Showing papers on "K-epsilon turbulence model published in 2000"

Scale-Invariance and Turbulence Models for Large-Eddy Simulation

Abstract: ▪ Abstract Relationships between small and large scales of motion in turbulent flows are of much interest in large-eddy simulation of turbulence, in which small scales are not explicitly resolved and must be modeled. This paper reviews models that are based on scale-invariance properties of high-Reynolds-number turbulence in the inertial range. The review starts with the Smagorinsky model, but the focus is on dynamic and similarity subgrid models and on evaluating how well these models reproduce the true impact of the small scales on large-scale physics and how they perform in numerical simulations. Various criteria to evaluate the model performance are discussed, including the so-called a posteriori and a priori studies based on direct numerical simulation and experimental data. Issues are addressed mainly in the context of canonical, incompressible flows, but extensions to scalar-transport, compressible, and reacting flows are also mentioned. Other recent modeling approaches are briefly introduced.

Electron temperature gradient driven turbulence

Abstract: Collisionless electron-temperature-gradient-driven (ETG) turbulence in toroidal geometry is studied via nonlinear numerical simulations To this aim, two massively parallel, fully gyrokinetic Vlasov codes are used, both including electromagnetic effects Somewhat surprisingly, and unlike in the analogous case of ion-temperature-gradient-driven (ITG) turbulence, we find that the turbulent electron heat flux is significantly underpredicted by simple mixing length estimates in a certain parameter regime (ŝ∼1, low α) This observation is directly linked to the presence of radially highly elongated vortices (“streamers”) which lead to very effective cross-field transport The simulations therefore indicate that ETG turbulence is likely to be relevant to magnetic confinement fusion experiments

Analysis and interpretation of instantaneous turbulent velocity fields

Abstract: Methods of analyzing and interpreting velocity-field data (both two- and three-dimensional) to understand the kinematics, dynamics, and scales of turbulence are discussed. Reynolds decomposition and vorticity are traditionally used; however, several other methods, including Galilean (constant convection velocity) and LES decompositions (low-pass filtering), in conjunction with critical-point analysis of the local velocity gradient tensor, reveal more about the structure of turbulence. Once the small-scale structures have been identified, it is necessary to assess their importance to the overall dynamics of the turbulence by visualizing the motions they induce and the stresses they impose both on other small-scale vortices and on the larger-scale field.

Suppression of turbulence and transport by sheared flow

Abstract: The role of stable shear flow in suppressing turbulence and turbulent transport in plasmas and neutral fluids is reviewed. Localized stable flow shear produces transport barriers whose extensive and highly successful utilization in fusion devices has made them the primary experimental technique for reducing and even eliminating the rapid turbulent losses of heat and particles that characterize fusion-grade plasmas. These transport barriers occur in different plasma regions with disparate physical properties and in a range of confining configurations, indicating a physical process of unusual universality. Flow shear suppresses turbulence by speeding up turbulent decorrelation. This is a robust feature of advection whenever the straining rate of stable mean flow shear exceeds the nonlinear decorrelation rate. Shear straining lowers correlation lengths in the direction of shear and reduces turbulent amplitudes. It also disrupts other processes that feed into or result from turbulence, including the linear instability of important collective modes, the transport-producing correlations between advecting fluid and advectants, and large-scale spatially connected avalanchelike transport events. In plasmas, regions of stable flow shear can be externally driven, but most frequently are created spontaneously in critical transitions between different plasma states. Shear suppression occurs in hydrodynamics and represents an extension of rapid-distortion theory to a long-time-scale nonlinear regime in two-dimensional stable shear flow. Examples from hydrodynamics include the emergence of coherent vortices in decaying two-dimensional Navier-Stokes turbulence and the reduction of turbulent transport in the stratosphere.

Elastic turbulence in a polymer solution flow

Abstract: Turbulence is a ubiquitous phenomenon that is not fully understood. It is known that the flow of a simple, newtonian fluid is likely to be turbulent when the Reynolds number is large (typically when the velocity is high, the viscosity is low and the size of the tank is large). In contrast, viscoelastic fluids such as solutions of flexible long-chain polymers have nonlinear mechanical properties and therefore may be expected to behave differently. Here we observe experimentally that the flow of a sufficiently elastic polymer solution can become irregular even at low velocity, high viscosity and in a small tank. The fluid motion is excited in a broad range of spatial and temporal scales, and we observe an increase in the flow resistance by a factor of about twenty. Although the Reynolds number may be arbitrarily low, the observed flow has all the main features of developed turbulence. A comparable state of turbulent flow for a newtonian fluid in a pipe would have a Reynolds number as high as 10(5) (refs 1, 2). The low Reynolds number or 'elastic' turbulence that we observe is accompanied by significant stretching of the polymer molecules, resulting in an increase in the elastic stresses of up to two orders of magnitude.

Turbulence Modeling in Rotating and Curved Channels: Assessing the Spalart-Shur Correction

Abstract: Aunie edapproachtosystem-rotationandstreamline-curvatureeffectsintheframeworkofsimpleeddy-viscosity turbulence models is exercised in a range of rotating and curved channel e ows. The Spalart ‐Allmaras (SA) oneequation turbulence model (Spalart, P. R., and Allmaras, S. R., “ A One-Equation Turbulence Model for Aerodynamic Flows,” AIAAPaper 92-0439, 1992 )modie ed in thismanner is shown to bequitecompetitivewith advanced nonlinear and Reynolds-stress models and to be much more accurate than the original SA model and other eddyviscosity models that are widely used for industrial e ow computations. The new term adds about 20% to the computing cost, but does not degrade convergence.

An Introduction to Turbulent Flow

Abstract: Most natural and industrial flows are turbulent. The atmosphere and oceans, automobile and aircraft engines, all provide examples of this ubiquitous phenomenon. In recent years, turbulence has become a very lively area of scientific research and application, attracting many newcomers who need a basic introduction to the subject. An Introduction to Turbulent Flow, first published in 2000, offers a solid grounding in the subject of turbulence, developing both physical insight and the mathematical framework needed to express the theory. It begins with a review of the physical nature of turbulence, statistical tools, and space and time scales of turbulence. Basic theory is presented next, illustrated by examples of simple turbulent flows and developed through classical models of jets, wakes, and boundary layers. A deeper understanding of turbulence dynamics is provided by spectral analysis and its applications. The final chapter introduces the numerical simulation of turbulent flows. This well-balanced text will interest graduate students in engineering, applied mathematics, and the physical sciences.

Length scales of turbulence in stably stratified mixing layers

Abstract: Turbulence resulting from Kelvin–Helmholtz instability in layers of localized stratification and shear is studied by means of direct numerical simulation. Our objective is to present a comprehensive description of the turbulence evolution in terms of simple, conceptual pictures of shear–buoyancy interaction that have been developed previously based on assumptions of spatially uniform stratification and shear. To this end, we examine the evolution of various length scales that are commonly used to characterize the physical state of a turbulent flow. Evolving layer thicknesses and overturning scales are described, as are the Ozmidov, Corrsin, and Kolmogorov scales. These considerations enable us to provide an enhanced understanding of the relationships between uniform-gradient and localized-gradient models for sheared, stratified turbulence. We show that the ratio of the Ozmidov scale to the Thorpe scale provides a useful indicator of the age of a turbulent event resulting from Kelvin–Helmholtz instability.

On the problem of turbulence

Abstract: A central theme in the history of the turbulence problem is about the method of ‘closure’ in the models and ‘theories’ which have been proposed. Closure has invariably been by empirical calibration with experimental data. In this note we draw attention to a paper by Morris, Giridharan and Lilley, in which for the first time empiricism is obviated. For the turbulent mixing layer, this is accomplished by including in its description the mechanism for production of turbulent shear stress (i.e. turbulent momentum transfer), by large-scale instability waves. Some implications for the theory of turbulent shear flows are discussed.

Shock Wave—Turbulence Interactions

Abstract: ▪ Abstract The idealized interactions of shock waves with homogeneous and isotropic turbulence, homogeneous sheared turbulence, turbulent jets, shear layers, turbulent wake flows, and two-dimensional boundary layers have been reviewed. The interaction between a shock wave and turbulence is mutual. A shock wave exhibits substantial unsteadiness and deformation as a result of the interaction, whereas the characteristic velocity, timescales and length scales of turbulence change considerably. The outcomes of the interaction depend on the strength, orientation, location, and shape of the shock wave, as well as the flow geometry and boundary conditions. The state of turbulence and the compressibility of the incoming flow are two additional parameters that also affect the interaction.

The Eddy Dissipation Turbulence Energy Cascade Model

Abstract: The turbulence energy cascade model used in the Eddy Dissipation Concept for combusting flow is presented and discussed in relation to existing knowledge of relevant turbulent flows. The cascade consists of a stepwise model for energy transfer from larger to smaller scales and for energy dissipation from each scale level by viscous forces. The cascade model makes a connection between the viscous fine structures, where combustion takes place, and the larger transporting eddies which are simulated by turbulence models. Thus, fine-structure quantities are expressed in terms of turbulence energy and dissipation. The model is compared to turbulence-energy-spectrum data for the inertial subrange and the dissipative range for nonreacting and reacting flows. The model is also discussed in relation to isotropic decaying turbulence in the transition from initial to final periods of decay. It is concluded that the energy cascade model captures important features of the turbulence structural interaction and ...

Scaling properties of three-dimensional isotropic magnetohydrodynamic turbulence

Abstract: A comprehensive picture of three-dimensional (3D) isotropic magnetohydrodynamic (MHD) turbulence is presented based on the first 5123-mode numerical simulations performed. Both temporal and spatial scaling properties are studied. For finite magnetic helicity H the energy decay is governed by the constancy of H and the decrease of the ratio of kinetic and magnetic energy Γ=EK/EM. A simple model consistent with a series of simulation runs predicts the asymptotic decay laws E∼t−1/2, EK∼t−1. For nonhelical MHD turbulence, H≃0, the energy decays faster, E∼t−1. The energy spectrum follows a k−5/3 law, clearly steeper than k−3/2 previously found in 2D MHD turbulence. The scaling exponents of the structure functions are consistent with a modified She–Leveque model ζpMHD=p/9+1−(1/3)p/3, which corresponds to a basic Kolmogorov scaling and sheet-like dissipative structures. The difference between the 3D and the 2D behavior can be related to the eddy dynamics in 3D and 2D hydrodynamic turbulence.

Compressibility effects in a turbulent annular mixing layer. Part 1. Turbulence and growth rate

Abstract: This work uses direct numerical simulations of time evolving annular mixing layers, which correspond to the early development of round jets, to study compressibility effects on turbulence in free shear flows. Nine cases were considered with convective Mach numbers ranging from Mc = 0.1 to 1.8 and turbulence Mach numbers reaching as high as Mt = 0.8.Growth rates of the simulated mixing layers are suppressed with increasing Mach number as observed experimentally. Also in accord with experiments, the mean velocity difference across the layer is found to be inadequate for scaling most turbulence statistics. An alternative scaling based on the mean velocity difference across a typical large eddy, whose dimension is determined by two-point spatial correlations, is proposed and validated. Analysis of the budget of the streamwise component of Reynolds stress shows how the new scaling is linked to the observed growth rate suppression. Dilatational contributions to the budget of turbulent kinetic energy are found to increase rapidly with Mach number, but remain small even at Mc = 1.8 despite the fact that shocklets are found at high Mach numbers. Flow visualizations show that at low Mach numbers the mixing region is dominated by large azimuthally correlated rollers whereas at high Mach numbers the flow is dominated by small streamwise oriented structures. An acoustic timescale limitation for supersonically deforming eddies is found to be consistent with the observations and scalings and is offered as a possible explanation for the decrease in transverse lengthscale.

On the prediction of gas–solid flows with two-way coupling using large eddy simulation

Abstract: The purpose of this paper is to examine the feasibility of large eddy simulation (LES) for predicting gas–solid flows in which the carrier flow turbulence is modified by momentum exchange with particles. Several a priori tests of subgrid-scale (SGS) turbulence models are conducted utilizing results from direct numerical simulation (DNS) of a forced homogeneous isotropic turbulent flow with the back effect of the particles modeled using the point-force approximation. Properties of the subgrid-scale field are computed by applying Gaussian filters to the DNS database. Similar to the behavior observed in single-phase flows, a priori test results show that, while the local energy flux is inaccurately estimated, the overall SGS dissipation is reasonably predicted using the conventional Smagorinsky model and underestimated using the Bardina scale-similarity model. Very good agreement between model predictions and DNS results are measured using closures whose coefficients are computed using the resolved field, the so-called dynamic subgrid models, with the mixed model yielding more accurate predictions than the dynamic Smagorinsky model. A priori test results are then confirmed in actual LES calculations used to investigate the sensitivity of the predictions to mesh refinement. The LES was performed at infinite turbulent Reynolds number and for a range of particle response times and mass loadings. Grid resolution in the LES was varied from 323 to 963 collocation points, with particle sample sizes of 885 000 for each response time. LES predictions of the flow with two-way coupling are independent of mesh refinement when using the dynamic mixed model and when the particle relaxation time becomes larger than the characteristic time scale of the unresolved fluid turbulent field.

A linear process in wall-bounded turbulent shear flows

Abstract: A linear process in wall-bounded turbulent shear flows has been investigated through numerical experiments. It is shown that the linear coupling term, which enhances non-normality of the linearized Navier–Stokes system, plays an important role in fully turbulent—and hence, nonlinear —flows. Near-wall turbulence is shown to decay without the linear coupling term. It is also shown that near-wall turbulence structures are not formed in their proper scales without the nonlinear terms in the Navier–Stokes equations, thus indicating that the formation of the commonly observed near-wall turbulence structures are essentially nonlinear, but the maintenance relies on the linear process. Other implications of the linear process are also discussed.

Coherent structure phenomena in drift wave-zonal flow turbulence

Abstract: Zonal flows are azimuthally symmetric plasma potential perturbations spontaneously generated from small-scale drift-wave fluctuations via the action of Reynolds stresses. We show that, after initial linear growth, zonal flows can undergo further nonlinear evolution leading to the formation of long-lived coherent structures which consist of self-bound wave packets supporting stationary shear layers. Such coherent zonal flow structures constitute dynamical paradigms for intermittency in drift-wave turbulence that manifests itself by the intermittent distribution of regions with a reduced level of anomalous transport.

Rough wall turbulent boundary layers in shallow open channel flow

Abstract: An experimental study was undertaken to investigate the effects of roughness on the structure of turbulent boundary layers in open channels. The study was carried out using a laser Doppler anemometer in shallow flows for three different types of rough surface, as well as a hydraulically smooth surface. The flow Reynolds number based on the boundary layer momentum thickness ranged from 1400 to 4000. The boundary layer thickness was comparable with the depth of flow and the turbulence intensity in the channel flow varied from 2 to 4 percent. The defect profile was correlated using an approach which allowed both the skin friction and wake strength to vary. The wake parameter was observed to vary significantly with the type of surface roughness in contradiction to the wall similarity hypothesis. Wall roughness also led to higher turbulence levels in the outer region of the boundary layer. The profound effect of surface roughness on the outer region as well as the effect of channel turbulence on the main flow indicates a strong interaction, which must be accounted for in turbulence models

Application of generalized thermostatistics to fully developed turbulence

Abstract: We apply the formalism of non-extensive statistical mechanics to fully developed turbulent flows. We obtain analytical formulas for probability density functions of velocity differences depending on distance r/η and Reynolds number Rλ, which are in very good agreement with turbulence experiments. The skewness is taken into account by analysing universal contributions due to higher-order correlations of the chaotic dynamics. We also calculate the moment scaling exponents ζm, which also agree well with experimental data.

A study of turbulence under conditions of transient flow in a pipe

Abstract: A detailed investigation of fully developed transient flow in a pipe has been undertaken using water as the working fluid. Linearly increasing or decreasing excursions of flow rate were imposed between steady initial and final values. A three-beam, two-component laser Doppler anemometer was used to make simultaneous measurements of either axial and radial, or axial and circumferential, components of local velocity. Values of ensemble-averaged mean velocity, root-mean-square velocity fluctuation and turbulent shear stress were found from the measurements.Being the first really detailed study of ramp-type transient turbulent flow, the present investigation has yielded new information and valuable insight into certain fundamental aspects of turbulence dynamics. Some striking features are evident in the response of the turbulence field to the imposed excursions of flow rate. Three different delays have been identified: a delay in the response of turbulence production; a delay in turbulence energy redistribution among its three components; and a delay associated with the propagation of turbulence radially. The last of these is the most pronounced under the conditions of the present study. A dimensionless delay parameter τ+[= √2τUτ0/D] is proposed to describe it. The first response of turbulence is found to occur in the region near the wall where turbulence production peaks. The axial component of turbulence responds earlier than the other two components and builds up faster. The response propagates towards the centre of the pipe through the action of turbulent diffusion at a speed which depends on the Reynolds number at the start of the excursion. In the core region, the three components of turbulence energy respond in a similar manner. Turbulence intensity is reduced in the case of accelerating flow and increased in decelerating flow. This is mainly as a result of the delayed response of turbulence. A dimensionless ramp rate parameter γ[= (dUb/dt) (1/Ub0)(D/Uτ0] is proposed, which determines the extent to which the turbulence energy differs from that of pseudo-steady flow as a result of the delay in the propagation of turbulence.

Quasi-two-dimensional turbulence

Abstract: We review the results of numerical and experimental studies in quasi-two-dimensional (Q2D) turbulence. We demonstrate that theoretical energy spectra with slopes –5/3 and –3 (Kraichnan–Batchelor–Leith) can be observed only for a special set of external parameters. The bottom drag, beta effect, finite Rossby–Obukhov radius or vertical stratification, which distinguish geophysical Q2D turbulence from its purely 2D counterpart, determine the organization of a Q2D flow on a large scale. Since the spectral energy flux in 2D turbulence is directed upscale, the bottom friction takes on a special role. In the absence of bottom drag the energy condenses on the largest resolvable scale and flow equilibration is not attained.

Recent Turbulence Model Advances Applied to Multi-Element Airfoil Computations

Abstract: A one-equation linear turbulence model and two-equation nonlinear explicit algebraic stress model (EASM) are applied to the flow over a multielement airfoil. The effect of the K-epsilon and K-omega forms of the two-equation model are explored, and the K-epsilon form is shown to be deficient in the wall-bounded regions of adverse pressure gradient flows. A new K-omega form of EASM is introduced. Nonlinear terms present in EASM are shown to improve predictions of turbulent shear stress behind the trailing edge of the main element and near midflap. Curvature corrections are applied to both the one- and two-equation turbulence models and yield only relatively small local differences in the flap region, where the flow field undergoes the greatest curvature. Predictions of maximum lifts are essentially unaffected by the turbulence model variations studied.

On the mechanisms of modifying the structure of turbulent homogeneous shear flows by dispersed particles

Abstract: The present study is concerned with answering the question: What are the physical mechanisms responsible for the modification of the turbulence structure by solid particles dispersed in a homogeneous shear flow? We employ DNS (direct numerical simulations) to examine the effects of the two-way interaction between the two phases on the turbulence structure. Our results indicate that particles affect the rate of production of turbulence energy via modifying the vorticity dynamics. It is known that regions of large production rate of turbulence energy are sandwiched between counter rotating vortices whose vorticity, ωs, is aligned with the axes of the longitudinal vortex tubes. These longitudinal vortex tubes are strongly inclined toward the streamwise direction due to the imposed mean shear. The stronger ωs is, the larger the production rate. The dispersed solid particles modify the alignment of the local vorticity vector, ω, with the axis of the longitudinal vortex tube. Increasing this alignment increases...

Sub-grid turbulence modeling for unsteady flow with acoustic resonance

Abstract: This paper proposes a novel combination of Reynoldsaveraged Navier-Stokes (RANS) and large-eddy simulation (LES) sub-grid models, which combines the best features of time-averaged and spatially-filtered models, yielding the superior near-wall stress predictions of (algebraic or full-transport) Reynolds-stress models with the ability to override any quasi-steady grid-converged RAN’S model solution in regions of sufficiently high grid density. The proposed hybrid formulation is well suited to the coupled simulation of all flow scales in resonating high-Reynolds number flows and contains no additional empirical constants beyond those appearing in the original RANS and LES sub-grid models.