Showing papers on "K-epsilon turbulence model published in 1985"
1,138 citations
TL;DR: In this article, experimental data have been obtained in an incompressible turbulent flow over a rearward-facing step in a diverging channel flow and mean velocities, Reynolds stresses, and triple products that were measured by a laser Doppler velocimeter are presented for two cases of tunnel wall divergence.
Abstract: Experimental data have been obtained in an incompressible turbulent flow over a rearward-facing step in a diverging channel flow. Mean velocities, Reynolds stresses, and triple products that were measured by a laser Doppler velocimeter are presented for two cases of tunnel wall divergence. Eddy viscosities, production, convection, turbulent diffusion, and dissipation (balance of kinetic energy equation) terms are extracted from the data. These data are compared with various eddy-viscosity turbulence models. Numerical calculations incorporating the k-epsilon and algebraic-stress turbulence models are compared with the data. When determining quantities of engineering interest, the modified algebraic-stress model (ASM) is a significant improvement over the unmodified ASM and the unmodified k-epsilon model; however, like the others, it dramatically overpredicts the experimentally determined dissipation rate.
635 citations
TL;DR: In this article, a new turbulence closure model was proposed to treat two-dimensional, turbulent boundary layers with strong adverse pressure gradients and attendant separation by using an ordinary differential equation derived from the turbulent kinetic energy equation to describe the stream wise development of the maximum Reynolds shear stress in conjunction with an assumed eddy viscosity distribution.
Abstract: A new turbulence closure model designed specifically to treat two-dimensional, turbulent boundary layers with strong adverse pressure gradients and attendant separation is presented The influence of history effects are modelled by using an ordinary differential equation derived from the turbulent kinetic energy equation to describe the stream wise development of the maximum Reynolds shear stress in conjunction with an assumed eddy viscosity distribution that has as its velocity scale the maximum Reynolds shear stress In the outer part of the boundary layer, the eddy viscosity is treated as a free parameter which is adjusted in order to satisfy the ODE for the maximum shear stress Because of this, the model is not simply an eddy viscosity model, but contains features of a Reynolds stress model Comparisons with experiment are presented that clearly show the proposed model to be superior to the Cebeci-Smith one in treating strongly retarded and separated flows In contrast to two-equation, eddy viscosity models, it requires only slightly more computational effort than simple models such as the Cebeci-Smith
378 citations
TL;DR: In this article, the authors examined the modeling of the subgrid-scale stresses in the large-eddy simulation of turbulence from a theoretical standpoint, and compared alternative models that have been proposed which are properly invariant.
Abstract: The modelling of the subgrid-scale stresses in the large-eddy simulation of turbulence is examined from a theoretical standpoint. While there are a variety of approaches that have been proposed, it is demonstrated that one of the more recent models gives rise to equations of motion for the large eddies of turbulence which are not Galilean-invariant. Consequently, this model cannot be of any general applicability, since it is inconsistent with the basic physics of the problem, which requires that the description of the turbulence be the same in all inertial frames of reference. Alternative models that have been proposed which are properly invariant are discussed and compared.
291 citations
TL;DR: In this paper, the E-e model is extended to the atmospheric boundary layer for which a modification of the dissipation equation is found to be necessary in order to give results comparable with observational data.
Abstract: In the so called E - e turbulence model, an eddy viscosity is evaluated from turbulent kinetic energy E and energy dissipation e. Although still a first-order closure method in its simpler form, the E- e model yields eddy viscosity for complex turbulent flows without a prior prescription of a length scale needed in so-called mixing-length models. The E - e model has been successfully applied to many flow problems in engineering applications for non-rotating boundary layers. In this paper, the E - e method is extended to the atmospheric boundary layer for which a modification of the dissipation equation is found to be necessary in order to give results comparable with observational data.
233 citations
TL;DR: In this article, a critical review of the turbulence models available for the prediction of complex turbulent shear layers is carried out, concentrating mainly on three-dimensional flows, flows subjected to curvature and body rotation, separated flows, and vortex flows.
Abstract: The turbulence models available for the prediction of complex turbulent shear layers are reviewed in this paper, concentrating mainly on three-dimensional flows, flows subjected to curvature and body rotation, separated flows, and vortex flows. A critical review of zero-equation, one-equation, two-equation, algebraic Reynolds stress, and full Reynolds stress models are carried out, with a specific emphasis on their applicability to complex flows. It is concluded that algebraic eddy viscosity models and kappa-epsilon/kappa-omega models, with a constant value of coefficients, are not adequate for complex flows. The models which include a description of stresses, either through an algebraic Reynolds stress model or a full Reynolds stress model, are essential for adequate prediction of these flows. It is recommended that systematic experimental investigations be carried out to isolate various complex interactions in order to understand and model the various effects and to carry out an extension of the present models to include complex flows.
180 citations
01 Jan 1985
TL;DR: In this article, a new and improved wall function method for compressible turbulent flows has been developed and tested, which is applicable to attached and separated flows, to both high and low Reynolds number flows, and to flows with adiabatic and nonadiabatic surfaces.
Abstract: A new and improved wall function method for compressible turbulent flows has been developed and tested. This method is applicable to attached and separated flows, to both high- and low-Reynolds number flows, and to flows with adiabatic and nonadiabatic surfaces. This wall function method has been applied to the Launder-Spalding k-epsilon two-equation model of turbulence. The tests consist of comparisons of calculated and experimental results for: (1) an axisymmetrical transonic shock-wave/boundary-wave interaction flow at low Reynolds number in an adiabatic tube, (2) an axisymmetrical high-Reynolds number transonic flow over a nonadiabatic bump, and (3) a two-dimensional supersonic high-Reynolds number flow on a nonadiabatic deflected flap. Each of these experiments had significant regions of flow separation. The calculations are performed with an implicit algorithm that solves the Reynolds-averaged Navier-Stokes equations. It is shown that the results obtained agree very well with the data for the complex compressible flows tested.
131 citations
TL;DR: In this article, a new propagation model is developed for the intensity fluctuations of a laser beam propagating through extended clear-air turbulence, where the field of the optical wave is modeled as the sum of a coherent component and a random component, the intensity of which is assumed governed by the generalized n distribution of Nakagami.
Abstract: A new propagation model is developed for the intensity fluctuations of a laser beam propagating through extended clear-air turbulence. The field of the optical wave is modeled as the sum of a coherent (deterministic) component and a random component, the intensity of which is assumed governed by the generalized n distribution of Nakagami. We further assume that the statistics are inherently nonstationary by treating the average intensity of the random portion of the field as a fluctuating quantity. The resulting unconditional I–K distribution for the intensity fluctuations is a generalized form of the K distribution that is applicable to all conditions of atmospheric turbulence for which data have been obtained, including weak turbulence for which the K distribution is not theoretically applicable.
129 citations
TL;DR: In this paper, the structure of turbulence in a strongly stratified nocturnal boundary layer is studied using fast-response aircraft data collected under clear sky conditions with weak ambient flow.
Abstract: The structure of turbulence in a strongly stratified nocturnal boundary layer is studied using fast-response aircraft data collected under clear sky conditions with weak ambient flow. The principal source of turbulence is shear generation near the top of the surface inversion layer. This shear is induced by the development of surface flow which appears to be cold air drainage. The downward heat flux in the turbulent shear zone acts to warm the upper part of the inversion layer and is opposed by clear-air radiative cooling and advection of cold air. The horizontal structure of the turbulence is studied using conditional means and other properties of the joint frequency distribution and analysis of the eigenvectors of the correlation matrix. Often, the turbulence exhibits statistical properties consistent with shear instability on horizontal scales near 300–400 m. Although modified by stratification, the main motions are turbulent-like with sharp horizontal boundaries and lead to net downward heat ...
116 citations
TL;DR: In this paper, a low-speed turbulent boundary layer in zero pressure gradient with an isolated, artificially generated vortex imbedded in it is studied, showing that the circulation around the vortex is almost conserved, being reduced only by the spanwise-component surface shear stress.
Abstract: Detailed mean-flow and turbulence measurements have been made in a low-speed turbulent boundary layer in zero pressure gradient with an isolated, artificially generated vortex imbedded in it. The vortex was generated by a half-delta wing on the floor of the wind-tunnel settling chamber, so that the vortex entering the working section had the same circulation as that originally generated, while axial-component velocity variations were very much reduced, relative to the local mean velocity, from values just behind the generator. The measurements show that the circulation around the vortex imbedded in the boundary layer is almost conserved, being reduced only by the spanwise-component surface shear stress. Therefore the region of flow affected by the vortex continues to grow downstream, its cross-sectional dimensions being roughly proportional to the local boundary-layer thickness. The behaviour of the various components of eddy viscosity, deduced from measured Reynolds stresses, and of the various triple products, suggests that the simple empirical correlations for these quantities used in present-day turbulence models are not likely to yield flow predictions which are accurate in detail.
112 citations
01 Jan 1985
TL;DR: In this article, a model for the relaxation process is proposed for the vorticity field from the study of the structure of homogeneous turbulence, and the behavior of the anisotropy in the Reynolds stress, dissipation and Vorticity fields has been analyzed to reveal new physics in distorting and relaxing turbulence.
Abstract: Full turbulence simulation has been conducted of homogeneous turbulence subject to irrotational strains and under relaxation from these. The behavior of the anisotropy in the Reynolds stress, dissipation and vorticity fields has been analyzed to reveal new physics in distorting and relaxing turbulence. A model for the relaxation process is proposed for the vorticity field from the study of the structure of homogeneous turbulence.
Book•
01 Jan 1985
TL;DR: In this article, the authors proposed a two-dimensional model of the small-scale structure of Turbulence in the Ocean and showed that it can be used to estimate the temperature variation in the ocean.
Abstract: I. Theory of Turbulence in Stratified Flows.- 1. Definition of Turbulence.- 2. Equations of Turbulent Flow.- 3. Mechanisms of Turbulence Generation in the Ocean.- 3.1 Instability of Vertical Velocity Gradients in Drifting Flow.- 3.2 Overturning of Surface Waves.- 3.3 Instability of Vertical Velocity Gradients in Stratified Large-Scale Oceanic Flows.- 3.4 Hydrodynamic Instability of Quasi-Horizontal Meso-Scale Non-Stationary Flows.- 3.5 Instability of Local Velocity Gradients in Internal Waves.- 3.6 Convection in Layers with Unstable Density Stratification.- 3.7 Instability of Vertical Velocity Gradients in a Bottom Boundary Layer (BBL).- 4. Stratification Effects.- 5. Theory of Turbulence Spectra.- 6. The Small-Scale Structure of Turbulence.- II. Small-Scale Turbulence.- 7. Instruments for The Measurement of Small-Scale Turbulence.- 7.1 Experimental Techniques.- 8. Statistical Characteristics of Turbulence.- 9. Velocity Fluctuations.- 9.1 Root-Mean-Square Values.- 9.2 Correlation Functions and Spectra.- 9.3 Dependence on Local Background Conditions.- 9.4 Spectra of Fluctuation Intensity and Energy Dissipation.- 9.5 Turbulent Energy Dissipation Rate.- 9.6 Climatology of Small-Scale Turbulence.- 10. Temperature Fluctuations.- 10.1 An Indirect Method of Estimating Temperature Fluctuations.- 10.2 Local Temperature Gradients in the Ocean.- 10.3 Variations in Fine-Structure Temperature Profiles.- 10.4 Direct Measurements of High-Frequency Temperature Fluctuations.- 10.5 Turbulent Heat Fluxes.- 10.6 Spectra of High-Frequency Temperature Fluctuations.- 10.7 Spectral Characteristics of the Temperature Variability in the Ocean.- 10.8 Dissipation Rate of Temperature Inhomogeneities.- 11. Fluctuations of Electrical Conductivity and Salinity.- 11.1 Fundamentals.- 11.2 Local Gradients of C and S.- 11.3 Spectral Characteristics.- 11.4 Dependence on Local Background Conditions.- 11.5 Intermittency of Electrical Conductivity Fluctuations.- 11.6 Deep-Sea Measurement Data.- 11.7 Determination of Salinity Fluctuations.- 11.8 Density Fluctuations and Turbulent Mass Flux.- 11.9 Climatology of Electrical Conductivity Fluctuations.- III. Large-Scale Horizontal Turbulence.- 12. Large-Scale Turbulence and Negative Eddy Viscosity.- 13. Theory of Two-Dimensional Turbulence.- 14. Horizontal Turbulence Spectra.- Notes.- References.- Name Index.
TL;DR: A review of the current ideas and theories about the basic mechanisms for dispersion from localized sources in complex turbulent flows can be found in this paper, where the authors summarize the main features of such flows: inhomogeneity and unsteadiness of the turbulence, the shear and the convergence and divergence of the mean flow, the non-Gaussianity of the turbulent, recirculation of the average flow, and the presence of surfaces.
Abstract: The dispersion of matter and heat in turbulent flows is generally analyzed in different ways depending on whether the matter and heat are released from distributed sources, such as heat at the wall of a pipe, or whether (as in this review) they are released from a single source that is small compared with the scale of the flow. There are many examples of such types of dispersion in engineering fluid mechanics, such as the spreading of a flame in a highly turbulent engine flow, the dispersion of one or more species emitted from pipes into large chemical reactors, and the heat released from local overheating in nuclear reactor subassembly channels. There are also many examples where continuous or sudden sources of pollutant or heat are discharged into the atmosphere or into aqueous environments. Usually these discharges occur in complex flows with inhomogeneous turbulence, such as boundary layers over level surfaces, or in flows impinging on surfaces, such as hills in the atmosphere or underwater ridges in the oceans. The aim of this review is primarily to summarize the current ideas and theories about the basic mechanisms for dispersion from localized sources in complex turbulent flows. A brief consideration of the examples already given indicates some of the characteristic features of such flows: inhomogeneity and unsteadiness of the turbulence, the shear and the convergence and divergence of the mean flow, the non-Gaussianity of the turbulence, recirculation of the mean flow, and the presence of surfaces. In most practical dispersion problems, many of these effects occur simultaneously, but in the dispersion from small sources and in the vicinity
01 Jan 1985
TL;DR: In this paper, the dynamics of low-dimensional nonlinear systems with chaotic solutions have been studied and the results of these studies have produced very interesting and profound results with several implications in many disciplines dealing with nonlinear equations.
Abstract: Recent studies of the dynamics of low-dimensional nonlinear systems with chaotic solutions have produced very interesting and profound results with several implications in many disciplines dealing with nonlinear equations. However, the interest of fluid dynamicists in these studies stems primarily from the expectation that they will help us understand better the onset as well as dynamics of turbulence in fluid flows. At this time, much of this expectation remains untested, especially in ‘open’ or unconfined fluid flows. This work is aimed at filling some of this gap.
TL;DR: In this article, the effects of turbulence are modeled by a variant of the k-e turbulence model incorporating curvature corrections, and the governing equations are solved by an efficient pressure-implicit split-operator algorithm.
Abstract: Turbulent flows over surface-mounted thin and thick ribs are investigated using a new computational method for incompressible recirculating flows. The method employs a differencing scheme which simultaneously satisfies the requirements of low numerical diffusion and positivity of coefficients. The effects of turbulence are modeled by a variant of the k-e turbulence model incorporating curvature corrections. The governing equations are solved by an efficient pressure-implicit split-operator algorithm. The predictions are compared with experimental data and previous calculations. The present results compare satisfactorily with most of the measurements and show a definite improvement over previous results. Nomenclature A = finite difference coefficient Ci,c2,cfji,ak,ffe,K = turbulence constants: 1.44, 1.92, 0.09, 1.0, *?/[(c2-ct)tf ],0.4187
01 Jan 1985
TL;DR: In this article, the effects of turbulent diffusion on particle dispersion, and hence on erosion, are demonstrated numerically, and the relative rate of erosion decreases and the location of maximum wear is displaced toward the stagnation point as the turbulence intensity increases.
TL;DR: In this paper, the structure of turbulence in compound channel flows is examined in a laboratory study and the mixing region's effect on the compound flow field for both wide and narrow channel conditions is investigated.
Abstract: The structure of turbulence in compound channel flows is examined in a laboratory study. Shear stresses and turbulence intensities are measured in a channel comprised of a deep central section flanked on either side by wide shallow berms (flood plains). The study concerns the nature of turbulence in the mixing regions separating the deep and shallow zones. Also studied is the mixing region’s effect on the compound flow field for both “wide” and “narrow” channel conditions. Under “narrow” channel conditions the mixing process extends to the center of the main channel flow field; however, under “wide” channel conditions, the central region is not affected and observed turbulence levels at the center of the main channel are in close agreement with theoretical values for a two-dimensional flow field. Apparent shear stress at the vertical main channel-flood plain interface was measured directly and compared favorably with estimated values based on momentum considerations.
Book•
11 Sep 1985
TL;DR: Theoretical approaches to fluid flow have been studied for a long time as discussed by the authors, including large eddy simulations and Lagrangian models of fluid flow. But the main focus of this paper is on three-dimensional fluid flow models.
Abstract: I. Turbulence Sensitivity and Control in Wall Flows.- II. Observations, Theoretical Ideas, and Modeling of Turbulent Flows -- Past, Present, and Future.- III. Large Eddy Simulation: Its Role in Turbulence Research.- IV. An Introduction and Overview of Various Theoretical Approaches to Turbulence.- V. Decimated Amplitude Equations in Turbulence Dynamics.- VI. Flat-Eddy Model for Coherent Structures in Boundary Layer Turbulence.- VII. Progress and Prospects in Phenomenological Turbulence Models.- VIII. Renormalisation Group Methods Applied to the Numerical Simulation of Fluid Turbulence.- IX. Statistical Methods in Turbulence.- X. The Structure of Homogeneous Turbulence.- XI. Vortex Dynamics.- XII. Two-Fluid Models of Turbulence.- XIII. Chaos and Coherent Structures in Fluid Flaws.- XIV. Connection Between Two Classical Approaches to Turbulence: The Conventional Theory and the Attractors.- XV. Remarks on Prototypes of Turbulence, Structures in Turbulence and the Role of Chaos.- XVI. Subgrid Scale Modeling and Statistical Theories in Three-Dimensional Turbulence.- XVII. Strange Attractors, Coherent Structures and Statistical Approaches.- XVIII. A Note on the Structure of Turbulent Shear Flows.- XIX. Lagrangian Modelling for Turbulent Flows.
TL;DR: In this paper, a simple model is developed for the wavenumber spectrum of the variance of a passive scalar quantity in an isotropic turbulence field, which can define the spectral distributions at all wavenumbers as an arbitrary function of a scalar Reynolds number Reθ=R Reλ and the Schmidt number Sc=ν/D (where R=τθ/τe is the scalar/kinetic energy time scale ratio and Reλ=u’λ/ν is the turbulence Reynolds number).
Abstract: A simple model is developed for the wavenumber spectrum of the variance of a passive scalar quantity in an isotropic turbulence field. The model can define the spectral distributions at all wavenumbers as an arbitrary function of a scalar Reynolds number Reθ=R Reλ and the Schmidt number Sc=ν/D (where R=τθ/τe is the scalar/kinetic energy time scale ratio and Reλ=u’λ/ν is the turbulence Reynolds number). The model is compared with one‐dimensional spectral data over a range of Reynolds numbers and for Sc=0.7, 7, and 700; model and data are shown to be in reasonable agreement.
TL;DR: In this paper, a two-equation turbulence model for steady incompressible two-phase flows including phase change has been developed for the flow of a turbulent axisymmetric gaseous jet laden with evaporating liquid droplets.
TL;DR: In this paper, it was shown that the reduction of broadband (even total) far-field jet noise can be achieved via controlled excitation of a jet at a frequency in the range 0.01 < Stθ < 0.02.
Abstract: It is shown that reduction of broadband (even total) far-field jet noise can be achieved via controlled excitation of a jet at a frequency in the range 0.01 < Stθ < 0.02, where Stθ is the Strouhal number based on the exit momentum thickness of the shear layer. Hot-wire measurements in the noise-producing region of the jet reveal that the noise suppression is a direct consequence of turbulence suppression, produced by early saturation and breakdown of maximally growing instability modes.
TL;DR: In this article, the authors describe a theoretical model that describes the competition between inertial effects in the distorted mean flow which tend to set up concentration gradients and turbulent diffusion which tends to counteract such gradients.
Abstract: The behavior of blunt dust samplers in turbulent air flow has received relatively little attention. This paper describes the development of a theoretical model which aims to identify the important controlling parameters and to form the basis of an experimental inquiry. Physically, the model describes the competition between inertial effects in the distorted mean flow which tend to set up concentration gradients and turbulent diffusion which tends to counteract such gradients. Experiments were carried out in a wind tunnel using a simple axisymmetric disk-shaped blunt sampler facing the wind. Its aspiration efficiency was investigated as a function of particle aerodynamic diameter, turbulence intensity, and turbulence length scale (for fixed sampler dimensions, sampling flow rate and wind speed). Experiments were also carried out to investigate the effects of turbulence on the performances of sharp-edged isokinetic sampling probes. The results of all these experiments were broadly consistent with the theore...
TL;DR: In this article, a system of equations governing turbulent shear flows is discussed, where the mean velocity, the mean pressure, and four statistical quantities related to the fluctuating field constitute the fundamental quantities for shear flow.
Abstract: A system of equations governing turbulent shear flows is discussed. In this system the mean velocity, the mean pressure, and four statistical quantities related to the fluctuating field constitute the fundamental quantities for shear flows. A closed system of equations for these quantities is derived statistically with the aid of the two‐scale direct‐interaction approximation, where the Reynolds stress is expressed in the form of the eddy‐viscosity representation. On this basis, some turbulence models are discussed from the statistical viewpoint.
TL;DR: In this paper, the authors examined the applicability of the SCIPVIS code as a basic part of a program for estimating broadband shock noise radiation and showed that good qualitative agreement exists between predicted and measured static pressure distributions for both underexpanded and overexpanded flow cases considered.
Abstract: SCIPVIS, the computational model discussed by Dash et al. (1985), is assessed in predicting the complicated flow structure associated with shock-containing plumes. In addition, the analysis in this study examines this code's applicability as a basic part of a program for estimating broadband shock noise radiation. The results of this study show that excellent agreement exists between predicted and measured static pressure distributions for both underexpanded and overexpanded flow cases considered. Of the three turbulence closure models incorporated in the SCIPVIS code, the kW model of Spalding produces the most uniform agreement with measurement. The k-epsilon-2 model of Launder consistently overestimates plume spreading for supersonic jets with exit Mach numbers in the 1-2 range. Dash's (1983) k-epsilon-2-cc, compressibility-corrected version of Launder's model underestimates plume spreading. Good qualitative agreement was also obtained between the measured longitudinal turbulence intensity and that predicted by the code for the same trial case. Comparison of measured and predicted broadband shock noise spectrum peak values were found to be in excellent agreement. This utilized a variant of the Harper-Bourne and Fisher (1973) phase-array model: the effective shock spacing was reinterpreted as the value of the end of the plume potential core, determined herein by the SCIPVIS code.
TL;DR: In this article, a mathematical model is presented for calculating the external heat transfer coefficients around gas turbine blades, based on a finite-difference procedure for solving the boundary-layer equations which describe the flow and temperature field around the blades.
Abstract: A mathematical model is presented for calculating the external heat transfer coefficients around gas turbine blades. The model is based on a finite-difference procedure for solving the boundary-layer equations which describe the flow and temperature field around the blades. The effects of turbulence are simulated by a low-Reynolds number version of the k -e turbulence model. This allows calculation of laminar and transitional zones and also the onset of transition. Applications of the calculation method are presented to turbine-blade situations which have recently been investigated experimentally. Predicted and measured heat transfer coefficients are compared and good agreement with the data is observed. This is true especially for the pressure-surface boundary layer which is of a rather complex nature because it remains in a transitional state over the full blade length. The influence of various flow phenomena like laminar-turbulent transition and of the boundary conditions (pressure gradient, free-stream turbulence) on the predicted heat transfer rates is discussed.
TL;DR: In this article, an experimental investigation was performed on turbulent boundary layers with injection and suction through a slit, and the velocity profile, turbulent energy, auto-correlation function, energy spectrum, and energy balance were measured in detail.
Abstract: An experimental investigation is performed on turbulent boundary layers with injection and suction through a slit. The velocity profile, turbulent energy, auto-correlation function, energy spectrum, and energy balance are measured in detail, and the influence of injection and suction through a slit on the turbulent boundary layers is presented. The process of recovery to an equilibrium state from non-equilibrium state is investigated. Main results are summarized as follows. The effects of injection and suction on velocity profiles and turbulence characteristics are small in the vicinity of the wall. On the other hand, the effects of injection clearly appear in the outer layer region of the turbulent boundary layer. Convection, production, and dissipation of turbulence energy increase with injection and decrease with suction.
TL;DR: In this article, the finite element method is applied to turbulent confined flow problems adopting a primitive-variables formulation, and the turbulence state is defined by a k-e model of turbulence.