Showing papers on "K-epsilon turbulence model published in 1988"

Reassessment of the scale-determining equation for advanced turbulence models

Abstract: A comprehensive and critical review of closure approximations for two-equation turbulence models has been made. Particular attention has focused on the scale-determining equation in an attempt to find the optimum choice of dependent variable and closure approximations. Using a combination of singular perturbation methods and numerical computations, this paper demonstrates that: 1) conventional A:-e and A>w formulations generally are inaccurate for boundary layers in adverse pressure gradient; 2) using "wall functions'' tends to mask the shortcomings of such models; and 3) a more suitable choice of dependent variables exists that is much more accurate for adverse pressure gradient. Based on the analysis, a two-equation turbulence model is postulated that is shown to be quite accurate for attached boundary layers in adverse pressure gradient, compressible boundary layers, and free shear flows. With no viscous damping of the model's closure coefficients and without the aid of wall functions, the model equations can be integrated through the viscous sublayer. Surface boundary conditions are presented that permit accurate predictions for flow over rough surfaces and for flows with surface mass addition.

Near-wall turbulence models for complex flows including separation

Abstract: Results of a computational experiment designed to investigate the performance of different near-wall treatments in a single turbulence model with a common numerical method are reported. The complete fully elliptic, Reynoldsaveraged Navier-Stokes equations have been solved using a low-Reynolds-number model, a new two-layer model, and a two-point wall-function method, in thek-s turbulence model, for the boundary layer and wake of two axisymmetric bodies. These tests enable the evaluation of the performance of the different approaches in flows involving longitudinal and transverse surface curvatures, streamwise and normal pressure gradients, viscous-inviscid interaction, and separation. The two-layer approach has been found to be quite promising for such flows and can be extended to other complex flows.

Design of a Nonsingular Level 2.5 Second-Order Closure Model for the Prediction of Atmospheric Turbulence

Abstract: The suitability of applying the Mellor and Yamada (1974, 1982) Level 2.5 second-order turbulence closure model to general circulation models is investigated by examining not only the scheme's simulation of fully (or nearly fully) developed turbulence, but also its simulation of rapidly growing or strongly decaying turbulence. The behavior of the model is presented over its entire domain of definition, with special consideration given to the pathologies of the model. The model is then modified for the case of growing turbulence to rectify some of its physical shortcomings for that case, and to remove the pathologies that prohibit its use in a general circulation model. The performance of the modified Level 2.5 model is compared to the performance of various other modified versions through the numerical simulation for a growing convective PBL. The results show that the modified Level 2.5 model is a viable candidate for the prediction of turbulence and the simulation of the PBL in general circulation models.

The subgrid‐scale modeling of compressible turbulence

Abstract: A subgrid‐scale model recently derived by Yoshizawa [Phys. Fluids 29, 2152 (1986)] for use in the large‐eddy simulation of compressible turbulent flows is examined from a fundamental theoretical and computational standpoint. It is demonstrated that this model, which is only applicable to compressible turbulent flows in the limit of small density fluctuations, correlates somewhat poorly with the results of direct numerical simulations of compressible isotropic turbulence at low Mach numbers. An alternative model, based on Favre‐filtered fields, is suggested which appears to reduce these limitations.

Turbulence structure near a sharp density interface

Abstract: The effects of a sharp density interface and a rigid flat plate on oscillating-grid induced shear-free turbulence were investigated experimentally. A two-component laser-Doppler velocimeter was used to measure turbulence intensities in and above the density interface (with matched refractive indices) and near the rigid flat plate. Energy spectra, velocity correlations, and kinetic energy fluxes were also measured. Amplification of the horizontal turbulent velocity, coupled with a sharp reduction in the vertical turbulent velocity, was observed near both the density interface and the flat plate. These findings are in agreement with some previous results pertaining to shear-free turbulence near rigid walls (Hunt & Graham 1978) and near density interfaces (Long 1978). The results imply that, near the density interface, the turbulent kinetic energy in the vertical velocity component is only a small fraction of the total turbulent kinetic energy and indicate that the effects of the anisotropy created by the density interface or the flat plate are confined to the large turbulence scales.

The Interaction of Acoustic Radiation with Turbulence

Abstract: We derive expressions for the spectral emissivity and absorptivity of acoustic radiation by low Mach number (M ≪ 1) turbulent fluids. The emissivity and absorptivity depend on the manner in which the turbulence is excited. We consider three types of turbulence. The first is free turbulence, that is, turbulence which is not subject to external forces. The second and third examples are special cases of forced turbulence, turbulence maintained by stirring with spoons and turbulent pseudoconvection. Acoustic quadrupoles are the lowest order acoustic multipoles present in free turbulence, and they control both its emissivity and absorptivity. Acoustic dipoles are created in forced turbulence, and they enhance the acoustic emissivity by M^(-2) compared to that of free turbulence. The acoustic absorptivity of forced turbulence is quite subtle. The absorptivity of turbulence which is maintained by stirring is dominated by acoustic dipoles and exceeds that of free turbulence by M^(-2). The dipole absorptivity of turbulent pseudoconvection is reduced by M^2 below that of turbulence maintained by stirring. Thus, the absorptivity of turbulent pseudoconvection is no larger than that of free turbulence. We apply our results to estimate the equilibrium energies of the acoustic modes in a box filled with fluid some of which is turbulent. For both free turbulence and turbulence maintained by stirring, the most highly excited acoustic modes attain energies E ~ Mv^2, where M and v are the typical mass and velocity of an energy bearing eddy. The quality factors, or Q's, of the modes are larger by M^(-2) in the former case than in the latter. For turbulent pseudoconvection, the most energetic acoustic modes have equilibrium energies E ~ Mc^2 , where c is the sound speed. Their Q's are comparable to those of modes in equilibrium with free turbulence. We evaluate the scattering of acoustic radiation by turbulent fluids. For all types of turbulence, the scattering opacity is smaller by M^3 than the absorptive opacity for frequencies near the peak of the acoustic spectrum. Radiation scattered by free turbulence and turbulent pseudoconvection suffers frequency shifts Δω ~ ω. The frequency shifts are much smaller, Δω ~ Mω, for radiation scattered by turbulence maintained by stirring. We investigate the rate at which nonlinear interactions transfer energy among the acoustic modes. If all of the fluid in the box is turbulent, this rate is slower, by M^3 for free turbulence, by M^5 for turbulence maintained by stirring, and by M for turbulent pseudoconvection, than the rate at which the individual acoustic modes exchange energy with the turbulence. If only a small portion of the fluid is turbulent, the nonlinear mode interactions can be significant, especially for modes in equilibrium with turbulent pseudoconvection. Our results have potential applications to the acoustic radiation in regions of extended turbulence which often arise in nature. In particular, they should prove useful in understanding the excitation of solar oscillations.

A Decaying Isotropic Turbulence Pursued by the Spectral Method

Abstract: The decaying isotropic turbulence starting with a typical initial energy spectrum was numerically investigated by the spectral method for Reynolds numbers 50–500, using up to 128 3 grid points. The microscale Reynolds number reached at a fully developed state was \({\lesssim}100\). Only the periodic boundary condition was set on the surfaces of the cube which contained the turbulence. As a result, the Kolmogorov spectrum law and other interesting characteristics of the turbulence were found, including the perspective of intermittent strong-vorticity regions randomly distributed in a fully developed turbulence.

Turbulence and Random Processes in Fluid Mechanics

Abstract: This book aims to give students the background to understand current research books on turbulence. To achieve this, it mixes a specialized review of advanced developments with elementary derivations of basic concepts or calculations. There is no complete theory of turbulence in fluid mechanics. The scope of this subject involves a wide spectrum of topics: fluid motion equations, statistical tools, stability theory, transition to turbulence, turbulence modeling, and so on. In few pages, this book presents a panorama of distinct approaches, in the manner of a handbook. A large number of items are at least mentioned, if not treated in depth.

Turbulent mixing at a shear-free density interface

Abstract: The interaction of a sharp density interface with oscillating-grid-induced shear-free turbulence was experimentally investigated. A linear photodiode array was used in conjunction with laser-induced fluorescence to measure the concentration of dye that was initially only in the less dense layer. A laser-Doppler velocimeter was used to measure the vertical velocity in and above the density interface at a point where the dye concentration was also measured. Potential refractive-index-fluctuation problems were avoided using solutes that provided a homogeneous optical environment across the density interface. Internal wave spectra, amplitudes and velocities, as well as the vertical mass flux were measured. The results indicate that mixing occurs in intermittent bursts and that the gradient (local) Richardson number remains constant for a certain range of the overall Richardson number R_j, defined in terms of an integral lengthscale, buoyancy jump and turbulence intensity. The spectra of the internal waves decay as f^(−3) at frequencies below the maximum Brunt-Vaisala frequency. These findings give support to a model for oceanic mixing proposed by Phillips (1977) in which the internal waves are limited in their spectral density by sporadic local instabilities and breakdown to turbulence. The results also indicate that, for a certain R_j range, the thickness of the interfacial layer (normalized by the integral lengthscale of the turbulence) is a decreasing function of R_j. At sufficiently high R_j the interfacial thickness becomes limited by diffusive effects. Finally, we discuss a simple model for entrainment at a density interface in the presence of shear-free turbulence.

Structure of Turbulent Sonic Underexpanded Free Jets

Abstract: Turbulent mixing in adapted and weakly underexpanded (underexpansion ratios less than 1.4) round jets, involving fully developed pipe flows injected into still air, was studied experimentally. Measurements included mean and fluctuating concentrations and mean static pressures using laser-induced iodine flourescence and mean and fluctuating streamwise velocities using laser Doppler anemometry. Predictions were used to help interpret the measurements and to initiate evaluation of methods for analyzing these processes. The predictions were based on k-e turbulence models, including a proposed extension to treat compressibility effects at high convection Mach numbers. In conjunction with other measurements, the results show that the near-field region of underexpanded jets is influenced by compressibility, which tends to reduce turbulent mixing rates at high convective Mach numbers, and high turbulence levels at the jet exit, which tends to increase turbulent mixing rates. Predictions based on effective-ada pted-jet exit conditions yielded reasonably good estimates of mixing levels near the exit of underexpanded jets for both fully developed and slug flow jet exit conditions; however, such methods provide no information concerning the near-field region containing the shock waves. Predictions based on solution of parabolized Navier-Stokes governing equations, using the SCIPVIS algorithm, were encouraging for slug flow exit conditions, but this approach must be extended to treat fully developed flow at the jet exit.

Contributions to the understanding of large-scale coherent structures in developing free turbulent shear flows

Abstract: Advances in the mechanics of boundary layer flow are reported. The physical problems of large scale coherent structures in real, developing free turbulent shear flows, from the nonlinear aspects of hydrodynamic stability are addressed. The presence of fine grained turbulence in the problem, and its absence, lacks a small parameter. The problem is presented on the basis of conservation principles, which are the dynamics of the problem directed towards extracting the most physical information, however, it is emphasized that it must also involve approximations.

Turbulence Structure of the Convective Boundary Layer. Part I. Variability of Normalized Turbulence Statistics

Abstract: Profiles of turbulence statistics from aircraft observations of the Phoenix 78 convective boundary layer experiment are compared with those from previous observational and modeling studies. The sources and degree of variability of the normalized results, both within and between experiments, are discussed. The intercomparison provides evidence that moderately rolling terrain does not bias convective boundary layer turbulence structure away from that observed over more uniform terrain. The manner in which cross inversion entrainment affects turbulence in the atmosphere and in models is also discussed.

Kinetic Energy Transfer between Internal Gravity Waves and Turbulence

Abstract: We describe a reliable method for distinguishing the mean, wave and turbulence fields when internal waves with changing amplitude perturb the turbulent boundary layer. By integrating the component wave and turbulence kinetic energy budgets through the turbulent layer, we show that only mechanism trasnferring energy between wave and turbulent fields is the work done by the periodic part of the turbulent stress against the wave rate of strain. When these components are π/2 out of phase. the net energy transfer is zero. Eight wave-turbulence interaction events of differing stability are analyzed and interpreted using rapid distortion theory. When density stratification is approximately steady, the phase relationship does not change from π/2 However, periodicity in the stratification changes the phase angle and leads to strong energy transfer from wave to turbulence.

Numerical Prediction of Turbulent Flow in Rotating Cavities

Abstract: Predictions of the isothermal, incompressible flow in the cavity formed between two corotating plane disks and a peripheral shroud have been obtained using an elliptic calculation procedure and a low turbulence Reynolds number k–e model for the estimation of turbulent transport. Both radial inflow and outflow are investigated for a wide range of flow conditions involving rotational Reynolds numbers up to ∼106 . Although predictive accuracy is generally good, the computed flow in the Ekman layers for radial outflow often displays a retarded spreading rate and a tendency to laminarize under conditions that are known from experiment to produce turbulent flow.

The Turbulence Structure of Nocturnal Slope Flow

Abstract: Measurements of the turbulence structure of nocturnal slope flow are used to test the hypothesis that slope flow turbulence in the region above the low-level wind maximum is decoupled from the surface and has a local structure similar to that found by Nieuwstadt for stably stratified flow over flat terrain. A turbulence covariance model is used to determine local scaling relations for slope flow. These relations predict that slope-flow turbulence variables, scaled with the local values of the momentum and heat fluxes, are nearly identical to those for stably stratified flow over flat terrain, the principal exception being the normalized eddy diffusivities. Comparison of observations with local scaling predictions above the slope flow wind maximum indicates that local scaling is a promising approach for the description of slope flow turbulence. In particular, the slope flow turbulent kinetic energy (TKE) is found to be proportional to the local stress, with the constant of proportionality in close...

Cosmic-ray pitch-angle scattering in isotropic turbulence

Abstract: A dissipation range is incorporated in the turbulence model to reconcile the divergent conclusions from studies of cosmic-ray pitch-angle scattering in isotropic magnetic turbulence. The Fokker-Planck coefficient for pitch-angle scattering is calculated. It is shown that the slab form of the Fokker-Plank coefficient (Jokipii, 1966) is valid at very low energies, while the nonslab form (Fisk, 1974) is valid at intermediate energies.

Recent insights into instability and transition to turbulence in open-flow systems

Abstract: Roads to turbulence in open-flow shear layers are interpreted as sequences of often competing instabilities. These correspond to primary and higher order restructurings of vorticity distributions which culminate in convected spatial disorder (with some spatial coherence on the scale of the shear layer) traditionally called turbulence. Attempts are made to interpret these phenomena in terms of concepts of convective and global instabilities on one hand, and of chaos and strange attractors on the other. The first is fruitful, and together with a review of mechanisms of receptivity provides a unifying approach to understanding and estimating transition to turbulence. In contrast, current evidence indicates that concepts of chaos are unlikely to help in predicting transition in open-flow systems. Furthermore, a distinction should apparently be made between temporal chaos and the convected spatial disorder of turbulence past Reynolds numbers where boundary layers and separated shear layers are formed.

Transport phenomena in turbulent flows

Abstract: These proceedings contain 65 papers grouped under the headings of: Fundamentals, Coherent Structures, Wall Shear Flows, Free Shear Flows, Scalar and Buoyant Transport, Modeling and Prediction of Turbulent Transport, Numerical Simulations of Turbulence, Measurement Techniques, Turbulent Transport in Applications.

Modeling Turbulent Transport in Stratified Estuary

Abstract: A finite difference mathematical model for the calculation of estuarine flow and transport processes is presented. Due to the emphasis on engineering applications, turbulence closure is formulated on the basis of mixing length and damping functions. The necessary empirical constants were determined from theoretical considerations and from data published in the literature from meteorological, oceanographic, and laboratory experiments, which yielded a set of parameters for eddy viscosity and eddy diffusivity not tuned to a particular system. Similarly, an integral model is derived to account for wind‐induced mixing in the case of highly variable meteorological conditions. Application of the model in a case study of the Trave estuary in northern Germany shows its predictive capability. A long‐term simulation of 85 days reproduced both total mixing events and strong stratification. The model showed good agreement with the extensive field data.

Two-Equation Low-Reynolds-Number Turbulence Modeling of Transitional Boundary Layer Flows Characteristic of Gas Turbine Blades. Ph.D. Thesis. Final Contractor Report

Abstract: The use of low Reynolds number (LRN) forms of the k-epsilon turbulence model in predicting transitional boundary layer flow characteristic of gas turbine blades is developed. The research presented consists of: (1) an evaluation of two existing models; (2) the development of a modification to current LRN models; and (3) the extensive testing of the proposed model against experimental data. The prediction characteristics and capabilities of the Jones-Launder (1972) and Lam-Bremhorst (1981) LRN k-epsilon models are evaluated with respect to the prediction of transition on flat plates. Next, the mechanism by which the models simulate transition is considered and the need for additional constraints is discussed. Finally, the transition predictions of a new model are compared with a wide range of different experiments, including transitional flows with free-stream turbulence under conditions of flat plate constant velocity, flat plate constant acceleration, flat plate but strongly variable acceleration, and flow around turbine blade test cascades. In general, calculational procedure yields good agreement with most of the experiments.

Turbulence modeling in non-inertial frames of reference

Abstract: The effect of an arbitrary change of frame on the structure of turbulence models is examined from a fundamental theoretical standpoint. It is proven, as a rigorous consequence of the Navier-Stokes equations, that turbulence models must be form invariant under arbitrary translational accelerations of the reference frame and should only be affected by rotations through the intrinsic mean vorticity. A direct application of the invariance property along with the Taylor-Proudman Theorem, material frame-indifference in the limit of two-dimensional turbulence and Rapid Distortion Theory is shown to yield powerful constraints on the allowable form of turbulence models. Most of the commonly used turbulence models are demonstrated to be in serious violation of these constraints and consequently are inconsistent with the Navier-Stokes equations in non-inertial frames. Alternative models with improved non-inertial properties are developed and some simple applications to rotating turbulent flows are considered.