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This paper outlines a methodology for the reduction of a complex computational fluid dynamics (CFD) model using data-based mechanistic (DBM) modelling technique. For this study a full scale, adiabatic walled ventilated installation was used. Primarily, a CFD model that is three dimensional, transient and turbulent was proposed and solved by a commercial package CFX 4.3 in order to obtain informative data that will be used to build a DBM model. At the inlet a step rise in temperature was applied and the ventilation rate is kept steady. Turbulence is modelled by the widely used standard k – ϵ model. Temperature responses at 36 monitoring positions inside the installation were extracted out of the simulation. In the second stage of the work, for the same ventilation system, a DBM model was formulated from an energy balance equation. The simplified refined instrumental variable (SRIV) algorithm is employed as model parameter identification tool. The obtained highly accurate model parameters for all monitoring positions demonstrate the possibility of reducing complex CFD models using identification technique.

This paper outlines a novel approach to model and control the internal dynamics of energy and mass transfer in an imperfectly mixed fluid. The essential element in the approach lies in the extension of a complex CFD simulation model with a simplified, low-order representation of the process using a mathematical identification technique. The reduced-order model that characterises the dominant modes of dynamic behaviour forms an excellent basis for on-line model-based control purposes. Most control algorithms are designed based on experimental time-series data, unlike the others this paper discusses a methodology to use numerical predictions for controller development. This has important practical advantage for control applications especially when experimentation is difficult or in some extreme cases impossible. Furthermore, the inspiration of using numerical predictions instead of experimental time-series data allows designing virtual climate control systems, which launches new possibilities to large number of applications. In this paper, the general methodology will be elaborated using multiple-input–multiple-output (MIMO) ventilation system, and later on the approach will be applied for a single-input–single-output (SISO) ventilation system.

A database of decaying homogeneous, isotropic turbulence is constructed including reference direct numerical simulations at two different Reynolds numbers and a large number of corresponding large-eddy simulations at various subgrid resolutions. Errors in large-eddy simulation as a function of physical and numerical parameters are investigated. In particular, employing the Smagorinsky subgrid parametrization, the dependence of modeling and numerical errors on simulation parameters is quantified. The interaction between these two basic sources of error is shown to lead to their partial cancellation for several flow properties. This leads to a central paradox in large-eddy simulation related to possible strategies that can be followed to improve the accuracy of predictions. Moreover, a framework is presented in which the global parameter dependence of the errors can be classified in terms of the “subgrid activity” which measures the ratio of the turbulent to the total dissipation rate. Such an analysis allows one to quantify refinement strategies and associated model parameters which provide optimal total simulation error at given computational cost. ispartof: Physics of Fluids vol:15 issue:9 pages:2740-2755 status: published

In the current study, we use a large-eddy simulation of a wind-farm boundary layer to generate the fluctuating wind fields that are observed at different turbines in the wind farm. Using these wind fields as inputs, we focus on the development of a benchmark framework in which we explore the trade-off between high energy extraction and low variability using optimal control of multiple turbines subject to a turbulent wind field. The controls variables that are optimized are the electric torque and the pitch angles of the individual turbines over time horizons of 10 minutes. Moreover, both optimal control of individual turbines and coordinated optimal control of groups of turbines are investigated. Optimal control results are presented in terms of Pareto fronts that show optimal trade-offs between energy extraction and power smoothing. We find that power variations can be significantly reduced with limited loss of extracted energy. Moreover, coordinated control can effectively reduce fluctuations over longer time scales. For instance, considering 24 optimally coordinated turbines, variability at a time scale of 50 seconds is reduced 4 times more than the normal statistical reduction of 24 uncoordinated turbines. © Published under licence by IOP Publishing Ltd. ispartof: Journal of Physics: Conference Series vol:524 issue:1 ispartof: The Science of Making Torque from Wind location:Lyngby date:18 Jun - 20 Jun 2014 status: published

In this study we consider large wind farms in a conventionally neutral atmospheric boundary layer. In large wind farms the energy extracted by the turbines is dominated by downward vertical turbulent transport of kinetic energy from the airflow above the farm. However, atmospheric boundary layers are almost always capped by an inversion layer which slows down the entrainment rate and counteracts boundary layer growth. In a suite of large eddy simulations the effect of the strength of the capping inversion on the boundary layer and on the performance of a large wind farm is investigated. For simulations with and without wind turbines the results indicate that the boundary layer growth is effectively limited by the capping inversion and that the entrainment rate depends strongly on the inversion strength. The power output of wind farms is shown to decrease for increasing inversions. © Published under licence by IOP Publishing Ltd. ispartof: Journal of Physics: Conference Series vol:524 issue:1 ispartof: The Science of Making Torque from Wind location:Lyngby date:18 Jun - 20 Jun 2014 status: published

Low-dimensional discrete linear ventilation models have been studied by Cao and Meyers (2012). In the present study, we investigate the validity and applicability of linear ventilation models for heavy-gas dispersion by employing Reynolds-averaged Navier-Stokes (RANS) simulations. A simple benchmark ventilation case is considered under isothermal condition. Considering large density differences from pollutant gas and fresh air, the effect of buoyancy force has been taken into account in turbulent production term to obtain correct diffusion behaviour. A low-Re k-ɛ model has been selected and the generalized gradient diffusion hypothesis is used for buoyancy source term. It is concluded that the flow equations decouple from the concentration equation when the ratio α of air mass-flow rate m_a to pollutant mass-flow rate m_p is larger than 10^5, which is 10 times higher than the range without density differences (α>10^4). The dependence of the coupling on Richardson number Ri is also studied. It is found that the higher the Richardson number, the larger the α should be to decouple equations. ispartof: Building Simulation vol:7 issue:2 pages:131-136 status: published

In the present work we couple flow simulations performed using Large Eddy Simulations (LES) with gradient based optimization to control individual turbine in a farm, so as to achieve an increase in the total power output. The controls in our optimization problem are the disk-based thrust coefficients C′T,n of individual turbines as function of time. We use a gradient-based algorithm for the optimization and the gradients are computed using the adjoint method; the adjoint equations are formulated directly from the LES equation and the cost functional. We employ a receding-horizon predictive control setting and solve the optimization problem iteratively at each time horizon based on the gradient information obtained from the evolution of the flow field and the adjoint computation. In this paper we further elaborate the optimization techniques, interpret the simulation of adjoint field and present results for the wind-farm boundary layer cases. We find that the extracted farm power increases by approximately 20%, during optimal control. However, the increased power output is also responsible for an increase in turbulent dissipation, and a deceleration of the boundary layer. These issues are further discussed. ispartof: 32nd ASME Wind Energy Symposium ispartof: AIAA SciTech 32nd ASME Wind Energy Symposium location:National Harbor, Maryland date:13 Jan - 17 Jan 2014 status: published

The current work focuses on the development and application of an efficient algorithm for optimization of three-dimensional turbulent flows, simulated using Direct Numerical Simulation (DNS) or large-eddy simulations, and further characterized by large-dimensional optimization-parameter spaces. The optimization algorithm is based on Sequential Quadratic Programming (SQP) in combination with a damped formulation of the limited-memory BFGS method. The latter is suitable for solving large-scale constrained optimization problems whose Hessian matrices cannot be computed and stored at a reasonable cost. We combine the algorithm with a line search merit function based an an L1-norm to enforce the convergence from any remote point. It is first shown that the proposed form of the damped L-BFGS algorithm is suitable for solving equality constrained Rosenbrock type functions. Then, we apply the algorithm to an optimal-control test problem that consists of finding the optimal initial perturbations to a turbulent temporal mixing layer such that mixing is improved at the end of a simulation time horizon T. The controls are further subject to a non-linear equality constraint on the total control energy. DNSs are used to resolve all turbulent scales of motion, and a continuous adjoint formulation is employed to calculate the gradient of the cost functionals. We compare the convergence speed of the SQP L-BFGS algorithm to a conventional non-linear conjugate gradient method (i.e. the current standard in DNS-based optimal control), and find that the SQP algorithm is more than an order of magnitude faster than the conjugate-gradient method. ispartof: Journal of Computational Physics vol:256 pages:1-16 status: published

Recently, new requirements have been imposed by grid regulators on power gradients or ramping rates of wind farms. These requirements are an important concern for wind farm operators, as they introduce additional losses in farm efficiency. In the current study, we investigate the use of optimal coordinated control of rotating kinetic energy reserves to smooth power gradients in a wind farm, while maximizing power extraction. To that end, we use turbulent velocity fields obtained from large eddy simulations of a large wind farm, and set up an elementary case in which we consider the coordinated control of two turbines only. We find that optimal control of kinetic energy reserves allows to significantly reduce power variations, keeping them within requirements on power gradients. Moreover, in comparison to a per-turbine limitation of gradients with a greedy power control, we extract on average 3% more power. © 2013 IEEE. ispartof: 2013 IEEE GRENOBLE POWERTECH (POWERTECH) ispartof: IEEE PowerTech location:Grenoble date:17 Jun - 20 Jun 2013 status: published

This paper addresses one of the most persisting problems in wall-modeled large eddy simulation (LES): the overshoot of the mean velocity gradient near the wall, often referred to as the “log-layer mismatch” problem. An analysis of the relationship between turbulent kinetic energy budgets and mean velocity gradient is elaborated for both direct numerical simulations and LES of fully developed channel flow at high Reynolds number. Based on the analysis, a self-adaptive Smagorinsky model for LES of high-Reynolds-number boundary layer flows is proposed, in which the Smagorinsky coefficient is dynamically adjusted so that a logarithmic mean velocity distribution is captured. The model is then implemented in a second-order finite-volume code, and applied to a high-Reynolds-number channel flow with rough walls. We find that the desired logarithmic mean velocity distribution is well predicted for different resolutions and grid aspect ratios. ispartof: Physics of Fluids vol:25 issue:1 status: published

Instrumented small-scale porous disk models are used to study the spectrum of a surrogate for the power output in a micro wind farm with 100 models of wind turbines. The power spectra of individual porous disk models in the first row of the wind farm show the expected $-5/3$ power law at higher frequencies. Downstream models measure an increased variance due to wake effects. Conversely, the power spectrum of the sum of the power over the entire wind farm shows a peak at the turbine-to-turbine travel frequency between the model turbines, and a near $-5/3$ power law region at a much wider range of lower frequencies, confirming previous LES results. Comparison with the spectrum that would result when assuming that the signals are uncorrelated, highlights the strong effects of correlations and anti-correlations in the fluctuations at various frequencies. ispartof: Journal of Physics - Conference Series vol:753 issue:7 ispartof: Torque 2016 location:Munich date:5 Oct - 7 Oct 2016 status: published

In wall-bounded turbulent flow simulations, periodic boundary conditions combined with insufficiently long domains lead to persistent spanwise locking of large-scale turbulent structures. This leads to statistical inhomogeneities of 10% to 15% that persist in time averages of 60 eddy turnover times and more. We propose a shifted periodic boundary condition that eliminates this effect without the need for excessive streamwise domain lengths. The method is tested based on a set of direct numerical simulations of a turbulent channel flow, and large-eddy simulations of a high Reynolds number rough wall half-channel flow. The method is very useful for precursor simulations that generate inlet conditions for simulations that are spatially inhomogeneous, but require statistically homogeneous inlet boundary conditions in the spanwise direction. The method's advantages are illustrated for the simulation of a developing wind-farm boundary layer. ispartof: Physics of Fluids vol:28 issue:2 status: published

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., Accepted for publication in Journal of Fluid Mechanics

Power-generating kite systems extract energy from the wind by periodically pulling a generator on the ground while flying fast in a crosswind direction. Kite systems are intrinsically unstable, and subject to atmospheric turbulences. As an alternative to closed-loop control, this paper investigates the open-loop stabilization and robustification of a kite system using techniques based on the solution of Lyapunov differential equation. A wind flow is computed as a solution to a time-dependent three dimensional Navier-Stokes equation. Open-loop stable trajectories for the power-generating kite system are computed based on the statistical properties of the wind field, and are robustified with respect to the system constraints. The stability and robustness of the resulting trajectories are assessed by simulating the system using the computed time- and space-dependent turbulent wind flow.

For high-Reynolds-numbers wall-bounded flows, large-eddy simulation (LES) combined with a wall stress model (WSM) is frequently used. The mean velocity of turbulent boundary layers at high-Reynolds-numbers follows a logarithmic distribution near the wall. However, in LES of high-Reynolds-number wallbounded flows, an overshoot of the mean velocity gradient near the wall is often reported. Many attempts have tried to suppress this overshoot of mean velocity gradient. However, a successful explanation on the relationship between the mean velocity gradient and flow properties, accounting for effects of subgrid-scale model, numerical scheme, and grid set-up has not yet been reported. In the current study, we elaborate a relationship between the mean shear and its budgets for the case of wall-modeled LES.We show that the overshoot of the mean shear is not necessarily caused by over-dissipation, as often reported in literature. Moreover, we proposed a novel hybrid scheme for the Smagorinsky model, where the model coefficient is determined dynamically near the wall, based on the relationship between the desired logarithmic mean shear and the SGS terms composing the bulk of the budgets for the mean shear. The normal Smagorinsky model is then employed far away from the wall. We show that this new model successfully yields the desired logarithmic velocity distribution near the wall.

The evolution of a mixing layer is very sensitive to upstream flow conditions (Moser and Rogers, 1993). We optimize the initial flow conditions of a temporal mixing layer. We use this case as a substitute experiment to study how long flow control can affect the evolution of the mixing layer solution. In earlier work, we showed that optimization of the initial condition can be used to, e.g. increase the rate of kinetic energy dissipation at the end of a selected optimization time window significantly (Delport et al., 2009). The current paper focusses on longer time windows and addresses the robustness of the optima in presence of white noise.

A review is presented of the error-landscape methodology. This approach evaluates the error-response surface of large-eddy simulations (LES) to essential model and numerical parameters by a systematic variation of these parameters. Using an error landscape constructed for LES of decaying homogeneous isotropic turbulence, it is shown that the determination of LES quality based on one error measure alone, can lead to misleading results, related to underlying error-balancing mechanisms. This problem can be avoided by considering a range of errors simultaneously, emphasizing different scales in the solution. Subsequently, the error-landscape method is further illustrated by comparing different numerical discretizations for Smagorinsky LES. Finally, a more complex case, i.e. a high (infinite) Reynolds number boundary layer, is considered.

As wind power grows as an important contributor to the worldwide overall energy portfolio, wind farms will cover increasingly larger surface areas. With the characteristic height of the atmospheric boundary layer (ABL) of about 1 km, wind farms with horizontal extents exceeding 10–20 km may therefore approach the asymptotic limit of ‘infinite’ wind farms, and the boundary layer flow may approach the fully developed regime. Envisioning such large-scale implementations calls for advancements in our understanding of the detailed interactions between wind turbines and the atmospheric surface layer. In the past, a number of studies have focussed on the effect wind-turbine arrays on the WTABL using elements of momentum theory, potential flow, and the superposition of wakes of individual turbines (cf. Lissaman 1979, and Frandsen 1992). Several recent studies have focused on such dynamics of Wind Turbine Array Boundary Layers (WTABL) (Calaf et al., 2010; Meyers and Meneveau, 2010; Cal et al., 2010).

A suite of large-eddy simulations (LESs) of decaying homogeneous isotropic turbulence at high Reynolds numbers is performed and compared to wind-tunnel experiments in the tradition of Comte-Bellot and Corrsin. The error-landscape approach is used for the evaluation of the Smagorinsky model, and the results are used to identify an optimal combination of model parameter and resolution in a statistically robust fashion. The use of experimental reference data in the error-landscape approach allows to evaluate the optimal Smagorinsky coefficient at high Reynolds numbers and to perform detailed comparisons with analytical predictions. We demonstrate, using a pseudospectral discretization, that the optimal so-called Smagorinsky trajectory obtained from the error-landscape analysis converges at high simulation resolutions to the high-Re theoretical Lilly prediction for the Smagorinsky coefficient. Using modified wavenumbers in the same spectral code, the current study also presents error-landscape results based on LES with “second-order” discretization errors. By slightly revising Lilly’s analysis, we show that including the effect of numerical discretization when evaluating the strain-rate tensor needed in the subgrid-scale model leads to a good prediction of the optimal Smagorinsky parameter obtained from the corresponding error-landscape. Using similar analytical tools, we further demonstrate that the dynamic procedure can also be adapted to better account for the effects of discretization and test-filter shape. ispartof: Physics of Fluids vol:22 issue:12 pages:1-14 status: published

We focus on the enhancement of mixing in a mixing layer using a combination of adjointbased optimization and DNS. The mixing of momentum in a temporal mixing layer is considered, where small initial perturbations on the mean velocity field are optimized to reach a well-mixed turbulent state at the end of the simulation time window. Optimization cases are presented for 6 different optimization time horizons. Based on this, the sensitivity of the mixing-layer flow properties to the initial controls is investigated, including the behavior for long time windows, for which the optimized layer seems to converge to a selfsimilar state much faster than usually reported in literature.

It is well known that when wind turbines are deployed in large arrays, their efficiency decreases due to complex interactions among themselves and with the atmospheric boundary layer (ABL). For wind farms whose length exceeds the height of the ABL by over an order of magnitude, a “fully developed” flow regime can be established. In this asymptotic regime, changes in the streamwise direction can be neglected and the relevant exchanges occur in the vertical direction. Such a fully developed wind-turbine array boundary layer (WTABL) has not been studied systematically before. A suite of large eddy simulations (LES), in which wind turbines are modeled using the classical “drag disk” concept, is performed for various wind-turbine arrangements, turbine loading factors, and surface roughness values. The results are used to quantify the vertical transport of momentum and kinetic energy across the boundary layer. It is shown that the vertical fluxes of kinetic energy are of the same order of magnitude as the power extracted by the forces modeling the wind turbines. In the fully developed WTABL, the kinetic energy extracted by the wind turbines is transported into the wind-turbine region by vertical fluxes associated with turbulence. The results are also used to develop improved models for effective roughness length scales experienced by the ABL. The effective roughness scale is often used to model wind-turbine arrays in simulations of atmospheric dynamics at larger (regional and global) scales. The results from the LES are compared to several existing models for effective roughness lengths. Based on the observed trends, a modified model is proposed, showing improvement in the predicted effective roughness length. ispartof: Physics of Fluids vol:22 issue:1 pages:1-16 status: published

The mixing in a temporal mixing layer after a selected simulation time horizon is maximized by optimizing the initial disturbances on the mean velocity field. We concentrate on algorithms which impose the necessary energy and continuity constraints on the initial disturbances. A constrained optimization method is selected and applied to five different cost functionals.

Large Eddy Simulations (LES) of arrays of wind turbines in the atmospheric turbulent boundary layer with many turbines often require simplified models for the effects of individual turbines,in order to avoid having to use very fine grid spacings near the individual (moving) turbine blades. This goal can be accomplished using the actuator disk model. This approach,ho wever,raises several issues when implemented in the context of LES. In particular,the question is raised of which reference velocity should be used when parameterizing the induced forces: instantaneous versus time averaged,undisturb ed velocity or the local one. Also,one may consider including tangential forces to represent the angular momentum in the wakes. In this paper we present several arguments to make the appropriate choices,and illustrate the effects of these choices in LES of two wind turbine arrays, one with an aligned and one with a staggered arrangement. Predicted power outputs,as well as features of the predicted flow fields are analyzed. Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc. ispartof: 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition ispartof: 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition location:Orlando, Florida, USA date:4 Jan - 7 Jan 2010 status: published

Reliability and robustness are two important required features of CFD results. While a huge amount of works address the issue of model and numerical scheme validation, the search for robust models (i.e. models that exhibit a low sensitivity with respect to tuning parameters) and methods which make it possible to measure the sensitivity of the results received much less attention. The present work addresses these two issues.

Part I Numerical and mathematical analysis of subgrid-scale-model and discretization errors. Architecture of approximate deconvolution models of turbulence, by A. Labovschii, W. Layton, C. Manica, M. Neda, L. Rebholz, I. Stanculescu, C. Trenchea Adaptive turbulence computation based on weak solutions and weak uniqueness, by Johan Hoffman On the application of wavelets to LES sub-grid modelling, by Marta de la Llave Plata, Stewart Cant Analysis of truncation errors and design of physically optimized discretizations, by Stefan Hickel, Nikolaus A. Adams Spectral behavior of various subgrid-scale models in LES at very high Reynolds number, by R. Cocle, L. Bricteux, G. Winckelmans Performance assessment of a new advective subgrid model through two classic benchmark test cases, by Luiz E.B. Sampaio, Angela O. Nieckele, Margot Gerritsen Assessment of dissipation in LES based on explicit filtering from the computation of kinetic energy budget, by Christophe Bogey, Christophe Bailly Optimal unstructured meshing for large eddy simulations, by Yacine Addad, Ulka Gaitonde, Dominique Laurence, Stefano Rolfo Analysis of uniform and adaptive LES in natural convection flow, by Andreas Hauser, Gabriel Wittum Part II Computational error-assessment Influence of time step size and convergence criteria on large eddy simulations with implicit time discretization, by Michael Kornhaas, Dorte C. Sternel, Michael Schafer Assessment of LES quality measures using the error landscape approach, by Markus Klein, Johan Meyers, Bernard J. Geurts Analysis of numerical error reduction in explicitly filtered LES using two-point turbulence closure, by Julien Berland, Christophe Bogey, Christophe Bailly Sensitivity of SGS models and of quality of LES to grid irregularity, by Ghader Ghorbaniasl, Chris Lacor Anisotropic grid refinement study for LES, by Peter Toth, Mate Marton Lohasz Part III Modelling and error-assessment of near-wallflows Expectations in the wall region of a large-eddy simulation, by Philippe R. Spalart, Mikhail Kh. Strelets, and Andrey Travin Large eddy simulation of atmospheric convective boundary layer with realistic environmental forcings, by Aaron M. Botnick, Evgeni Fedorovich Accuracy close to the wall for large-eddy simulations of flow around obstacles using immersed boundary methods, by Mathieu J. B. M. Pourquie On the control of the mass errors in finite volume-based approximate projection methods for large eddy simulations, by Andrea Aprovitola, Filippo Maria Denaro Part IV Error assessment in complex applications Reliability of large-eddy simulation of nonpremixed turbulent flames: scalar dissipation rate modeling and 3D-boundary conditions, by L. Vervisch, G. Lodato, P. Domingo LES at work: quality management in practical large-eddy simulations, by Christer Fureby, Rickard E. Bensow Quality of LES predictions of isothermal and hot round jet, by Artur Tyliszczak, Andrzej Boguslawski, Stanislaw Drobniak LES for street-scale environments and its prospects, by Zheng-Tong Xie, Ian P. Castro Large eddy simulations of the Richtmyer-Meshkov instability in a converging geometry, by Manuel Lombardini, Ralf Deiterding, D.I. Pullin Quality assessment in LES of a compressible swirling mixing layer, by Sebastian R. Muller, Leonhard Kleiser Accuracy of large-eddy simulation of premixed turbulent combustion, by A.W. Vreman, R.J.M. Bastiaans, B.J. Geurts Mesh dependency of turbulent reacting large-eddy simulations of a gas turbine combustion chamber, by Guillaume Boudier, Gabriel Staffelbach, Laurent Y.M. Gicquel, Thierry J. Poinsot Analysis of SGS particle dispersion model in LES of channel flow, by Jacek Potorski, Miroslaw Luniewski Numerical Data for Reliability of LES for Non-isothermal Multiphase Turbulent Channel Flow, by Marek Jaszczur, Luis M. Portela Lagrangian tracking of heavy particles in large-eddy simulation of turbulent channel fl

In recent years, variational multiscale (VMS) Smagorinsky models have emerged as new models for large-eddy simulations (LES). A common version is the small-small variant, which uses a small-scale extraction of the LES solution, obtained by high-pass filtering the resolved velocity field, to express a Smagorinsky term. The subsequent small-scale extraction of this term is used as a model. In the current work, three formulations of the small-small VMS model are investigated in large-eddy simulations of the plane channel flow. The basic small-small formulation (Model A) is modified to explicitly incorporate effects of the LES filter and the high-pass filter (Model B). A third modification (Model C) is further inertial-range consistent, allowing the use of constant model coefficients for filters widths which are situated in a finite Reynolds-number inertial subrange. We aim to evaluate the performance of these models in the presence of walls. Therefore, channel-flow simulations are performed for Reτ=110Reτ=110 , 300, 400, and 650. Further, the effect of changes in the shape of the high-pass filter used for the three models is investigated. A sharp cutoff filter and a Gaussian high-pass filter are considered. In addition, a range of high-pass-filter widths is included in the analysis. Evaluations of the skin-friction, mean-velocity profiles, Reynolds stresses, and spanwise velocity spectra are presented. We show that Model C is most insensitive to changes in Reynolds number and filter shape, closely followed by Model B. Model A is the most sensitive to the considered variations, and simulation quality depends in particular on variations in the filter shape. ispartof: Physics of Fluids vol:19 issue:9 status: published

We address the sensitivity of large-eddy simulations (LES) to parametric uncertainty in the subgrid-scale model. More specifically, we investigate the sensitivity of the LES statistical moments of decaying homogeneous isotropic turbulence to the uncertainty in the Smagorinsky model free parameterCs(i.e. the Smagorinsky constant). Our sensitivity methodology relies on the non-intrusive approach of the generalized Polynomial Chaos (gPC) method; the gPC is a spectral non-statistical numerical method well-suited to representing random processes not restricted to Gaussian fields. The analysis is carried out at Reλ, =, 100 and for different grid resolutions andCsdistributions. Numerical predictions are also compared to direct numerical simulation evidence. We have shown that the different turbulent scales of the LES solution respond differently to the variability inCs. In particular, the study of the relative turbulent kinetic energy distributions for differentCsdistributions indicates that small scales are mainly affected by changes in the subgrid-model parametric uncertainty.

Under conventionally-neutral conditions, the boundary layer is frequently capped by an inversion layer, which counteracts vertical entrainment of kinetic energy. Very large wind farms are known to depend on vertical entrainment to transport energy from above the farm towards the turbines. In this study, large eddy simulations (LES) of an infinite wind-turbine array in a conventionally neutral atmospheric boundary layer are performed. By carefully selecting the initial potential temperature profile, the influence of the height and the strength of a capping inversion on the power output of a wind farm is investigated. Results indicate that both the height and the strength have a significant effect on the boundary layer flow, and that the height of the neutral boundary layer is effectively controlled by the capping inversion. In addition, it is shown that the vertical entrainment rate decreases for increasing inversion strength or height. In our infinite wind-farm simulations, varying the inversion characteristics leads to differences in power extraction on the order of 13 ± 0.2 % (for increasing the strength from 2.5 to 10 K), and 31 ± 0.4 % (for increasing the height from 500 to 1500 m). A detailed analysis of the mean kinetic-energy equation is included, showing that the variation in power extraction originates from the work done by the driving pressure gradient related to the boundary layer height and the geostrophic angle, while entrainment of kinetic energy from the free atmosphere does not play a significant role. Also, the effect of inversion strength on power extraction is energetically not related to different amounts of energy entrained, but explained by a difference in boundary layer growth, leading to higher boundary layers for lower inversion strengths. We further present a simple analytical model that allows to obtain wind-farm power output and driving power for the fully developed regime as function of Rossby number, and boundary layer height. ispartof: Physics of Fluids vol:27 issue:6 status: published

A methodology is proposed for the assessment of error dynamics in large-eddy simulations. It is demonstrated that the optimization of model parameters with respect to one flow property can be obtained at the expense of the accuracy with which other flow properties are predicted. Therefore, an approach is introduced which allows to assess the total errors based on various flow properties simultaneously. We show that parameter settings exist, for which all monitored errors are "near optimal," and refer to such regions as "multi-objective optimal parameter regions." We focus on multi-objective errors that are obtained from weighted spectra, emphasizing both large- as well small-scale errors. These multi-objective optimal parameter regions depend strongly on the simulation Reynolds number and the resolution. At too coarse resolutions, no multi-objective optimal regions might exist as not all error-components might simultaneously be sufficiently small. The identification of multi-objective optimal parameter regions can be adopted to effectively compare different subgrid models. A comparison between large-eddy simulations using the Lilly-Smagorinsky model, the dynamic Smagorinsky model and a new Re-consistent eddy-viscosity model is made, which illustrates this. Based on the new methodology for error assessment the latter model is found to be the most accurate and robust among the selected subgrid models, in combination with the finite volume discretization used in the present study.

We present a framework which can be used to rigorously assess and compare large-eddy simulation methods. We apply this to LES of homogeneous isotropic turbulence using a Smagorin-sky model and three different discretizations. By systematically varying the simulation resolution and the Smagorinsky coefficient, one can determine parameter regions for which one, two or multiple flow predictions are simultaneously predicted with approximately minimal error. To this end errors on the predicted longitudinal integral length scale, the resolved kinetic energy and the resolved enstrophy are considered. Parameter regions where all considered errors are simultaneously (nearly) minimal are entitled ‘multi-objective optimal’ parameter regions. Surprisingly, we find that a standard second-order method has a larger ‘multi-objective optimal’ parameter region than two considered fourth order methods. Moreover, the errors in the respective ‘multi-objective optimal’ regions are also lowest for the second-order scheme.

We present a database analysis to obtain a precise evaluation of the accuracy limitations associated with the popular dynamic eddy-viscosity model in large-eddy simulation. We consider decaying homogeneous isotropic turbulence at two different Reynolds numbers, i.e., Reλ=50Reλ=50 and 100. The large-eddy simulation errors associated with the dynamic model are compared with those arising in the “static” Smagorinsky model. A large number of systematically varied simulations using the Smagorinsky model provides a detailed impression of the dependence of the total simulation error on (i) the spatial resolution and (ii) the resolution of the subgrid dissipation length. This error behavior also induces an “optimal refinement trajectory” which specifies the particular Smagorinsky parameter, in terms of the spatial resolution, for which the total error is minimal. In contrast, the dynamic model gives rise to a self-consistently determined “dynamic trajectory” that represents the dependence of the dynamic coefficient on the spatial resolution. This dynamic trajectory is compared with the optimal refinement trajectory as obtained from the full database analysis of the Smagorinsky fluid. It is shown that the dynamic procedure in which the top-hat test filter is adopted, predicts values for the eddy viscosity as function of resolution and Reynolds number, which quite closely follow the main trends established in the optimal refinement trajectory. Furthermore, a sensitivity analysis, including dependency on test-filter width and filter shape, is discussed. Total simulation errors, due to interacting discretization, and modeling errors associated with the dynamic procedure may be a factor 2 higher compared to the optimum; still the dynamic procedure represents one of the very few self-contained and efficient error-reduction strategies when increasing the spatial resolution. ispartof: Physics of Fluids vol:17 issue:4 pages:045108- status: published

This paper aims at determining the most influential initial flow field parameters on the evolution of turbulent mixing phenomena. To this end a stochastic method is developed to generate a divergence-free random velocity field with a prescribed energy distribution in physical and wave-number space. In addition, predetermined integral length scales are established. Eight direct numerical simulations of a temporally evolving turbulent mixing layer are examined in detail. Simulation results show a large disparity in mean and instantaneous turbulent quantities, mainly effected by the energy spectrum, the integral length scale and the divergence freeness of the initial field.

We study the near field of a zero-net-mass-flux (ZNMF) actuated round jet using direct numerical simulations. The Reynolds number of the jet Re D = 2000 and three ZNMF actuators are used, evenly distributed over a circle, and directed towards the main jet. The actuators are triggered in phase, and have a relatively low momentum coefficient of C μ = 0.0049 each. We study four different control frequencies with Strouhal numbers ranging from St D = 0.165 to St D = 1.32; next to that, also two uncontrolled baseline cases are included in the study. We find that this type of ZNMF actuation leads to strong deformations of the near-field jet region that are very similar to those observed for non-circular jets. At the end of the jet's potential core (x/D = 5), the jet-column cross section is deformed into a hexagram-like geometry that results from strong modifications of the vortex structures. Two mechanisms lead to these modifications, i.e., (i) self-deformation of the jet's primary vortex rings started by distortions in their azimuthal curvature by the actuation, and (ii) production of side jets by the development and subsequent detachment of secondary streamwise vortex pairs. Further downstream (x/D = 10), the jet transforms into a triangular pattern, as the sharp corner regions of the hexagram entrain fluid and spread. We further investigate the global characteristics of the actuated jets. In particular when using the jet preferred frequency, i.e., St D = 0.33, parameters such as entrainment, centerline decay rate, and mean turbulent kinetic energy are significantly increased. Furthermore, high frequency actuation, i.e., St D = 1.32, is found to suppress the mechanisms leading to large scale structure growth and turbulent kinetic energy production. The simulations further include a passive scalar equation, and passive scalar mixing is also quantified and visualized. ispartof: Physics of Fluids vol:26 issue:7 status: published

In the current study, an Actuator-Line Model (ALM) is implemented in our in-house pseudo-spectral LES solver SP-WIND, including a turbine controller. Below rated wind speed, turbines are controlled by a standard-torque-controller aiming at maximum power extraction from the wind. Above rated wind speed, the extracted power is limited by a blade pitch controller which is based on a proportional-integral type control algorithm. This model is used to perform a series of single turbine and wind farm simulations using the NREL 5MW turbine. First of all, we focus on below-rated wind speed, and investigate the effect of the farm layout on the controller calibration curves. These calibration curves are expressed in terms of nondimensional torque and rotational speed, using the mean turbine-disk velocity as reference. We show that this normalization leads to calibration curves that are independent of wind speed, but the calibration curves do depend on the farm layout, in particular for tightly spaced farms. Compared to turbines in a lone-standing set-up, turbines in a farm experience a different wind distribution over the rotor due to the farm boundary-layer interaction. We demonstrate this for fully developed wind-farm boundary layers with aligned turbine arrangements at different spacings (5D, 7D, 9D). Further we also compare calibration curves obtained from full farm simulations with calibration curves that can be obtained at a much lower cost using a minimal flow unit. © Published under licence by IOP Publishing Ltd. ispartof: Journal of Physics: Conference Series vol:524 issue:1 ispartof: The Science of Making Torque from Wind location:Lyngby date:18 Jun - 20 Jun 2014 status: published

In the present paper, an implicit time accurate approach, combined with multigrid is used for the Large-Eddy Simulation (LES) of compressible flows. The multigrid scheme is used as a driver for a fully implicit time stepping scheme. The time derivative is approximated by a second order backward difference formulation. The channel flow is considered as test case. Comparison with a purely explicit approach using a second order and four stages Runge-Kutta method shows that the explicit scheme is 40–50% more expensive in CPU time.

Introduction Connexins (Cx) comprise a family of homologous proteins that are involved in the intercellular exchange of ions and small metabolites between adjacent cells. So far, mutations in seven different connexins have been found in humans, each resulting in a genetic disease. Methods Based on the sequence alignment of known human Cx genes, we developed degenerate PCR primers that we anticipated would amplify members of the Cx gene family, in order to identify novel Cx genes. Results By subcloning and sequencing the PCR products, we identified a previously unidentified connexin gene that we named Cx59 (GJA11). Using FISH we localized the GJA11 gene to chromosome 1p34, and by the analysis of a YAC contig of this region, we mapped this gene within the linkage interval of an Indonesian family with autosomal dominant nonsyndromic hearing loss (ADNSHL). Because mutations in other connexins, namely GJB3 (Cx31) and GJB6 (Cx30), lead to similar forms of ADNSHL, GJA11 (Cx59) was a very strong candidate gene. Therefore, we performed mutation analysis of the coding region of GJA11 in patients of this Indonesian family, but no disease-causing mutation was found.

Upstream flow conditions have a large impact on mixing in shear layers. Optimizing these flow conditions can significantly improve mixing effectiveness. We focus on the evolution of a mixing layer in a temporal framework using direct numerical simulations, and optimize the initial disturbances on the layer such that maximal mixing is achieved after a selected simulation time horizon. A gradient-based optimization strategy is used, which employs adjoint-based gradient calculations formulated in a continuous framework. This allows us to limit disk storage needed for the adjoint simulation. We further concentrate on algorithms which impose the necessary energy and continuity constraints on the initial perturbations. For the continuity constraints, parameter elimination is used. For the energy constraint two methods are compared: the gradient projection and the augmented Lagrangian. Optimization with the gradient projection method is shown to be the more robust methodology. We found that the augmented Lagrang...

A functional form for the energy spectrum is proposed, which includes a predissipative bottleneck effect and an intermittency correction. The form contains five parameters for which five constraints are formulated. Three of them are related to the condition that the integrals of the spectrum,E(k)E(k), k2E(k)k2E(k), and k4E(k)k4E(k), should yield appropriate values for total energy, enstrophy, and derivative skewness. Two extra conditions are inferred from the location and height of the intermittency corrected dissipation peak, which is found to be independent of Reynolds number(70

This paper aims at determining the most influential inlet turbulence parameters on the downstream transitional mixing region. To this end, a stochastic method is developed to generate a divergence-free random velocity field with a prescribed energy distribution in physical and wave-number space. In addition, predetermined integral length scales can be established. Ten direct numerical simulations of a temporally evolving transitional turbulent mixing layer are examined in detail. Simulation results show a large disparity in mean and instantaneous turbulent quantities, mainly effected by the energy spectrum, the integral length scale and the divergence freeness of the initial field.