Papers by Richard J A M Stevens
A comparative experimental and numerical study of rotating Rayleigh-Bénard convection in a cylindrical cell
APS, Nov 1, 2019
Bulletin of the American Physical Society, Nov 22, 2020
The Fluid Physics Modeling Challenges of Wind Plants 1 RICHARD STEVENS, University of Twente -The... more The Fluid Physics Modeling Challenges of Wind Plants 1 RICHARD STEVENS, University of Twente -The performance of large wind farms depends on the development of turbulent wind turbine wakes and the interaction between these wakes. Turbulence also plays a crucial role in transporting kinetic energy from the large-scale geostrophic winds in the atmospheric boundary layer towards heights where wind farms can harvest this energy. High-resolution large eddy simulations (LES) are ideally suited to understand these flow phenomena. Much has been learned from wind farm simulations, which initially focused on 'idealized' situations. Nowadays, the community increasingly focuses on modeling more complex situations, such as the effect of complex terrain and different atmospheric stability conditions. As wind farms become larger, the need to improve their design and develop control strategies to mitigate wake effects increases. However, due to the large separation of length scales and the number of cases, it is unfeasible to use LES for wind farm design. Therefore, LES are used to further develop computationally more tractable modeling approaches ranging from Reynolds Average Navier Stokes (RANS) models to analytical modeling approaches. With the increasing size of wind turbines and wind farms, an emerging challenge will be to also account for mesoscale flow phenomena.
Renewable Energy, May 1, 2022
High-fidelity large-eddy simulations are suitable to obtain insight into the complex flow dynamic... more High-fidelity large-eddy simulations are suitable to obtain insight into the complex flow dynamics in extended wind farms. In order to better understand these flow dynamics, we use dynamic mode decomposition (DMD) to analyze and reconstruct the flow field in large-scale numerically simulated wind farms by large-eddy simulations (LES). Different wind farm layouts are considered, and we find that a combination of horizontal and vertical staggering leads to improved wind farm performance compared to traditional horizontal staggering. We analyze the wind farm flows using the amplitude selection (AP) and sparsity-promoting (SP method) DMD approach. We find that the AP method tends to select modes with a small length scale and a high frequency, while the SP method selects large coherent structures with low frequency. The latter are somewhat reminiscent of modes obtained using proper orthogonal decomposition (POD). We find that a relatively limited number of SP-DMD modes is sufficient to accurately reconstruct the flow field in the entire wind farm, whereas the AP-DMD method requires more modes to achieve an accurate reconstruction. Thus, the SP-DMD method has a smaller performance loss compared to the AP-DMD method in terms of the reconstruction of the flow field.
European Journal of Mechanics - B/Fluids
Understanding how blockage influences large wind farms is essential as the first row produces the... more Understanding how blockage influences large wind farms is essential as the first row produces the most energy and is often used as a reference for the subsequent rows. We use large-eddy simulations to investigate wind farm blockage by comparing a stand-alone turbine, an infinite row of turbines, and a wind farm with eight rows. We find that the blockage effect for dense turbine arrays is highly dependent on the non-dimensional turbine spacing. Spanwise neighboring turbines appear to benefit from deflected flow, while close downstream turbines enhance flow over the wind farm, reducing productivity at the front. In agreement with the uniform inflow wind tunnel measurements by Segalini and Dahlberg (2020), we find that the effect of downstream turbines follows a universal trend as a function of the average inter-turbine spacing when the performance of the first wind farm row is normalized with the corresponding isolated row case. However, we also demonstrate that the wind farm layout strongly affects blockage as the results do not follow a universal trend when normalized with the performance of a stand-alone turbine.
28th AIAA/CEAS Aeroacoustics 2022 Conference, Jun 13, 2022
A good understanding of wind turbine noise propagation is relevant to better measure the impact o... more A good understanding of wind turbine noise propagation is relevant to better measure the impact of turbines on the environment. In this study, we developed numerical simulations to study the impact of a 2D hill on the sound propagation for a turbine in non flat terrain. The simulations employed a propagation model derived from the linearized Euler equations, solved in a moving frame following the wavefront. The wind turbine noise was modeled using a point source approach. The flow structure in the atmospheric boundary layer and the wind turbine wake were obtained from large-eddy simulations. We find that the wind turbine wake acts as a waveguide that focuses sound propagation towards the ground. This effect is most pronounced for the flat terrain case and when the turbine is placed on the hill. The sound attenuation is more localized and closer to the turbine when the wind turbine is placed on the hilltop than in the flat case. As the wind speed increases, the sound focusing is observed closer to the turbine. For a turbine placed in front of the hill, the sound propagation is mainly determined by the flow over the hill. This demonstrates that terrain topography can have surprising effects on wind turbine noise propagation.
Bulletin of the American Physical Society, Nov 18, 2012
i.e. the convection of a fluid enclosed between two plates that is driven by a temperature gradie... more i.e. the convection of a fluid enclosed between two plates that is driven by a temperature gradient, is the idealized setup of a phenomenon ubiquitous in nature and technical applications. Of special interest for this system are the statistics of turbulent temperature fluctuations, which we are investigating for a fluid enclosed in a cylindrical vessel. To this end, we derive an exact evolution equation for the probability density function (PDF) of temperature from first principles. Appearing unclosed terms are expressed as conditional averages of velocities and heat diffusion, which are estimated from direct numerical simulations. Our theoretical framework allows to connect the statistical quantities to the dynamics of Rayleigh-Bénard convection, giving deeper insights into the temperature statistics and transport mechanisms in different regions of the fluid volume, i.e. in the boundary layers, the bulk and the sidewall regions. Furthermore, a minimalistic model of the conditional averages that still incorporates the core features is developed by physical reasoning to highlight the overall character of the heat transport processes.
Bulletin of the American Physical Society, Nov 21, 2010
Discontinuous transitions between different turbulent states are rare, since turbulence is expect... more Discontinuous transitions between different turbulent states are rare, since turbulence is expected to sample all of phase space over wide parameter ranges. However, it was found 2 in turbulent rotating thermal convection of a fluid between two parallel horizontal plates that the Nusselt number Nu is strongly enhanced when the inverse Rossby number 1/Ro, which is proportional to the rotation rate Ω, exceeds a critical value 1/Ro c. The enhancement is due to the formation of Ekman vorticies that extract additional fluid out of the thermal boundary layers at the sample top and bottom. As found in experiments and numerical simulations in cylindrical systems, 1/Ro c is proportional to 1/Γ where Γ ≡ D/L (with D being the cell diameter and L the cell height). We present a Ginzburg-Landau like model that explains the existence of a bifurcation at finite 1/Ro c as a finite-size effect, and yields the proportionality between 1/Ro c and 1/Γ.
Bulletin of the American Physical Society, Nov 24, 2009
heat transfer in Rayleigh-Bénard convection (RBC) is determined by the Rayleigh number Ra and the... more heat transfer in Rayleigh-Bénard convection (RBC) is determined by the Rayleigh number Ra and the Prandtl number P r 2. In case of rotation about the vertical axis the third dimensionless control parameter is the Rossby number Ro. Here we present numerical data for the heat transfer in rotating RBC for Ra = 10 8 as a function of P r and Ro. When Ro is fixed the heat transfer enhancement with respect to the non-rotating value as function of P r shows a maximum. This maximum is due to the reduced efficiency of Ekman pumping when P r becomes too small or too large. When P r becomes too small the heat that is carried by the vertical vortices spreads out in the middle of the cell, i.e. it makes Ekman pumping less efficient, due to the larger thermal diffusivity 3. For higher P r the thermal boundary layers (BLs) are much thinner than the kinetic BLs and therefore the Ekman vortices do not reach the thermal BL. This means that the fluid that is sucked into the vertical vortices is colder than for lower P r and this limits the efficiency of Ekman pumping at high P r.
Heat transport in turbulent rotating Rayleigh-Bénard convection
No abstract
Journal of Fluid Mechanics
The wind energy industry relies on computationally efficient engineering-type models to design wi... more The wind energy industry relies on computationally efficient engineering-type models to design wind farms. Typically these models do not account for the effect of atmospheric stratification in either the boundary layer or the free atmosphere. This study proposes a new analytical model for fully developed wind-turbine arrays in conventionally neutral atmospheric boundary layers frequently encountered in nature. The model captures the effect of the free-atmosphere stratification, Coriolis force, wind farm layout and turbine operating condition on the wind farm performance. The model is developed based on the physical insight derived from large-eddy simulations. We demonstrate that the geostrophic drag law (GDL) for flow over flat terrain can be extended to flow over fully developed wind farm arrays. The presence of a vast wind farm significantly increases the wind farm friction velocity compared with flow over flat terrain, which is modelled by updated coefficients in the GDL. The dev...
Bulletin of the American Physical Society, 2017
Submitted for the DFD17 Meeting of The American Physical Society Large eddy simulation study on t... more Submitted for the DFD17 Meeting of The American Physical Society Large eddy simulation study on the effect of vertical staggering in large-scale wind farms 1 RICHARD STEVENS, MARK ARENDSHORST, MENGQI ZHANG, University of Twente-We present results from large eddy simulations (LES) of extended aligned windfarms. We vary the hub height of consecutive downstream turbine rows in order to create vertically staggered windfarms and we study the effect of streamwise turbine spacing, turbine rotor diameter, and the hub height difference between consecutive rows on the average turbine power output. The results show that the production of the second turbine row increases when the first turbine row is lower than the second row. Consequently, we find that the average turbine power output increases significantly in the entrance region of the windfarm. However, we find that the relative benefit of vertical staggering, compared to the non-staggered case, decreases further inside the windfarm. The reason is that the vertical kinetic energy transfer, which brings high velocity fluid from above the windfarm towards the hub-height plane, does not significantly increase by vertically staggering wind turbines. This limits the potential benefit of vertical staggering in extended windfarms. We find, for a fixed hub height difference between consecutive rows, that vertical staggering is more beneficial for the average windfarm power output when the streamwise turbine spacing and turbine diameter are smaller.
Bulletin of the American Physical Society, 2015
University-We present results from large eddy simulations (LES) of wind farms consisting of tens ... more University-We present results from large eddy simulations (LES) of wind farms consisting of tens to hundreds of turbines with respective streamwise and spanwise spacings approaching 35 and 12 turbine diameters. Even in staggered farms where the distance between consecutive turbines in the flow direction is more than 50 turbine diameters, we observe visible wake effects. In aligned farms, the performance of the turbines in the fully developed regime, where the power output as function of the downstream position becomes constant, is shown to primarily depend on the streamwise distance between consecutive turbine rows. However, for other layouts the power production in the fully developed regime mainly depends on the geometrical mean turbine spacing (inverse turbine density). These findings agree very well with predictions from our recently developed coupled wake boundary layer (CWBL) model, which introduces a two way coupling between the wake (Jensen) and top-down model approaches (Stevens et al. JRSE 7, 023115, 2015). To further validate the CWBL model we apply it to the problem of determining the optimal wind turbine thrust coefficient for power maximization over the entire farm. The CWBL model predictions agree very well with recent LES results (Goit & Meyers, JFM 768, 5-50, 2015).
Computers & Fluids, 2020
Modeling the effect of complex terrain on high Reynolds number flows is important to improve our ... more Modeling the effect of complex terrain on high Reynolds number flows is important to improve our understanding of flow dynamics in wind farms and the dispersion of pollen and pollutants in hilly or mountainous terrain as well as the flow in urban areas. Unfortunately, simulating high Reynolds number flows over complex terrain is still a big challenge. Therefore, we present a simplified version of the wall modeled immersed boundary method by Chester et al. (J. Comput. Phys. 2007; 225: 427-448). By preventing the extrapolation and iteration steps in the original method, the proposed approach is much easier to implement and more computationally efficient. Furthermore, the proposed method only requires information that is available to each processor and thus is much more efficient for simulations performed on a large number of cores. These are crucial considerations for algorithms that are deployed on modern supercomputers and will allow much higher grid resolutions to be considered. We validate our method against wind tunnel measurements for turbulent flows over wall-mounted cubes, a two-dimensional ridge, and a three-dimensional hill. We find very good agreement between the simulation results and the measurement data, which shows this method is suitable to model high Reynolds number flows over complex terrain.
Renewable Energy, 2016
Validation of four LES and a vortex model against stereo-PIV measurements in the near wake of an ... more Validation of four LES and a vortex model against stereo-PIV measurements in the near wake of an actuator disc and a wind turbine In this paper we report the results of a workshop organised by the Delft University of Technology in 2014, aiming at the comparison between different state-of-the-art numerical models for the simulation of wind turbine wakes. The chosen benchmark case is a wind tunnel measurement, where stereoscopic Particle Image Velocimetry was employed to obtain the velocity field and turbulence statistics in the near wake of a two-bladed wind turbine model and of a porous disc, which mimics the numerical actuator used in the simulations. Researchers have been invited to simulate the experimental case based on the disc drag coefficient and the inflow characteristics. Four large eddy simulation (LES) codes from different institutions and a vortex model are part of the comparison. The purpose of this benchmark is to validate the numerical predictions of the flow field statistics in the near wake of an actuator disc, a case that is highly relevant for full wind farm applications. The comparison has shown that, despite its extreme simplicity, the vortex model is capable of reproducing the wake expansion and the centre line velocity with very high accuracy. Also all tested LES models are able to predict the velocity deficit in the very near wake well, contrary to what was expected from previous literature. However, the resolved velocity fluctuations in the LES are below the experimentally measured values.
Submitted for the DFD12 Meeting of The American Physical Society Collective phenomena in large-ed... more Submitted for the DFD12 Meeting of The American Physical Society Collective phenomena in large-eddy simulations of extended wind farms 1 RICHARD STEVENS, CHARLES MENEVEAU, Johns Hopkins University-A major issue with respect to the incorporation of large wind farms in power grids is that their power output strongly fluctuates over time. Understanding these fluctuations, especially its spatio-temporal characteristics, is important for the design of the backup power that must be available. The power fluctuations of the turbines depend on the effect of the wakes, created by a prior row of turbines, on the operation of the turbines, the inter-turbine correlations, and the interaction between the turbines and the atmospheric boundary layer (ABL). We analyze the power fluctuations in large eddy simulations of extended wind-parks in the ABL. We consider various aggregates of wind turbines such as the total average power signal, or sub-averages within the wind farm. In particular, we find that the power variations of the total wind park decreases more than one would expect if one assumes the power output of the turbines to be uncorrelated. The non-trivial correlations are due to the interactions between turbines placed downstream from each other. Surprisingly, the frequency spectra of the total wind-farm output show a decay that follows approximately a-5/3 power-law scaling regime, qualitatively consistent with observations made in field-scale operational wind parks (Apt, 2007).
Springer proceedings in physics, 2009
DOI to the publisher's website. • The final author version and the galley proof are versions of t... more DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:
Physical Review Letters, Apr 6, 2018
The possible transition to the so-called ultimate regime, wherein both the bulk and the boundary ... more The possible transition to the so-called ultimate regime, wherein both the bulk and the boundary layers are turbulent, has been an outstanding issue in thermal convection, since the seminal work by Kraichnan [Phys. Fluids 5, 1374 (1962)]. Yet, when this transition takes place and how the local flow induces it is not fully understood. Here, by performing two-dimensional simulations of Rayleigh-Bénard turbulence covering six decades in Rayleigh number Ra up to 10 14 for Prandtl number Pr = 1, for the first time in numerical simulations we find the transition to the ultimate regime, namely at Ra * = 10 13. We reveal how the emission of thermal plumes enhances the global heat transport, leading to a steeper increase of the Nusselt number than the classical Malkus scaling Nu ∼ Ra 1/3 [Proc. R. Soc. London A 225, 196 (1954)]. Beyond the transition, the mean velocity profiles are logarithmic throughout, indicating turbulent boundary layers. In contrast, the temperature profiles are only locally logarithmic, namely within the regions where plumes are emitted, and where the local Nusselt number has an effective scaling Nu ∼ Ra 0.38 , corresponding to the effective scaling in the ultimate regime.
Bulletin of the American Physical Society, Nov 20, 2017
Submitted for the DFD17 Meeting of The American Physical Society Direct numerical simulations of ... more Submitted for the DFD17 Meeting of The American Physical Society Direct numerical simulations of Couette flow with unstable stratifications ALEXANDER BLASS, XIAOJUE ZHU, ROBERTO VERZICCO, DETLEF LOHSE, RICHARD STEVENS, Univ of Twente-A series of direct numerical simulations of Couette flow with unstable stratification have been performed with a second-order finite difference code, optimized for a GPU cluster (AFiD GPU). Defining h as the channel height, shear Reynolds numbers up to Re τ = hu τ /ν ≈ 370 have been achieved. Looking at the different mean temperatures and velocities of the datasets, it can be seen that, as expected, the convection and shear regimes compete with each other. For low Ra, the statistics show a shear dominated flow field, whereas it becomes more difficult for the shear to dominate in the higher Ra regime. Studying the the Nusselt number (N u) as function of the Re number for different Ra numbers shows that for higher Ra the heat transfer first decreases with increasing shear before it increases strongly for higher mechanical driving. This unexpected non-monotonic change of N u as a function of Re is due to a breakup of the large scale convection rolls formed by the buoyancy forces when moderate shear is applied. The large scale dynamics of pure thermal and pure mechanical driving can be observed in the extreme cases.
Physical Review Letters, Jan 29, 2009
Experimental and numerical data for the heat transfer as a function of the Rayleigh-, Prandtl-, a... more Experimental and numerical data for the heat transfer as a function of the Rayleigh-, Prandtl-, and Rossby numbers in turbulent rotating Rayleigh-Bénard convection are presented. For relatively small Ra ≈ 10 8 and large P r modest rotation can enhance the heat transfer by up to 30%. At larger Ra there is less heat-transfer enhancement, and at small P r < ∼ 0.7 there is no heat-transfer enhancement at all. We suggest that the small-P r behavior is due to the breakdown of the heattransfer-enhancing Ekman pumping because of larger thermal diffusion.
Authorea (Authorea), Aug 4, 2023
The interior oceans of several icy moons are considered as "moderately rotating". Observations su... more The interior oceans of several icy moons are considered as "moderately rotating". Observations suggest a larger heat transport around the poles than at the equator. Rotating Rayleigh-Bénard convection (RRBC) in planar configuration is known to show an enhanced heat transport compared to the non-rotating case for such "moderate" rotation. We investigate the potential for such a (polar) heat transport enhancement in these sub-glacial oceans by direct numerical simulations of RRBC in spherical geometry for Ra=10 6 and 0.7[?]Pr[?]4.38. We find an enhancement up to 28% in the "polar tangent cylinder", which is globally compensated by a reduced heat transport at low latitudes. As a result, the polar heat transport can exceed the equatorial by up to 50%. The enhancement is mostly insensitive to different radial gravity profiles, but decreases for thinner shells. In general, polar heat transport and its enhancement in spherical RRBC follow the same principles as in planar RRBC.
Uploads
Papers by Richard J A M Stevens