Showing papers on "K-epsilon turbulence model published in 1968"

The distortion of turbulence by irrotational plane strain

Abstract: : The experiments extend those of Townsend which form the basis of his model of free turbulence. Here straining is carried to a strain ratio of 6:1, while Townsend's straining went only to 4:1. Two kinds of distorting ducts are used to produce the uniform mean strain applied to initially nearly isotropic grid turbulence. The results differ from Townsend's in that (1) a considerably higher degree of anisotropy is achieved, Townsend's measure of anisotropy attaining values up to 0.6, rather than the maximum of 0.42 he found; (2) there is no evidence that an equilibrium structure is attained; and (3) the strained turbulence rapidly becomes less anisotropic when the straining ceases. It is found to be possible to predict the variation of the total turbulence energy using rapid-distortion theory with a correction for decay. However, the individual components cannot be accurately predicted in this way. (Author)

Load Fluctuations in Turbulent Flow

Abstract: Measurements of lift and drag force fluctuations on elementary building shapes in turbulent flow are reported. It is shown that fluctuations in the drag force can be related to the turbulent velocity fluctuations with the use of a simple momentum model. Tests were conducted in a uniform stream, with a relative intensity of turbulence of approximately 10% and a scale of turbulence of the same order as the major dimensions of the models used. The investigation of load fluctuations in turbulent flow was carried out as part of a study directed towards the assessment of wind loads and wind effects on tall buildings.

Formulation of the Theory of Turbulence

Abstract: A theory of homogeneous, isotropic turbulence in an incompressible fluid is formulated. This theory provides a basis for the dynamics of fully developed turbulence. A hierarchy of equations to determine the time evolution of single‐time moments of the velocity field is derived. Various properties of this hierarchy are exhibited, such as positivity of the dynamically determined energy density. The theory is applied to the study of the inertial range, where the Kolmogoroff theory is justified. A generalized inertial‐range theory is formulated. This “semilocal” theory is characterized by local energy transfer and nonlocal relaxation of triple moments. The generalized theory is applied to the study of hydromagnetic turbulence, which is shown to possess a semilocal inertial range.

Structure of Turbulence in a Curved Mixing Layer

Abstract: Earlier conclusions about the nature of the turbulent energy budgets, the value of the inertial subrange spectral constant α, and the turbulence Reynolds number Rλ in a curved mixing layer are revised in view of the results of a recent investigation.

Measurement of Turbulence in Water

Abstract: A study of hot-film anemometer measurements in water resulted in a hypothesis that: Dirt and air bubbles accumulating on the hot-film sensor change the mean voltage for a given velocity, but have only a minor, outside the frequency domain in water, effect on the frequency response of the sensor to velocity fluctuations. And for a given sensor there is a unique family of voltage/velocity relations that can be defined by calibration with different overheat ratios. The hypothesis was experimentally verified by comparing turbulence measurements made in the same flow field with well filtered and with very dirty water. The method was used to measure the characteristics of turbulence measurements made in ordinary laboratory water for flow over hydraulically-rough and hydraulically-smooth boundaries. Reynolds numbers ranged from 8,000 to 20,000 and mean velocities from 0.3 fps to 2.8 fps. Relative turbulent intensities for flow over the smooth boundary were in good agreement with Laufer's measurements in air. Power spectrum analysis of the turbulence showed very little energy in frequencies larger than 100 Hz.

An experimental study of turbulence production near a smooth wall in a turbulent boundary layer with zero pressure-gradient,

Abstract: : Detailed study of the structure of a turbulent boundary layer near a smooth wall is presented including instantaneous values of: velocity profiles, fluctuation data, and turbulence production rates. It is shown that essentially all the turbulence production occurs during 'bursting times.' The details of the bursting process are described in three stages: low-speed streak lifting, oscillatory growth, and breakup. It is shown that the streak-lifting creates an unstable (inflexional) region in the instantaneous velocity profile. This unstable region is followed, in the downstream flow, by oscillatory growth and breakup. Short duration energy spectra, auto-correlation data, fluctuation data in mean value and for bursting and non-bursting times, detailed photos of the flow processes, and comparison of measured frequencies with calculated unstable frequencies all suggest that the process of turbulence production near smooth walls is due to the formation of a local instability of the Kelvin-Helmholz type arising from the interaction of the wall model with the outer flow, that is from low-speed streak lifting. (Author)

Compressible Turbulent Magnetohydrodynamic Boundary Layers

Abstract: A closed analytical model for compressible magnetohydrodynamic boundary layers is formulated by using transport equations for the turbulent fluctuations of species mass density, velocity, and temperature, and thus avoiding a priori relations between turbulent fluxes and mean flow quantities. The equations for both the mean and the fluctuating motion are simplified according to the boundary‐layer approximation, and closure of the system is achieved by the introduction of “universal turbulence structure parameters” that only relate turbulent correlations among themselves. This model accounts for convection and diffusion of turbulent fluxes as well as for the effect of turbulence suppression by applied magnetic fields. It is shown that if convection, diffusion, and electromagnetic effects were omitted in the equations of fluctuating motion, the latter would reduce to algebraic forms defining the concepts of mixing length, turbulent Prandtl number, and turbulent Schmidt number in terms of turbulence structure parameters.

Prediction of drag reduction with a viscoelastic model

Abstract: Drag reduction prediction in turbulent flow with viscoelastic model, discussing solutions exhibiting elastic properties in laminar flow

The structure of canopy flow field.

Abstract: : A model study of canopy flow over high roughness elements was carried out using roughness consisting of pegs 9. cm high and 0.48 cm in diameter arranged in four patterns. The mean velocity and the turbulence intensity were measured within and above the roughness elements. Empirical expressions derived from field measurements for mean velocity profiles, turbulent velocity, and turbulence intensity were used to examine the data obtained in this model study. The logarithmic profile was adapted to analyze the data of mean velocity above the canopy. In this analysis, the friction velocity and the roughness parameter were calculated from the mean velocity profiles and related to the density of roughness elements to show the effects of roughness density on the flow field. The growth of the internal boundary layer was estimated from the mean velocity profiles and the turbulence intensity. The results of estimation were compared with semi-imperical equations. Although the coefficient of anisotropy above the canopy in this model study is larger than in the field, the model study gave data about the turbulent flow field similar to the field data. Hence, this model was verified to be suitable for the study of diffusion. (Author)

The damping of gravity waves in shallow water by energy dissipation in a turbulent boundary layer

Abstract: The method of matched asymptotic expansions is applied to the determination of the damping of gravity waves propagating in turbulent conditions. The effect of the turbulence is introduced by a general system of coefficients of eddy viscosity, whilst the turbulence itself is supposed to be confined to boundary layers adjacent to a rigid impermeable bottom and the free surface. The lowest order damping in the system is found to be independent of surface turbulence and computations are made for a physically meaningful distribution of eddy viscosity in the lower boundary layer. DOI: 10.1111/j.2153-3490.1968.tb00375.x

Simulation of Horizontal Turbulent Diffusion of Particles under Waves

Abstract: By oscillation of an array of turbulence-generating grids in still water, the turbulent fluid velocity field m shoaling waves near the bottom is simulated in a laboratory channel. Solid particles with fall velocities varying between 1 and 40 mm/sec are introduced into the test volume from above. Multiple- image photography using ultraviolet lighting techniques and a suitably placed mirror allow recording of the gram trajectories as functions of time and three space dimensions simultaneously. The Lagrangian intensities of turbulence and diffusion coefficients are then directly measured from the photographic data. The scale times, scale lengths, and the frequencies of the power spectra modes can then be calculated. Properties of the fluid turbulence are inferred from the quasi-neutral particles. The analysis, which is restricted to the component of diffusion in the hori2ontal direction normal to the grid motion, shows that the turbulent velocity distributions of both fluid and heavy particles are Gaussian, and that their standard deviations (intensities of turbulence) increase regularly with increasing grid Reynolds numbers (grid speeds). Diffusion coefficients likewise generally increase with increasing grid Reynolds numbers. Diffusivities of the heavy particles relative to the fluid are a function of both particle fall velocity and the structure of the fluid turbulence itself.

Drag Reduction in a Model of Shear-Flow Turbulence

Abstract: Turbulent shear flow model for studying drag reduction in Burgers type system with nonlinearity

Two‐Dimensional Magnetohydrodynamic Turbulence

Abstract: For a system governed by a generalized Ohm's law, an arbitrary velocity field cannot independently maintain magnetic field fluctuations in a two‐dimensional situation.

Production of negative eddy conductivities and viscosities in the presence of buoyancy and shear.

Abstract: An analysis of weak turbulence indicates that under certain stabilizing conditions, the eddy conductivity and viscosity can become negative. It is shown that for the model considered, the occurrence of the negative values depends on the fact that the turbulence decays with time.

Undulance and turbulence in stably stratified media

Abstract: : The origin and the structure of undulance and turbulence in stably stratified media are investigated through theoretical reasoning and laboratory experiments. The mechanisms for generating turbulence in stably stratified media are linked with the mechanisms for generating vorticity - shear and stratification. The dual role of stable stratification -- the capability for generating and attenuating turbulence -- is pointed out. The turbulence induced by stable stratification is evidenced in two experimental results: (1) turbulent rotors in the lee of a barrier in a stably stratified fluid, and (2) the breaking of traveling internal waves on a sloping surface. The ability of stable stratification to generate turbulence is also indicated from an exact solution for an inviscid stably stratified flow past a barrier. The structure of undulance and turbulence in stably stratified media is investigated in a stratified salt water towing tank, with schlieren photographs, quartz-coated hot-film probes, and single electrode conductivity probes. The schlieren photographs show clearly the collapse of a turbulent wake and the attenuation of turbulence by stable stratification. Auto-correlations and -spectra for the streamwise turbulent velocity field and for the turbulent concentration field are obtained. From the measured correlations and spectra, the combined wave-turbulence behavior is clearly shown, and the turbulence is strongly anisotropic. (Author)

A kinetic (non-linear) theory of turbulence in incompressible fluids

Abstract: : In principle, a turbulence field is to be governed by the Navier- Stokes equations. In order to avoid the difficulty of treatment due to the non- linear characteristics of the Navier-Stokes equations, one begins with the assumption that a turbulence field may be represented by a proper distribution of many elementary vortex lines, each of which, being a particular solution of the Navier-Stokes equations, exhibits full characteristics of the non-linear equations. Based on this assumption, an equation is introduced which governs the distribution of those elementary vortex lines, in the same way as the Liouville equation governs the distribution of particles. With respect to a two-dimensional field, it is shown that Taylor's parabolic correlation mode for short distances and Kolmogoroff's 2/3-power correlation mode for moderate distances are unified to one correlation mode which is valid for the entire range of correlation distances. With respect to three-dimensional cases, introducing remarks are given. (Author)