Showing papers on "K-epsilon turbulence model published in 2006"

A new version of detached-eddy simulation, resistant to ambiguous grid densities

Abstract: Detached-eddy simulation (DES) is well understood in thin boundary layers, with the turbulence model in its Reynolds-averaged Navier–Stokes (RANS) mode and flattened grid cells, and in regions of massive separation, with the turbulence model in its large-eddy simulation (LES) mode and grid cells close to isotropic. However its initial formulation, denoted DES97 from here on, can exhibit an incorrect behavior in thick boundary layers and shallow separation regions. This behavior begins when the grid spacing parallel to the wall Δ∥ becomes less than the boundary-layer thickness δ, either through grid refinement or boundary-layer thickening. The grid spacing is then fine enough for the DES length scale to follow the LES branch (and therefore lower the eddy viscosity below the RANS level), but resolved Reynolds stresses deriving from velocity fluctuations (“LES content”) have not replaced the modeled Reynolds stresses. LES content may be lacking because the resolution is not fine enough to fully support it, and/or because of delays in its generation by instabilities. The depleted stresses reduce the skin friction, which can lead to premature separation.

Solver and Turbulence Model Upgrades to OVERFLOW 2 for Unsteady and High-Speed Applications

Abstract: An implicit unfactored SSOR algorithm has been added to the overset Navier-Stokes CFD code OVERFLOW 2 for unsteady and moving body applications. The HLLEM and HLLC third-order spatial upwind convective flux models have been added for high-speed flow applications. A generalized upwind transport equation has been added for solution of the two-equation turbulence models and the species equations. The generalized transport equation is solved using an unfactored SSOR implicit algorithm. Three hybrid RANS/DES turbulence models have been added for unsteady flow applications. Wall function boundary conditions that include compressibility and heat transfer effects have been also been added to OVERFLOW 2.

Study of the near-wall-turbulent region of the high-Reynolds-number boundary layer using an atmospheric flow

Abstract: (Received 31 March 2005 and in revised form 29 July 2005) Data from the near-wall-turbulent region of the high-Reynolds-number atmospheric surface layer are used to analyse the attached-eddy model of wall turbulence. All data were acquired during near-neutral conditions at the Surface Layer Turbulence and Environmental Science Test (SLTEST) facility located in the western Utah Great Salt Lake Desert. Instantaneous streamwise and wall-normal components of velocity were collected with a wall-normal array of two-component hot wires within the first 2 m above the surface of the salt flats. Streamwise and wall-normal turbulence intensities and spectra are directly compared to corresponding laboratory data and similarity formulations hypothesized from the attached-eddy model of wall turbulence. This affords the opportunity to compare results with Reynolds numbers varying over three orders of magnitude. The wall-normal turbulence-intensity similarity formulation is extended. The results show good support for the similarity arguments forwarded by the attached-eddy model as well as Townsend’s (1956) Reynolds-number similarity hypothesis and lack of the ‘inactive’ motion influence on the wall-normal velocity component. The effects of wall roughness and the spread in the convection velocity due to this roughness are also discussed. An experimental investigation of the near-wall-turbulent (logarithmic) region of the high-Reynolds-number turbulent boundary layer was conducted. The main purpose of this work is to use these data to investigate the attached-eddy model of wallbounded turbulence at high Reynolds numbers. (A good review of the importance of understanding high-Reynolds-number wall-bounded flow is given by Gad-el-Hak & Bandyopadhyay 1994.) The attached-eddy model essentially provides a kinematic description for wall-bounded turbulence. The foundation of the model, which is based on the attached-eddy hypothesis of Townsend (1976), is the observation that wallbounded turbulence contains a collection of coherent structures or eddies. Therefore, the model proposes that the statistical features of wall-bounded turbulence can be modelled by a linear superposition of such eddies. The model has been refined and developed over the past three decades on the data of low-to-moderate Reynoldsnumber wall-bounded turbulence experiments (e.g. pipe and boundary-layer flow) and has led to a number of similarity laws. For a complete review of the attached-eddy model see Perry & Marusic (1995) and the references therein.

Enhancement and Suppression of Heat Transfer by MHD Turbulence

Abstract: We study the effect of turbulence on heat transfer within magnetized plasmas for energy injection velocities both larger and smaller than the Alfven speed. We find that in the latter regime the heat transfer is partially suppressed, while in the former regime the effects of turbulence depend on the intensity of driving. In fact, the scale lA at which the turbulent velocity is equal to the Alfven velocity is an important new parameter. When the electron mean free path λ is larger than lA, the stronger the turbulence, the lower the thermal conductivity by electrons. The turbulent motions, however, induce their own advective heat transport, which, for the parameters of intracluster medium, provides effective heat diffusivity that exceeds the classical Spitzer value.

Decay of turbulence in pipe flow.

Abstract: A novel experiment has been devised which provides direct evidence for critical point behavior in the longstanding problem of the transition to turbulence in a pipe. The novelty lies in the quenching of turbulence by reducing the Reynolds number and observing the decay of disordered motion. Divergence of the time scales implies underlying deterministic dynamics which are analogous to those found in boundary crises in dynamical systems. A modulated wave packet emerges from the long term transients and this coherent state provides evidence for connections with recent theoretical developments.

Euler Equations, Navier-Stokes Equations and Turbulence

Abstract: In 2004 the mathematical world will mark 120 years since the advent of turbulence theory ([80]). In his 1884 paper Reynolds introduced the decomposition of turbulent flow into mean and fluctuation and derived the equations that describe the interaction between them. The Reynolds equations are still a riddle. They are based on the Navier-Stokes equations, which are a still a mystery. The Navier-Stokes equations are a viscous regularization of the Euler equations, which are still an enigma. Turbulence is a riddle wrapped in a mystery inside an enigma ([11]).

On a wave-induced turbulence and a wave-mixed upper ocean layer

Abstract: [1] A concept of wave-amplitude-based Reynolds number is suggested which is hypothesised to indicate a transition from laminarity to turbulence for the wave-induced motion If the hypothesis is correct, the wave-induced motion can be turbulent and the depth of upper ocean mixing due to such wave-generated turbulence can be predicted based on knowledge of the wave climate Estimates of the critical wave Reynolds number provide an approximate value of Recr = 3000 This number was tested on mechanically-generated laboratory waves and was confirmed Once this number is used for ocean conditions when mixing due to heating and cooling is less important than that due to the waves, quantitative and qualitative characteristics of the ocean's Mixed Layer Depth (MLD) are shown to be predicted with a satisfactory degree of agreement with observations Testing the hypothesis against other known results in turbulence generation and wave attenuation is also conducted

A Modified-Leray-α subgrid scale model of turbulence

Abstract: Inspired by the remarkable performance of the Leray-α (and the Navier–Stokes alpha (NS-α), also known as the viscous Camassa–Holm) subgrid scale model of turbulence as a closure model to Reynolds averaged equations (RANS) for flows in turbulent channels and pipes, we introduce in this paper another subgrid scale model of turbulence, the modified Leray-α (ML-α) subgrid scale model of turbulence. The application of the ML-α to infinite channels and pipes gives, due to symmetry, similar reduced equations as Leray-α and NS-α. As a result the reduced ML-α model in infinite channels and pipes is equally impressive as a closure model to RANS equations as NS-α and all the other alpha subgrid scale models of turbulence (Leray-α and Clark-α). Motivated by this, we present an analytical study of the ML-α model in this paper. Specifically, we will show the global well-posedness of the ML-α equation and establish an upper bound for the dimension of its global attractor. Similarly to the analytical study of the NS-α and Leray-α subgrid scale models of turbulence we show that the ML-α model will follow the usual k−5/3 Kolmogorov power law for the energy spectrum for wavenumbers in the inertial range that are smaller than 1/α and then have a steeper power law for wavenumbers greater than 1/α (where α > 0 is the length scale associated with the width of the filter). This result essentially shows that there is some sort of parametrization of the large wavenumbers (larger than 1/α) in terms of the smaller wavenumbers. Therefore, the ML-α model can provide us another computationally sound analytical subgrid large eddy simulation model of turbulence.

Gyro-kinetic simulation of global turbulent transport properties in tokamak experiments

Abstract: A general geometry gyro-kinetic model for particle simulation of plasma turbulence in tokamak experiments is described. It incorporates the comprehensive influence of noncircular cross section, realistic plasma profiles, plasma rotation, neoclassical (equilibrium) electric fields, and Coulomb collisions. An interesting result of global turbulence development in a shaped tokamak plasma is presented with regard to nonlinear turbulence spreading into the linearly stable region. The mutual interaction between turbulence and zonal flows in collisionless plasmas is studied with a focus on identifying possible nonlinear saturation mechanisms for zonal flows. A bursting temporal behavior with a period longer than the geodesic acoustic oscillation period is observed even in a collisionless system. Our simulation results suggest that the zonal flows can drive turbulence. However, this process is too weak to be an effective zonal flow saturation mechanism.

A speculative study of 2/3-order fractional Laplacian modeling of turbulence: Some thoughts and conjectures

Abstract: This study makes the first attempt to use the 2∕3-order fractional Laplacian modeling of Kolmogorov −5∕3 scaling of fully developed turbulence and enhanced diffusing movements of random turbulent particles. Nonlinear inertial interactions and molecular Brownian diffusivity are considered to be the bifractal mechanism behind multifractal scaling of moderate Reynolds number turbulence. Accordingly, a stochastic equation is proposed to describe turbulence intermittency. The 2∕3-order fractional Laplacian representation is also used to model nonlinear interactions of fluctuating velocity components, and then we conjecture a fractional Reynolds equation, underlying fractal spacetime structures of Levy 2∕3 stable distribution and the Kolmogorov scaling at inertial scales. The new perspective of this study is that the fractional calculus is an effective approach to modeling the chaotic fractal phenomena induced by nonlinear interactions.

Numerical study of the subgrid fluid turbulence effects on the statistics of heavy colliding particles

Abstract: The main purpose of this article is to investigate the effects of the subgrid fluid turbulence on the motion of nonsettling colliding particles suspended in steady homogeneous isotropic turbulent flow An additional goal is to characterize the statistical properties of the subgrid fluid turbulence “viewed” by inertial particles to support the development of large eddy simulation (LES) approach for particle-laden turbulent flows Two types of numerical experiments have been carried out: first, the discrete particle trajectories were computed using the fluid velocity field given by direct numerical simulation (DNS) in order to characterize the small-scale fluid velocity fluctuations “seen” by the particles In a second stage, the particle trajectory simulations were performed using several filtered velocity fields computed from the DNS data to evaluate the effect of the subgrid fluid turbulence on the particle statistics (turbulent dispersion, kinetic energy, accumulation efficiency, particle-particle relat

Approach to the 4/5 law in homogeneous isotropic turbulence

Abstract: Kolmogorov's similarity hypotheses and his 4/5 law are valid at very large Reynolds numbers. For flows encountered in the laboratory, the effect of a finite Reynolds number and of the non-stationarity or inhomogeneity associated with the large scales can affect the behaviour of the scales in the inertial range significantly. This paper focuses on the source of inhomogeneity in two types of flows, those dominated mainly by a decay of energy in the streamwise direction and those which are forced, through a continuous injection of energy at large scales. Results based on a parameterization of the second-order velocity structure function indicate that the normalized third-order structure function approaches 4/5 much more rapidly for forced than for decaying turbulence. This trend is supported by grid turbulence measurements and numerical data in a periodic box.

K-L turbulence model for the self-similar growth of the Rayleigh-Taylor and Richtmyer-Meshkov instabilities

Abstract: A turbulence model is developed to described the self-similar growth of the Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities. The model describes the dominant eddies in the mixing zone with evolutionary equations for their characteristic dimension L and energy per unit mass K≡V2∕2. The equations are based on the successful buoyancy-drag models for RT and RM flows, but constructed only with local parameters so that it can be applied to multidimensional flows with multiple shells of materials. The model has several unknown coefficients that are determined by comparing analytical and numerical solutions with RT and RM experiments.

Extremely Weak Mixing in Stable Conditions

Abstract: Transport by extremely weak turbulence occurring on nights with clear skies and weak winds is examined from seven tower levels of eddy-correlation data taken from each of two field programs. The very small flux is systematic, provided that the perturbations are computed from a record-dependent averaging length, which must be as small as 10 s in very stable conditions. With traditional methods for computing the flux, these fluxes were considered too small to estimate, in that the computed values behaved erratically. For extremely weak turbulence, the fluxes decrease systematically with height and often indicate very shallow boundary-layer depths on the order of 10 m. However, in one field program, the turbulence slowly increases with height above the surface flux-based boundary layer apparently due to horizontal advection of stronger turbulence driven by modest surface heterogeneity. For very weak turbulence, the eddy diffusivity for momentum is systematically greater than that for heat in both field programs. The dependence of the turbulence strength and its variability with stability is examined in some detail.

A quasi-normal scale elimination model of turbulence and its application to stably stratified flows

Abstract: . Models of planetary, atmospheric and oceanic circulation involve eddy viscosity and eddy diffusivity, KM and KH, that account for unresolved turbulent mixing and diffusion. The most sophisticated turbulent closure models used today for geophysical applications belong in the family of the Reynolds stress models. These models are formulated for the physical space variables; they consider a hierarchy of turbulent correlations and employ a rational way of its truncation. In the process, unknown correlations are related to the known ones via "closure assumptions'' that are based upon physical plausibility, preservation of tensorial properties, and the principle of the invariant modeling according to which the constants in the closure relationships are universal. Although a great deal of progress has been achieved with Reynolds stress closure models over the years, there are still situations in which these models fail. The most difficult flows for the Reynolds stress modeling are those with anisotropy and waves because these processes are scale-dependent and cannot be included in the closure assumptions that pertain to ensemble-averaged quantities. Here, we develop an alternative approach of deriving expressions for KM and KH using the spectral space representation and employing a self-consistent, quasi-normal scale elimination (QNSE) algorithm. More specifically, the QNSE procedure is based upon the quasi-Gaussian mapping of the velocity and temperature fields using the Langevin equations. Turbulence and waves are treated as one entity and the effect of the internal waves is easily identifiable. This model implies partial averaging and, thus, is scale-dependent; it allows one to easily introduce into consideration such parameters as the grid resolution, the degree of the anisotropy, and spectral characteristics, among others. Applied to turbulent flows affected by anisotropy and waves, the method traces turbulence anisotropization and shows how the dispersion relationships for linear waves are modified by turbulence. In addition, one can derive the internal wave frequency shift and the threshold criterion of internal wave generation in the presence of turbulence. The spectral method enables one to derive analytically various one-dimensional and three-dimensional spectra that reflect the effects of waves and anisotropy. When averaging is extended to all scales, the method yields a Reynolds-averaged, Navier-Stokes equations based model (RANS). This RANS model shows that there exists a range of Ri, approximately between 0.1 and 1, in which turbulence undergoes remarkable anisotropization; the vertical mixing becomes suppressed while the horizontal mixing is enhanced. Although KH decreases at large Ri and tends to its molecular value, KM remains finite and larger than its molecular value. This behavior is attributable to the effect of internal waves that mix the momentum but do not mix a scalar. In the Reynolds stress models, this feature is not replicated; instead, all Reynolds stress models predict KM→0 at some value of Ri≤1 which varies from one model to another. The presented spectral model indicates that there is no a single-valued critical Richardson number Ri at which turbulence is fully suppressed by stable stratification. This result is in agreement with large volume of atmospheric, oceanic and laboratory data. The new spectral model has been implemented in the K-e format and tested in simulations of the stably stratified atmospheric boundary layers. The results of these simulations are in good agreement with the data collected in BASE, SHEBA and CASES99 campaigns. Implementation of the QNSE-derived KM and KH in the high-resolution weather prediction system HIRLAM results in significant improvement of its predictive skills.

Polarization Intermittency and Its Influence on MHD Turbulence

Abstract: The Goldreich-Sridhar model of incompressible turbulence provides us with an elegant approach to describing strong MHD turbulence. It relies on the fact that interacting Alfvenic waves are independent and have random polarization. However, in case of strong interaction, a spontaneous local axial asymmetry can arise. We used direct numerical simulations to show that polarization alignment occurs and that it grows larger at smaller scales. Assuming critical balance, this effect could lead to a shallower spectrum and stronger anisotropy. Even small changes in these two properties will have important astrophysical consequences, e.g., for the cosmic-ray physics.

Mechanism of flow instability and transition to turbulence

Abstract: In this paper, a new mechanism of flow instability and turbulence transition is proposed for wall bounded shear flows. It is stated that the total energy gradient in the transverse direction and that in the streamwise direction of the main flow dominate the disturbance amplification or decay. Thus, they determine the critical condition of instability initiation and flow transition under given initial disturbance. A new dimensionless parameter K for characterizing flow instability is proposed which is expressed as the ratio of the energy gradients in the two directions for the flow without energy input or output. It is suggested that flow instability should first occur at the position of K max which may be the most dangerous position. This speculation is confirmed by Nishioka et al.'s experimental data. Comparison with experimental data for plane Poiseuille flow and pipe Poiseuille flow indicates that the proposed idea is really valid. It is found that the turbulence transition takes place at a critical value of K max of about 385 for both plane Poiseuille flow and pipe Poiseuille flow, below which no turbulence will occur regardless the disturbance. More studies show that the theory is also valid for plane Couette flows which holds a critical value of K max of about 370.

K-L turbulence model for the self-similar growth of the Rayleigh-Taylor and Richtmyer-Meshkov instabilities

Abstract: A turbulence model is developed to described the self-similar growth of the Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities. The model describes the dominant eddies in the mixing zone with evolutionary equations for their characteristic dimension L and energy per unit mass K≡V2∕2. The equations are based on the successful buoyancy-drag models for RT and RM flows, but constructed only with local parameters so that it can be applied to multidimensional flows with multiple shells of materials. The model has several unknown coefficients that are determined by comparing analytical and numerical solutions with RT and RM experiments.

Small-scale anisotropy in Lagrangian turbulence

Abstract: We report measurements of the second-order Lagrangian structure function and the Lagrangian velocity spectrum in an intensely turbulent laboratory flow. We find that the asymmetries of the large-scale flow are reflected in the small-scale statistics. In addition, we present new measurements of the Lagrangian structure function scaling constant C0, which is of central importance to stochastic turbulence models as well as to the understanding of turbulent pair dispersion and scalar mixing. The scaling of C0 with the turbulence level is also investigated, and found to be in agreement with an existing model.

Energy transfers in forced MHD turbulence

Abstract: The energy cascade in magnetohydrodynamics is studied using high resolution direct numerical simulations of forced isotropic turbulence. The magnetic Prandtl number is unity and the large scale forcing is a function of the velocity that injects a constant rate of energy without generating a mean flow. A shell decomposition of the velocity and magnetic fields is proposed and is extended to the Elsasser variables. The analysis of energy exchanges between these shell variables shows that the velocity and magnetic energy cascades are mainly local and forward, though non-local energy transfer does exist between the large, forced, velocity scales and the small magnetic structures. The possibility of splitting the shell-to-shell energy transfer into forward and backward contributions is also discussed.