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Showing papers on "K-epsilon turbulence model published in 2001"


Journal ArticleDOI
TL;DR: In this paper, the first analytical description of anomalous scaling laws in turbulent transport has been obtained and the underlying physical mechanism reveals the role of statistical integrals of motion in nonequilibrium systems.
Abstract: The understanding of fluid turbulence has considerably progressed in recent years. The application of the methods of statistical mechanics to the description of the motion of fluid particles, i.e., to the Lagrangian dynamics, has led to a new quantitative theory of intermittency in turbulent transport. The first analytical description of anomalous scaling laws in turbulence has been obtained. The underlying physical mechanism reveals the role of statistical integrals of motion in nonequilibrium systems. For turbulent transport, the statistical conservation laws are hidden in the evolution of groups of fluid particles and arise from the competition between the expansion of a group and the change of its geometry. By breaking the scale-invariance symmetry, the statistically conserved quantities lead to the observed anomalous scaling of transported fields. Lagrangian methods also shed new light on some practical issues, such as mixing and turbulent magnetic dynamo.

1,186 citations


Book
13 Feb 2001
TL;DR: In this paper, the authors present a general framework for single point closure in the context of turbulent flow models, which is based on the Cayley-hampton tensor model.
Abstract: Preface. Preface to second edition. Preface to first edition. Motivation. Epitome. Acknowledgements. Part I FUNDAMENTALS OF TURBULENCE. 1 Introduction. 1.1 The turbulence problem. 1.2 Closure modeling. 1.3 Categories of turbulent flow. Exercises. 2 Mathematical and statistical background. 2.1 Dimensional analysis. 2.1.1 Scales of turbulence. 2.2 Statistical tools. 2.2.1 Averages and probability density functions. 2.2.2 Correlations. 2.3 Cartesian tensors. 2.3.1 Isotropic tensors. 2.3.2 Tensor functions of tensors Cayley-Hamilton theorem. Exercises. 3 Reynolds averaged Navier-Stokes equations. 3.1 Background to the equations. 3.2 Reynolds averaged equations. 3.3 Terms of kinetic energy and Reynolds stress budgets. 3.4 Passive contaminant transport. Exercises. 4 Parallel and self-similar shear flows. 4.1 Plane channel flow. 4.1.1 Logarithmic layer. 4.1.2 Roughness. 4.2 Boundary layer. 4.2.1 Entrainment. 4.3 Free-shear layers. 4.3.1 Spreading rates. 4.3.2 Remarks on self-similar boundary layers. 4.4 Heat and mass transfer. 4.4.1 Parallel flow and boundary layers. 4.4.2 Dispersion from elevated sources. Exercises. 5 Vorticity and vortical structures. 5.1 Structures. 5.1.1 Free-shear layers. 5.1.2 Boundary layers. 5.1.3 Non-random vortices. 5.2 Vorticity and dissipation. 5.2.1 Vortex stretching and relative dispersion. 5.2.2 Mean-squared vorticity equation. Exercises. Part II SINGLE-POINT CLOSURE MODELING. 6 Models with scalar variables. 6.1 Boundary-layer methods. 6.1.1 Integral boundary-layer methods. 6.1.2 Mixing length model. 6.2 The k -epsilon model. 6.2.1 Analytical solutions to the k -epsilon model. 6.2.2 Boundary conditions and near-wall modifications. 6.2.3 Weak solution at edges of free-shear flow free-stream sensitivity. 6.3 The k -omega model. 6.4 Stagnation-point anomaly. 6.5 The question of transition. 6.5.1 Reliance on the turbulence model. 6.5.2 Intermittency equation. 6.5.3 Laminar fluctuations. 6.6 Eddy viscosity transport models. Exercises. 7 Models with tensor variables. 7.1 Second-moment transport. 7.1.1 A simple illustration. 7.1.2 Closing the Reynolds stress transport equation. 7.1.3 Models for the slow part. 7.1.4 Models for the rapid part. 7.2 Analytic solutions to SMC models. 7.2.1 Homogeneous shear flow. 7.2.2 Curved shear flow. 7.2.3 Algebraic stress approximation and nonlinear eddy viscosity. 7.3 Non-homogeneity. 7.3.1 Turbulent transport. 7.3.2 Near-wall modeling. 7.3.3 No-slip condition. 7.3.4 Nonlocal wall effects. 7.4 Reynolds averaged computation. 7.4.1 Numerical issues. 7.4.2 Examples of Reynolds averaged computation. Exercises. 8 Advanced topics. 8.1 Further modeling principles. 8.1.1 Galilean invariance and frame rotation. 8.1.2 Realizability. 8.2 Second-moment closure and Langevin equations. 8.3 Moving equilibrium solutions of SMC. 8.3.1 Criterion for steady mean flow. 8.3.2 Solution in two-dimensional mean flow. 8.3.3 Bifurcations. 8.4 Passive scalar flux modeling. 8.4.1 Scalar diffusivity models. 8.4.2 Tensor diffusivity models. 8.4.3 Scalar flux transport. 8.4.4 Scalar variance. 8.5 Active scalar flux modeling: effects of buoyancy. 8.5.1 Second-moment transport models. 8.5.2 Stratified shear flow. Exercises. Part III THEORY OF HOMOGENEOUS TURBULENCE. 9 Mathematical representations. 9.1 Fourier transforms. 9.2 Three-dimensional energy spectrum of homogeneous turbulence. 9.2.1 Spectrum tensor and velocity covariances. 9.2.2 Modeling the energy spectrum. Exercises. 10 Navier-Stokes equations in spectral space. 10.1 Convolution integrals as triad interaction. 10.2 Evolution of spectra. 10.2.1 Small-k behavior and energy decay. 10.2.2 Energy cascade. 10.2.3 Final period of decay. Exercises. 11 Rapid distortion theory. 11.1 Irrotational mean flow. 11.1.1 Cauchy form of vorticity equation. 11.1.2 Distortion of a Fourier mode. 11.1.3 Calculation of covariances. 11.2 General homogeneous distortions. 11.2.1 Homogeneous shear. 11.2.2 Turbulence near a wall. Exercises. Part IV TURBULENCE SIMULATION. 12 Eddy-resolving simulation. 12.1 Direct numerical simulation. 12.1.1 Grid requirements. 12.1.2 Numerical dissipation. 12.1.3 Energy-conserving schemes. 12.2 Illustrations. 12.3 Pseudo-spectral method. Exercises. 13 Simulation of large eddies. 13.1 Large eddy simulation. 13.1.1 Filtering. 13.1.2 Subgrid models. 13.2 Detached eddy simulation. Exercises. References. Index.

562 citations


Journal ArticleDOI
TL;DR: In this article, a nonlinearly dispersive Navier-stokes-alpha (NS-α) model of incompressible fluid turbulence was derived by filtering the velocity of the fluid loop in Kelvin's circulation theorem.

439 citations


Journal ArticleDOI
TL;DR: A two-fluid model of turbulent, adiabatic bubbly flow was implemented in the computational fluid dynamics (CFD) CFX4.2 program and validated.

320 citations


Journal ArticleDOI
TL;DR: In this article, a stochastic interparticle collision model for particle-laden flows to be applied in the frame of the Euler/Lagrange approach is introduced, relying on the generation of a fictitious collision partner with a given size and velocity, whereby no information is required on the actual position and direction of motion of the surrounding real particles.

317 citations


Journal ArticleDOI
TL;DR: In this paper, the authors describe the wide range of free-surface deformations that occur when there is turbulence at the surface, and focus on turbulence in the denser, liquid, medium.
Abstract: A free surface may be deformed by fluid motions; such deformation may lead to surface roughness, breakup, or disintegration. This paper describes the wide range of free-surface deformations that occur when there is turbulence at the surface, and focuses on turbulence in the denser, liquid, medium. This turbulence may be generated at the surface as in breaking water waves, or may reach the surface from other sources such as bed boundary layers or submerged jets. The discussion is structured by consideration of the stabilizing influences of gravity and surface tension against the disrupting effect of the turbulent kinetic energy. This leads to a two-parameter description of the surface behaviour which gives a framework for further experimental and theoretical studies. Much of the discussion is necessarily heuristic, and is often limited by a lack of appropriate experimental observations. It is intended that such experiments be stimulated, to test the value or otherwise of our two-parameter description.

288 citations


Journal ArticleDOI
TL;DR: In this paper, the authors explore the character of transport in a plasma turbulence model with avalanche transport, and the motion of tracer particles has been followed, both the time evolution of the moments of the distribution function of the tracer particle radial positions, 〈|r(t)−r(0)|n〉, and their finite scale Lyapunov number are used to determine the anomalous diffusion exponent, ν.
Abstract: To explore the character of transport in a plasma turbulence model with avalanche transport, the motion of tracer particles has been followed. Both the time evolution of the moments of the distribution function of the tracer particle radial positions, 〈|r(t)−r(0)|n〉, and their finite scale Lyapunov number are used to determine the anomalous diffusion exponent, ν. The numerical results show that the transport mechanism is superdiffusive with an exponent ν close to 0.88±0.07. The distribution of the exit times of particles trapped into stochastic jets is also determined. These particles have the lowest separation rate at the low resonant surfaces.

270 citations


Journal ArticleDOI
TL;DR: In this paper, the authors derive analytic criteria for the existence of hyperbolic (attracting or repelling), elliptic, and parabolic material lines in two-dimensional turbulence.
Abstract: We derive analytic criteria for the existence of hyperbolic (attracting or repelling), elliptic, and parabolic material lines in two-dimensional turbulence. The criteria use a frame-independent Eulerian partition of the physical space that is based on the sign definiteness of the strain acceleration tensor over directions of zero strain. For Navier–Stokes flows, our hyperbolicity criterion can be reformulated in terms of strain, vorticity, pressure, viscous and body forces. The special material lines we identify allow us to locate different kinds of material structures that enhance or suppress finite-time turbulent mixing: stretching and folding lines, Lagrangian vortex cores, and shear jets. We illustrate the use of our criteria on simulations of two-dimensional barotropic turbulence.

244 citations


Journal ArticleDOI
TL;DR: In this paper, four different algebraic second-moment turbulence closure models are investigated in detail, and their performance in terms of Prandtl number, Monin-Obukhov similarity theory, and length scale ratios are first tested against data for simple flows.
Abstract: In this comparative study, four different algebraic second-moment turbulence closure models are investigated in detail. These closure schemes differ in the number of terms considered for the closure of the pressure–strain correlations. These four turbulence closures result in the eddy-diffusivity principle such that the closure assumptions are contained in dimensionless so-called stability functions. Their performance in terms of Prandtl number, Monin–Obukhov similarity theory, and length scale ratios are first tested against data for simple flows. The turbulence closure is then completed by means of a k–ϵ two-equation model, but other models such as the two-equation model by Mellor and Yamada could also be used. The concept of the steady-state Richardson number for homogeneous shear layers is exploited for calibrating the sensitivity of the four models to shear and stable stratification. Idealized simulations of mixed layer entrainment into stably stratified flow due to surface stress and due to...

243 citations


Journal ArticleDOI
TL;DR: In this article, a numerical model is used to simulate wave breaking, the large scale water motions and turbulence induced by the breaking process, and the model consists of a free surface model using the surface markers method combined with a three-dimensional model that solves the flow equations.

217 citations


Journal ArticleDOI
TL;DR: In this article, the authors deal with the numerical simulation of cavitation phenomena inside injector nozzles and combine the volume-of-fluid technique (VOF) with a model predicting the growth and collapse of bubbles.
Abstract: This paper deals with the numerical simulation of cavitation phenomena inside injector nozzles. The numerical approach combines the Volume-of-Fluid technique (VOF) with a model predicting the growth and collapse of bubbles. To model the turbulence effect a k–ω model is introduced for the two-phase flow. Calculations show that the numerical method is able to reproduce complex cavitation phenomena as observed in injection nozzle experiments.

Journal ArticleDOI
TL;DR: In this paper, mean and turbulence characteristics in nonuniform open-channel flows were measured using a 3D acoustic Doppler velocimeter, both accelerating and decelerating flows were inve...
Abstract: Measurements of the mean and turbulence characteristics in nonuniform open-channel flows were carried out using a 3D acoustic Doppler velocimeter. Both accelerating and decelerating flows were inve...

Journal ArticleDOI
TL;DR: In this paper, the role of turbulence structure in the evolution of one-point turbulence statistics is explored and five statistical measures of the energy-containing turbulence structure are introduced and used with direct numerical simulations to analyse the role in several cases of homogeneous and inhomogeneous turbulence undergoing diverse modes of mean deformation.
Abstract: The dynamics of the evolution of turbulence statistics depend on the structure of the turbulence. For example, wavenumber anisotropy in homogeneous turbulence is known to affect both the interaction between large and small scales (Kida & Hunt 1989), and the non-local effects of the pressure–strain-rate correlation in the one-point Reynolds stress equations (Reynolds 1989; Cambon et al. 1992). Good quantitative measures of turbulence structure are easy to construct using two-point or spectral data, but one-point measures are needed for the Reynolds-averaged modelling of engineering flows. Here we introduce a systematic framework for exploring the role of turbulence structure in the evolution of one-point turbulence statistics. Five one-point statistical measures of the energy-containing turbulence structure are introduced and used with direct numerical simulations to analyse the role of turbulence structure in several cases of homogeneous and inhomogeneous turbulence undergoing diverse modes of mean deformation. The one-point structure tensors are found to be useful descriptors of turbulence structure, and lead to a deeper understanding of some rather surprising observations from DNS and experiments.

Journal ArticleDOI
TL;DR: In this paper, the boundary conditions appropriate for use with averaged equations in the body of the water are obtained by integrating across the two-phase surface layer, where the mean pressure and the mean rate of strain have similarities to those for a compressible fluid.
Abstract: Strong turbulence at a water–air free surface can lead to splashing and a disconnected surface as in a breaking wave. Averaging to obtain boundary conditions for such flows first requires equations of motion for the two-phase region. These are derived using an integral method, then averaged conservation equations for mass and momentum are obtained along with an equation for the turbulent kinetic energy in which extra work terms appear. These extra terms include both the mean pressure and the mean rate of strain and have similarities to those for a compressible fluid. Boundary conditions appropriate for use with averaged equations in the body of the water are obtained by integrating across the two-phase surface layer.A number of ‘new’ terms arise for which closure expressions must be found for practical use. Our knowledge of the properties of strong turbulence at a free surface is insufficient to make such closures. However, preliminary discussions are given for two simplified cases in order to stimulate further experimental and theoretical studies.Much of the turbulence in a spilling breaker originates from its foot where turbulent water meets undisturbed water. A discussion of averaging at the foot of a breaker gives parameters that may serve to measure the ‘strength’ of a breaker.

Journal ArticleDOI
TL;DR: In this paper, a method is proposed to reduce the noise contribution to mean turbulence parameters obtained by 3D acoustic Doppler velocity profiler measurements based on a noise spectrum reconstruction from cross-spectra evaluations.
Abstract: A method is proposed to reduce the noise contribution to mean turbulence parameters obtained by 3D acoustic Doppler velocity profiler measurements. It is based on a noise spectrum reconstruction from cross-spectra evaluations of two independent and simultaneous measurements of the same vertical velocity component over the whole water depth. The noise spectra and the noise variances are calculated and removed for the three fluctuating velocity components measured in turbulent, open-channel flow. The corrected turbulence spectra show a −5/3 slope over the whole inertial subrange delimited by the frequency band of the device, while the uncorrected turbulence spectra have flat high-frequency regions typical for noise effects. This method does not require any hypothesis on the flow characteristics nor does it depend on device-dependent parameters. The corrected profiles of turbulence intensities, turbulent kinetic energy, shear stress, and turbulent energy balance equation terms, such as production, t...

Journal ArticleDOI
TL;DR: In this paper, the authors present the results of three-dimensional fluid global simulations of electrostatic ion turbulence in tokamaks with reversed magnetic shear, and show that a transport barrier appears at the location of magnetic reversal, due to a rarefaction of resonant surfaces in this region.
Abstract: This paper presents the results of three-dimensional fluid global simulations of electrostatic ion turbulence in tokamaks with reversed magnetic shear. It is found that a transport barrier appears at the location of magnetic shear reversal. This is due to a rarefaction of resonant surfaces in this region. For the same reason, the barrier is more pronounced when the minimum of the safety factor is a simple rational number. The barrier is broadened by velocity shear effects. It is also found that large-scale transport events hardly cross a transport barrier. Finally, a significant amount of toroidal rotation is generated by the turbulence. This rotation changes its sign at the position of magnetic shear reversal, as expected from a quasi-linear estimate of the Reynolds stresstensor.

Book
20 Nov 2001
TL;DR: In this paper, the authors discuss the properties of Turbulence and chaos in the context of empirical algorithms and analytic theories and mathematical aspects, and develop developed and developed Turbulences.
Abstract: 1 Continua and Generalities About Their Equations.- 2 Empirical Algorithms.- 3 Analytical Theories and Mathematical Aspects.- 4 Incipient Turbulence and Chaos.- 5 Ordering Chaos.- 6 Developed Turbulence.- 7 Statistical Properties of Turbulence.- Name Index.- Citations Index.

Journal ArticleDOI
TL;DR: The role of the wall in creating turbulence diminishes greatly at large drag reductions; Warholic et al. as discussed by the authors showed that a turbulent flow with zero Reynolds stress exists at maximum drag reduction.
Abstract: Particle-image velocimetry has been used to study the effect of drag-reducing polymers on the structure of turbulence in a channel flow, under conditions of 41% and 55% drag reduction. The fluctuating velocity fields in the x-y plane and in one x-z plane were measured. The striking features of these results are the damping of small scales and the repression of fluctuations of the velocity component normal to the wall. The role of the wall in creating turbulence diminishes greatly at large drag reductions; Warholic et al. (1999) have shown that a turbulent flow with zero Reynolds stress exists at maximum drag reduction. Velocity fields presented for conditions approaching this critical behavior are of particular interest.

Journal ArticleDOI
TL;DR: In this paper, the conditionally averaged Navier-Stokes equations are used to simulate transitional skin friction or heat transfer, and a turbulence weighting factor τ is used to describe the diffusion of freestream turbulence into the boundary layer and the intermittent laminar-turbulent flow behavior during transition.
Abstract: To simulate transitional skin friction or heat transfer, the conditionally averaged Navier-Stokes equations are used. To describe the diffusion of freestream turbulence into the boundary layer and the intermittent laminar-turbulent flow behavior during transition, a turbulence weighting factor τ is used. A transport equation is presented for this τ-factor including convection, diffusion, production, and sink terms, In combination with the conditioned Navier-Stokes equations, this leads to an accurate calculation of flow characteristics within the transitional layer. The method is validated on transitional skin friction and heat transfer measurements, respectively on a flat plate and in a linear turbine cascade

Journal ArticleDOI
TL;DR: In this paper, a model is presented to investigate the driving of coronal turbulence in open field line regions, powered by low-frequency oscillatory field line motions at the coronal base.
Abstract: A model is presented to investigate the driving of coronal turbulence in open field line regions, powered by low-frequency oscillatory field line motions at the coronal base. The model incorporates the combined effects of wave propagation, reflection associated with gradients of Alfven speed, and low-frequency quasi-two-dimensional turbulence, which is treated using a one-point closure phenomenology appropriate to a transverse cascade in the reduced magnetohydrodynamic regime. Considering a sample of the corona and employing open boundary conditions, we use the model to investigate the dynamical efficiency of turbulent dissipation, which competes with propagation of fluctuations away from the coronal base. We examine the dependence of the heating efficiency on wave-forcing frequency, the sensitivity to parameters controlling the Alfven speed profile, the behavior of the model for varying the phenomenological correlation length of turbulence, including asymptotic limits of negligible or very intense nonlinearities, and the confinement of turbulent dissipation to the region near the coronal base. Each of these issues may be of importance in understanding the heating of the corona and the origin of the solar wind.

Journal ArticleDOI
TL;DR: In this paper, the authors investigated the flow field of dual, parallel planar turbulent jets using an x-type hot-wire probe and numerically by solving the Reynolds-averaged Navier-Stokes equations.
Abstract: The flowfield of dual, parallel planar turbulent jets is investigated experimentally using an x-type hot-wire probe and numerically by solving the Reynolds-averaged Navier-Stokes equations. The performance of both differential Reynolds stress (RSM) and standard k-e turbulence models is evaluated. Results show that the numerical models predict the merge and combined point characteristics to good accuracy. However, both turbulence models show a narrower width of the jet envelope than measured by experiment

Journal ArticleDOI
TL;DR: In this article, the authors investigate the performance of standard stochastic models of single-particle dispersion in two-dimensional turbulence and introduce a family of two-process models that provide a better parameterization of turbulent dispersion for rotating barotropic flows.
Abstract: We investigate the performance of standard stochastic models of single-particle dispersion in two-dimensional turbulence. Owing to the presence of coherent vortices, particle dispersion in two-dimensional turbulence is characterized by a non-Gaussian velocity distribution and a non-exponential velocity autocorrelation, and it cannot be properly captured by either linear or nonlinear stochastic models with a single component process. Based on physical and dynamical considerations, we introduce a family of two-process stochastic models that provide a better parameterization of turbulent dispersion in rotating barotropic flows.

Journal ArticleDOI
TL;DR: In this article, the authors measured the radial correlation length of the turbulence Lc,r is shown to scale with the local ion gyroradius, Lc r ≈ 5ρi, while the decorrelation times scale with local acoustic velocity as τ c~a/cs.
Abstract: Plasma turbulence characteristics, including radial correlation lengths, decorrelation times, amplitude profile and flow velocity, have been measured during a ρ* scan on DIII-D while all other transport relevant dimensionless quantities (e.g., β, ν*, κ, q, Te/Ti) are held nearly constant. The turbulence is measured by examining the correlation properties of the local long wavelength (k⊥ρi ≤ 1) density fluctuations, measured with beam emission spectroscopy. The radial correlation length of the turbulence Lc,r is shown to scale with the local ion gyroradius, Lc,r ≈ 5ρi, while the decorrelation times scale with the local acoustic velocity as τc~a/cs. The turbulent diffusivity parameter, D~(Lc,r2/τc), scales in a roughly gyro-Bohm-like fashion, as predicted by the gyrokinetic equations governing turbulent transport. The experimental one fluid power balance heat diffusivity scaling and that from GLF23 modelling compare reasonably well.

Journal ArticleDOI
TL;DR: In this article, the authors studied numerically a one-dimensional model of dispersive wave turbulence, which admits a very precise and detailed realization of these turbulent cycles and their components.

Journal ArticleDOI
TL;DR: In this paper, a spatially periodic array is used to simulate the turbulent flow field inside an elementary control volume representing a porous medium, and mean flow and turbulence equations are discretized by means of the control-volume approach.
Abstract: A spatially periodic array is used to simulate the turbulent flow field inside an elementary control volume representing a porous medium. The low Reynolds (Re) version of the κ - e model is employed. Mean flow and turbulence equations are discretized by means of the control-volume approach. Boundary treatment includes symmetry lines and spatially periodic conditions. A generalized coordinate system is used to generate the computational grid. Solution of the flow equations is accomplished through the SIMPLE method. Detailed computations are used to close the proposed macroscopic turbulence model. Overall pressure drop and volume-averaged turbulence kinetic energy (TKE) are presented

Journal ArticleDOI
TL;DR: In this paper, the effect of the initial conditions and the size of the computational box on the turbulent statistics and structures is examined in detail, and a series of calculations was initialized using two different realizations of a spatially developing turbulent boundary-layer with their free streams moving in opposite directions.
Abstract: Large-eddy simulations of temporally evolving turbulent mixing layers have been carried out. The effect of the initial conditions and the size of the computational box on the turbulent statistics and structures is examined in detail. A series of calculations was initialized using two different realizations of a spatially developing turbulent boundary-layer with their free streams moving in opposite directions. Computations initialized with mean flow plus random perturbations with prescribed moments were also conducted. In all cases, the initial transitional stage, from boundary-layer turbulence or random noise to mixing-layer turbulence, was followed by a self-similar period. The self-similar periods, however, differed considerably: the growth rates and turbulence intensities showed differences, and were affected both by the initial condition and by the computational domain size. In all simulations the presence of quasi-two-dimensional spanwise rollers was clear, together with ‘braid’ regions with quasi-streamwise vortices. The development of these structures, however, was different: if strong rollers were formed early (as in the cases initialized by random noise), a well-organized pattern persisted throughout the self-similar period. The presence of boundary layer turbulence, on the other hand, inhibited the growth of the inviscid instability, and delayed the formation of the roller–braid patterns. Increasing the domain size tended to make the flow more three-dimensional.

Journal ArticleDOI
TL;DR: In this paper, the authors investigated inertial subrange energy spectra associated with turbulent flows developed by the Rayleigh-Taylor instability and Richtmyer-Meshkov instability (RMI).
Abstract: We investigate inertial subrange energy spectra associated with turbulent flows developed by the Rayleigh–Taylor instability and Richtmyer–Meshkov instability (RMI). We argue that the extended Kolmogorov–Kraichnan phenomenology originally developed for turbulent flows with an external agent should also be applicable to these instability driven turbulent flows. A prediction of the mixing zone width for the RMI induced turbulent flow is presented using the RMI modified energy spectrum and a two-equation turbulence model. A possible application to subgrid modeling for large-eddy simulation is discussed briefly.

Journal ArticleDOI
TL;DR: In this paper, a review of existing mathematical models for turbulence models for flow through permeable structures is presented, where the authors classified models in terms of the order of application of time and volume averaging operators, among other peculiarities.
Abstract: Turbulence models proposed for flow through permeable structures depend on the order of application of time and volume average operators. Two developed methodologies, following the two orders of integration, lead to different governing equations for the statistical quantities. The flow turbulence kinetic energy resulting in each case is different. This paper reviews recently published mathematical models developed for such flows. The concept of double decomposition is discussed and models are classified in terms of the order of application of time and volume averaging operators, among other peculiarities. A total of four major classes of models are identified and a general discussion on their main characteristics is carried out. Proposed equations for turbulence kinetic energy following time-space and space-time integration sequences are derived and similar terms are compared. Treatment of the drag coefficient and closure of the interfacial surface integrals are discussed

Journal ArticleDOI
TL;DR: In this paper, the authors used two groups of turbulence models in a sub-critical flow regime: the non-linear k-e model with extended models, such as renormalization group (RNG) and the anisotropic model, and the large eddy simulation (LES) method, which is based on a standard sub-grid scale model with a near-wall approach.
Abstract: The numerical simulation of transitional flow around a two-dimensional stationary circular cylinder is presented using two groups of turbulence models in a sub-critical flow regime. In the first group, enhanced two-equation turbulence models based on the eddy viscosity concept are used. They include the non-linear k–e model with extended models, such as renormalization group (RNG) and the anisotropic model. In the second group, flow simulation is carried out using the large eddy simulation (LES) method, which is based on a standard sub-grid scale (SGS) model with a near-wall approach. This near-wall model, without using the ‘law of wall’, is achieved in a finite element code. The numerical results extracted from these simulations are compared with each other and with the experimental data in order to determine the relative performance of these turbulence models and to find the best model for the flow of interest. Although most of the LES simulations have been previously carried out using finite volume methods, results from using the present model show that the finite element method (FEM) can also be used with confidence. Copyright © 2001 John Wiley & Sons, Ltd.

Journal ArticleDOI
TL;DR: In this article, the viability of multiscale lattice Boltzmann schemes for numerical simulation of turbulent flows is discussed and numerically demonstrated for turboaxial machine applications, and the extension of boundary-fitting formulas based on wall functions is proposed, which enables the efficient computation of turbulent flow in complex curvilinear geometry using a simple Cartesian grid.