surface layer (0-100m)
• Experimental values 10 min average Standard
  Deviation s

• Vertical speed-up profiles overestimaded
• Minimum mae for STD_LS, STD_PNF and STD_RH
• Modelled roughness lt Real roughness

CROSS-VALIDATION (WIND SPEED)
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5. RESULTS
5.2 Turbulent characteristics. Horizontal
evolution of K - LINE A
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5. RESULTS
5.2 Turbulent characteristics. Vertical Turbulent
Intensity evolution

• Vertical profiles in the surface layer (0-100m)
• Experimental values 10 min average

Z (m)
Z (m)
Z (m)
TI_Alaiz2
TI_Alaiz3
TI_Alaiz6

• Vertical TI profiles underestimated
• Minimum mae for STD_PNF and STD_RH
• Modelled roughness lt Real roughness

CROSS-VALIDATION (TURBULENCE INTENSITY)
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6. CONCLUSIONS

• TASK A sensitivity analysis and assessment of
  isotropic ke turbulence models through field data
  from Alaiz hill site.
• Standard Panofsky and Standard Richards Hoxey
  set of constants provide globally better results
  at the hilltop for this configuration of the
  model.
• The results concern the assessment on the
  hilltop of Alaiz hill site and could differ on
  the lee side where unsteady flow patterns usually
  exist.

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6. CONCLUSIONS

• Further work
• Optimize the code in the near wall region
  adapting the present wall funtions especially for
  highly roughed areas.
• Undertake a sensitivity analysis on the inlet
  profiles assessing its impact on the results
• Extend the measurement campaign at other
  locations with Lidar/sonic anemometry
• Test anisotropic models like RSM (Reynolds Stress
  Model). Compare error decrease to computing time
  increase
• Test modifying the default configuration of RNG
  and Realizable models.
• Investigate RANS-LES hybrid solutions. Compare
  error decrease to computing time increase

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