arXiv subjects

Johan Meyers

Publications and source records attributed to Johan Meyers.

18 recordsLinked to original sources

arXiv2026

A machine-learned probability distribution in the phase space of turbulent channel flow for synthetic turbulence and flow reconstruction

Although a complete characterisation of the probability distribution in the phase space of turbulent flows remains elusive, accurately sampling this distribution is essential for both synthetic turbulence generation and turbulent flow reconstruction. Motivated by these applications, we examine to what extent a machine-learned distribution can approximate the physical invariant distribution of turbulent channel flow at $\mathrm{Re}_\tau=180$. We assess three important properties of the approximation: physical ensemble statistics, consistent conditional sampling, and dynamical invariance. To this end, a flow-based generative model is trained on a minimal conditional flow unit, which we define as the smallest domain outside which conditional fields, given a single observation at the domain centre, are indistinguishable from unconditional fields in terms of mean-square discrepancy to other conditional fields. We also introduce a consistent procedure for sampling from the conditional learned distribution. Comparisons with direct numerical simulation show that synthetic turbulent fields reproduce key statistical and dynamical features of turbulence, including intermittency and nonlinear energy transfer. The consistency of conditional sampling is demonstrated in a flow reconstruction problem, and subsequently used to generate synthetic turbulent velocity fields on a large domain. When adopted as initial conditions in direct numerical simulations, these fields yield physical and statistically stationary ensemble statistics, indicating that the learned distribution provides a good approximation to the natural distribution of the turbulent dynamical system.

physics.flu-dyn↗

arXiv2024

How thermally-induced secondary motions in offshore hybrid wind-solar farms improve wind-farm efficiency

Integrating floating photovoltaic (FPV) installations into offshore wind farms has been proposed as a major opportunity to scale up offshore renewable energy generation. The interaction between these hybrid wind-solar farms and the atmospheric boundary layer (ABL) is for the first time addressed in the present study. Idealized large-eddy simulations (LES) are used to investigate the flow through both isolated wind and solar farms, as well as combined wind-solar farms, in varying configurations and under different atmospheric conditions. When the FPV modules are arranged in long strips parallel to the flow direction, secondary motions arise due to the temperature difference between the warm FPV modules and colder sea surface, significantly affecting the horizontal distribution of mean wind speed in the ABL. Associated downdrafts between the strips increase entrainment of high-speed momentum from above, thereby increasing the wind speed at these locations. LES of hybrid wind-solar farms reveals that this is beneficial for wind turbines when they are located between the FPV arrays, leading, for the cases that we considered, to a farm-averaged power increase of up to 30% compared to an isolated wind farm. It is shown that the ratio between inertial and buoyancy forces, quantified by a heterogeneity Richardson number $Ri_h$, plays a crucial role in the formation of secondary flows and the resulting wind-farm power enhancement. We further show that no significant power gains, but also no losses emerge in situations when the solar panels are aligned perpendicular to the flow. Although the present results suggest a large potential for wind-solar hybridization, future research should focus on a wider range of scenarios, obtained from a realistic distribution of wind directions and speeds to quantify the potential beneficial impact on real annual power production.

physics.flu-dyn↗

arXiv2024

Wind-farm wake recovery mechanisms in conventionally neutral boundary layers

Synthetic-aperture radar images and mesoscale model results show that wind-farm wakes behave very differently than single-turbine wakes, e.g. with wakes that seemingly narrow and do not disperse over long distances. In the current work, we aim at better understanding the physical mechanisms that govern wind-farm wake behaviour and recovery. Hence, we study the wake properties of a 1.6 GW wind-farm operating in conventionally neutral boundary layers with four capping-inversion heights, i.e. 203, 319, 507 and 1001 m. In shallow boundary layers, we find strong flow decelerations which reduce the Coriolis force magnitude, leading to an anticlockwise wake deflection in the Northern Hemisphere. In deep boundary layers, the vertical turbulent entrainment of momentum adds clockwise-turning flow from aloft into the wake region, leading to a faster recovery rate and a clockwise wake deflection. To estimate the wake properties, we develop a simple model that fits the velocity magnitude profiles along the spanwise direction. Based on this, we observe that the wake narrows along the downstream direction in all cases. Further, a detailed momentum budget analysis shows that the wake is mostly replenished by turbulent vertical entrainment in deep boundary layers. In shallow boundary layers, the capping inversion limits vertical motions and wakes are mostly replenished by mean flow entrainment in the spanwise direction. Moreover, in these cases, we observe a counterclockwise flow rotation near the left edge of the wake, which persists at each location downstream of the farm, giving rise to local strong streamwise velocity gradients along the spanwise direction.

physics.flu-dyn↗

arXiv2024

Stable Boundary Layers with Subsidence: Scaling and Similarity of the Truly Steady State

The stable boundary layer (SBL) subjected to large-scale subsidence is studied through large-eddy simulations (LESs) with fixed surface temperature and a linear subsidence velocity profile. These boundary layers reach a truly steady state, where thermal equilibrium is established by a balance between surface cooling and subsidence-induced heating. We identify three governing dimensionless groups by scaling the governing equations with the geostrophic wind and Coriolis frequency, and systematically investigate the impact of these external parameters on global flow properties and mean profiles in the steady state. The SBL depth, low-level jet, and the magnitude of the turbulent momentum flux are reduced when the subsidence rate or Buoyancy number increases, while surface heat flux is enhanced. The shape of normalized mean profiles of temperature and heat flux is mainly determined by the subsidence rate, while they collapse for varying buoyancy and surface Rossby numbers. We develop empirical correlations for the stability parameter $h_{\theta}/L_O$ and a thermal shape factor, and propose a new unidirectional geostrophic drag law, to form a closed set of equations that estimates relevant flow properties from external parameters. The estimation errors compared to the LES data are less than 5% for friction velocity and surface heat flux, and at most 10% for the SBL depth $h_{\theta}$. Within the surface layer, dimensionless velocity and temperature gradients in the steady SBL with subsidence show acceptable agreement to Monin-Obukhov similarity theory, while the collapse is improved when a recently proposed mixed scaling parameter, that includes $h_{\theta}/L_O$, is used.

physics.flu-dyn↗

arXiv2023

A meso-micro atmospheric perturbation model for wind farm blockage

As wind farms continue to grow in size, mesoscale effects such as blockage and gravity waves become increasingly important. Allaerts & Meyers (J. Fluid Mech., 2019) proposed an atmospheric perturbation model (APM) that can simulate the interaction of wind farms and the atmospheric boundary layer while keeping computational costs low. The model resolves the meso-scale flow, and couples to a wake model to estimate the turbine inflow velocities at the micro-scale. This study presents a new way of coupling the mesoscale APM to a wake model, based on matching the velocity between the models throughout the farm. This method performs well, but requires good estimates of the turbine-level velocity fields by the wake model. Additionally, we investigate the mesoscale effects of a large wind farm, and find that aside from the turbine forces and increased turbulence levels, the dispersive stresses due to subgrid flow heterogeneity also play an important role at the entrance of the farm, and contribute to the global blockage effect. By using the wake model coupling, we can explicitly incorporate these stresses in the model. The resulting APM is validated using 27 LES simulations of a large wind farm under different atmospheric conditions. The APM and LES results are compared on both meso- and turbine-scale, and on turbine power output. The APM captures the overall effects gravity waves have on wind farm power production, and significantly outperforms standard wake models.

physics.flu-dyn↗

arXiv2023

A parametric large-eddy simulation study of wind-farm blockage and gravity waves in conventionally neutral boundary layers

We present a suite of large-eddy simulations of a wind farm operating in conventionally neutral atmospheric boundary layers (CNBLs). A fixed 1.6 GW wind farm is considered for 40 different atmospheric stratification conditions to investigate effects on wind-farm efficiency and blockage, as well as related gravity-wave excitation. A tuned Rayleigh damping layer and a wave-free fringe region method (Lanzilao & Meyers, Bound. Layer Meteor. 186, 2023) are used to avoid spurious excitation of gravity waves, and a domain-size study is included to evaluate and minimize effects of artificial domain blockage. A fully neutral reference case is also considered, to distinguish between a case with hydrodynamic blockage only, and cases that include hydrostatic blockage excited by gravity waves. We discuss in detail the dependence of gravity-wave excitation, flow fields, and wind-farm blockage on capping-inversion height, strength and free-atmosphere lapse rate. In all cases, an unfavourable pressure gradient is present in front of the farm, and a favourable pressure gradient in the farm, with hydrostatic contributions arising from gravity waves at least an order of magnitude larger than hydrodynamic effects. Using respectively non-local and wake efficiencies $η_\textit{nl}$ and $η_\textit{w}$ (Allaerts & Meyers, Bound. Layer Meteor. 166, 2018), we observe a strong negative correlation between unfavourable upstream pressure rise and $η_\textit{nl}$, and a strong positive correlation between the favourable pressure drop in the farm and $η_\textit{w}$. Using a simplified linear gravity-wave model, we formulate a simple scaling for $η_\textit{nl}/η_\textit{w}$, which matches reasonably well with the LES results.

physics.flu-dyn↗

arXiv2023

Quasi-static closed-loop wind-farm control for combined power and fatigue optimization

We develop a methodology for combined power and loads optimization by coupling a surrogate loads model with an analytical quasi-static Gaussian wake merging model. The look-up table based fatigue model is developed offline through a series of OpenFast simulations, covering different operational states of a DTU 10 MW reference wind turbine, and verified against large eddy simulations with aeroelastic coupling. Subsequently, optimal control set points for the TotalControl reference wind power plant are obtained using the analytical model, and tested in a wind farm emulator that is based on large eddy simulations. The wake model is calibrated online using in a quasi-static closed-loop manner. Benefits of the closed-loop controller are exhibited via comparison of farm performance against greedy operation and against open-loop control results obtained without feedback or calibration. Results show that the closed-loop control out performs open-loop control, with farm configurations with deep turbine arrays showcasing the highest gains. Inclusion of fatigue in the cost function through the developed LUT also leads to interesting insights, with reduced blade root fatigue loading without significant decrease in power production when compared to open-loop control. A case study is also performed which showcases real world applications for the developed closed-loop controller and the load LUT, in which the closed-loop controller is shown to react to scenarios with turbine operation shut-down, optimizing the yaw angles online to maximize performance for the new layout.

eess.SY↗

arXiv2023

Bayesian uncertainty quantification framework for wake model calibration and validation with historical wind farm power data

The expected growth in wind energy capacity requires efficient and accurate models for wind farm layout optimization, control, and annual energy predictions. Although analytical wake models are widely used for these applications, several model components must be better understood to improve their accuracy. To this end, we propose a Bayesian uncertainty quantification framework for physics-guided data-driven model enhancement. The framework incorporates turbulence-related aleatoric uncertainty in historical wind farm data, epistemic uncertainty in the empirical parameters, and systematic uncertainty due to unmodelled physics. We apply the framework to the wake expansion parameterization in the Gaussian wake model and employ historical power data of the Westermost Rough offshore wind farm. We find that the framework successfully distinguishes the three sources of uncertainty in the joint posterior distribution of the parameters. On the one hand, the framework allows for wake model calibration by selecting the maximum a posteriori estimators for the empirical parameters. On the other hand, it facilitates model validation by separating the measurement error and the model error distribution. In addition, the model adequacy and the effect of unmodelled physics are assessable via the posterior parameter uncertainty and correlations. Consequently, we believe that the Bayesian uncertainty quantification framework can be used to calibrate and validate existing and upcoming physics-guided models.

physics.flu-dyn↗

arXiv2022

An improved fringe-region technique for the representation of gravity waves in large-eddy simulation with application to wind farms

Large-eddy simulations of the atmospheric boundary layer are often performed using pseudo-spectral methods, which adopt a fringe-region approach to introduce inflow boundary conditions. However, we notice that a standard fringe-region technique excites spurious gravity waves when stratified atmospheres are considered, therefore enhancing the amount of energy reflected from the top of the domain and perturbing the velocity and pressure fields downstream. In this work, we develop a new fringe-region method that imposes the inflow conditions while limiting spurious effects on the surrounding flow. This is achieved by locally damping the convective term in the vertical momentum equation. We first apply the standard and wave-free fringe-region techniques to two-dimensional inviscid-flow simulations subjected to 169 different atmospheric states. A similar study is performed on a three-dimensional domain using a couple of atmospheric states. In all cases, the new fringe-region technique outperforms the standard method, imposing the inflow conditions with a minimal impact on the surrounding flow. Moreover, we also investigate the performance of two already existing non-reflective upper boundary conditions, that is a Rayleigh damping layer (RDL) and a radiation condition (RC). Results highlight the importance of carefully tuning the RDL to limit the distortion of the numerical solution. Also, we find that the tuned RDL outperforms the RC in all cases. Finally, the tuned RDL together with the wave-free fringe-region method are applied to an LES of a wind farm operating in a conventionally neutral boundary layer, for which we measure a reflectivity of only 0.75%.

physics.flu-dyn↗

arXiv2020

Study of the energy convergence of the Karhunen-Loeve decomposition applied to the large-eddy simulation of a high-Reynolds-number pressure-driven boundary layer

We study the energy convergence of the Karhunen-Loève decomposition of the turbulent velocity field in a high-Reynolds-number pressure-driven boundary layer as a function of the number of modes. An energy-optimal Karhunen-Loève (KL) decomposition is obtained from wall-modeled large-eddy simulations at "infinite" Reynolds number. By explicitly using Fourier modes for the horizontal homogeneous directions, we are able to construct a basis of full rank, and we demonstrate that our results have reached statistical convergence. The KL dimension, corresponding to the number of modes per unit volume required to capture 90% of the total turbulent kinetic energy, is found to be $2.4 \times 10^5 |Ω|/H^3$ (with $|Ω|$ the domain volume and $H$ the boundary layer height). This is significantly higher than current estimates, which are mostly based on the method of snapshots. In our analysis, we carefully correct for the effect of subgrid scales on these estimates.

physics.flu-dyn↗

arXiv2020

A new wake-merging method for wind-farm power prediction in presence of heterogeneous background velocity fields

Many wind farms are placed near coastal regions or in proximity of orographic obstacles. The meso-scale gradients that develop in these zones make wind farms operating in velocity fields that are rarely uniform. However, all existing wake-merging methods in engineering wind-farm wake models assume a homogeneous background velocity field in and around the farm, relying on a single wind-speed value usually measured several hundreds of meters upstream of the first row of turbines. In this study, we derive a new momentum-conserving wake-merging method capable of superimposing the waked flow on a heterogeneous background velocity field. We couple the proposed wake-merging method with four different wake models, i.e. the Gaussian, super-Gaussian, double-Gaussian and Ishihara model, and we test its performance against LES data, dual-Doppler radar measurements and SCADA data from the Horns Rev, London Array, and Westermost Rough farm. Next to this, as an additional point of reference, the standard Jensen model with quadratic superposition is also included. Results show that the new method performs similarly to linear superposition of velocity deficits in homogeneous conditions but it shows better performance when a spatially varying background velocity is used. The most accurate estimates are obtained when the wake-merging method is coupled with the double-Gaussian and Gaussian single-wake model. The Ishihara model also shows good agreements with observations. In contrast to this, the Jensen and super-Gaussian wake model underestimate the farm power output for all wind speeds, wind directions and wind farms considered in our analysis.

physics.flu-dyn↗

arXiv2020

Reconstruction of turbulent flow fields from lidar measurements based on large-eddy simulation

We investigate the reconstruction of a turbulent flow field in the atmospheric boundary layer from a time series of lidar measurements, using Large-Eddy Simulations (LES) and a 4D-Var data assimilation algorithm. This leads to an optimisation problem in which the error between measurements and simulations is minimised over an observation time horizon. To exploit the spatial coherence of the turbulence, we use a quadratic regularisation in the objective function, that is based on the two-point covariance matrix. Moreover, to improve conditioning, and remove continuity constraints, the problem is transformed into a Karhunen-Loève basis. For the optimisation, we use a quasi-Newton limited-memory BFGS algorithm combined with an adjoint approach for the gradient. We also consider reconstruction based on a Taylor's frozen turbulence (TFT) model as point of comparison. To evaluate the approach, we construct a series of virtual lidar measurements from a fine-grid LES of a pressure-driven boundary-layer. The reconstruction uses LES on a coarser mesh and smaller domain, and results are compared to the fine-grid reference. Two lidar scanning modes are considered: a classical plan-position-indicator mode, which swipes the lidar beam in a horizontal plane, and a 3D pattern that is based on a Lissajous curve. We find that normalised errors lie between 15% and 25% (error variance normalised by background variance) in the scanning region, and increase to $100\%$ over a distance that is comparable to the correlation length scale outside this scanning region. Moreover, LES outperforms TFT by 30% to 70% depending on scanning mode and location.

physics.flu-dyn↗

arXiv2018

On the decay of dispersive motions in the outer region of rough-wall boundary layers

In rough-wall boundary layers, wall-parallel non-homogeneous mean-flow solutions exist that lead to so-called dispersive velocity components and dispersive stresses. They play a significant role in the mean-flow momentum balance near the wall, but typically disappear in the outer layer. A theoretical framework is presented to study the decay of dispersive motions in the outer layer. To this end, the problem is formulated in Fourier space, and a set of governing ordinary differential equations per mode in wavenumber space is derived by linearizing the Reynolds-averaged Navier-Stokes equations around a constant background velocity. With further simplifications, analytically tractable solutions are found consisting of linear combinations of $\exp(-kz)$ and $\exp(-Kz)$, with $z$ the wall distance, $k$ the magnitude of the horizontal wavevector $\mathbf{k}$, and where $K(\mathbf{k},\textit{Re})$ is a function of $\mathbf{k}$ and the Reynolds number $\textit{Re}$. Moreover, for $k\rightarrow \infty$ or $k_1\rightarrow 0$, $K\rightarrow k$ is found, in which case solutions consist of a linear combination of $\exp(-kz)$ and $z\exp(-kz)$, and are Reynolds number independent. These analytical relations are verified in the limit of $k_1=0$ using the rough boundary layer experiments by Vanderwel and Ganapathisubramani (J. Fluid Mech. 774, R2, 2015) and are in good agreement for $\ell_k/δ\leq 0.5$, with $δ$ the boundary-layer thickness and $\ell_k = 2π/k$.

physics.flu-dyn↗

arXiv2018

Effect of layout on asymptotic boundary layer regime in deep wind farms

The power output of wind farms depends strongly on spatial turbine arrangement, and the resulting turbulent interactions with the atmospheric boundary layer. The main goal of this work is to study the effect of turbine layout on the power output for large wind farms approaching a fully-developed regime. For this purpose we employ an experimental setup of a scaled wind farm with one-hundred porous disk models, of which sixty are instrumented with strain gages. Our experiments cover a parametric space of fifty-six different layouts for which the turbine-area-density is constant, focusing on different turbine arrangements including non-uniform spacings. The strain-gage measurements are used to deduce surrogate power and unsteady loading on turbines for each layout. Our results indicate that the power asymptote at the end of the wind farm depends on the layout in different ways. Firstly, for layouts with a relatively uniform spacing we find that the power asymptote in the fully developed regime reaches approximately the same value, similarly to the prediction of available analytical models. Secondly, we show that the power asymptote in the fully-developed regime can be lowered by inefficient turbine placement, for instance when a large number of the turbines are located in the near wake of upstream turbines. Thirdly, our experiments indicate that an uneven spacing between turbines can improve the overall power output for both the developing and fully-developed part of large wind farms. Specifically, we find a higher power asymptote for a turbine layout with a significant streamwise uneven spacing (i.e. a large streamwise spacing between pairs of closely spaced rows that are slightly staggered). Our results thereby indicate that such a layout may promote beneficial flow interactions in the fully-developed regime for conditions with a strongly prevailing wind direction.

physics.flu-dyn↗

arXiv2018

Periodic Shadowing Sensitivity Analysis of Chaotic Systems

The sensitivity of long-time averages of a hyperbolic chaotic system to parameter perturbations can be determined using the shadowing direction, the uniformly-bounded-in-time solution of the sensitivity equations. Although its existence is formally guaranteed for certain systems, methods to determine it are hardly available. One practical approach is the Least-Squares Shadowing (LSS) algorithm (Q Wang, SIAM J Numer Anal 52, 156, 2014), whereby the shadowing direction is approximated by the solution of the sensitivity equations with the least square average norm. Here, we present an alternative, potentially simpler shadowing-based algorithm, termed periodic shadowing. The key idea is to obtain a bounded solution of the sensitivity equations by complementing it with periodic boundary conditions in time. We show that this is not only justifiable when the reference trajectory is itself periodic, but also possible and effective for chaotic trajectories. Our error analysis shows that periodic shadowing has the same convergence rates as LSS when the time span $T$ is increased: the sensitivity error first decays as $1/T$ and then, asymptotically as $1/\sqrt{T}$. We demonstrate the approach on the Lorenz equations, and also show that, as $T$ tends to infinity, periodic shadowing sensitivities converge to the same value obtained from long unstable periodic orbits (D Lasagna, SIAM J Appl Dyn Syst 17, 1, 2018) for which there is no shadowing error. Finally, finite-difference approximations of the sensitivity are also examined, and we show that subtle non-hyperbolicity features of the Lorenz system introduce a small, yet systematic, bias.

nlin.CD↗

arXiv2016

Wake Structure of Wind Turbines in Yaw under Uniform Inflow Conditions

Reducing wake losses in wind farms by deflecting the wakes through turbine yawing has been shown to be a feasible wind farm controls approach. Nonetheless, the effectiveness of yawing depends not only on the degree of wake deflection but also on the resulting shape of the wake. In this work, the deflection and morphology of wakes behind a wind turbine operating in yawed conditions are studied using wind tunnel experiments of a wind turbine modeled as a porous disk in a uniform inflow. First, by measuring velocity distributions at various downstream positions and comparing with prior studies, we confirm that the non-rotating wind turbine model in yaw generates realistic wake deflections. Second, we characterize the wake shape and make first observations of what is termed a curled wake, displaying significant spanwise asymmetry. The wake curling observed in the experiments is also reproduced qualitatively in large eddy simulations using both actuator disk and actuator line models. When a wind turbine is yawed for the benefit of downstream turbines, the asymmetric shape of the wake must be taken into account since it affects how much of it intersects the downstream turbines.

physics.flu-dyn↗

arXiv2014

HPC realization of a controlled turbulent round jet using OpenFOAM

The present paper investigates high performance computing abilities of OpenFOAM for a low Reynolds number ($Re_D=2000$) axisymmetric jet subject to multiple zero net mass flux (ZNMF) actuators. First, parallel performance of OpenFOAM is tested by performing a scaling study up to $2048$ processors on a supercomputer of Flemish Supercomputer Center(VSC). Then, a method to improve the parallel efficiency is proposed. The method is based on developing a hybrid concept to calculate the statistical moments. This new concept combines ensemble and time averaging in order to allow data sampling in parallel. The motivation is obtaining a reduction in the walltime to collect turbulent statistics which is observed to be the dominating part in the ZNMF controlled jet flow. Employing this parallel statistical averaging approach in combination with regular grid partitioning parallelism, allowed us conducting DNS cases on $P=624$ processors with an overall speed-up of $S_e=540.56$ and a parallel efficiency of $E_e=0.87$. The parallelization using only grid partitioning exhibited inferior performance with $S_e=423.94$ and $E_e=0.68$. In addition to develop a methodology to increase the parallel performance, we reduced the time step cost of the existing unsteady solver as well. To this end, an incremental projection method is implemented into OpenFOAM and a performance gain above $30\%$ is realized.

physics.flu-dyn↗

arXiv2012

Flow visualization using momentum and energy transport tubes and applications to turbulent flow in wind farms

As a generalization of the mass-flux based classical stream-tube, the concept of momentum and energy transport tubes is discussed as a flow visualization tool. These transport tubes have the property, respectively, that no fluxes of momentum or energy exist over their respective tube mantles. As an example application using data from large-eddy simulation, such tubes are visualized for the mean-flow structure of turbulent flow in large wind farms, in fully developed wind-turbine-array boundary layers. The three-dimensional organization of energy transport tubes changes considerably when turbine spacings are varied, enabling the visualization of the path taken by the kinetic energy flux that is ultimately available at any given turbine within the array.

physics.flu-dyn↗