Basics of Wind Meteorology - Dynamics of Horizontal Flow
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WIND ENERGY METEOROLOGY SS 2011 Detlev Heinemann ENERGY METEOROLOGY GROUP INSTITUTE OF PHYSICS OLDENBURG UNIVERSITY FORWIND – CENTER FOR WIND ENERGY RESEARCHMontag, 18. April 2011
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WIND ENERGY METEOROLOGY Contents I. Basic Meteorology - Dynamics of Horizontal Flow (forces, equation of motion, geostrophic wind, frictional effects, primitive equations, general circulation) - Atmospheric Boundary Layer (turbulence, vertical structure, special BL effects) II. Atmospheric Flow Modeling - Model classes: Linear, RANS, LES, .. - Application: Wind farm modeling III. Offshore-Specific Conditions IV. Resource Assessment & Wind Power Forecasting V. Wind Measurements & Statistics 2Montag, 18. April 2011
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WIND ENERGY METEOROLOGY INTRODUCTION Research related to wind energy meteorology at the Institute of Physics / ForWind 3Montag, 18. April 2011
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WIND ENERGY METEOROLOGY RESEARCH TOPICS Forecasting of wind power Offshore wind energy meteorology Numerical modelling of wind flow Turbulent characteristics of wind flow 4Montag, 18. April 2011
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WIND ENERGY METEOROLOGY WIND POWER FORECASTING Numerical Weather Prediction Wind speed, direction Spatial Refinement roughness, orography, thermal stability Forecasting local Wind farm power output power characteristics, shading losses Correction of systematic errors 28 13 5Montag, 18. April 2011
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WIND ENERGY METEOROLOGY WIND POWER FORECASTING PHYSICAL MODELS Input: - wind speed forecasts at hub height - roughness parameter / orography - thermal stability - wind farm geometry - power curve - produced power (measurement) for correction (model output statistics) 6Montag, 18. April 2011
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WIND ENERGY METEOROLOGY WIND POWER FORECASTING STATISTICAL MODELS Input: - wind speed forecasts at hub height - produced power (measurement) as training data (e.g., in a Neural Net) statistically derived wind power curve includes: - wind farm effects (wake effects) - regional/local situation (roughness, orography, etc.) - regular updates ensure adaptation to changes 7Montag, 18. April 2011
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WIND ENERGY METEOROLOGY Example: Vertical wind profile comparison of different theoretical vertical profiles with IEC standard large deviations of real profiles importance of atmospheric stability over the ocean 8Montag, 18. April 2011
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WIND ENERGY METEOROLOGY Example: Vertical wind profile comparison of different theoretical vertical profiles with IEC standard large deviations of real profiles importance of atmospheric stability over the ocean 8Montag, 18. April 2011
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WIND ENERGY METEOROLOGY Offshore Wind Energy 9Montag, 18. April 2011
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WIND ENERGY METEOROLOGY Offshore Wind Energy measurement platform FINO-1 test field Alpha Ventus 9Montag, 18. April 2011
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WIND ENERGY METEOROLOGY Numerical Modelling of Atmospheric Boundary Layer Flow Application: Offshore, complex terrain, thermally induced flow Tasks: - Parametrisation of local and small-scale effects (turbulence!) - coupling of differnet scales e.g: meso scale models and Large Eddy Simulation (LES) to couple the synoptic scale flow and wakes behind wind turbines important for: turbine design, resource assessment, forecasting 10Montag, 18. April 2011
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WIND ENERGY METEOROLOGY Offshore Wind Resources Modelling the atmospheric boundary layer wind field in offshore wind farms extension of knowledge of the marine atmopheric boundary layer with respect to wind energy applications vertical structure of wind fields over the ocean turbulence in offshore wind farms influence of wakes in large offshore wind farms on local wind fields modlling the influence of air sea interaction interaction of wind and waves reliable data for turbine design 11Montag, 18. April 2011
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WIND ENERGY METEOROLOGY OFFSHORE WIND RESOURCES Meso Scale Modelling high resolution up to 1 km Resource assesment and forecasting Offshore and coastal regions complex terrain extreme events on long time scales time scales from hours to decades no small-scale turbulence resolved 12Montag, 18. April 2011
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WIND ENERGY METEOROLOGY OFFSHORE WIND RESOURCES mean wind speed in m/s for the period 2004-2006. calculated with the mesoscale model WRF and data from the measurement platform FINO-1 13Montag, 18. April 2011
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WIND ENERGY METEOROLOGY WAKE MODELLING IN WIND FARMS Calculation of wind speed deficit in single wake with Ainslie model (Reynolds-Solver) ‣Superposition of multiple wakes (wind farm situation) ‣Influence of turbulence intensity on wake shape ‣Estimation of yearly power production based on the wind speed distribution ‣Application of Large Eddy Simulation (LES) 14Montag, 18. April 2011
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WIND ENERGY METEOROLOGY TURBINE DYNAMICS wind induced turbine dynamics are in time scale of sec and below knowledge of wind characteristics in time scale of sec necessary 15Montag, 18. April 2011
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WIND ENERGY METEOROLOGY Windböe - was ist dies? WIND GUSTS uτ := v(t + τ ) − v(t) ur := v(x + r) − v(x) 16Montag, 18. April 2011
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WIND ENERGY METEOROLOGY STATISTICS OF WIND GUSTS (Wind fluctuations) P(uτσ−1) τ=4s 1/hour ~106 1/100 years Boundary-Layer Meteorology 108 (2003) 17Montag, 18. April 2011
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WIND ENERGY METEOROLOGY WIND TURBINE POWER CURVES: data sheets vs. reality Wind turbine power output is result of nonlinear dynamic processes But: power curve P(v) is usually taken from simplified data sheets 18Montag, 18. April 2011
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WIND ENERGY METEOROLOGY WIND TURBINE POWER CURVES: data sheets vs. reality individual power curves according to the meteorological situation governing parameter: - wind direction, - atmospheric stability, - turbulence intensity aim: „learning“ power curves integration in forecasting schemes 19Montag, 18. April 2011
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WIND ENERGY METEOROLOGY I BASIC METEOROLOGY I-1 Dynamics of Horizontal Flow 20Montag, 18. April 2011
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WIND ENERGY METEOROLOGY Dynamics of Horizontal Flow Newton’s second law in each of the three directions in the If the coordinate system is accelerated, coordinate system, the acceleration a apparent forces are introduced to experienced by a body of mass m in compensate for this acceleration of the response to a resultant force ΣF is given coordinate system. by In a rotating frame of reference two different apparent forces are required: ‣ a centrifugal force that is experienced by all bodies, irrespective of their motion, This equation describes the motion in an ‣ and a Coriolis force that depends on inertial (i.e. nonaccelerating) frame of the relative velocity of the body in the reference. plane perpendicular to the axis of rotation (i.e., in the plane parallel to the equatorial plane). 21Montag, 18. April 2011
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WIND ENERGY METEOROLOGY Real Forces ‣ Gravitation ‣ Pressure gradient force ‣ Frictional force 22Montag, 18. April 2011
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WIND ENERGY METEOROLOGY Insert: Total & local time derivatives Atmospheric variables typically depend on both time and space: ψ = ψ(t,x,y,z) total time derivative d/dt rate of change following an air parcel as it moves along its three- dimensional trajectory through the atmosphere (Eulerian) local derivative ∂/∂t rate of change at a fixed point in rotating (x, y, z) space (Lagrangian) Related by chain rule: advection terms 23Montag, 18. April 2011
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WIND ENERGY METEOROLOGY Hydrostatic Equation & Geopotential (I) Atmopheric pressure at any height is due to the force per unit area exerted by the weight of the air above that + height. --> atmospheric pressure decreases with increasing height Net upward force due to the decrease in atmospheric pressure with height: -δp Wallace & Hobbs (2006) Net downward force due to gravi- tational force acting on the slab: gρδz If the net upward force on the slab equals the downward force: Atmosphere is in hydrostatic balance. 24Montag, 18. April 2011
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WIND ENERGY METEOROLOGY Hydrostatic Equation & Geopotential (II) For an atmosphere in hydrostatic balance, the balance of forces in the vertical requires that Note: δp is negative! or, with δz -> 0: Balance of gravitational force Hydrostatic Equation and vertical component of pressure gradient force Integration then yields: 25Montag, 18. April 2011
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WIND ENERGY METEOROLOGY Hydrostatic Equation & Geopotential (III) The geopotential at any point in the Earth’s atmosphere is defined as the work that must be done against the Earth’s gravitational field to raise a mass of 1 kg from sea level to that point. In other words, is the gravitational potential per unit mass. units of geopotential: Jkg-1 or m2s2. dΦ = gdz = - 1/ρ dp The geopotential Φ(z) at height z is thus given by with Φ(z=0) = 0 at sea level. 26Montag, 18. April 2011
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WIND ENERGY METEOROLOGY Hydrostatic Equation & Geopotential (IV) Definition of the geopotential height Z: g0 is the globally averaged acceleration due to gravity at the Earth’s surface (9.81ms-2). Geopotential height is often used as the vertical coordinate in atmospheric applications in which energy plays an important role (e.g., in large-scale atmospheric motions). The values of z and Z are almost the same in the lower atmosphere where g≅g0. 27Montag, 18. April 2011
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WIND ENERGY METEOROLOGY Pressure Gradient Force The pressure gradient force is directed down the horizontal pressure gradient ∇p from higher toward lower pressure. The x-component of the pressure gradient force acting on a fluid element: The horizontal components of the pressure gradient force and acceleration, respectively, then are: 28Montag, 18. April 2011
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WIND ENERGY METEOROLOGY Frictional Force frictional force (per unit mass): τ represents the vertical compo- Free atmosphere (above the nent of the shear stress (i.e., the boundary layer): rate of vertical exchange of hori- Frictional force << pressure zontal momentum) in units of gradient force, Coriolis force Nm-2 due to the presence of smal- Within the boundary layer: ler, unresolved scales of motion. Frictional force ~ other terms in the horizontal equation of motion 29Montag, 18. April 2011
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WIND ENERGY METEOROLOGY Shear Stress The shear stress σs at the Earth’s surface is in the opposing direction to the surface wind vector Vs. Approximation by the empirical relationship: where ρ density of the air CD dimensionless drag coefficient (varying with surface roughness and static stability Vs surface wind vector Vs (scalar) surface wind speed 30Montag, 18. April 2011
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WIND ENERGY METEOROLOGY Coriolis Force – Mathematical Description transformation of coordinates between the inertial reference frame and 1 the reference frame rotating with the angular velocity of the earth ... 2 … and applied to the wind velocity vector v=d‘r/dt … …and substituting (1) in (2) adds two new 3 components: the Coriolis acceleration (2nd term) plus the centripetal acceleration (3rd term) 4 The Coriolis force and acceleration in vector notation … 5 … and the horizontal component only. 32Montag, 18. April 2011
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WIND ENERGY METEOROLOGY Coriolis Force – Properties ‣ The Coriolis force is proportional the the object’s velocity, i.e., it is only acting on moving objects. ‣ The Coriolis force acts perpendicular to the direction of a moving object. ‣ In the northern hemisphere this results in a deflection of the horizontal wind vector to the right, in the southern hemisphere to the left. ‣ Consequently, the Coriolis force only affects the direction, not the velocity. No work on the object is performed. ‣ The Coriolis force vanishes at the equator and is maximum at the poles. Ω = (0, Ω cos φ , Ω sin φ) is the vector of the earth’s rotation with (|Ω| = 7.29 · 10−5 rad s−1). f = 2 Ω sin φ ( ~10 −4 s −1 in midlatitudes) is the Coriolis parameter. 33Montag, 18. April 2011
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WIND ENERGY METEOROLOGY Equation of Motion (I) Horizontal motions of fluid In component form: elements in the atmosphere are governed by the acting forces: Fh = Fp,h + Fc,h + Ffr,h The individual acceleration of fluid elements (air parcels) thus is: dvh/dt = ah = ap,h + ac,h + afr,h 1) Notes: 1) dvh/dt is the Lagrangian time derivative Then the horizontal equation of motion can be written: of the horizontal velocity component experienced by an air parcel as it moves about in the atmosphere. 2 ) Accelaration is due to a change in velocity of the motion as well as due to a change in direction of the motion. 34Montag, 18. April 2011
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WIND ENERGY METEOROLOGY Equation of Motion (II) The density dependence can be eliminated by substituting Fp = -1/ρ ∇p by Fp = - ∇Φ: Here, the horizontal wind field is defined on surfaces of constant pressure (∇p=0) instead of surfaces of constant geopotential (∇Φ=0). 35Montag, 18. April 2011
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WIND ENERGY METEOROLOGY The Geostrophic Wind: Example Low pressure system over Great Britain Δp = 32 hPa Δx = 600 km latitude: Φ = 54°N Coriolis parameter: f = 2 Ω sinΦ = 1.18 10-4 s -1 vg = - 1 / (1.2 kgm -3 x 1.18 10-4 s -1) x (32 hPa / 0.6 106 m) = 38 ms-1 38Montag, 18. April 2011
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WIND ENERGY METEOROLOGY Balances of the Horizontal Wind Field The geostrophic balance Balance of boundary layer flow The horizontal components of the The pressure gradient force Fp,h is balanced pressure gradient force Fp,h and the by the sum of the Coriolis force Fc,h and the Coriolis force Fc,h are balanced. vg is the frictional force Ffr. geostrophic wind. The stronger the frictional force Ffr, the larger the angle between vfr and vg and the more subgeostrophic the surface wind speed vfr. 39Montag, 18. April 2011
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WIND ENERGY METEOROLOGY The Primitive Equations (I) The horizontal equation of motion is part of a complete system of equations that governs the evolution of large-scale atmospheric motions – the socalled primitive equations. The other primitive equations relate to the vertical component of the motion and to the time rates of change of the thermodynamic variables p, ρ, and T. Equations containing time derivatives are prognostic equations. The remaining so-called diagnostic equations describe relationships between the dependent variables that apply at any instant in time. 40Montag, 18. April 2011
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WIND ENERGY METEOROLOGY The Primitive Equations (II) horizontal equation of motion hydrostatic/hypsometric equation thermodynamic energy equation (κ=0.286, ω=dp/dt) continuity equation Five equations in five dependent variables: u, v, ω, Φ, and T. The fields of diabatic heating J and friction F need to be parameterized. 41Montag, 18. April 2011
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