Showing papers on "K-epsilon turbulence model published in 1984"

A Large-Eddy-Simulation Model for the Study of Planetary Boundary-Layer Turbulence

Abstract: A large-eddy-simulation (LFS) model explicitly calculates the large-eddy field and parameterizes the small eddies. The large eddies in the atmospheric boundary layer are believed to be much more important and more flow-dependent than the small eddies. The LES model results are therefore believed to be relatively insensitive to the parameterization scheme for the small eddies. Deardorff first applied this type of numerical model to boundary-layer turbulence. In order to continue his important work, and to take advantage of the fast Fourier transformation algorithm, a new LES model code which uses a mixed pseudospectral finite-difference method was developed. This LES model is described here and tested with a simple vortex flow and with the Wangara day-33 data. This model will be used to systematically investigate fundamental problems in the area of boundary-layer turbulence. It is hoped that three-dimensional simulations will give useful statistical information about turbulence structural and impr...

Local isotropy and the decay of turbulence in a stratified fluid

Abstract: The validity of the assumption of local isotropy is investigated using measurements of three orthogonal components of the turbulent velocity fields associated with initially high-Reynolds-number geophysical turbulence The turbulent fields, generated by various large-scale internal motions caused by tidal flows over an estuarine sill, decay under the influence of stable mean density gradients With measurements from sensors mounted on a submersible, we examine the evolution of spectral shapes and of ratios of cross-stream to streamwise components, as well as the degree of high-wavenumber universality, for the observational range of the parameter I≡ ks/kb = lb/ls This ratio is a measure of separation between the Kolmogoroff wavenumber ks≡ (e/ν3)¼ ≡ 2π/ls typical of scales by which turbulent kinetic energy has been dissipated (at rate e), and the buoyancy wavenumber kb ≡ (N3/e)½ ≡ 2π/lb typical of scales at which the ambient stratification parameter N ≡ (−gρz/ρ0)½ becomes important For values of I larger than ∼ 3000, inertial subranges are observed in all spectra, and the spectral ratio ϕ22/ϕ11 of cross-stream to streamwise spectral densities reaches the isotropic value of 4/3 for about a decade in wavenumber As ks/kb decreases, inertial subranges vanish, but spectra of the cross-stream and streamwise components continue to satisfy isotropic relationships at dissipation wavenumbers We provide a criterion for when e may safely be estimated from a single measured component of the dissipation tensor, and also explore questions of appropriate low-wavenumber normalization for buoyancy-modified turbulence

The mixing layer: deterministic models of a turbulent flow. Part 3. The effect of plane strain on the dynamics of streamwise vortices

Abstract: … in hydrodynamic turbulence … the fate of vortices extending in the direction of motion is of great importance (J. M. Burgers 1948).We examine an elementary model of the dynamics of streamwise vorticity in a plane mixing layer. We assume that the vorticity is unidirectional and subjected to a two-dimensional spatially uniform strain, positive along the direction of vorticity. The equations of motion are solved numerically with initial conditions corresponding to a strain-viscous-diffusion balance for a layer with a sinusoidal variation of vorticity. The numerical results are interpreted physically and compared to those of an asymptotic analysis of the same problem by Neu. It is found that strained vortex sheets are fundamentally unstable unless their local strength nowhere exceeds a constant (somewhat larger than 2) times the square root of the product of strain and viscosity. The instability manifests itself by the spanwise redistribution of the vorticity towards the regions of maximum strength. This is accompanied by the local rotation of the layer and the intensification of the vorticity. The end result of this evolution is a set of discrete round vortices whose structure is well approximated by that of axially symmetric vortices in an axially symmetric strain. The phenomenon can proceed (possibly simultaneously) on two separate lengthscales and with two correspondingly different timescales. The first lengthscale is the initial spanwise extent of vorticity of a given sign. The second, relevant to initially thin and spanwise slowly varying vortex layers, is proportional to the layer thickness. The two types of vorticity focusing or collapse are studied separately. The effect of the first on the diffusion rate of a scalar across the layer is calculated. The second is examined in detail for a spanwise-uniform layer: First we solve the eigenvalue problem for infinitesimal perturbations and then use the eigenfunctions as initial conditions for a numerical finite-differences solution. We find that the initial instability is similar to that of unstrained layers, in that roll-up and pairings also follow. However, at each stage a strain-diffusion balance eventually imposes the same cross-sectional lengthscale and each of these events leads to an intensification of the local value of the vorticity.The parameters upon which collapse and its timescale depend are related to those which are known to govern a mixing layer. The results suggest that the conditions for collapse of strained vortex sheets into concentrated round vortices are easily met in a mixing layer, even at low Reynolds numbers, so that these structures whose size is the Taylor microscale are far more plausibly typical than are vortex sheets on that scale. We found that they raise significantly the diffusion rate of scalar attributes by enhancing the rate of growth of material surfaces across which diffusion takes place. Finally, experimental methods that rely on the visualization of the gradient of scalar concentration are shown to be unable to reveal the presence of streamwise vorticity unless that vorticity has already gathered into concentrated vortex tubes.

Structure of particle-laden jets - Measurements and predictions

Abstract: Measurements of mean and fluctuating velocities of both phases as well as particle mass fluxes were completed in turbulent, particle-laden jets containing monodisperse particles with well-defined initial and boundary conditions. The new measurements were used to evaluate a stochastic separated flow model of the process which treated effects of interphase slip and turbulent dispersion using random-walk computations for particle motion. The continuous phase was treated using a modified k-epsilon model allowing for direct contributions of interphase transport to both mean and turbulence properties. The model performed reasonably well over the new data base, with all empirical parameters fixed from earlier work. In contrast, simplified models ignoring either interphase slip or turbulent dispersion yielded poor agreement with the measurements.

Turbulence structure in thermal convection and shear-free boundary layers

Abstract: This paper is a study of turbulence near rigid surfaces, in the absence of any mean shear. Different sources of turbulence are considered, including thermal convection and grid turbulence. It is shown that, ifa rigid boundary is introduced into the flow, then for short times the linear theory of Hunt & Graham (1978) reveals the common structure of these flows near the boundary, if the parameters used are the rate of energy dissipation per unit mass 6 and the distance z from the surface. Over longer times nonlinear effects develop, such as large 'eddies straining smaller eddies near the boundary. Some new estimates are suggested here and compared with the computations of Biringen & Reynolds (1981) and experiments of Thomas BE Hancock (1977). It is shown that calculations based on the linear theory agree well with many measurements of the vertical profiles of turbulence in thermal convection layers, including those of the vertical variance, the low-frequency end of the spectrum of the vertical turbulence (w), the integral scale of w, and two-point cross-correlations of tu. (The latter was aprediction, subsequently tested by atmospheric measurements.) Some discussion of the reasons for this agreement are suggested. The observations of the effects of mean-velocity gradients near the surface are also shown to be consistent with the theoretical arguments proposed here.

The Interaction between an Internal Gravity Wave and Turbulence in the Stably-Stratified Nocturnal Boundary Layer

Abstract: Observations have been made of a stably-stratified nighttime boundary layer perturbed by Kelvin-Helmholtz internal waves with critical levels around 600 m. Significant turbulence intensities were measured although the time-mean gradient Richardson numbers were large and positive. It is shown by constructing energy budgets of wave and turbulent components separately that there is an essential flow of kinetic energy from wave to turbulence and that the mechanics of this exchange process depend upon the nonlinear character of the wave field. Turbulent energy budgets were followed through a wave cycle and revealed that turbulence production occurred during only one quarter of a wave period, the rest of the time being taken up by redistribution of turbulent kinetic energy (tke) among the three orthogonal components, relaxation under the effects of density stratification and dissipation. The principal path of energy dissipation is through conversion of vertical component tke to density fluctuations, wh...

A turbulent-transport model for concentration fluctuations and fluxes

Abstract: A second-order closure model describing the diffusion of a passive scalar from a small source is presented. The model improves upon the earlier work of Lewellen & Teske (1976) by ensuring the early stage of the release, the so-called meander phase, is accurately described. In addition to the mean concentration and scalar fluxes, a model equation for the evolution of the scalar variance is proposed. The latter introduces a new lengthscale which represents the scale of the concentration fluctuations. The model predictions are compared with the recent experimental data of Fackrell & Robins (1982a, b).

A Synthesized Model of the Near-Wall Behavior in Turbulent Boundary Layers.

Abstract: : A model of the near-wall behavior of turbulent boundary layers is presented Based on an extensive series of primarily visualization experiments, which are described in overview, the model proposes a sequence of events which give rise to the bursting behavior responsible for turbulence production in the near-wall region The model illustrates how hairpin vortex flow structures, generated during low-speed streak break down and ejection, are also reponsible for the streak regeneration process, thus defining a clear cycle of turbulence generation for the near-wall region (Author)

The effects of turbulence on the mean flow past two-dimensional rectangular cylinders

Abstract: There are two main effects of turbulence on the mean flow past rectangular cylinders, just as found earlier for square rods. Small-scale turbulence increases the growth rate of the separated shear layers through increased mixing. Large-scale turbulence weakens regular vortex shedding by reducing spanwise correlation. The consequences of increased mixing and weakened regular vortex shedding depend on the depth-to-height ratio of a rectangular cylinder. In particular, the mean base pressure of a rectangular cylinder can be varied significantly by both the scale and intensity of turbulence.

The Baldwin-Lomax Turbulence Model for Two-Dimensional Shock-Wave/Boundary-Layer Interactions

Abstract: The algebraic turbulent eddy viscosity model of Baldwin and Lomax has been critically examined for the case of two-dimension al (2-D) supersonic compression corner interactions. The flowfields are computed using the Navier-Stokes equations together with three different versions of the Baldwin-Lomax model, including the incorporation of a relaxation technique. The turbulence models are evaluated by a detailed comparison with available experimental data for compression ramp flows over a range of corner angle and Reynolds number. The Baldwin-Lomax outer formulation is found to be unsuitable for separated 2-D supersonic interactions due to the unphysical streamwise variation of the computed length scale in the vicinity of separation. Minor modifications are proposed to partially remedy this difficulty. The use of relaxation provides significant improvement in the flowfield prediction upstream of the corner. However, the relaxation length required is one-tenth of that employed in a previous computational study. AH of the turbulence models tested here fail to simulate the rapid recovery of the boundary layer downstream of reattachment.

Resistive fluid turbulence and energy confinement

Abstract: The invariance properties of the underlying equations under scale transformations provide information about plasma transport. By applying this argument to specific models, in which the magnetic configuration and the physical mechanism of transport are identified, this information can be sufficient to completely determine the transport coefficients in a turbulent plasma. In this way the electron energy transport due to resistive fluid turbulence is examined in tokamak and reversed field pinch configuration. The resulting confinement times have interesting implications for the performance of the two systems.

Description and prediction of transition in two-dimensional, incompressible flow

Abstract: : This paper deals with a survey of transition problems in two-dimensional, incompressible flows. The first chapter is devoted to a general description of phenomena leading to turbulence under the influence of various factors: free-stream turbulence, sound, pressure gradient, oscillations of the external flow, roughness, suction, wall curvature. Then, linear and non-linear stability theories are briefly discussed. This chapter ends with a review of results concerning the structure and growth of turbulent spots and the progressive disappearance of intermittency phenomenon when positive pressure gradients are applied. The second chapter describes practical methods for calculating the transition onset as well as the transition region itself. Methods based on linear stability theory, empirical criteria, intermittency methods and turbulence models are presented successively. Some applications of these techniques are also given. (Author)

The structure of mesoscale turbulence and horizontal spreading at ocean fronts

Abstract: We report results of experiments with a field of two-layer geostrophic turbulence that is driven internally by baroclinic instability. Turbulence is first produced at a sharp, unstable density front and propagates horizontally until all of the stratified fluid contains quasi two-dimensional eddy motions. Continuing instability blocks the inverse energy cascade that is otherwise characteristic of two-dimensional turbulence, and causes the dominant length scale to be approximately constant. Ekman friction, however, causes the turbulence intensity to decay exponentially in time. Measurements of the dispersion of neutrally buoyant particles indicate an energy spectrum of the form E ( k ) ∼ k −2.46±0.02 , where k is the horizontal wavenumber, at scales less than that of energy injection. The experiments also have implications for horizontal mixing by mesoscale turbulence at density fronts. The spreading of the upper-layer fluid proceeds like t 1 2 over time scales much less than that for the exponential decay of fluid velocities, but on larger time scales mixing is reduced, and can be halted, by Ekman dissipation.

Species Concentrations and Turbulence Properties in Buoyant Methane Diffusion Flames

Abstract: Past measurements of mean velocities and temperatures in buoyant turbulent, axisymmetric methane diffusion flames burning in still air have been extended to included mean species concentrations (CH/sub 4/, N/sub 2/, O/sub 2/, CO/sub 2/, H/sub 2/O, CO, and H/sub 2/) and turbulence quantitites. The new measurements were used to evaluate a Favre-averaged, k-epsilon-g turbulence model of the process- with all empirical constants fixed by measurements in noncombusting flows. Use of the laminar flamelet method to treat scalar properties yielded reasonably good predictions of mean properties. Turbulence predictions were less satisfactory, generally underestimating fluctuation levels and Reynolds stresses in highly regions of the flows. Measurements indicating significant anisotropy of turbulence properties in the same regions. These findings suggest the need for multistress closure to adequately model turbulence properties in buoyant flames.

Turbulence structure and turbulent diffusion near gas-liquid interfaces

Abstract: In this paper the general features of the turbulence structure and mass and heat transfer at gas-liquid interfaces are reviewed and analysed with particular reference to recent research on large-scale structures in turbulent shear flows, turbulence near boundaries in the absence of mean velocity gradients, numerical simulations of turbulence and of turbulent diffusion.

Collision rate of small particles in a homogeneous and isotropic turbulence

Abstract: A theoretical equation is derived for the collision rate of aerosol particles in a homogeneous and isotropic turbulent system. This equation takes into account the relative velocity between fluid and particles. The calculated results indicate that the relative velocity between fluid and particles is the main factor in the turbulent coagulation (agglomeration, coalescence) of unequally sized particles in an air flow. This hold true, even when the particle sizes are less than 1 micron. For particles of equal radii the coagulation coefficient reaches its minimum value, because the effect of motion relative to the fluid now becomes zero and only the spatial variation of turbulent motion remains to cause collisions between the particles. For particles following a fluid motion completely, as in a water stream, the equation for the collision rate reduces to the Saffman and Turner equation.

A new turbulence closure model for boundary layer flows with strong adverse pressure gradients and separation

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 modeled by using an ordinary differential equation (ODE) derived from the turbulence kinetic-energy equation, to describe the streamwise development of the maximum Reynolds shear stress in conjunction with an assumed eddy-viscosity distribution which 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 s not simply an eddy-viscosity model, but contains features of a Reynolds-stress model. Comparisons with experiments are presented which clearly show the proposed model to be superior to the Cebeci-Smith model 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 like the Cebeci-Smith model.

Probing turbulence via large eddy simulation

Abstract: Two examples of the application of a large-eddy simulation data base to the study of organized structures in fully developed turbulent channel flow are presented. In the first study, it is shown that the flow contains an appreciable number of hairpin vortices among other flow structures. In the second study, the Karhunen-Loeve expansion and Lumley's characteristic eddy decomposition were used to extract deterministic structures from the flow. It is shown that the extracted eddies are energetic, make a significant contribution to turbulence production, and display some of the features of the organized motions observed in turbulent boundary layers.

Numerical predictions of flows over backward‐facing steps

Abstract: Predictions are reported for two-dimensional, steady, incompressible flows over rearward-facing steps for both laminar and turbulent conditions. The standard k-ϵ turbulence model was used for the turbulent flow. Attention was focused on obtaining accurate solutions to the differential equations. It is concluded that some of the serious discrepancies that have occurred between prediction and observation, and attributed in earlier studies to the inadequacy of the turbulence model, may have been due to the inaccuracy of the solution.

LIMITATIONS AND EMPIRICAL EXTENSIONS OF THE k-ε MODEL AS APPLIED TO TURBULENT CONFINED SWIRLING FLOWS

Abstract: Shortcomings and recommended corrections to the standard two-equation k-epsilon turbulence model suggested by previous investigators are presented. They are assessed regarding their applicability to turbulent swirling recirculating flow. Recent experimental data on swirling confined flows, obtained with a five-hole pitot probe and a six-orientation hot-wire probe, are used to obtain optimum values of the turbulence parameters C-mu, C2, and sigma-epsilon for swirling flows. General predictions of moderately and strongly swirling flows with these values are more accurate than predictions with the standard or previous simple extensions of the k-epsilon turbulence model.

Fractal structures in turbulence

Abstract: We present a qualitative overview of our work on the issue of fractal structures in turbulence. We explain why fully developed turbulence is not space filling and describe how its fractal dimension can be estimated theoretically. The implications of the fractal nature of turbulence on transport processes like turbulent diffusion and on fluctuations in passive scalars are discussed. The latter affect wave propagation in turbulent media and these effects are examined. In addition we consider clouds in the atmosphere which are claimed to have fractal perimeters (or surfaces) and outline the physical reasons for this phenomenon. The fractal dimension of clouds is tied to the theory of turbulent diffusion and is computed theoretically. Indications of the road ahead are given.

Turbulence in phase-separating binary mixtures

Abstract: When a turbulent binary fluid mixture is quenched below its consolute point, turbulent mixing competes with an instability toward phase separation. A linear stability analysis in the viscous-convective range of concentration fluctuations shows that spinodal decomposition can be suppressed entirely by sufficiently strong stirring. An instability reappears, however, for deep quenches, when the injection rate of concentration fluctuations exceeds the rate of turbulent mixing. The growing concentration fluctuations which result appear to be confined to the viscous-convective range.

Numerical calculation of decaying isotropic turbulence using the LET theory

Abstract: The local-energy-transfer (LET) theory (McComb 1978) was used to calculate freely decaying turbulence for four different initial spectra at low-to-moderate values of microscale Reynolds numbers (Rλ up to about 40). The results for energy, dissipation and energy-transfer spectra and for skewness factor all agreed quite closely with the predictions of the well-known direct-interaction approximation (DIA: Kraichnan 1964). However, LET gave higher values of energy transfer and of evolved skewness factor than DIA. This may be related to the fact that LET yields the k−5/3 law for the energy spectrum at infinite Reynolds number.The LET equations were then integrated numerically for decaying isotropic turbulence at high Reynolds number. Values were obtained for the wavenumber spectra of energy, dissipation rate and inertial-transfer rate, along with the associated integral parameters, at an evolved microscale Reynolds number Rλ of 533. The predictions of LET agreed well with experimental results and with the Lagrangian-history theories (Herring & Kraichnan 1979). In particular, the purely Eulerian LET theory was found to agree rather closely with the strain-based Lagrangian-history approximation; and further comparisons suggested that this agreement extended to low Reynolds numbers as well.

The effect of rotation on turbulence structure

Abstract: Rotating turbulent channel flow has been simulated numerically using the large-eddy-simulation technique. With a three-dimensional, time-dependent, numerical simulation of turbulence, it was possible to obtain detailed flow-field information which had not been available previously from experiments. This information was used to study the structure and statistical properties of the flow with externally imposed rotation. It was found that in agreement with experimental observations, the Coriolis force introduced by the system rotation could stabilize/destabilize turbulence. The large-scale motion observed in the experiment was also found to exist in the computed flow field.

Final stages of transition to turbulence in plane channel flow

Abstract: This paper involves a numerical simulation of the final stages of transition to turbulence in plane channel flow at a Reynolds number of 1500. Three-dimensional incompressible Navier-Stokes equations are numerically integrated to obtain the time evolution of two- and three-dimensional finite-amplitude disturbances. Computations are performed on the CYBER-203 vector processor for a 32 x 51 x 32 grid. Solutions indicate the existence of structures similar to those observed in the laboratory and characteristics of the various stages of transition that lead to final breakdown. In particular, evidence points to the formation of a upside-down-V-shaped vortex and the subsequent system of horseshoe vortices inclined to the main flow direction as the primary elements of transition. Details of the resulting flow field after breakdown indicate the evolution of streaklike formations found in turbulent flows. Although the flow field does approach a steady state (turbulent channel flow), the introduction of subgrid-scale terms seems necessary to obtain fully developed turbulence statistics.

A numerical study of a separating and reattaching flow by using Reynolds-stress turbulence closure

Abstract: The numerical study of the Reynolds-stress turbulence closure for separating, reattaching, recirculating and redeveloping flow is summarized. The calculations were made for two different closure models of pressure - strain correlation. The results were compared with the experimental data. Furthermore, these results were compared with the computations made by using the one layer and three layer treatment of k-epsilon turbulence model which were developed. Generally the computations by the Reynolds-stress model show better results than those by the k-epsilon model, in particular, some improvement was noticed in the redeveloping region of the separating and reattaching flow in a pipe with sudden expansion.