Showing papers on "K-epsilon turbulence model published in 1991"

A dynamic subgrid‐scale model for compressible turbulence and scalar transport

Abstract: The dynamic subgrid-scale (SGS) model of Germano et al. (1991) is generalized for the large eddy simulation (LES) of compressible flows and transport of a scalar. The model was applied to the LES of decaying isotropic turbulence, and the results are in excellent agreement with experimental data and direct numerical simulations. The expression for the SGS turbulent Prandtl number was evaluated using direct numerical simulation (DNS) data in isotropic turbulence, homogeneous shear flow, and turbulent channel flow. The qualitative behavior of the model for turbulent Prandtl number and its dependence on molecular Prandtl number, direction of scalar gradient, and distance from the wall are in accordance with the total turbulent Prandtl number from the DNS data.

Local Structure Of Turbulence in an Incompressible Viscous Fluid at Very Large Reynolds Numbers

Abstract: §1. We denote by ua(P) = ua(xl, x2, x3, t), a= 1,2,3, the velocity components at time t at a point with rectangular Cartesian coordi­nates xi, x2, x3. When studying turbulence it is natural to regard the velocity components ua(P) at each point P = (xi, x2, x3, t) of the region G under consideration belonging to the four-dimensional space (xi, x2i X3, t) as random variables in the sense of probability theory (for this approach, see the paper by Millionshchikov [1]).

The minimal flow unit in near-wall turbulence

Abstract: Direct numerical simulations of unsteady channel flow were performed at low to moderate Reynolds numbers on computational boxes chosen small enough so that the flow consists of a doubly periodic (in x and z) array of identical structures. The goal is to isolate the basic flow unit, to study its morphology and dynamics, and to evaluate its contribution to turbulence in fully developed channels. For boxes wider than approximately 100 wall units in the spanwise direction, the flow is turbulent and the low-order turbulence statistics are in good agreement with experiments in the near-wall region. For a narrow range of widths below that threshold, the flow near only one wall remains turbulent, but its statistics are still in fairly good agreement with experimental data when scaled with the local wall stress. For narrower boxes only laminar solutions are found. In all cases, the elementary box contains a single low-velocity streak, consisting of a longitudinal strip on which a thin layer of spanwise vorticity is lifted away from the wall. A fundamental period of intermittency for the regeneration of turbulence is identified, and that process is observed to consist of the wrapping of the wall-layer vorticity around a single inclined longitudinal vortex.

Preferential concentration of particles by turbulence

Abstract: Direct numerical simulation of isotropic turbulence was used to investigate the effect of turbulence on the concentration fields of heavy particles. The hydrodynamic field was computed using 643 points and a statistically stationary flow was obtained by forcing the low‐wave‐number components of the velocity field. The particles used in the simulations were time advanced according to Stokes drag law and were also assumed to be much more dense than the fluid. Properties of the particle cloud were obtained by following the trajectories of 1 000 000 particles through the simulated flow fields. Three values of the ratio of the particle time constant to large‐scale turbulence time scale were used in the simulations: 0.075, 0.15, and 0.52. The simulations show that the particles collect preferentially in regions of low vorticity and high strain rate. This preferential collection was most pronounced for the intermediate particle time constant (0.15) and it was also found that the instantaneous number density was as much as 25 times the mean value for these simulations. The fact that dense particles collect in regions of low vorticity and high strain in turn implies that turbulence may actually inhibit rather than enhance mixing of particles.

Near-wall turbulence closure modeling without ``damping functions''

Abstract: An elliptic relaxation model is proposed for the strongly inhomogeneous region near the wall in wall-bounded turbulent shear flow. This model enables the correct kinematic boundary condition to be imposed on the normal component of turbulent intensity. Hence, wall blocking is represented. Means for enforcing the correct boundary conditions on the other components of intensity and on the k — ɛ equations are discussed. The present model agrees quite well with direct numerical simulation (DNS) data. The virtue of the present approach is that arbitrary “damping functions” are not required.

The analysis and modelling of dilatational terms in compressible turbulence

Abstract: It is shown that the dilatational terms that need to be modeled in compressible turbulence include not only the pressure-dilatation term but also another term - the compressible dissipation. The nature of these dilatational terms in homogeneous turbulence is explored by asymptotic analysis of the compressible Navier-Stokes equations. A non-dimensional parameter which characterizes some compressible effects in moderate Mach number, homogeneous turbulence is identified. Direct numerical simulations (DNS) of isotropic, compressible turbulence are performed, and their results are found to be in agreement with the theoretical analysis. A model for the compressible dissipation is proposed; the model is based on the asymptotic analysis and the direct numerical simulations. This model is calibrated with reference to the DNS results regarding the influence of compressibility on the decay rate of isotropic turbulence. An application of the proposed model to the compressible mixing layer has shown that the model is able to predict the dramatically reduced growth rate of the compressible mixing layer.

Turbulent open-channel flows with variable depth across the channel

Abstract: The flow of water in straight open channels with prismatic complex cross-sections is considered. Lateral distributions of depth-mean velocity and boundary shear stress are derived theoretically for channels of any shape, provided that the boundary geometry can be discretized into linear elements. The analytical model includes the effects of bed-generated turbulence, lateral shear turbulence and secondary flows. Experimental data from the Science and Engineering Research Council (SERC) Flood Channel Facility are used to illustrate the relative importance of these three effects on internal shear stresses. New experimental evidence concerning the spatial distribution of Reynolds stresses τyx and τzx is presented for the particular case of compound or two-stage channels. In such channels the vertical distributions of τzx are shown to be highly nonlinear in the regions of strongest lateral shear and the depth-averaged values of τyx are shown to be significantly different from the depth mean apparent shear stresses. The importance of secondary flows in the lateral shear layer region is therefore established. The influence of both Reynolds stresses and secondary flows on eddy viscosity values is quantified. A numerical study is undertaken of the lateral distributions of local friction factor and dimensionless eddy viscosity. The results of this study are then used in the analytical model to reproduce lateral distributions of depth-mean velocity and boundary shear stress in a two stage channel. The work will be of interest to engineers engaged in flood channel hydraulics and overbank flow in particular.

A one-equation turbulence transport model for high Reynolds number wall-bounded flows

Abstract: A one-equation turbulence model that avoids the need for an algebraic length scale is derived from a simplified form of the standard k-epsilon model equations. After calibration based on well established properties of the flow over a flat plate, predictions of several other flows are compared with experiment. The preliminary results presented indicate that the model has predictive and numerical properties of sufficient interest to merit further investigation and refinement. The one-equation model is also analyzed numerically and robust solution methods are presented.

Analytical methods for the development of reynolds-stress closures in turbulence

Abstract: Analytical methods for the development of Reynolds stress models in turbulence are reviewed in detail. Zero, one and two equation models are discussed along with second-order closures. A strong case is made for the superior predictive capabilities of second-order closure models in comparison to the simpler models. The central points are illustrated by examples from both homogeneous and inhomogeneous turbulence. A discussion of the author's views concerning the progress made in Reynolds stress modeling is also provided along with a brief history of the subject.

Turbulence in the liquid phase of a uniform bubbly air-water flow

Abstract: The paper describes studies of the turbulence of the liquid in a bubbly, grid-generated turbulent flow field. Laser-Doppler and hot-film anemometry are used for the experimental investigation. It is found that the turbulent kinetic energy increases strongly with the void fraction α. Roughly speaking, there exist two distinct regimes: the first one corresponds to low value of α, where hydrodynamic interactions between bubbles are negligible, and the second one to higher values, for which, owing to their mutual interactions, the bubbles transfer a greater amount of kinetic energy to the liquid. The Reynolds stress tensor shows that the quasi-isotropy is not altered. At low enough values of α, the difference between the turbulent kinetic energy in the liquid phase and the energy associated with the grid-generated turbulence proves to be approximately equal to the intensity of the pseudo-turbulence, defined as the fluctuating energy that would be induced by the motion of the bubbles under non-turbulent conditions. The one-dimensional spectra exhibit a large range of high frequencies associated with the wakes of the bubbles and the classical dependence.

Theory of mean poloidal flow generation by turbulence

Abstract: The mechanism for generation of mean poloidal flow by turbulence is identified and elucidated. Two methods of calculating poloidal flow acceleration are given and shown to yield predictions which agree. These methods link flow generation to the quasilinear radial current or the Reynolds stress 〈VrVθ〉. It is shown that poloidal acceleration will occur if the turbulence supports radially propagating waves and if radial gradients in the turbulent Reynolds stress and wave energy density flux are present. In practice, these conditions are met in the tokamak edge region when waves propagate through the outermost closed flux surface or when convection cells with large radial correlation length are situated in steep gradient regions. The possible impact of these results on the theory of the L→H transition is discussed.

Direct observation of the intermittency of intense vorticity filaments in turbulence.

Abstract: Cavitation in a liquid seeded with bubbles is used as a new visualization technique to single out the regions of very low pressure of a fully developed turbulent flow. By this means, the sudden appearance of high vorticity filaments is observed. These structures are very thin and short lived and display a high degree of temporal as well as spatial intermittency. They contribute to the flow organization: In particular their disintegration corresponds to the formation of large eddies.

Assumed β-pdf Model for Turbulent Mixing: Validation and Extension to Multiple Scalar Mixing

Abstract: Many engineering calculations of turbulent reacting flows employ the assumed-pdf approach. On the form of the assumed pdf, however, there has been little consensus and the choice has often been ad hoc. The objective of this work is to investigate the validity of the assumed β-pdf model for the case of the inert mixing of two scalars and extend the applicability of the model to multiple scalar mixing. By comparing the β-pdf model favorably with the two-scalar mixing data obtained from direct numerical simulations (DNS), it is demonstrated that the use of this model is justified for all stages of the mixing process in statistically-stationary, isotropic turbulence. It is also shown analytically that during the final stages of mixing the model β-pdf reduces to a Gaussian-pdf, consistent with the observations from experiments and DNS, The suggested multivariate β-pdf model for multiple-scalar mixing relates algebraically, The mean scalar concentrations and the turbulent scalar-energy—to the joint pdf...

Structure and dynamics of homogeneous turbulence: models and simulations

Abstract: This paper presents a review of recent results on homogeneous turbulence. We discuss results obtained by direct numerical simulation as well as phenomenological models for the interpretation and understanding of these flows. In particular, we show that homogeneous turbulence can be well described in terms of a weakly correlated, random background field that is generally consistent with the classical Kolmogorov theory of turbulence, and strongly correlated, highly localized structures, that are largely responsible for intermittency effects and deviations from Kolmogorov scaling. These results give a unified dynamical picture of turbulence that describes both the energetics and intermittency of homogeneous turbulence, and allows us to develop a quantitative model for the description of the statistics of turbulence at small scales.

Application of a Reynolds stress turbulence model to the compressible shear layer

Abstract: Theoretically based turbulence models have had success in predicting many features of incompressible, free shear layers However, attempts to extend these models to the high-speed, compressible shear layer have been less effective In the present work, the compressible shear layer was studied with a second-order turbulence closure, which initially used only variable density extensions of incompressible models for the Reynolds stress transport equation and the dissipation rate transport equation The quasi-incompressible closure was unsuccessful; the predicted effect of the convective Mach number on the shear layer growth rate was significantly smaller than that observed in experiments Having thus confirmed that compressibility effects have to be explicitly considered, a new model for the compressible dissipation was introduced into the closure This model is based on a low Mach number, asymptotic analysis of the Navier-Stokes equations, and on direct numerical simulation of compressible, isotropic turbulence The use of the new model for the compressible dissipation led to good agreement of the computed growth rates with the experimental data Both the computations and the experiments indicate a dramatic reduction in the growth rate when the convective Mach number is increased Experimental data on the normalized maximum turbulence intensities and shear stress also show a reduction with increasing Mach number

Locally axisymmetric turbulence

Abstract: The failure of local isotropy to describe the experimentally obtained derivative moments in turbulent shear flows has previously been well-documented, but is briefly reviewed. The same data are then used to evaluate the hypothesis that the turbulence is locally axisymmetric. Locally axisymmetric turbulence is defined herein as turbulence which is locally invariant to rotations about a preferred axis.The derivative moment relations are derived from the general form of the two-point velocity correlation tensor near the origin for axisymmetric turbulence. These are used to derive relations for the rate of dissipation of kinetic energy, the mean-square vorticity, and the components of each. Almost all of the experimental derivative moment data are shown to be consistent with these equations, and thus with local axisymmetry.

Evolution and dynamics of shear-layer structures in near-wall turbulence

Abstract: Near-wall flow structures in turbulent shear flows are analyzed, with particular emphasis on the study of their space-time evolution and connection to turbulence production. The results are obtained from investigation of a database generated from direct numerical simulation of turbulent channel flow at a Reynolds number of 180 based on half-channel width and friction velocity. New light is shed on problems associated with conditional sampling techniques, together with methods to improve these techniques, for use both in physical and numerical experiments. The results clearly indicate that earlier conceptual models of the processes associated with near-wall turbulence production, based on flow visualization and probe measurements need to be modified. For instance, the development of asymmetry in the spanwise direction seems to be an important element in the evolution of near-wall structures in general, and for shear layers in particular. The inhibition of spanwise motion of the near-wall streaky pattern may be the primary reason for the ability of small longitudinal riblets to reduce turbulent skin friction below the value for a flat surface.

Some characteristics of small-scale turbulence in a turbulent duct flow

Abstract: The fine-scale structure of turbulence in a fully developed turbulent duct flow is examined by considering the 3D velocity derivative field obtained from direct numerical simulations at two relatively small Reynolds numbers. The magnitudes of all mean-square derivatives (normalized by wall variables) increase with the Reynolds number, the increase being largest at the wall. These magnitudes are not consistent with the assumption of local isotropy except perhaps near the duct center-line. When the assumption of local isotropy is relaxed to one of local axisymmetry, or invariance with respect to rotation about a coordinate axis (here chosen in the streamwise direction), satisfactory agreement is indicated by the data outside the wall region. Support for axisymmetry is demonstrated by anisotropy invariant maps of the dissipation and vorticity tensors.

Second-Order Near-Wall Turbulence Closures: A Review

Abstract: Advances in second-order near-wall turbulence closures are summarized All closures under consideration are based on high-Reynolds-number models Most near-wall closures proposed to date attempt to modify the high-Reynolds-number models for the dissipation function and the pressure redistribution term so that the resultant models are applicable all the way to the wall The asymptotic behavior of the near-wall closures is examined and compared with the proper near-wall behavior of the exact Reynolds-stress equations It is found that three second-order near-wall closures give the best correlations with simulated turbulence statistics However, their predictions of near-wall Reynolds-stress budgets are considered to be incorrect A proposed modification to the dissipitation-rate equation remedies part of those predictions It is concluded that further improvements are required if a complete replication of all the turbulence properties and Reynolds-stress budgets by a statistical model of turbulence is desirable

Reynolds shear stress measurements in a separated boundary layer flow

Abstract: Turbulence measurements were obtained for two cases of boundary layer flow with an adverse pressure gradient, one attached and the other separated. A three-component laser Doppler velocimeter system was used to measure three mean velocity components, all six Reynolds stress components, and all ten velocity triple product correlations. Independent measurements of skin-friction obtained with a laser oil-flow interferometer were used to examine the law of the wall in adverse pressure gradient flows where p(+) is less than 0.05. Strong similiarities were seen between the two adverse pressure gradient flows and free shear layer type flows. Eddy viscosities, dissipation rates, and pressure-strain rates were deduced from the data and compared to various turbulence modeling assumptions.

Lagrangian statistical simulation of the turbulent motion of heavy particles

Abstract: A Lagrangian stochastic model for the motion of heavy particles has been developed by coupling a stochastic model for the motion of fluid elements to the Stokes equations of motion of a particle in a turbulent flow. The effects of crossing trajectories and continuity are incorporated by generalising Csanady's (1963) ideas developed for stationary homogeneous turbulence; effects of turbulence inhomogeneity and nonstationarity are embodied in the stochastic model for the fluid motion.

Near-wall modeling of the dissipation rate equation

Abstract: Near-wall modeling of the dissipation rate equation is investigated and its asymptotic behavior is studied in detail using a k-epsilon model. It is found that all existing modeled dissipation rate equations predict an incorrect behavior for the dissipation rate near a wall. An improvement is proposed and the resulting near-wall dissipation rate distribution is found to be similar to that given by numerical simulation data. To further validate the improved k-epsilon model, it is used to calculate flat-plate turbulent boundary-layer flows at high- as well as low-turbulence Reynolds numbers, and the results are compared with measurements, numerical simulation data, and the calculations of three different two-equation models. These comparisons show that all the models tested give essentially the same flow properties away from the wall; significant differences only occur in a region very close to the wall. In this region, the calculations of the improved k-epsilon model are in better agreement with measurements and numerical simulation data. In particular, the modeled distribution of the dissipation rate is significantly improved and a maximum is predicted at the wall instead of away from the wall. Furthermore, the improved k-epsilon model is found to be the most asymptotically consistent among the four different two-equation models examined.

"Alfvénic" versus "standard" turbulence in the solar wind.

Abstract: We study the variation of the properties of turbulence with stream structure, on time scales of hours and minutes, in the inner heliosphere at solar minimum. Between fast hot streams, this turbulence is found to show many properties typical of standard weakly compressible magnetohydrodynamic (MHD) turbulence such as excess of turbulent magnetic energy and a relative level of density fluctuation approximately equal to the turbulent Mach number squared. We discuss whether or not the more peculiar properties of Alfvenic turbulence, found within fast streams, represent some genuinely different state of MHD turbulence at large distances from the sun and the ecliptic plane. The Ulysses spacecraft data should allow these possibilities to be distinguished

Electron diamagnetic effects on the resistive pressure-gradient-driven turbulence and poloidal flow generation

Abstract: The nonlinear evolution of resistive pressure‐gradient‐driven turbulence with diamagnetic effects included generates a dc electric field (poloidal velocity) through the convective nonlinearity in the momentum balance equation. This radial electric field has a strong shear and contributes to the saturation of the turbulence; its effect on the saturation level of turbulence is more important than the change of the time and length scales of the modes by the direct ω* effects.

Transport asymmetry in skewed turbulence

Abstract: Large‐eddy simulations have shown that passive, conservative scalars emitted into the convective boundary layer (CBL) of the atmosphere have unusual diffusion properties. A species introduced through an area source at the layer top and having zero flux through the bottom (i.e., one undergoing ‘‘top‐down’’ diffusion) has a well‐behaved eddy diffusivity, but one introduced at the bottom, with zero flux at the top (‘‘bottom‐up’’ diffusion) has a much different diffusivity profile in the same turbulence field. It is suggested that the roots of this transport asymmetry lie in the interaction between skewness of the transporting turbulence and the gradient of the flux of the transported scalar. A kinematic model is used to show that this interaction can indeed induce transport asymmetry in small‐time‐scale, homogeneous turbulence. The present simulations with a Lagrangian particle model confirm that this asymmetry extends to large‐time‐scale, inhomogeneous turbulence. A heuristic model of convective turbulence suggests that its asymmetric transport is also described by the kinematic model but with the small‐time‐scale restriction removed. In all cases the transport asymmetry effects scale with the parameter SσwTL/h, where S, σw, and TL are the skewness, standard deviation, and Lagrangian integral time scale of the transporting turbulence, and h is the layer depth; a scalar flux gradient is required as well.