Showing papers on "K-epsilon turbulence model published in 1994"

Two-equation eddy-viscosity turbulence models for engineering applications

Abstract: Two new two-equation eddy-viscosity turbulence models will be presented. They combine different elements of existing models that are considered superior to their alternatives. The first model, referred to as the baseline (BSL) model, utilizes the original k-ω model of Wilcox in the inner region of the boundary layer and switches to the standard k-e model in the outer region and in free shear flows. It has a performance similar to the Wilcox model, but avoids that model's strong freestream sensitivity

Toward a theory of interstellar turbulence. 2. Strong Alfvenic turbulence

Abstract: We continue to investigate the possibility that interstellar turbulence is caused by nonlinear interactions among shear Alfven waves. Here, as in Paper I, we restrict attention to the symmetric case where the oppositely directed waves carry equal energy fluxes. This precludes application to the solar wind in which the outward flux significantly exceeds the ingoing one. All our detailed calculations are carried out for an incompressible magnetized fluid. In incompressible magnetohydrodynamics (MHD), nonlinear interactions only occur between oppositely direct waves. Paper I contains a detailed derivation of the inertial range spectrum for the weak turbulence of shear Alfven waves. As energy cascades to high perpendicular wavenumbers, interactions become so strong that the assumption of weakness is no longer valid. Here, we present a theory for the strong turbulence of shear Alfven waves. It has the following main characteristics. (1) The inertial-range energy spectrum exhibits a critical balance beween linear wave periods and nonlinear turnover timescales. (2) The "eddies" are elongated in the direction of the field on small spatial scales; the parallel and perpendicular components of the wave vector, k_z and k_⊥, are related by k_z ≈ k^(2/3) _⊥L^(-1/3), where L is the outer scale of the turbulence. (3) The "one-dimensional" energy spectrum is proportional to k^(-5/3) _⊥-an anisotropic Kolmogorov energy spectrum. Shear Alfvenic turbulence mixes specific entropy as a passive contaminant. This gives rise to an electron density power spectrum whose form mimics the energy spectrum of the turbulence. Radio, wave scattering by these electron density fluctuations produces anisotropic scatter-broadened images. Damping by ion-neutral collisions restricts Alfvenic turbulence to highly ionized regions of the interstellar medium. We expect negligible generation of compressive MHD waves by shear Alfven waves belonging to the critically balanced cascade. Viscous and collisionless damping are also unimportant in the interstellar medium (ISM). Our calculations support the general picture of interstellar turbulence advanced by Higdon.

A New K-epsilon Eddy Viscosity Model for High Reynolds Number Turbulent Flows: Model Development and Validation

Abstract: A new k-epsilon eddy viscosity model, which consists of a new model dissipation rate equation and a new realizable eddy viscosity formulation, is proposed. The new model dissipation rate equation is based on the dynamic equation of the mean-square vorticity fluctuation at large turbulent Reynolds number. The new eddy viscosity formulation is based on the realizability constraints: the positivity of normal Reynolds stresses and Schwarz' inequality for turbulent shear stresses. We find that the present model with a set of unified model coefficients can perform well for a variety of flows. The flows that are examined include: (1) rotating homogeneous shear flows; (2) boundary-free shear flows including a mixing layer, planar and round jets; (3) a channel flow, and flat plate boundary layers with and without a pressure gradient; and (4) backward facing step separated flows. The model predictions are compared with available experimental data. The results from the standard k-epsilon eddy viscosity model are also included for comparison. It is shown that the present model is a significant improvement over the standard k-epsilon eddy viscosity model.

The spatial structure of neutral atmospheric surface-layer turbulence

Abstract: Modelling of the complete second-order structure of homogeneous, neutrally stratified atmospheric boundary-layer turbulence, including spectra of all velocity components and cross-spectra of any combination of velocity components at two arbitrarily chosen points, is attempted. Two models based on Rapid Distortion Theory (RDT) are investigated. Both models assume the velocity profile in the height interval of interest to be approximately linear. The linearized Navier–Stokes equation together with considerations of ‘eddy’ lifetimes are then used to modify the spatial second-order structure of the turbulence. The second model differs from the first by modelling the blocking by the surface in addition to the shear. The resulting models of the spectral velocity tensor contain only three adjustable parameters: a lengthscale describing the size of the largest energy-containing eddies, a non-dimensional number used in the parametrization of ‘eddy’ lifetime, and the third parameter is a measure of the energy dissipation.Two atmospheric experiments, both designed to investigate the spatial structure of turbulence and both running for approximately one year, are used to test and calibrate the models. Even though the approximations leading to the models are very crude they are capable of predicting well the two-point second-order statistics such as cross-spectra, coherences and phases, on the basis of measurements carried out at one point. The two models give very similar predictions, the largest difference being in the coherences involving vertical velocity fluctuations, where the blocking by the surface seems to have a significant effect.

Vorticity and turbulence

Abstract: This is an introduction to turbulence in vortex systems, and to turbulence theory for incompressible flow described in terms of the vorticity field. It is the author's hope that by the end of the book the reader will believe that these subjects are identical, and constitute a special case of fairly standard statistical mechanics, with both equilibrium and non-equilibrium aspects. The author's main goal is to relate turbulence to statistical mechanics. The first three chapters of the book constitute a fairly standard introduction to homogeneous turbulence in incompressible flow; a quick review of fluid mechanics; a summary of the appropriate Fourier theory; and a summary of Kolmogorov's theory of the inertial range. The next four chapters present the statistical theory of vortex notion, and the vortex dynamics of turbulence. The book ends with the major conclusion that turbulence can no longer be viewed as incomprehensible.

Natural convection flow in a square cavity revisited: Laminar and turbulent models with wall functions

Abstract: Numerical simulations have been undertaken for the benchmark problem of natural convection flow in a square cavity. The control volume method is used to solve the conservation equations for laminar and turbulent flows for a series of Rayleigh numbers (Ra) reaching values up to 1010. The k-ϵ model has been used for turbulence modelling with and without logarithmic wall functions. Uniform and non-uniform (stretched) grids have been employed with increasing density to guarantee accurate solutions, especially near the walls for high Ra-values. ADI and SIP solvers are implemented to accelerate convergence. Excellent agreement is obtained with previous numerical solutions, while some discrepancies with others for high Ra-values may be due to a possibly different implementation of the wall functions. Comparisons with experimental data for heat transfer (Nusselt number) clearly demonstrates the limitations of the standard k-ϵ model with logarithmic wall functions, which gives significant overpredictions.

Analysis of the K-epsilon turbulence model

Abstract: This book is aimed at applied mathematicians interested in numerical simulation of turbulent flows. The book is centered around the k - {epsilon} model but it also deals with other models such as subgrid scale models, one equation models and Reynolds Stress models. The reader is expected to have some knowledge of numerical methods for fluids and, if possible, some understanding of fluid mechanics, the partial differential equations used and their variational formulations. This book presents the k - {epsilon} method for turbulence in a language familiar to applied mathematicians, stripped bare of all the technicalities of turbulence theory. The model is justified from a mathematical standpoint rather than from a physical one. The numerical algorithms are investigated and some theoretical and numerical results presented. This book should prove an invaluable tool for those studying a subject that is still controversial but very useful for industrial applications. (authors). 71 figs., 200 refs.

Intermittency in fully developed turbulence: Log-Poisson statistics and generalized scale covariance.

Abstract: Some properties of a model of intermittency in fully developed turbulence due to She and L\'ev\^eque [Phys. Rev. Lett. 72, 336 (1994)] are explored. The probability functions solution of the model is shown to be simply related to the log-Poisson statistics of local nondimensional energy dissipation. It is also shown that the intermittency obtained by She and L\'ev\^eque can be interpreted as the consequence of the scale covariance of the energy dissipation. Based on these observations, a new picture of turbulence is presented, in which scale covariance plays a central role.

The influence of a mean magnetic field on three- dimensional magnetohydrodynamic turbulence

Abstract: Building on results from two-dimensional magnetohydrodynamic (MHD) turbulence (Shebalin, Matthaeus & Montgomery 1983), the development of anisotropic states from initially isotropic ones is investigated numerically for fully three-dimensional incompressible MHD turbulence. It is found that when an external d.c. magnetic field (B0) is imposed on viscous and resistive MHD systems, excitations are preferentially transferred to modes with wavevectors perpendicular to B0). The anisotropy increases with increasing mechanical and magnetic Reynolds numbers, and also with increasing wavenumber. The tendency of B0 to inhibit development of turbulence is also examined.

The stabilizing effect of compressibility in turbulent shear flow

Abstract: Direct numerical simulation of turbulent homogeneous shear flow is performed in order to clarify compressibility effects on the turbulence growth in the flow. The two Mach numbers relevant to homogeneous shear flow are the turbulent Mach number M_t and the gradient Mach number M_g. Two series of simulations are performed where the initial values of M_g and M_t are increased separately. The growth rate of turbulent kinetic energy is observed to decrease in both series of simulations. This `stabilizing'' effect of compressibility on the turbulent energy growth rate is observed to be substantially larger in the DNS series where the initial value of M_g is changed. A systematic comparison of the different DNS cases shows that the compressibility effect of reduced turbulent energy growth rate is primarily due to the reduced level of turbulence production and not due to explicit dilatational effects. The reduced turbulence production is not a mean density effect since the mean density remains constant in compressible homogeneous shear flow. The stabilizing effect of compressibility on the turbulence growth is observed to increase with the gradient Mach number M_g in the homogeneous shear flow DNS. Estimates of M_g for the mixing layer and the boundary layer are obtained. These estimates show that the parameter M_g becomes much larger in the high-speed mixing layer relative to the high-speed boundary layer even though the mean flow Mach numbers are the same in the two flows. Therefore, the inhibition of turbulent energy production and consequent `stabilizing'' effect of compressibility on the turbulence (over and above that due to the mean density variation) is expected to be larger in the mixing layer relative to the boundary layer in agreement with experimental observations.

Bottleneck phenomenon in developed turbulence

Abstract: It is shown how viscosity increases turbulence level in the inertial interval by suppressing turbulent transfer.

Reynolds Number Effects in Wall-Bounded Turbulent Flows

Abstract: This paper reviews the state of the art of Reynolds number effects in wall-bounded shear-flow turbulence, with particular emphasis on the canonical zero-pressure-gradient boundary layer and two-dimensional channel flow problems. The Reynolds numbers encountered in many practical situations are typically orders of magnitude higher than those studied computationally or even experimentally. High-Reynolds number research facilities are expensive to build and operate and the few existing are heavily scheduled with mostly developmental work. For wind tunnels, additional complications due to compressibility effects are introduced at high speeds. Full computational simulation of high-Reynolds number flows is beyond the reach of current capabilities. Understanding of turbulence and modeling will continue to play vital roles in the computation of high-Reynolds number practical flows using the Reynolds-averaged Navier-Stokes equations. Since the existing knowledge base, accumulated mostly through physical as well as numerical experiments, is skewed towards the low Reynolds numbers, the key question in such high-Reynolds number modeling as well as in devising novel flow control strategies is: what are the Reynolds number effects on the mean and statistical turbulence quantities and on the organized motions? Since the mean flow review of Coles (1962), the coherent structures, in low-Reynolds number wall-bounded flows, have been reviewed several times. However, the Reynolds number effects on the higher-order statistical turbulence quantities and on the coherent structures have not been reviewed thus far, and there are some unresolved aspects of the effects on even the mean flow at very high Reynolds numbers. Furthermore, a considerable volume of experimental and full-simulation data have been accumulated since 1962. The present article aims at further assimilation of those data, pointing to obvious gaps in the present state of knowledge and highlighting the misunderstood as well as the ill-understood aspects of Reynolds number effects.

On particle adhesion and removal mechanisms in turbulent flows

Abstract: Particle removal mechanisms in a turbulent flow are examined and two models which are based on the structure of turbulence near wall flow are described. The theory of critical moment, along with the sliding detachment models, is used, and the effects of the near-wall coherent vortices, as well as turbulence burst/inrush phenomena, are included. The down sweep flow patterns are modeled as viscous stagnation point flows. The hydrodynamic force and torque acting on a spherical particle attached to a wall are used in the model developments. For different adhesion models, the minimum critical shear velocities for removing particles of different sizes are evaluated. The model predictions are compared with the available data and discussed.

Development of a k-ε Model for Bubbly Two-Phase Flow

Abstract: An extension of the k-[epsilon] model for bubbly two-phase flow is proposed and tested against experimental data. The basic assumption made is that the shear-induced turbulence and bubble-induced turbulence may be linearly superposed. This assumption results in a model with two time constants that matches both homogeneous two-phase turbulence data (Lance and Bataille, 1991) and pipe data (Serizawa, 1986). The coefficients of the single-phase k-[epsilon] model have not been modified and only one additional coefficient is required: the virtual volume coefficient of the bubbles, which may be determined from first principles. This model not only agrees with the data trends, but it also predicts the turbulence suppression which has been measured for high Reynolds number bubbly air/water flows in pipes.

Oscillating grids as a source of nearly isotropic turbulence

Abstract: Turbulence generated by vertical oscillations of a horizontal monoplanar grid in homogeneous water contained in a tank was used to study certain properties of nearly isotropic turbulence. The cases of sustained oscillations and the removal of forcing after a period of oscillations were considered. The former was used to evaluate the Eulerian‐frequency spectra of nearly isotropic turbulence, and the velocity–time power law and spectral behavior of decaying turbulence were studied using the latter. The experimental observations are compared with available theoretical formulations as well as previous experimental observations.

Decay of Isotropic Turbulence at Low Reynolds Number

Abstract: Decay of isotropic turbulence is computed using direct numerical simulations. Comparisons with experimental spectra at moderate and low Reynolds numbers (R(sub lambda) less than 70) show good agreement. At moderate to high Reynolds numbers (R(sub lambda) greater 50), the spectra are found to collapse with Kolmogorov scaling at high wave numbers. However, at low Reynolds numbers (R(sub lambda) less than 50) the shape of the spectra at the Kolmogorov length scales is Reynolds number dependent. Direct simulation data from flowfields of decaying isotropic turbulence are used to compute the terms in the equation for the dissipation rate of the turbulent kinetic energy. The development of the skewness and the net destruction of the turbulence dissipation rate in the limit of low Reynolds numbers are presented. The nonlinear terms are found to remain active at surprisingly low Reynolds numbers.

Observations of turbulence in the surf zone

Abstract: : The turbulence generated by waves breaking on a natural beach is examined using hotfilm anemometer data. Turbulence intensity is estimated from the dissipation rate and an appropriate length scale (a fraction of the water depth). The dissipation rates are determined from wavenumber spectra found by applying Taylor's hypothesis to frequency spectra of short (1/8s) hotfilm time series. The resulting Froude-scaled turbulence intensities are relatively uniform throughout the water column and are similar in vertical structure but lower in magnitude than in existing laboratory studies. The magnitudes of the turbulence intensity observed in both the field and laboratory are consistent with an existing macroscopic model of bore dissipation in the surf zone. Scaling by this bore model relates turbulence intensity levels of monochromatic waves in small-scale laboratory experiments to random waves in the natural surf zone.... Surfzone, Turbulence, Wave breaking, Wave dissipation.

Charged-Particle Motion in Multidimensional Magnetic Field Turbulence

Abstract: We present a new analysis of the fundamental physics of charged-particle motion in a turbulent magnetic field using a numerical simulation. The magnetic field fluctuations are taken to be static and to have a power spectrum which is Kolmogorov. The charged particles are treated as test particles. It is shown that when the field turbulence is independent of one coordinate (i.e., k lies in a plane), the motion of these particles across the magnetic field is essentially zero, as required by theory. Consequently, the only motion across the average magnetic field direction that is allowed is that due to field-line random walk. On the other hand, when a fully three-dimensional realization of the turbulence is considered, the particles readily cross the field. Transport coefficients both along and across the ambient magnetic field are computed. This scheme provides a direct computation of the Fokker-Planck coefficients based on the motions of individual particles, and allows for comparison with analytic theory.

A family of stochastic models for two-particle dispersion in isotropic homogeneous stationary turbulence

Abstract: A family of Lagrangian stochastic models for the joint motion of particle pairs in isotropic homogeneous stationary turbulence is considered. The Markov assumption and well-mixed criterion of Thomson (1990) are used, and the models have quadratic-form functions of velocity for the particle accelerations. Two constraints are derived which formally require that the correct one-particle statistics are obtained by the models. These constraints involve the Eulerian expectation of the ‘acceleration’ of a fluid particle with conditioned instantaneous velocity, given either at the particle, or at some other particle's position. The Navier-Stokes equations, with Gaussian Eulerian probability distributions, are shown to give quadratic-form conditional accelerations, and models which satisfy these two constraints are found. Dispersion calculations show that the constraints do not always guarantee good one-particle statistics, but it is possible to select a constrained model that does. Thomson's model has good one-particle statistics, but is shown to have unphysical conditional accelerations. Comparisons of relative dispersion for the models are made.

A note on the spectra and decay of rotating homogeneous turbulence

Abstract: In this Letter, the dynamics of spectral energy transfer in rotating homogeneous turbulence is investigated. It is shown that the wave number kΩ=(Ω3/e)1/2 (defined by the rotation speed Ω and dissipation e) determines the turbulence length scale, above which rotation effects on spectral transfer and on energy spectrum form are important. From the rotation‐modified spectrum, turbulence decay laws are also inferred.

Turbulence: the chief outstanding difficulty of our subject

Abstract: A review of interesting current topics in turbulence research is decorated with examples of popular fallacies about the behaviour of turbulence. Topics include the status of the Law of the Wall, especially in compressible flow; analogies between the effects of Reynolds number, pressure gradient, unsteadiness and roughness change; the status of Kolmogorov's universal equilibrium theory and local isotropy of the small eddies; turbulence modelling, with reference to universality, pressure-strain modelling and the dissipation equation; and chaos. Fallacies include the mixing-length concept; the effect of pressure gradient on Reynolds shear stress; the separability of time and space derivatives; models of the dissipation equation; and chaos.

Evolution of energy-containing turbulent eddies in the solar wind

Abstract: Previous theoretical treatments of fluid-scale turbulence in the solar wind have concentrated on describing the state and dynamical evolution of fluctuations in the inertial range, which are characterized by power law energy spectra. In the present paper a model for the evolution of somewhat larger, more energetic magnetohydrodynamic (MHD) fluctuations is developed by analogy with classical hydrodynamic turbulence in the quasi-equilibrium range. The model is constructed by assembling and extending existing phenomenologies of homogeneous MHD turbulence, as well as simple two-length-scale models for transport of MHD turbulence in a weekly inhomogeneous medium. A set of equations is presented for the evolution of the turbulence, including the transport and nonlinear evolution of magnetic and kinetic energy, cross helicity, and their correlation scales. Two versions of the model are derived, depending on whether the fluctuations are distributed isotropically in three dimensions or restricted to the two-dimensional plane perpendicular to the mean magnetic field. This model includes a number of potentially important physical effects that have been neglected in previous discussions of transport of solar wind turbulence.

Effects of Free-Stream Turbulence and Adverse Pressure Gradients on Boundary Layer Transition

Abstract: Boundary layer measurements are presented through transition for six different free- stream turbulence levels and a complete range of adverse pressure gradients for attached laminar flow. Measured intermittency distributions provide an excellent similarity basis for characterizing the transition process under all conditions tested when the Narasimha procedure for determining transition inception is used. This inception location procedure brings consistency to the data. Velocity profiles and integral parameters are influenced by turbulence level and pressure gradient and do not provide a consistent basis

Computation of oscillating airfoil flows with one- and two-equation turbulence models

Abstract: The ability of one- and two-equation turbulence models to predict unsteady separated flows over airfoils is evaluated. An implicit, factorized, upwind-biased numerical scheme is used for the integration of the compressible, Reynolds-averaged Navier-Stokes equations. The turbulent eddy viscosity is obtained from the computed mean flowfield by integration of the turbulent field equations. One- and two-equation turbulence models are first tested for a separated airfoil flow at fixed angle of incidence. The same models are then applied to compute the unsteady flowfields about airfoils undergoing oscillatory motion at low subsonic Mach numbers. Experimental cases where the flow has been tripped at the leading-edge and where natural transition was allowed to occur naturally are considered. The more recently developed turbulence models capture the physics of unsteady separated flow significantly better than the standard kappa-epsilon and kappa-omega models. However, certain differences in the hysteresis effects are observed. For an untripped high-Reynolds-number flow, it was found necessary to take into account the leading-edge transitional flow region to capture the correct physical mechanism that leads to dynamic stall.