Showing papers on "K-epsilon turbulence model published in 1996"

Dominant two‐dimensional solar wind turbulence with implications for cosmic ray transport

Abstract: Two new methods for distinguishing two-dimensional (2D) turbulence from slab turbulence are applied to Helios magnetometer data. Two-component models with varying slab and 2D ingredients are considered. Both methods indicate that solar wind magnetic turbulence possesses a dominant (∼85 % by energy) 2D component. The presence of such a large 2D component provides a natural solution to the long-standing problem of “too small” cosmic ray mean free paths derived from quasilinear scattering theory when using the slab model.

Numerical models for two-phase turbulent flows

Abstract: Numerical models for turbulent fluid-particle flows are reviewed. The two approaches typically used for modelling the dispersed (particle) phase are the trajectory and two-fluid formulations, while volume- averaged models are most common for the continuous (fluid) phase. The review is structured according to the turbulence models used for the continuous phase: turbulence energy-dissipation models, large- eddy simulations, direct numerical simulations, and discrete vortex models. The applications of these models to simulate particle dispersion due to fluid turbulence and the adjustments to the models to account for the modulation of the carrier phase turbulence by the particles are addressed.

Towards better uncertainty estimates for turbulence statistics

Abstract: Methods for calculating the statistical uncertainty associated with the sampling of random processes such as those which occur in turbulence research are given. In particular, formulas based on normal distribution assumptions and on any general distribution shape are given for means, variances, Reynolds stresses, correlation coefficients, homogeneous and mixed turbulent triple products and fourth order turbulence moments. In addition, two resampling algorithms, the “bootstrap” and “jackknife”, are presented and compared using actual turbulence data. The availability of these methods will allow turbulence data to be presented with statistical uncertainty error bars on all turbulence quantities.

Review of Lagrangian Stochastic Models for Trajectories in the Turbulent Atmosphere

Abstract: We review the theoretical basis for, and the advantages of, random flight models for the trajectories of tracer particles in turbulence. We then survey their application to calculate dispersion in the principal types of atmospheric turbulence (stratified, vertically-inhomogeneous, Gaussian or non-Gaussian turbulence in the surface layer and above), and show that they are especially suitable for some problems (e.g., quantifying ground emissions).

Compressible mixing layer growth rate and turbulence characteristics

Abstract: Direct numerical simulation databases have been used to study the effect of compressibility on mixing layers. The simulations cover convective Mach numbers from 0.2 to 1.2 and all contain a fully resolved turbulent energy cascade to small spatial scales. Statistical information is extracted from the databases to determine reasons for the reduced growth rate that is observed as the convective Mach number is increased. It is found that the dilatational contribution to dissipation is negligible even when eddy shocklets are observed in the flow. Also pressure-dilatation is not found to be significant. Using an accurate relation between the momentum thickness growth rate and the production of turbulence kinetic energy together with integrated equations for the Reynolds stress tensor it is shown that reduced pressure fluctuations are responsible for the changes in growth rate via the pressure–strain term. A deterministic model for the required pressure fluctuations is given based on the structure of variable-density vortices and the assumption that the limiting eddies are sonic. Simple anisotropy considerations are used to close the averaged equations. Good agreement with turbulence statistics obtained from the simulations is found.

Stellar Turbulent Convection: A Self-consistent Model

Abstract: We present a self-consistent model for stellar turbulent convection that is similar in spirit to the CM model (Canuto & Mazzitelli 1991) since it accounts for the full spectrum of the turbulent eddies rather than only one eddy, as done in the mixing length theory (MLT). The model differs from the CM model in the treatment of the rate of energy input ns(k) from the source that generates the turbulence. In the present model, ns(k) is controlled by both the source and the turbulence it ultimately generates, thus ensuring a self-consistent modeling of the turbulence. This improves the CM model in which ns(k) was taken to be equal to the growth rate of the linear unstable convective modes.However, since the formulation of a self-consistent treatment is far from simple, we were forced to use a representation of the nonlinear interactions less complete than the one in the CM model. The ensuing equations were solved numerically for a wide range of convective efficiencies. The results are the convective flux, the mean square turbulent velocity, the root mean squared turbulent pressure and the turbulent viscosity.We implemented the model in the ATON stellar structure code and computed the evolution of a solar model. The results are generally similar to those of the CM model and thus quite different from the MLT. The present model requires a smaller overshoot into the upper radiative zone than does the CM model, in accord with recent empirical estimates. Application to Population II stars and comparison with the very metal-poor globular cluster M68 yields an age in the range 11-12 Gyr. This is somewhat younger than the CM age, which in turn is younger than the corresponding MLT age, a result of possible cosmological interest.

Velocity fidelity of flow tracer particles

Abstract: Recent developments concerning the unsteady dynamic forces on a spherical particle at finite Reynolds number are reviewed for solid particles and clean micro-bubble. A particle frequency :response function and an energy transfer function are derived for a solid particle or a contaminated micro-bubble in gas or liquid flow. A simple, unified method for estimating the cut-off frequency, or cut-off size, of a solid particle or a contaminated bubble is developed. Particle motion in isotropic turbulence is examined. Responses of the tracer particle to integral length scale structure, to turbulence energy, and to Taylor micro-scale structure are discussed in terms of the particle turbulence diffusivity, the particle turbulence intensity, and the ensemble average of the second invariant of fluid turbulence deformation tensor evaluated on the particle trajectory.

Computation of turbulent axisymmetric and nonaxisymmetric jet flows using the K-epsilon model

Abstract: It is known that the standard K-e model does not provide an accurate prediction of the mean flow of turbulent jets. This is so even when the Pope and Sarkar correction terms are included. It is suggested that the K-e model, together with the Pope and Sarkar terms for nonplanar and high convective Mach number flow corrections, does contain the essential ingredients of turbulence physics for adequate jet mean flow prediction. The problem lies in the standard coefficients that were calibrated by using boundary-layer and low Mach number plane mixing layer data. By replacing these coefficients by a new set of empirical coefficients, it is demonstrated that the model can offer good predictions of axisymmetric, rectangular, and elliptic jet mean flows over the Mach number range of 0.4-2.0 and jet total temperature to ambient temperature ratio of 1.0-4.0. The present result conveys the message that it is possible that there is no universally applicable turbulence model. The reason is that although the characteristics and dynamics of fine-scale turbulence may be the same for all turbulent flows, the large turbulence structures, having dimensions comparable to the local length scale of the flow, are significantly influenced by local boundary conditions and geometry. Thus overall turbulence dynamics are somewhat problem type dependent.

Direct numerical simulation of near-interface turbulence in coupled gas-liquid flow

Abstract: Turbulence structures near the interface between two flowing fluids have been resolved by direct numerical simulation. As a first step the interface has been kept flat, corresponding closely to the recent gas‐liquid flow experiments of Rashidi and Banerjee [Phys. Fluids A 2, 1827 (1990)], with the fluids coupled through continuity of velocity and shear stress boundary conditions. For density ratios between the fluids typical of air and water, the turbulence characteristics on the gas side are quite similar to that in wall regions. The liquid side shows larger velocity fluctuations close to the interface and ejections originate closer to the interface. The mean velocity distribution, turbulence intensities, Reynolds stress and various other statistical measures are significantly altered compared to those in the wall region of channel flows. Quasi‐streamwise vortices form in the areas between high and low shear stress on both sides of the interface. At any given instant, about a fifth of these appear to be ...

Turbulence in the Ocean, Atmosphere, Galaxy, and Universe

Abstract: Flows in natural bodies of fluid often become turbulent, with eddy-like motions dominated by inertial-vort ex forces. Buoyancy, Coriolis, viscous, self-gravitational, electromagnetic, and other force constraints produce a complex phase space of wave-like hydrodynamic states that interact with turbulence eddies, masquerade as turbulence, and preserve information about previous hydrodynamic states as fossil turbulence. Evidence from the ocean, atmosphere, galaxy and universe are compared with universal similarity hypotheses of Kolmogorov (1941, 1962) for turbulence velocity u, and extensions to scalar fields θ like temperature mixed by turbulence. Universal u and θ spectra of natural flows can be inferred from laboratory and computer simulations with satisfactory accuracy, but higher order spectra and the intermittency constant μ of the third Kolmogorov hypothesis (1962) require measurements at the much larger Reynolds numbers found only in nature. Information about previous hydrodynamic states is preserved by Schwarz viscous and turbulence lengths and masses of self-gravitat ing condensates (rarely by the classical Jeans length and mass), as it is by Ozmidov, Hopfinger and Fernando scales in hydrophysical fields of the ocean and atmosphere. Viscous-gravitational formation occurred 10 4 -10 5 y after the Big Bang for supercluster, cluster, and then galaxy masses of the plasma, producing the first turbulence. Condensation after plasma neutralization of the H- 4 He gas was to a primordial fog of sub-solar particles that persists today in galactic halos as "dark matter". These gradually formed all stars, star clusters, etc. (humans!) within.

High freestream turbulence effects on turbulent boundary layers

Abstract: High freestream turbulence levels significantly alter the characteristics of turbulent boundary layers. Numerous studies have been conducted with freestreams having turbulence levels of 7 percent or less, but studies using turbulence levels greater than 10 percent have been essentially limited to the effects on wall shear stress and heat transfer. This paper presents measurements of the boundary layer statistics for the interaction between a turbulent boundary layer and a freestream with turbulence levels ranging from 10 to 20 percent. The boundary layer statistics reported in this paper include mean and rms velocities, velocity correlation coefficients, length scales, and power spectra. Although the freestream turbulent eddies penetrate into the boundary layer at high freestream turbulence levels, as shown through spectra and length scale measurements, the mean velocity profile still exhibits a log-linear region. Direct measurements of total shear stress (turbulent shear stress and viscous shear stress) confirm the validity of the log-law at high freestream turbulence levels. Velocity defects in the outer region of the boundary layer were significantly decreased resulting in negative wake parameters. Fluctuating rms velocities were only affected when the freestream turbulence levels exceeded the levels of the boundary layer generated rms velocities. Length scales and power spectra measurements showed large scale turbulent eddies penetrate to within y+ = 15 of the wall.

Action at distance and Bohm scaling of turbulence in tokamaks

Abstract: Recent transport experiments in tokamaks have suggested the concept of ‘‘action at distance’’ in which the local turbulence depends on gradients at a distance larger than the correlation length. Furthermore, the scaling of the ion thermal diffusivity is not always consistent with local gyro‐Bohm‐like transport but rather scales worse than Bohm‐like. This work is an attempt to reconcile these observations with simplified numerical simulations of toroidal ion temperature gradient (ITG) mode turbulence using a fast two‐dimensional (2‐D) inhomogeneous full radius turbulence code. It is found that action at a distance is possible, but only at weak damping rates, since the propagation range is given simply by the curvature drift group velocity divided by the average damping rate. The correlation lengths always scale linearly with the gyroradius. It is found that Bohm scaling or worse is possible when the gradients are close to the ITG threshold and the radial modes keep the turbulence level small enough to avoi...

Spectral transport model for turbulence

Abstract: The spectrum of inhomogeneous turbulence is modeled by an approach that is not limited to regimes of large Reynolds numbers or small mean-flow strain rates. In its simplest form and applied to incompressible flow, the model depends on five phenomenological constants defining the strength of turbulence coupling to mean flow, turbulence transport in physical and wave-number space, and mixing of stress-tensor components. The implications for homogeneous isotropic turbulence are investigated in detail and found to correspond well to the conclusions from more fundamental theories. Under appropriate limiting conditions, a turbulent system described by the model will relax over time into a state of approximate spectral equilibrium permitting a reduction to a “one-point” model for the system that is substantially like the familiar K-e model. This yields preliminary estimates of the present model's parameters and points to the way to improved modeling of flows beyond the applicability of the K-e method.

Experimental evidence of the rapid distortion of turbulence in the air flow over water waves

Abstract: Detailed observations of the air flow velocity, pressure and Reynolds stresses above water waves in a wave flume are presented. The static pressure fluctuations induced by the waves are observed following a new procedure that eliminates acoustical contamination by the wave maker. The measurements are analysed by comparing them with numerical simulations of the air flow over waves. In these numerical simulations the sensitivity to the choice of turbulence closure is studied. We considered both first-order turbulence closure schemes based on the eddy viscosity concept, and a second-order Reynolds stress model. The comparison shows that turbulence closure schemes based on the eddy viscosity concept overestimate the modulation of the Reynolds stress in a significant part of the vertical domain. When an eddy viscosity closure is used, the overestimated modulation of the Reynolds stress gives a significant contribution to the wave growth rate. Our results confirm the conclusions Belcher & Hunt reached on the basis of the rapid distortion theory.The ratio of the wind speed to the phase speed of the paddle wave in the experiment varies between 3 and 6. The observed amplitudes of the velocity and pressure perturbation are in excellent agreement with the simulations. Comparison of the observed phases of the pressure and velocity perturbations shows that the numerical model underpredicts the downwind phase shift of the undulating flow.The sheltering coefficients for the flow over hills and the growth rates of waves that are slow compared to the wind calculated with the Reynolds stress model are in excellent agreement with the analytical model of Belcher & Hunt. Extending the calculations to fast waves, we find that the energy flux to waves travelling almost as fast as the wind is increased on going from the mixing length turbulence closure to the Reynolds stress model.

Pipe flow of a thixotropic liquid

Abstract: Detailed measurements of mean velocity and velocity fluctuation levels (axial, tangential and radial) have been carried out using a laser Doppler anemometer for fully developed pipe flow of an aqueous solution of Laponite, a synthetic clay. The equilibrium rheological structure of this thixotropic liquid is well characterised by the Herschel-Bulkley model. Velocity profiles calculated for a Herschel-Bulkley fluid prove to be a very accurate representation of the measurements for laminar flow at reynolds numbers below about 1500. The measured profiles develop an unexplained asymmetry for higher Reynolds numbers until the flow undergoes transition to turbulence. The fluid is drag reducing under turbulent flow conditions with relative levels of tangential and radial turbulence intensity suppressed in comparison with water whilst the axial turbulence intensity is little different. Under all flow conditions it is evident that the fluid rheology is far from structural equilibrium, with values for the apparent yield stress and effective viscosity determined from near-wall velocity measurements considerably below those obtained from a rheometer.

Numerical Model of Turbulent Flow over Sand Dune

Abstract: A two-dimensional numerical model, based on solution of the Reynolds-averaged Navier-Stokes equations and the k -ω turbulence model, which takes into account sand-grain roughness, is developed to describe the flow in a fixed dune-bed channel. The model predicts the velocity and turbulence fields, as well as the pressure and friction distributions along the dune. The details of the flow in the separation eddy are calculated. The model predictions are in general agreement with existing detailed experimental data in a rectangular channel with two-dimensional dunes of typical but regular shape. The calculated pressure and friction distributions enable determination of the resistance components of the channel without further empiricism. However, compared to a well-known and representative semiempirical engineering formula for the prediction of resistance of natural dune-bed channels, the two-dimensional numerical model predicts significantly different contributions of friction and pressure to the total resista...

A numerical study of the nonlinear cascade of energy in magnetohydrodynamic turbulence

Abstract: Power spectra of solar wind magnetic field and velocity fluctuations more closely resemble those of turbulent fluids (spectral index of −5/3) than they do predictions for magnetofluid turbulence (a −3/2 index). Furthermore, the amount the solar wind is heated by turbulence is uncertain. To aid in the study of both of these issues, we report numerically derived energy cascade rates in magnetohydrodynamic (MHD) turbulence and compare them with predictions of MHD turbulence phenomenologies. Either of the commonly predicted spectral indices of 5/3 and 3/2 are consistent with the simulations. Explicit calculation of inertial range energy cascade rates in the simulations show that for unequal levels of fluctuations propagating parallel and antiparallel to the magnetic field, the majority species always cascades faster than does the minority species, and the cascade rates are in better agreement with a Kolmogoroff-like MHD turbulence phenomenology than with a generalized Kraichnan phenomenology even in situations where the fluctuations are much smaller than the mean magnetic field. The “Kolmogoroff constant” for MHD turbulence for small normalized cross helicity is roughly 6.7 in two dimensions and 3.6 for one calculation in three dimensions. For large normalized cross helicity, however, none of the existing models can account for the numerical results, although the Kolmogoroff-like case still works somewhat better than the Kraichnan-like. In particular, the applied magnetic field has much less influence than expected, and Alfvenicity is more important than predicted. These results imply the need for better phenomenological models to make clear predictions about the solar wind.

Using direct numerical simulations to understand premixed turbulent combustion

Abstract: In the last 10 years, direct numerical simulations (DNS) have become one of the most effective tools to undersland and model premixed turbulent combustion. Examples of application reviewed in this article illustrate the potential of DNS techniques in studies of turbulence structure, flame wrinkling by turbulence, flame geometry, quenching, stretch, curvature, turbulent diffusion, and flame-generated turbulence. Interactions of flames with vortices, turbulence and walls, triple flame structures, or flame ignition in turbulent flows are specifically discussed. Implications of DNS results for turbulent combustion modeling are presented through different examples. The capacities and limitations of DNS tools are reviewed in terms of physics and computational requirements. The presentation starts with the simplest, most inexpensive tools ends with codes able to deal with complex chemistry, transport, and thermodynamics.

A Numerical Study of a Bluff-body Stabilized Diffusion Flame. Part 1. Influence of Turbulence Modeling and Boundary Conditions

Abstract: This is the first part of a paper on numerical prediction of a bluff-body stabilized turbulent diffusion flame of syngas and air. This part considers the influence of turbulence modeling and boundary conditions on the predictions. Part 2 investigates the effect of the turbulence-chemistry interaction model and the effect of finite-rate chemistry. Results based on the “standard” k-s model and a Reynolds-stress-equation (RSE) model are compared. Measurements are taken from the literature. The RSE model predicts results in better agreement with the measurements than the k-e model. The two models predict significantly different composition and temperature levels in the recirculation bubble created by the bluff body. The specification of the turbulence level in the fuel-jet has a substantial influence on the axial decay of mixture fraction. Grid-resolution studies show that a relatively coarse grid is capable of representing the present flow with sufficient accuracy to evaluate the various sub-models.