CFD for Atmospheric Flow and Wind Engineering Wind energy applications using RANS VKI Lecture Series Niels N. Sørensen Department of Wind Energy · DTU 24-02-2015
DTU Wind Energy Department DTU - Excellence since 1829 Niels N. Sørensen, CFD for Atmospheric Flow and Wind EngineeringWind energy 2 of 51 Department of Wind Energy · DTU 24-02-2015
DTU Wind Energy Department DTU organization Niels N. Sørensen, CFD for Atmospheric Flow and Wind EngineeringWind energy 3 of 51 Department of Wind Energy · DTU 24-02-2015
DTU Wind Energy Department Wind Technology Expertise Niels N. Sørensen, CFD for Atmospheric Flow and Wind EngineeringWind energy 4 of 51 Department of Wind Energy · DTU 24-02-2015
DTU Wind Energy Department DTU Wind Energy Niels N. Sørensen, CFD for Atmospheric Flow and Wind EngineeringWind energy 5 of 51 Department of Wind Energy · DTU 24-02-2015
DTU Wind Energy Department Wind-power Meteorology � Atmospheric flow modeling � Methods for atmospheric model verification � Fundamental atmospheric processes Determination of external wind � conditions for siting and design of wind turbines Niels N. Sørensen, CFD for Atmospheric Flow and Wind EngineeringWind energy 6 of 51 Department of Wind Energy · DTU 24-02-2015
DTU Wind Energy Department Modeling of Turbulent Flow in Wind Farms Wake flow in a 5 × 5 turbine park computed by the Actuator Disk method Niels N. Sørensen, CFD for Atmospheric Flow and Wind EngineeringWind energy 7 of 51 Department of Wind Energy · DTU 24-02-2015
DTU Wind Energy Department Advanced Wind Turbine Aerodynamics -modeling and exp. validation Niels N. Sørensen, CFD for Atmospheric Flow and Wind EngineeringWind energy 8 of 51 Department of Wind Energy · DTU 24-02-2015
DTU Wind Energy Department Experiments, Validation and Test Niels N. Sørensen, CFD for Atmospheric Flow and Wind EngineeringWind energy 9 of 51 Department of Wind Energy · DTU 24-02-2015
Introduction CFD in wind energy siting Today we will focus on CFD applications within the area of wind turbine siting: � Pin-pointing of rough flow conditions � Determination of optimal turbine positions � Determination of Annual Energy Production (AEP) Advanced flow physics, thermal stratification and forested terrain � Niels N. Sørensen, CFD for Atmospheric Flow and Wind EngineeringWind energy 10 of 51 Department of Wind Energy · DTU 24-02-2015
What are we typically looking for Locating rough wind conditions The studies are typically connected to siting of wind turbines, and typically we are looking for sever flow conditions. The cases are typically ones where the linear models are insufficient. High levels of turbulence � High velocity gradients � High values of directional � shear � High flow inclination � Recirculating flow Niels N. Sørensen, CFD for Atmospheric Flow and Wind EngineeringWind energy 11 of 51 Department of Wind Energy · DTU 24-02-2015
What are we typically looking for Determination of optimal turbine positions To determine the optimal position of wind turbines based on the available wind resources is slightly more difficult. The previously discussed rough conditions must be avoided � The actual variation of the wind direction should be accounted for � through a statistical description The optimum depend on much more than just the wind resource � Niels N. Sørensen, CFD for Atmospheric Flow and Wind EngineeringWind energy 12 of 51 Department of Wind Energy · DTU 24-02-2015
What are we typically looking for Wind Resources Wind resources are more than just the CFD computations: The wind rose gives the � frequency of a given wind sector The Weibull distribution gives � the frequency of a given wind speed in a selected sector � k − 1 � � k � � U � U k f ( U ) = exp − A A A Niels N. Sørensen, CFD for Atmospheric Flow and Wind EngineeringWind energy 13 of 51 Department of Wind Energy · DTU 24-02-2015
What are we typically looking for Comparing computations with measurements When comparing computed results with measurements in the Atmospheric Boundary Layer (ABL), we are comparing with a time varying signal where the wind speed is changing along with the wind direction: Mast-7, ~15 [m] AGL � Typically, a CFD simulation would be 1 deg. a steady-state simulation for one 2 5 deg. specific flow direction 1 � In reality, the statistical distribution of the wind direction and a series of 0 computations are needed -1 It is impossible to control the � experimental conditions, and data will -2 be contaminated by unwanted effects -5 -4 -3 -2 -1 0 Niels N. Sørensen, CFD for Atmospheric Flow and Wind EngineeringWind energy 14 of 51 Department of Wind Energy · DTU 24-02-2015
Atmospheric flows Solving flow in the atmosphere There are a several features characterizing flow in natural terrain, and below the most prominent are listed � The atmosphere is to a good approximation incompressible ( M < 0 . 1) � High Reynolds number flows (turbulence) � A large span of geometrical scales are involved (0-50 km) Complex surface geometries � The wall boundary is nearly always rough � Thermal stratification � Earth rotation, Coriolis effects � Forested terrain � Niels N. Sørensen, CFD for Atmospheric Flow and Wind EngineeringWind energy 15 of 51 Department of Wind Energy · DTU 24-02-2015
Atmospheric flows The Nature of turbulence Irregularity � Turbulence is irregular or random. � Diffusivity � Turbulent flow causes rapid mixing, increases heat transfer and flow � resistance. These are the most important aspect of turbulence from a engineering point of view. Three-dimensional vorticity fluctuations (rotational) � � Turbulence is rotational, and vorticity dynamics plays an important role. Energy is transferred from large to small scale by the interaction of vortices’s. Dissipation � � Turbulent flow are always dissipative. Viscous shear stresses perform deformation work which increases the internal energy of the fluid at the expenses of kinetic energy of turbulence. � Continuum Even though they are small the smallest scale of turbulence are ordinary far � lager than any molecular length scale � Flow feature Turbulence is a feature of the flow not of the fluid. � Niels N. Sørensen, CFD for Atmospheric Flow and Wind EngineeringWind energy 16 of 51 Department of Wind Energy · DTU 24-02-2015
Atmospheric flows The Scales of Turbulent Flows Modeling a channel flow at low Reynolds number: N 3 N 3 N 3 Re H Re τ DNS LES RANS 2 . 1 × 10 9 1 . 0 8 1 . 0 × 10 4 230 . 000 4 . 650 Where: Re τ = u τ H / 2 . ν � 0 . 4 � N 3 DNS ≥ Re 2 . 25 ,and N 3 Re 2 . 25 LES ≥ τ τ Re 0 . 25 τ Using approximate boundary conditions, e.g. in the form of log-law conditions, these numbers can be lowered. Niels N. Sørensen, CFD for Atmospheric Flow and Wind EngineeringWind energy 17 of 51 Department of Wind Energy · DTU 24-02-2015
Governing equations Reynolds Averaged Navier-Stokes Reynolds averaging of the Navier-Stokes equation, splitting the velocities in the mean and the fluctuating component � t + T 1 u i ( � r , t ) = U i ( � r ) + u ′ ( � r , t ) , where U i ( � u i ( � r ) = lim r , t ) dt T T →∞ t Inserting the Reynolds decomposed velocity in the Navier-Stokes and continuity equations Perform time averaging of the equations. The equations are in principle time independent, or steady state. Niels N. Sørensen, CFD for Atmospheric Flow and Wind EngineeringWind energy 18 of 51 Department of Wind Energy · DTU 24-02-2015
Governing equations The Reynolds Averaged Navier-Stokes The flow equations and additional equations have the following form: Continuity equation: ∂ t ( ρ ) + ∂ ∂ ( ρ U j ) = 0 ∂ x j Momentum equations: � � ∂ U i + ∂ U j �� ∂ t ( ρ U i ) + ∂ ∂ ) − ∂ + ∂ P U i U j + u ′ i u ′ ( ρ � � µ = S v , j ∂ x j ∂ x j ∂ x j ∂ x i ∂ x i Auxiliary equations: ∂ t ( ρφ ) + ∂ ∂ j φ ′ )) − ∂ � µ ∂φ � ( ρ ( U j φ + u ′ = S φ ∂ x j ∂ x j ∂ x i Niels N. Sørensen, CFD for Atmospheric Flow and Wind EngineeringWind energy 19 of 51 Department of Wind Energy · DTU 24-02-2015
Governing equations Boussinesq Eddy Viscosity Approximation Reynolds Stresses: � ∂ U i + ∂ U j � j = 2 ρ u ′ i u ′ 3 ρ k δ ij − µ t , ∂ x j ∂ x i Scalar flux: � ∂φ i φ ′ = − µ t � ρ u ′ . σ φ ∂ x i Pressure: ∂ ˆ P = ∂ P − ρ g . ∂ x i ∂ x i Niels N. Sørensen, CFD for Atmospheric Flow and Wind EngineeringWind energy 20 of 51 Department of Wind Energy · DTU 24-02-2015
Governing equations Closing the Equations To close the flow equations we need an expression for the µ t , this is typically handled by the turbulence model: For atmospheric flow in equilibrium over flat terrain we have a very simple model: µ t = ρκ u τ z . Typically a two equation model will be used for more complex cases, e.g.. the k − ǫ or the k − ω model µ t = ρ C µ k 2 ǫ . The two additional transport equations has a form similar to the previous stated general transport equation, and mainly the deviation between the models are in the source terms on the RHS. Niels N. Sørensen, CFD for Atmospheric Flow and Wind EngineeringWind energy 21 of 51 Department of Wind Energy · DTU 24-02-2015
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