Showing papers on "K-epsilon turbulence model published in 1969"
TL;DR: In this article, the Kolmogorov-Prandtl turbulence energy hypothesis is formulated in a way which is valid for the laminar sublayer as well as the fully turbulent region of a one-dimensional flow.
1,018 citations
TL;DR: In this article, the authors distinguish rigorously between wave motion and turbulence in a stratified fluid, although useful approximations seem feasible, although the task is made more difficult by the fact that properties of turbulence are very little like those described in most theories of turbulence, even when the Reynolds number is quite high.
Abstract: To distinguish rigorously between wave motion and turbulence in a stratified fluid seems impossible, although useful approximations seem feasible. The task is made more difficult by the fact that properties of turbulence are very little like those described in most theories of turbulence, even when the Reynolds number is quite high.
128 citations
TL;DR: In this article, the Townsend-Bakewell model of the eddies in the wall regions of turbulent shear flows is used to show that viscoelastic fluid properties must lead to significant reductions in the rate of production of turbulent energy.
Abstract: An analysis based on the Townsend-Bakewell model of the eddies in the wall regions of turbulent shear flows shows that viscoelastic fluid properties must lead to significant reductions in the rate of production of turbulent energy. This analysis in turn leads to the proper form of the similarity laws for drag reducing fluids, heretofore deduced empirically.
Measurements of the axial and radial turbulence intensities for flow through smooth round tubes are reported, as are measurements of the time-averaged velocity profiles and the drag coefficients. These indicate that for solutions exhibiting drag reduction at all Reynolds numbers the flow may be transitional to Reynolds numbers of the order of 105. This transitional flow consists of alternating patches of laminar and turbulent fluid, within each of which the flow characteristics are approximately similar to those of Newtonian fluids. At high Reynolds number conditions with the turbulent field fully developed the velocity profile in the core is flatter under drag-reducing conditions than for turbulent Newtonian fluids, a change dependent on the increased isotropy of the turbulent field of the drag-reducing fluid. These effects appear to be a result of increases in the time scales of the radial fluctuations caused by the fluid properties.
Design calculations based upon the present results suggest that in large diameter pipelines, or in boundary layers on large objects, drag reduction may not be attainable under conditions of practical interest until fluids having relaxation times an order of magnitude larger than those presently available, but with comparable viscosity levels, are developed or, alternately, until fluids exhibiting Weissenberg numbers which do not change with deformation rate, can be found.
126 citations
TL;DR: In this article, hot-film anemometry was used to measure the characteristics of turbulence in hydrodynamically smooth and hydroynamically rough open-channel flow and showed that the relative turbulent intensity of the vertical velocity component was about 60% of the longitudinal, and spectral energy distribution was not significantly affected by the type of flow.
Abstract: Measurements of the characteristics of turbulence in hydrodynamically smooth and hydrodynamically rough open-channel flow using hot-film anemometry technics showed: (a) that the relative turbulent intensity of the vertical velocity component was about 60% of the longitudinal, (b) that the spectral energy distribution was not significantly affected by the type of flow, (c) that most of the turbulent energy is contained in frequencies less than 5 hertz, (d) the macroscale of the turbulence as determined from the autocorrelation function was on the same order as the depth and (e) the ratio of the microscale to depth ranged from 0.1 to 0.2. The measurements were used to verify experimentally the longitudinal direction momentum terms in the Navier-Stokes equation and to determine qualitatively the magnitude of the production, diffusion, and dissipation terms in the energy equation.
70 citations
TL;DR: In this article, an artificial random force is introduced into Burgers' model equation for turbulence and the forced model equation is solved numerically as an initial value problem, where both the driving force and initial velocity field are assumed Gaussian and are generated by a white noise process.
Abstract: An artificial random force is introduced into Burgers' model equation for turbulence. This forced model equation is solved numerically as an initial‐value problem. Both the driving force and initial velocity field are assumed Gaussian and are generated by a white noise process. Many statistical properties of this model for turbulence are studied. By adjusting the external force, the turbulence can reach an equilibrium state. The velocity correlation function and energy spectrum are calculated for the equilibrium turbulence. It is found that the energy spectrum falls off as the inverse second power of the wavenumber. The velocity correlation function is similar to the result obtained in real turbulence experiments. With Gaussian random driving force and Gaussian initial velocity field, it is found that the velocity field remains very nearly Gaussian by comparing the fourth‐order velocity correlation with the quasinormal assumption. Although the process remains very nearly Gaussian, it is found that the projection of the process on the initial white noise process becomes smaller and smaller. This is to be expected, since the dynamic system is escaping from the original random base.
43 citations
Abstract: : A study was made of the mean flow field of free turbulent layers of variable density showing that if the velocity distribution in a particular constant-density flow is known, it is possible to obtain the corresponding variable-density velocity field without the introduction of a compressible turbulent viscosity. This is accomplished by a Dorodnitsyn-Howarth type of transformation applied to the time-dependent equations of motion rather than to the mean equations of motion, as has been done previously. When the transformed equations are averaged, using Reynolds' method, the incompressible turbulent equations for the mean flow are obtained. These equations can then be handled by conventional methods. Predictions obtained by this procedure agree well with experimental results.
30 citations
TL;DR: In this article, a method of this type is presented, in which the turbulence is characterized by three field variables: a turbulence energy density, a turbulence viscosity, and a turbulence scale of size.
Abstract: Two aspects of turbulence can be studied with existing computer technology. One of these is the study of the initial stages in the breakdown of a laminar flow into turbulence. The other is the study of the gross effects of turbulence on a mean flow. The laminar instability problem is hampered by difficulties in calculating high Reynolds number flows, because finite difference approximations introduce diffusionlike truncation errors that can obscure the effects of a real viscosity. These errors also influence the computational stability of numerical solutions. If only the mean effects of turbulence on a flow are of interest, the difficulties in calculating high Reynolds number flows can usually be avoided, because the effective turbulent viscosity is often larger than the molecular viscosity and is not as likely to be obscured by finite difference errors. A method of this type is presented, in which the turbulence is characterized by three field variables: a turbulence energy density, a turbulence viscosity, and a turbulence scale of size. These variables satisfy transport equations describing convection, creation, diffusion, and decay processes. Since these equations are highly nonlinear, numerical solutions are necessary to extract their full potential.
30 citations
01 Jan 1969
TL;DR: In this paper, the effect of soluble polymer additives on the structure of wall turbulence is examined in the light of a new theoretical model, and explained in terms of the ability of the polymer macromolecules to substantially increase the hydrodynamic stability of the viscous sublayer flow.
Abstract: The effect of soluble polymer additives on the structure of wall turbulence is examined in the light of a new theoretical model of wall turbulence, and explained in terms of the ability of the polymer macromolecules to substantially increase the hydrodynamic stability of the viscous sublayer flow. Drag reduction, increase in sublayer thickness and apparent ‘slip’ of the velocity profile, which have been observed experimentally are shown to result directly from increased sublayer stability. Specific examples are presented of the predicted effect of polymer additives on the distributions of mean velocity, turbulent shear stress, turbulence production and longitudinal velocity fluctuations. In particular, it is shown that while turbulence intensity may decrease in dilute polymer solutions, the overall longitudinal velocity fluctuations may be greatly enhanced by increased (non-turbulent) time-dependent activity in the sublayer. It is consequently suggested that considerable caution should be exercised in interpreting ‘turbulence’ measurements in drag-reducing solutions. The effect of surface roughness on wall turbulence and in particular on the flow of dilute polymer solutions is also considered briefly.
21 citations
19 citations
TL;DR: In this paper, the dispersion of small particles floating on the surface of an open channel with uniform flow and wide rectangular cross section was investigated, which was exclusively due to the diffusion caused by surface turbulence.
Abstract: An investigation is given of the dispersion of small particles floating on the surface of an open channel with uniform flow and wide rectangular cross section. The dispersion was exclusively due to the diffusion caused by surface turbulence. The surface turbulence is two-dimensional, homogeneous and nondecaying. The dispersion experiments were supplemented by measurements of the turbulence intensities and correlation functions just below the surface of the water. The turbulence was found to be anisotropic, the longitudinal dispersion being nearly twice the lateral dispersion. By the application of an established relation between the Lagrangian and Eulerian correlation functions and a principle of Reynolds' number similarity, a simple description of the one-particle diffusion is obtained.
19 citations
TL;DR: In this paper, the average three-dimensional line lengths were inferred by an intersection-counting method carried out on one-plane photographs, using small hydrogen bubbles in the nearly isotropic turbulence behind a regular grid.
Abstract: Fluid material line growth in turbulent flow has been measured by tagging lines with small hydrogen bubbles in the nearly isotropic turbulence behind a regular grid in a water tunnel. The average three-dimensional line lengths were inferred by an intersection-counting method carried out on one-plane photographs. The measurements cover ‘small’ time intervals only.
TL;DR: In this paper, the convective mass transfer of smooth and rough sphere test particles over a range of Reynolds numbers between 3 × 103 and 105 was studied by means of an electrochemical method at a Schmidt number of 2170.
Abstract: The convective mass transfer of smooth and rough sphere test particles over a range of Reynolds numbers between 3 × 103and 105 was studied by means of an electrochemical method at a Schmidt number of 2170. The experiments were carried out in a liquid tunnel where the electrolyte is forced past the stationary test particles at variable flow rates. Three distinctly different levels of turbulence intensity of the flow allowed an evaluation of the turbulence effect on the transfer rates. An extrapolation of the results to the heat and mass transfer coefficients of hailstone models in the atmosphere shows that surface roughness may account for increases in the transfer rates of up to a factor of 2. For relatively large roughness elements (cluster Particles) the increase in the convective transfer coefficients at equal Reynolds numbers (based on equal volume diameters) is approximated by the increase in surface area. Atmospheric turbulence is not expected to change these transfer coefficients significa...
TL;DR: In this article, the results of Champagne and Sleicher on the errors incurred in turbulence measurements by assuming normal component cooling of hot wires are extended to include greater tangential cooling were presented.
Abstract: Results of Champagne and Sleicher on the errors incurred in turbulence measurements by assuming normal‐component cooling of hot wires are extended to include greater tangential cooling. Results are also presented for errors in turbulence heat‐flux measurements.
01 Jan 1969
TL;DR: In this article, an apparatus that permits the measurement of turbulence intensity in diffusion flames of city gas with air by an optical method is described, where light intensity fluctuations are measured at wavelengths from 300 to 1800 nm and frequency analyzed up to 12 kHz.
Abstract: An apparatus that permits the measurement of turbulence intensity in diffusion flames of city gas with air by an optical method is described. Light-intensity fluctuations are measured at wavelengths from 300 to 1800 nm and frequency analyzed up to 12 kHz. The results are compared with those of longitudinal and perpendicular velocity fluctuations in isothermal jets as obtained by other methods. The degree of turbulence is mapped along and across the flame, and turbulence spectral functions are derived.
31 Jan 1969
TL;DR: In this article, experimental data are presented for various properties of the turbulence in the transition region of a low speed air jet (4.5 to 9 diameters downstream) and the overlap of results is generally quite reasonable.
Abstract: : Experimental data are presented for various properties of the turbulence in the transition region of a low speed air jet (4.5 to 9 diameters downstream). Previous investigations have been restricted to either the mixing region or the region of fully developed flow, the two regions of distinctly different, yet self-preserving turbulence structure. An attempt is made to tie in the present data for the intervening transition region with that of earlier works. The overlap of results is generally quite reasonable. (Author)
TL;DR: In this paper, the authors used the time-mean average concept to describe the turbulent flow and the conservation of species and energy equations are solved by two different numerical integration schemes; both methods are shown to yield similar results.
TL;DR: In this paper, an analysis is made to find the transport properties of a free turbulent flow using an entity model previously shown to have good prediction capability for pipe flow, where the double structure of the turbulent eddies and the anisotropic shape of the larger eddies can be satisfactorily incorporated into the model without undue complexity.
TL;DR: In this article, a simple method is presented for measuring time-average velocity, turbulence intensity, and concentration of droplets in two-phase (air-liquid) turbulent flows, and the method is applied to measure the time average velocity and turbulence intensity of air-liquid turbulent flows.
Abstract: A simple method is presented for measuring time-average velocity, turbulence intensity, and concentration of droplets in two-phase (air-liquid) turbulent flows.
01 Feb 1969
TL;DR: In this article, a generalized eddy-viscosity approximation is used to study the turbulence spectra of thermally stratified shear flows, and numerical solutions of the turbulent spectra are investigated.
Abstract: : A generalized eddy-viscosity approximation is used to study the turbulence spectra of thermally stratified shear flows. Numerical solutions of turbulence spectra are investigated. Modified hypothesis in the buoyancy subrange of stably stratified flow is given.
TL;DR: Ballistic wake structure and jump conditions for plane plasma shock waves with electrostatic turbulence with a single-passenger aircraft were investigated in this article. But the results were limited to the case of a single plane.
Abstract: Ballistic wake structure and jump conditions for plane plasma shock waves with electrostatic turbulence
TL;DR: In this article, the authors applied the method of Champagne to the flow downstream of a grid of parallel rods and found the turbulence to have become isotropic by a distance of approximately 30 mesh lengths.
Abstract: Careful corrections of measured turbulent intensities following the method of Champagne, have been applied to the flow downstream of a grid of parallel rods. Results show the turbulence to have become isotropic by a distance of approximately 30 mesh lengths.
TL;DR: In this paper, a Fourier transform is used to treat the Burgers one-dimensional model equation for homogeneous turbulence, and a dynamical equation for the energy spectrum is obtained with the aid of the Bogoliubov-expansion method, with the assumption of a quasinormal distribution for the velocity field, and an initial state of fully developed turbulence.
TL;DR: In this article, the spectral distribution of turbulent energy is considered, where the turbulence is assumed to be homogeneous and axisymmetric with a vertically directed axis of symmetry, and it is shown that the spectrum of the vertical energy behaves like k−5/3 for large wave numbers.
Abstract: In this paper the spectral distribution of turbulent energy is considered. The turbulence is assumed to be homogeneous and axisymmetric with a vertically directed axis of symmetry.The spectral representation of the velocity correlation equation was the starting point for determining the spectra of turbulent energy. Transfer of energy in axisymmetric turbulence was approximated by adopting a Heisenberg-type hypothesis. The general solution obtained presents as special cases the −5/3 law and the −11/5 law for the spectrum of total energy.It is shown that the spectrum of the vertical energy behaves like k−5/3 for large wave numbers and like k−5/3 for buoyancy subrange. The spectrum of temperature fluctuations is also investigated.
TL;DR: In this paper, a model for statistically isotropic homogeneous turbulence in an incompressible fluid is constructed, representing the turbulence as a superposition of individual vortex sheets, each vortex sheet moves in the velocity field of the other sheets which have larger scale.
Abstract: A model for statistically isotropic homogeneous turbulence in an incompressible fluid is constructed, representing the turbulence as a superposition of individual vortex sheets. Each vortex sheet moves in the velocity field of the other sheets which have larger scale. Each sheet is stretched out, and intensified, until obliterated by viscosity at high wavenumber. The rate of stretching is related to the symmetric part of the strain tensor ∂νi/∂κj, which is postulated to be statistically independent of the antisymmetric part. Representing the turbulence by the usual energy spectrum function F(k) leads to a set of integrodifferential equations. Solution of the equations gives a spectrum which is in close agreement with experimental spectra of turbulence over both the inertial and viscous subranges, suggesting that the model may be of some real physical interest. The model is sufficiently explicit so as to give information on the correlation between different Fourier components of the turbulence. The calcula...