Showing papers on "K-epsilon turbulence model published in 1981"

Numerical experiments in homogeneous turbulence

Abstract: The direct simulation methods developed by Orszag and Patternson (1972) for isotropic turbulence were extended to homogeneous turbulence in an incompressible fluid subjected to uniform deformation or rotation. The results of simulations for irrotational strain (plane and axisymmetric), shear, rotation, and relaxation toward isotropy following axisymmetric strain are compared with linear theory and experimental data. Emphasis is placed on the shear flow because of its importance and because of the availability of accurate and detailed experimental data. The computed results are used to assess the accuracy of two popular models used in the closure of the Reynolds-stress equations. Data from a variety of the computed fields and the details of the numerical methods used in the simulation are also presented.

Parameterization of Small Scales of Three-Dimensional Isotropic Turbulence Utilizing Spectral Closures

Abstract: A spectral equation derived from two-point closures applied to three-dimensional isotropic turbulence is studied from the subgrid-scale modeling point of view, with a cutoff wavenumber kc located in the inertial range of turbulence. Ideas of Kraichnan concerning eddy viscosities are then used to evaluate the parameterized subgrid-scale transfer. This, together with a suitable boundary condition at kc, allows us to predict statistically the large scales (k kc). A k−5/3 energy spectrum extending to kc is recovered without any artificial dissipation range in the neighborhood of kc. This procedure is valid both for forced stationary turbulence and for freely decaying turbulence. The same eddy-viscosity is then introduced in a direct numerical simulation of three-dimensional homogeneous isotropic turbulence without external forcing. Again, the energy spectrum, evaluated by averaging on a spherical shell of radius k, follows the Kolmogorov law u...

Conditional Sampling in Turbulence Measurement

Abstract: (a) Shear flows which exhibit a turbulent-nonturbulent interface; (b) Shear layers perturbed by interaction with another field of turbu­ lence; (c) Quasi-periodic or periodic flows (these include flows behind pass­ ing blades in rotating machinery, boundary layers over a solid or liquid surface with stationary or progressive periodic waves, and more generally flows subjected to either internal or external peri­ odic perturbations); (d) Coherent structures in different shear flows (these structures are currently receiving close attention by the turbulence community in view of their importance to the flow dynamics).

Anisotropic magnetohydrodynamic turbulence in a strong external magnetic field

Abstract: A strong external dc magnetic field introduces a basic anisotropy into incompressible magnetohydrodynamic turbulence. The modifications that this is likely to produce in the properties of the turbulence are explored for the high Reynolds number case. The conclusion is reached that the turbulent spectrum splits into two parts: an essentially two dimensional spectrum with both the velocity field and magnetic fluctuations perpendicular to the dc magnetic field, and a generally weaker and more nearly isotropic spectrum of Alfven waves. A minimal characterization of the spectral density tensors is given. Similarities to measurements from the Culham-Harwell Zeta pinch device and the UCLA Macrotor Tokamak are remarked upon, as are certain implications for the Belcher and Davis measurements of magnetohydrodynamic turbulence in the solar wind.

Turbulence Production in Premixed Turbulent Flames

Abstract: —A second order closure theory developed earlier is used to study the processes influencing the turbulent velocity field in a premixed turbulent flame with degrees of heat release of practical interest. The flow field is chosen so that the time-averaged flame structure is one-dimensional and statistically stationary. Earlier work suggests that in the absence of turbulence production due to Reynolds stresses as is the case in a flame orthogonal to the oncoming reactants, the case we consider, dilatation resulting from heat release reduces the level of turbulence. In contrast it is shown here that with sufficient heat release turbulence increases on passage through the flame because of a buoyancy production mechanism arising from the self-induced, mean pressure gradient. This mechanism overwhelms the effects of dilatation at temperature ratios characteristic of combustion. The same buoyancy mechanism also causes counter-gradient diffusion as predicted in an earlier paper and as observed in recent e...

Turbulence structure of a reattaching mixing layer

Abstract: Hot-wire measurements of second- and third-order mean products of velocity fluctuations have been made in the flow behind a backward-facing step with a thin, laminar boundary layer at the top of the step. Measurements extend to a distance of about 12 step heights downstream of the step, and include parts of the recirculating-flow region: approximate limits of validity of hot-wire results are given. The Reynolds number based on step height is about 105, the mixing layer being fully turbulent (fully three-dimensional eddies) well before reattachment, and fairly close to self-preservation in contrast to the results of some previous workers. Rapid changes in turbulence quantities occur in the reattachment region: Reynolds shear stress and triple products decrease spectacularly, mainly because of the confinement of the large eddies by the solid surface. The terms in the turbulent energy and shear stress balances also change rapidly but are still far from the self-preserving boundary-layer state even at the end of the measurement region.

Some developments in the theory of turbulence

Abstract: This is in no way intended as a review of turbulence- the subject is far too big for adequate treatment within a reasonably finite number of pages; the monumental treatise of Monin & Yaglom (1971, 1075) bears witness to this statement. It is rather a discourse on those aspects of the problem of turbulence with which I have myself had contact over the last twenty years or so. My choice of topics therefore has a very personal bias - but that is perhaps consistent with the style and objectives of this rather unusual issue of JFM. I have approached the dynamical problem of turbulence via two simpler (but nevertheless far from trivial) problems - viz the convection and diffusion of a passive scalar field and of a passive vector field by turbulence of known statistical properties. Particular emphasis is given to the method of successive averaging (a simplified version of the renormalization-group technique) which seems to me to have considerable potential. The difficulty of extending this method to the dynamical problem is discussed. In a final section (§ 6) I have allowed myself the luxury of discussing a somewhat esoteric topic - the problem of inviscid invariants and their relationship with the topological structure of a complex vorticity field. The helicity invariant is the prototype; it is identifiable with the Hopf invariant (1931) and it may be obtained from appropriate manipulation of Noether's theorem (Moreau 1977). A suggestion is made concerning possible measurement of this fundamental measure of ' lack of reflexional symmetry ' in a turbulent flow.

Large-eddy simulation of a passive scalar in isotropic turbulence

Abstract: TEMTY, a code for large-eddy simulation of a passive scalar in isotropic turbulence, is developed and proved by successful simulation of experiment. The role of each term in the scalar equation and the concept of prefiltering the scalar equation is examined. The ratio of the exponents in the decay of velocity and temperature intensities is found to parametrize with the ratio Λu/Λ0, where Λu, Λ0, are the velocity and temperature Taylor microscales respectively.

Spectral modelling of homogeneous non-isotropic turbulence

Abstract: The paper describes a method to calculate homogeneous anisotropic turbulent fields associated with a constant mean velocity gradient. The equations governing the Fourier transform of the triple velocity correlations are closed by using an extended eddy-damped quasi-normal approximation. An angular parametrization of the second-order spectral tensor is introduced in order to integrate analytically all the directional terms over a spherical shell. Numerical solutions of the model are presented for typical homogeneous anisotropic flows.

A Reynolds-stress closure model of turbulence applied to the calculation of a highly curved mixing layer

Abstract: The measurements in a highly curved mixing layer reported by Castro & Bradshaw (1976) are used to evaluate the performance of a calculation method based on the solution of modelled transport equations for the Reynolds stresses and the dissipation rate of turbulent energy. The model reproduces the suppression of turbulence by stabilizing curvature and, downstream of the curved region, where the flow returns asymptotically to being a plane mixing layer, calculated values of turbulent intensity and shear stress overshoot the plane-layer values in accordance with the experimental observations. The results are compared with those obtained by Townsend (1980) from a rapid-distortion model which correctly predicts the streamwise variation of the shear stress to intensity ratio. By contrast, calculations based on a conventional two-equation eddy-viscosity model fail badly to account for curvature effects on this flow.

A study of the interactions between large-scale coherent structures and fine-grained turbulence in a round jet

Abstract: Our recent studies of the interactions between large-scale structures and fine-grained turbulence in plane mixing layers have shown that many physical features of the problem may easily be obtained from an approximate energy integral description (Liu & Merkine 1976; Alper & Liu 1978), and this is confirmed by computational models (Gatski & Liu 1980). In this work, therefore, the approximate description is used to study at length the development of large-scale coherent structures in the technologically important problem of the round turbulent jet. The analysis begins from the radially integrated form of the kinetic energy equations of the mean flow, the large scale structure and the fine-grained turbulence, which are obtained through the use of the usual Reynolds time average and a conditional average with reference to the frequency of the idealized monochromatic component of the large-scale wavelike structure. This forms the basis for obtaining the ‘amplitude equations’ for the three components of the flow in terms of the mean flow momentum thickness, the large-scale structure kinetic energy and the fine-grained turbulence kinetic energy across the jet. These are obtained via the accompanying shape assumptions which also implicitly address the closure problems. The large-scale structure is also characterized by the Strouhal number St = fd/U e , where f is the frequency, d is the jet diameter and U e is the jet exit velocity, and by the azimuthal wave number n . The calculations are compared with the well controlled forced-jet observations of Binder & Favre-Marinet (1973), Favre-Marinet (1975), Favre-Marinet & Binder (1979) and Moore (1977). Although the present approximate considerations are not directed at structural details, the comparisons with observations on this aspect are most encouraging. Further theoretical work is presented that addresses the fundamental understanding of the mechanisms leading to the development of large-scale structures in turbulent jets. In general, large-scale structures in the range 0.02 ^ St St is increased, the streamwise location of the peak signal moves upstream, and the streamwise lifespan shortens. Consequently, high-frequency components of the large-scale structure dominate upstream while low-frequency components prevail further downstream. The Strouhal number that gives rise to maximum amplification is about 0.70 for weak initial levels of the large-scale structure and decreases to about 0.35 for very strong initial levels. As the initial energy level of the large-scale structure increases, its maximum relative amplification decreases until a level is reached beyond which the large-scale structure decays immediately downstream. This is explained in terms of the modification of the mean flow by the increasingly high energy levels of the large-scale structure in such a manner that it chokes off its own energy supply from the mean flow. At low Strouhal numbers the n = 1 helical component amplifies initially more than the n = 0 axisymmetric component for the same initial energy level. However, the n = 1 mode decays subsequently much faster than the n = 0 mode for all Strouhal numbers. This is attributable to the azimuthally-related wave-induced turbulent shear stresses in the n = 1 mode which give rise to additional mechanisms for energy transfer to the fine-grained turbulence. The possible control of the large-scale structure is fully explored through considering adjustments of the energy levels of the fine-grained turbulence and changes in initial mean velocity profile through changes in the momentum thickness at the nozzle exit. Increasing the initial turbulence levels and smoothing the mean nozzle exit velocity profile places restraints upon the downstream amplification of the large-scale structure. The non-equilibrium development of the large-scale structure is sensitive to its own initial conditions and spectral content, the initial condition of the fine-grained turbulence and the mean flow. Physical and quantitative studies of the large-scale structure in turbulent shear flows thus necessitate that the nature of such an initial environment be established and understood.

Near-surface turbulence measurements in a lake

Abstract: One of the most important but least understood regions of oceans and lakes is the near-surface zone. Exchanges of energy and momentum between the atmosphere and the waters below are controlled by turbulent mixing processes in the surface zone. Major advances in understanding these processes have been hampered by a lack of observations of turbulence near the surface. We have recently constructed a probe which can be used to estimate an important variable in theories of turbulence, the rate at which the kinetic energy of turbulence is dissipated, and have found a surprising though simple result: to a first approximation, scaling laws devised to describe dissipation in the atmospheric boundary layer may also be applicable in the water near the surface.

Calculation of turbulent boundary layers on curved surfaces

Abstract: Published data from boundary layers on convex surfaces are used to assess the performance of a calculation method based on the solution of modeled transport equations for the Reynolds’ stresses and the dissipation rate of turbulence energy. For flows with large curvature, the model closely reproduces the suppression of turbulence and the diminished growth rate and skin friction. The recovery of flow distorted by curvature is also predicted with results broadly in accord with the measurements.

Numerical Analysis of Flow in Sedimentation Basins

Abstract: The equations governing two-dimensional, steady flow in circular and rectangular primary settling basins are formulated. Mean-flow equations expressing conservation of mass and momentum are combined with a two-equation turbulence model (k-ϵ model) to compute velocity fields in sedimentation basins. The turbulence is characterized by a turbulent kinematic eddy viscosity which is computed directly as part of the solution. A numerical solution to the mathematical model is formulated by application of the Galerkin finite element method to the equation residuals. The resulting non-linear system of equations is solved by a variation of Newton's method. The model is applied to predict the flow pattern in a rectangular settling basin. A vector plot of the basin velocity field and contour plot of the turbulent kinematic eddy viscosity are presented.

Some interesting properties of two‐dimensional turbulence

Abstract: The effect of superimposed rigid body motions on the structure of two‐dimensional turbulence is examined. It is found that with regard to the fluctuation dynamics of the flow, the rotational behavior of two‐dimensional turbulence is quite different from its three‐dimensional counterpart. The implications that this has on turbulence modeling are discussed briefly.

Theory of saturation of optical scintillation by strong turbulence for arbitrary refractive-index spectra

Abstract: There is strong evidence that the amplitude of a light wave propagating through turbulence becomes Rayleigh distributed (i.e., the irradiance becomes exponentially distributed) in the limit of strong turbulence, which implies that the log-amplitude variance tends to π2/24. We find that the theory by Clifford et al. [ J. Opt. Soc. Am.64, 148– 154 ( 1974)] for saturation of scintillation by strong refractive turbulence can be made to obey this limit for power-law refractive-index spectra. However, for a nonzero inner scale of turbulence (no matter how small), the theory predicts that log-amplitude variance tends to zero in the limit of strong turbulence. A generalization of the theory is derived that obeys the π2/24 limit for arbitrary refractive-index spectra, a nonzero inner scale being a particular case. The new theory has no arbitrary parameters. Both old and new modulation transfer functions have different behavior for nonzero inner scale at both very large and very small spatial wave numbers when compared with the case of zero inner scale. This differing behavior affects the log-amplitude variance even if the Fresnel-zone size is much greater than the inner scale, provided that the lateral coherence length of phase is less than the inner scale. This differing behavior also applies at all spatial wave numbers if the Rytov variance is strongly affected by the inner scale. For strong (but finite) turbulence strength, the predicted log-amplitude variance is larger for a smaller ratio of Fresnel-zone size to inner scale, which is in quantitative agreement with observations.

Turbulence Reynolds number and the turbulent kinetic energy balance in the atmospheric surface layer

Abstract: The relation between the turbulence Reynolds numberR λ and a Reynolds numberz* based on the friction velocity and height from the ground is established using direct measurements of the r.m.s. longitudinal velocity and turbulent energy dissipation in the atmospheric surface layer. Measurements of the relative magnitude of components of the turbulent kinetic energy budget in the stability range 0 >z/L ≥ 0.4 indicate that local balance between production and dissipation is maintained. Approximate expressions, in terms of readily measured micrometeorological quantities, are proposed for the Taylor microscale λ and the Kolmogorov length scale η.

Turbulence in plane channel flows

Abstract: This paper complements an earlier study of the mean velocities in turbulent flows in a flat channel, one of whose walls can move relative to the other, so that the role of the stress gradient within the wall layers can be varied widely and in a controlled manner.Measurements of longitudinal, normal and lateral velocity fluctuation intensities (u′,v′,w′) and of shear stresses have been made in essentially fully developed flows established by various combinations of pressure gradient and wall velocity The channel aspect ratio (breadth/height) has been varied between 12 and 28 and the development ratio (development length/height) between 20 and 45. The introduction of a turbulence-generating grid at the entrance to the duct increases the effective development length.The study has considered twenty-six flows that are two-dimensional in the mean, which have been established by blowing and relative motion either in the same direction or directly opposed. Empirical descriptions, based on similarity laws incorporating either the wall stress or the local stress, are developed for the turbulence near the walls and in the core. The profiles of u′, v′ and w′ coalesce, to a reasonable approximation, when normalized with appropriate length and velocity scales. Extensive ‘plateau’ regions are identified, in which the scaled intensities are sensibly constant.A number of quantities characteristic of the structure of the turbulence are considered, in order to elucidate the effect of the stress gradient on the wall layer, and stages in the erosion of the constant-stress layer are identified.

The Transition to Turbulence in Nematic Liquid Crystals

Abstract: The article is divided in two parts. In part I we review the present state of knowledge on the problem of the transition to turbulence in isotropic liquids and we discuss analogies/differences with the case of nematics. In the well known Rayleigh-Benard case, experiments on ordinary liquids show that one must distinguish between confined and extended geometries (small or large “aspect ratios”). This difference is quite general and arises from the more or less large number of variables required to describe the structure. In confined geometry a Ruelle-Takens type of sequence seems relevant, with subharmonic bifurcation or intermittency as special cases. In extended geometry, slowly evolving imperfect structures (which may arise from an instability of the phase of rolls) result in a broad noise which can be viewed as a precursor of turbulence. In nematic liquid crystals (NLC) much less is known on the transition to turbulence. Nematic flows are verystrongly non-linear and are in large part controlle...

Two-position, two-frequency mutual-coherence function in turbulence

Abstract: By using the extended Huygens–Fresnel principle, an expression has been obtained for the generalized two-position, two-frequency mutual-coherence function of an electromagnetic beam in a turbulent medium. That result has been examined for different states of source coherence and for different turbulence conditions.