The interplay of wakes, blockage, and topographic effects in stratified flow

Atmospheric Flow, Loads and pOwer for Wind energy The interplay of wakes, blockage, and topographic effects in stratified flow James Bleeg DNV Common practice: Terrain not included in the wind farm flow simulation 2 Elevation Freestream simulation freestream wind speeds Wind farm simulation wake and blockage loss Stretched and extruded Witch of Agnesi 3 Quasi-2D Hill Definition Distorted view True view Elevation [m] 4 Wind farm definition Stretched view •5.1 MW, D = 160m, HH = 115m •Turbines organized in rows. 34 turbines in each row. 2D hub-to-hub •Rows are either on the crest, 15 D downstream of the rest, and/or 15D upstream of the crest. 5 Wind farm definition Stretched view •5.1 MW, D = 160m, HH = 115m •Turbines organized in rows. 34 turbines in each row. 2D hub-to-hub •Rows are either on the crest, 15 D downstream of the rest, and/or 15D upstream of the crest. Conventionally neutral boundary layer simulated in steady-state RANS FLOW Atmospheric Flow, Loads and pOwer for Wind energy 6 •zi = 960 m or 640 m •𝜃 lapse rate in free atmosphere = 3.3 K/km •Maximum 𝜃 lapse rate in inversion layer = 10.0 K/km •Thickness of inversion layer = 0.7 km •Latitude = 43°; z0 = 0.028 m •All turbines operate on plateau of the CT curve FLOW Atmospheric Flow, Loads and pOwer for Wind energy 7 Pressure coefficient* relative to conditions on the hill crest • Favorable pressure gradient on the windward side • Adverse pressure gradient on the leeward side • Pressure variation is much less pronounced if buoyancy is neglected (same is true for velocity) *The pressure field balancing the Coriolis force is removed DNV © 23 MAY 2023 Two rows of turbines 8 FLOW Atmospheric Flow, Loads and pOwer for Wind energy 9 flat hill, windward hill, leeward Two rows of turbines, zi = 960 m Percent change in wind speed relative to freestream The hill has a substantial influence on wake recovery downstream of the array and blockage effects upstream Regular and narrow hill, zi = 960 m Loss = 8.97% CP, turb = 0.437 •Loss is higher in the narrow hill, where there is a sharper pressure rise downstream, causing deeper wakes and stronger blockage •Turbine power efficiency is also 2% lower •CT is lower for thin hill case (but stronger wake downstream) Loss = 6.94% CP, turb = 0.446 Hill Narrow Hill Loss = 15.61% CP, turb = 0.408 Loss = -1.80% CP, turb = 0.477 Leeward rows, hill and valley; zi = 640 m •Both the array efficiency and the turbine efficiency are approximately 17% higher in the valley case than in the hill case. •The wake in the valley case recovers rapidly. Valley Hill Discussion •Simulations indicate that terrain can influence energy production in ways that are not accounted for in current practices for estimating energy yield •Terrain influences both wake and blockage effects •Implications for both array and turbine efficiency •Trends amplified by stable stratification •Paper to be submitted for publication •More simulation results •Hopefully, relevant measurements •Physical explanation •Streamwise pressure variations •Gravity wave/Froude effects •More? FLOW Atmospheric Flow, Loads and pOwer for Wind energy 18 DNV © 23 MAY 2023DNV © 23 MAY 2023 www.dnv.com Thank you for listening 19 [email protected] Turbine interaction loss 20 The turbine interaction loss for any wind farm turbine is simply the difference between its production in isolation (𝑃𝐼) and its production in a wind farm (𝑃) Turbine interaction loss for the full wind farm is therefore simply: 𝐿𝑜𝑠𝑠 =σ𝑃𝐼−σ𝑃 σ𝑃𝐼 Turbine interaction loss factor (array efficiency): 𝜂𝐴=1−𝐿𝑜𝑠𝑠 = σ𝑃 σ𝑃𝐼 minus T10 T10 T07 T08 T09 T11 T12 T13 Power and thrust coefficients 𝐶𝑝=𝑃 1 2𝜌ത 𝑉∞ 3𝐴 𝐶𝑇=𝑇 1 2𝜌ഥ 𝑉∞ 2𝐴 ത 𝑉∞Is the average of the axial component of wind speed over the disk in the freestream simulation 2 2 Onshore Reference Turbine Stretched view •Ct and Cp curves from IEA 3.4 MW, 130 m rotor diameter turbine •Scaled up to 5.0 MW and 160 m to be more consistent with modern onshore turbines •Ct and Cp curves not changed •IEA 5.0-160 •Documents > general > WP3