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Showing papers on "K-epsilon turbulence model published in 1974"



Journal ArticleDOI
TL;DR: There has been extensive work in the development of turbulence models, particularly for use in boundary layer calculations as mentioned in this paper, and substantial advances made over the past decade in the prediction of turbulent flows are discussed.
Abstract: Substantial advances made over the past decade in the prediction of turbulent flows are discussed. There was extensive work in the development of turbulence models, particularly for use in boundary layer calculations. Basic aspects of several important methods based on partial differential equations for the mean velocity field and turbulence quantities, including the relationship between the methods and suggestions for future development were reviewed. Work on three-dimensional time-dependent large eddy simulations is discussed. The emphasis is on the hydrodynamics of incompressible flows, but sources for consideration of heat transfer and compressibility are mentioned.

383 citations


Journal ArticleDOI
TL;DR: In this paper, the effects of an abrupt change of surface roughness on the mean flow and turbulence structure in the neutral surface layer are numerically investigated by higher-order turbulence closure theory, which includes dynamical equations for Reynolds stresses and the viscous dissipation rate.
Abstract: The effects of an abrupt change of surface roughness on the mean flow and turbulence structure in the neutral surface layer are numerically investigated by a higher-order turbulence closure theory, which includes dynamical equations for Reynolds stresses and the viscous dissipation rate. The closed system of governing equations, together with the specified initial and boundary conditions, is solved by an explicit finite-difference method on a digital computer. The numerical model predicts the distributions of mean wind, shear stress, turbulent energy and other quantities, with no a priori assumptions regarding the distributions of any of these variables in the transition region. The distributions of the nondimensional wind shear, the dissipation and mixing length scales, and the ratio of stress to turbulent kinetic energy are shown to differ significantly from their equilibrium flow variations.

224 citations


Journal ArticleDOI
TL;DR: In this article, various statistical properties of the truncated streamwise and normal velocity components u and v and of their product uv have been determined in an attempt to characterize quantitatively the motions of the flow.
Abstract: Measurement results of turbulent shear flows are re-examined. Various statistical properties of the truncated streamwise and normal velocity components u and v and of their product uv have been determined in an attempt to characterize quantitatively the motions of the flow. Average values and probability density distributions both of the truncated and untruncated signals have been taken.

169 citations


Journal ArticleDOI
TL;DR: In this paper, the evolution of the boundary layer on day 33 of the Wangara experiment in southeast Australia is calculated with a higher-order-closure turbulence model, which includes equations for the mean field as well as the second moments of the turbulent field.
Abstract: The evolution of the boundary layer on day 33 of the Wangara experiment in southeast Australia is calculated with a higher-order-closure turbulence model. This model, which includes equations for the mean field as well as the second moments of the turbulent field, is described in detail. The mean profiles of wind, temperature, and humidity, the profiles of heat and humidity fluxes, the Reynolds stress distributions, and the height of the boundary layer are shown between 10 a.m. and 6 p.m. The results agree well with those from Deardorff's 3-D simulation and take relatively little computer time.

151 citations


Journal ArticleDOI
TL;DR: In this paper, a set of turbulence model equations, originally postulated by Saffman, forms the basis of this three-part study of steady turbulent-boundary-layer structure above a flat plate.
Abstract: A set of turbulence model equations, originally postulated by Saffman, forms the basis of this three-part study of steady turbulent-boundary-layer structure above a flat plate In one part of the study the turbulence equations are integrated through the viscous sublayer by means of time-marching numerical integration techniques and the constant in the law of the wall is predicted as a function of wall roughness In a second part, the Van Driest compressible law of the wall is deduced by classical mathematical methods Then, using the Van Driest law as a wall boundary condition, the model equations are integrated through the entire boundary layer, again by time-marching methods, for a freestream Mach number of 296 NCREASINGLY, turbulent-flow studies have concentrated on phenomenologi cal-model equations describing turbulent motion The most promising approach seeks rate equations which describe evolution of the Reynolds stresses; development of equations of this type has progressed for both low- and highspeed flows1"5 This paper focuses upon one such set of turbulence-mo del equations originally devised by Saffman 2 and subsequently modified by Wilcox and Alber3 to account for the effects of compressibility; the model equations are based on the hypothesis that transfer of momentum and heat by turbulence can be described by an eddy viscosity which is a function of two turbulence densities, viz, an energy density, e, and a pseudovorticity density, Q Previous work 2'3 has concentrated mostly on formulation of the nonlinear diffusion equations satisfied by the turbulence densities; included in the present study is some model development which is directed primarily to the boundary conditions imposed at or near a solid boundary As a result, uncertainties regarding boundary conditions have been eliminated A concurrent study has been made of the predictions of the model equations for boundary layers on a flat plate under both compressible and incompressible flow conditions Past studies have left at least two areas of boundary-condition uncertainty On the one hand, Saffman2 indicated that the most natural boundary conditions for the mean velocity and the turbulence densities follow from matching to the law of the wall Matching is valid for the incompressible Saffman model because law-of-the-wall behavior near a solid boundary is contained within the equations; however, Wilcox and Alber3 did not generalize the matching concept for compressible flows On the other hand, for some applications, integration through the sublayer might be necessary (because of, eg, numerical reasons or sublayer-structure uncertainties) Thus, the question of boundary conditions for the turbulence densities appropriate to a solid boundary was considered briefly by Saffman and in a little more detail by Wilcox and Alber Although the boundary condition on e is straightforward (it vanishes at solid boundaries), both studies fall short of specifying a boundary condition on the vorticity density

126 citations


Journal ArticleDOI
TL;DR: In this paper, the effect of flow channel geometry on fully developed turbulent flow in clean rod bundle flow channels was investigated and it was shown that rod gap spacing (pitch-to-diameter ratio) is the most significant geometric parameter affecting the flow structure.

119 citations


Journal ArticleDOI
TL;DR: In this article, the fair-weather trade wind boundary layer was used to measure air velocity, temperature, and humidity from an aircraft in the fair weather boundary layer, and mean winds, turbulence quantities and thermodynamic variables were measured in both a clear and a partly cloudy region.
Abstract: Measurements of air velocity, temperature and humidity were made from an aircraft in the fair-weather trade wind boundary layer. On the day of the experiment, the region studied was characterized by north-south bands of cloud-free and moderately clouded areas roughly 40 km in width. Mean winds, turbulence quantities, and thermodynamic variables were measured in both a clear and a partly cloudy region. Production of turbulence energy in the subcloud layer of both regions was mainly from wind shear. In the cloud-free region, the turbulence energy and momentum flux budgets were measured. One of the most striking features was the large region (covering almost two-thirds of the depth of the mixed layer) of negative production of turbulence energy by wind shear. Notwithstanding this unusual feature, the terms of the turbulence energy budget agree quite well with a model developed by Lenschow. In the cloudy area, a layer of strong wind shear was observed near cloud base. This, coupled with corresponding...

117 citations


Journal ArticleDOI
TL;DR: In this article, the spectrum of blade leading and the associated noise caused by interference of a propeller, helicopter rotor, or fan rotor with inlet turbulence are studied experimentally and theoretically.
Abstract: The spectrum of blade leading and the associated noise caused by interference of a propeller, helicopter rotor, or fan rotor with inlet turbulence are studied experimentally and theoretically. One test with hot‐wire anemometers in a static inlet and another test with pressure transducers on the blades of a fan rotor reveal inlet turbulence to be highly anisotropic. The intensity of the transverse velocity component was found to be 2.5% of the mean flow and the streamwise component was 0.9%, with ambient winds of about 2 mph. The transverse integral scale of the turbulence is a fraction of an inlet diameter, while the streamwise integral scale is over 100 diameters. Evidence indicates the source of these disturbances is atmospheric turbulence. The associated noise is partially coherent with spectrum peaks which are so narrow as to be difficult to distinguish from true harmonics. A novel blade loading model is developed using concepts from random pulse modulation theory. Theoretical spectrum predictions ind...

103 citations


Journal ArticleDOI
TL;DR: In this article, a model for the variation with height of the terms in the turbulence kinetic energy budget throughout an unstably stratified barotrople planetary boundary layer is proposed.
Abstract: A model is proposed for the variation with height of the terms in the turbulence kinetic energy budget throughout an unstably stratified barotrople planetary boundary layer. The model is based upon aircraft measurements throughout the boundary layer that are presented here and previous results from surface layer measurements. The model assumes that at the limit of neutral stability, the transport term in the budget equation is at a minimum. When the height above the ground is greater than about ten times the absolute value of the Obukhov length, the shear-generation term is negligible, while the rate of dissipation of turbulence energy becomes almost constant, and the transport term increases almost linearly with height to balance the almost linear decrease of the buoyancy-generation term. Measurements of the ratio of the vertical flux of the horizontal part of the turbulence kinetic energy to the vertical part show good agreement with a model based upon surface layer observations and a laborator...

92 citations


Journal ArticleDOI
TL;DR: In this paper, it is shown that the spectrum of kinetic energy generated by a steady input of momentum at a discrete wavelength shows a rapid decrease (as k−5) towards shorter wavelengths but a much slower decrease towards longer wavelengths.
Abstract: Two-dimensional incompressible motion is generated by a steady external body force varying sinusoidally with a transverse co-ordinate. Such flow is found to be unstable for Reynolds numbers greater than 2½, and under these conditions evolves towards a new steady state. This ‘steady-eddy’ state is itself unstable in a sense, and its breakdown suggests the catastrophic onset of a cascade of turbulence. The mechanics of this cascade can be represented by a kind of recursion system in which the turbulence dynamics of one scale is repeated in the next, and a law of turbulent stress results. The spectrum of kinetic energy generated by a steady input of momentum at a discrete wavelength shows a rapid decrease (as k−5) towards shorter wavelengths but a much slower decrease (as k) towards longer wavelengths.

Journal ArticleDOI
TL;DR: Comte-Bellot and Corrsin this article measured the heat dispersion behind a heated wire stretched across a wind tunnel and determined the Lagrangian velocity autocorrelation in an approximately isotropic, grid-generated turbulent flow.
Abstract: By measuring the heat dispersion behind a heated wire stretched across a wind tunnel (Taylor 1921, 1935), the Lagrangian velocity autocorrelation was determined in an approximately isotropic, grid-generated turbulent flow. The techniques were similar to previous ones, but the scatter is less. Assuming self-preservation of the Lagrangian velocity statistics in a form consistent with recent measurements of decay in this flow (Comte-Bellot & Corrsin 1966, 1971), a stationary and an approximately self-preserving form for the dispersion were derived and approximately verified over the range of the experiment.Possibly the most important aspect of this experiment is that data were available in the same flow on the simplest Eulerian velocity autocorrelation in time, the correlation at a fixed spatial point translating with the mean flow (Comte-Bellot & Corrsin 1971). Thus, the Lagrangian velocity autocorrelation coefficient function calculated from the dispersion data could be compared with this corresponding Eulerian function. It was found that the Lagrangian Taylor micro-scale is very much larger than the analogous Eulerian microscale (76 ms compared with 6.2ms), contrary to an estimate of Corrsin (1963). The Lagrangian integral time scale is roughly equal to the Eulerian one, being larger by about 25 %.

Journal ArticleDOI
TL;DR: In this article, the authors considered the modification of that result when weak long-wave turbulence is present, in addition to the background inhomogeneity, and found that the convective saturation disappears when the turbulence exceeds a certain level, absolute growth occurring instead.
Abstract: It is known that parametric instabilities involving two coupled modes, with oppositely directed group velocities, saturate convectively if the medium is inhomogeneous. This work considers the modification of that result when weak long-wave turbulence is present, in addition to the background inhomogeneity. We find that the convective saturation disappears when the turbulence exceeds a certain level, absolute growth occurring instead.


Journal ArticleDOI
TL;DR: In this article, it is pointed out that by allowing the entrainment of free stream turbulence into the turbulent boundary layer and performing an overall turbulent energy balance, very satisfactory quantitative predictions can be made.

Journal ArticleDOI
TL;DR: In this paper, a method for measurement of turbulence quantities of fluid flow is proposed, where the motion of a swarm of small tracer particles supplied to turbulent flow is continually followed by high speed cine-photography, from which velocity correlations and energy spectra are evaluated.


Journal ArticleDOI
TL;DR: In this paper, it was shown that turbulent flame speed increases with scale under conditions of weak turbulence and decreases with increase in scale under condition of strong turbulence, and the two regions are separated by a transition region, which occurs when the turbulence intensity is about twice the laminar flame speed.

Book ChapterDOI
TL;DR: A brief account of the state-of-the-art of turbulent flow computations and its recent advancements using mean-velocity field closure, mean Turbulent Energy (MTE) closure, and mean Reynolds-Stress (MRS) closure through citation of appropriate theories and examples can be found in this paper.
Abstract: Publisher Summary This chapter discusses the central themes of contemporary methods with reference to individual sources for more detailed descriptions. It provides a brief account of the state-of-the-art of turbulent-flow computations and explains the computation of turbulent flows and its recent advancements using mean-velocity field (MVF) closure, Mean Turbulent Energy (MTE) Closure, and Mean Reynolds-Stress (MRS) Closure through citation of appropriate theories and examples. The MVF equations assume that the turbulence adjusts immediately to changes in mean conditions and that a universal relationship exists between the turbulent stresses and the mean strain rates. To avoid these assumptions, differential equations must be included for the Reynolds stresses. There is a more fundamental objection to the structural mean turbulent energy (MTES) idea. The homogeneous flows do not really reach equilibrium and that instead the turbulence time (and length) scales continually increase. It is required to employ the structure of the turbulence to compute the same. In this chapter, the approach has been to construct a comprehensive model, with numerous universal constants, and then to select these constants by optimizing the average fit to a number of selected flows.


01 Mar 1974
TL;DR: A survey of turbulence measurements in compressible flows is presented in this paper, where the majority of the measurements at super-and hypersonic speeds were made for the zero pressure gradient, turbulent boundary layer.
Abstract: A survey of turbulence measurements in compressible flows is presented. The majority of turbulence measurements at super- and hypersonic speeds were made for the zero pressure gradient, turbulent boundary layer. It was found that the nondimensional turbulent stress terms for the zero pressure gradient flow appear to agree closely with equivalent incompressible measurements in the outer part of the boundary layer. The stress terms were nondimensionalized by the wall value of shear stress and plotted versus the distance from the wall, nondimensionalized by the boundary-layer thickness. Indirect evaluation of the total shear stress distribution from mean velocity measurements for both super- and hypersonic flows (zero pressure gradient, two-dimensional flows) indicate a near universal distribution. These total shear stress curves also agree very closely with measured incompressible shear stress distributions. Recent laser anemometer measurements of the turbulent Reynolds shear stress (puv), reported by Johnson and Rose for a Mach number 2.9 flow, are in reasonable agreement with the expected total shear stress curve over the outer 60% of the boundary layer.

Journal ArticleDOI
TL;DR: In this article, a high Reynolds number turbulence model and its mixing-length derivative are employed to predict a variety of swirling boundary layers. But the results showed a serious lack of universality in the applicability of stress turbulence models in sublayer regions.
Abstract: Axisymmetrical swirling boundary layers and fully three-dimensional layers have in common a two-component shear stress Since the former are amenable to treatment by two-dimension al computational methods, they constitute useful and economical testing terrain for advanced turbulence models Traditional "effective-viscosity" based turbulence models, arbitrarily extended to account for the influence of a swirl component of velocity, display a serious lack of universality A high Reynolds number turbulence model is developed in the present study which provides algebraic equations for all six Reynolds stresses The model and its mixing-length derivative are both employed to predict a variety of swirling boundary layers A promising improvement in universality of predictive power is exhibited The principal conclusion is that future research should concentrate on extending the applicability of stress turbulence models into the sublayer region since the effective-viscosity based models are least satisfactory there

Journal ArticleDOI
TL;DR: The second-order invariant modeling technique for turbulent flows as developed by Donaldson is applied to axisymmetric wakes in this article, where all empirical model parameters are chosen from data on jets and shear layers leaving the wake completely determined as a function of initial conditions.
Abstract: The second-order invariant modeling technique for turbulent flows as developed by Donaldson is applied to axisymmetric wakes. All empirical model parameters are chosen from data on jets and shear layers leaving the wake completely determined as a function of initial conditions. Model predictions for the mean velocity distribution and the distributions of the four components of the second-order stress tensor are verified by comparison with the experimental observations of Chevray for a wake with significant mean momentum and Naudascher for the wake behind a self-propelled body. Nomenclature a, b = model constants defined in Eq. (12) D = diameter of the generating body M = normalized momentum defect in the wake, see Eq. (15) p = pressure q = square root of twice the turbulent kinetic energy per unit mass r = radial coordinate r* = radius at which 1/2 reaches one half its maximum

Journal ArticleDOI
TL;DR: In this paper, Cebeci et al. presented some numerical predictions of the turbulent flow of a mixture of CC1 4 vapour and air over a vertical plate onto which the vapour condenses.

Journal ArticleDOI
TL;DR: In this article, a turbulence representation consisting of a generalized set of transport equations for the Reynolds stress tensor and the turbulence energy decay rate is applied to the study of convective heat transport between parallel plates at moderate Rayleigh numbers, 5 × 103 ≤ Ra ≤ 6·4 × 105.
Abstract: A turbulence representation, consisting of a generalized set of transport equations for the Reynolds stress tensor and the turbulence energy decay rate, is applied to the study of convective heat transport between parallel plates at moderate Rayleigh numbers, 5 × 103 ≤ Ra ≤ 6·4 × 105. A series of heat flux transitions, in good agreement with those observed experimentally, is detect, ed in this study and found to correlate with changes in the turbulence structure. In the order of increasing Rayleigh number these structural changes correspond to: the transition from laminar to turbulent flow, the transition from low to locally high intensity turbulence, the transition to uniformly high intensity turbulence, and the transition from a buoyancy dominated turbulence to a shear dominated turbulence. An analysis is made of the effect of each of these transitions on the mechanism for heat transfer between the plates.


Journal ArticleDOI
TL;DR: In this paper, the authors demonstrate the ability of a laser velocimeter to measure the turbulence transport properties of high-speed compressible flows in a Mach-2.9 turbulent boundary layer.
Abstract: Measurements taken in a Mach-2.9 turbulent boundary layer are shown to demonstrate the ability of a laser velocimeter to measure the turbulence transport properties of high-speed compressible flows. This demonstrated ability, combined with the nonperturbing quality and relative insensitivity to environmental conditions of the laser velocimeter, opens the way to compressible flow measurements never considered possible with more conventional measurement techniques.

Journal ArticleDOI
TL;DR: In this article, a new and simple version of the Prandtl mixing length hypothesis for flow past smooth surfaces was proposed, which has been used in obtaining extensive predictions of boundary layers on porous surfaces including flows with steep density and pressure gradients measured in the present study.

Journal ArticleDOI
TL;DR: In this article, Boussinesq's concept from the lateral gradient of the mean velocity and the turbulence shear-stress was used to compute the eddy-viscosity in a turbulent boundary layer downstream of a hemi-spherical cap attached onto the plane rigid wall.
Abstract: Measurements have been made of the distributions of mean velocity, turbulence intensities and turbulence shear-stress in a turbulent boundary-layer downstream of a hemi-spherical cap attached onto the plane rigid wall. The eddy-viscosity, when computed in the classical way according to Boussinesq's concept from the lateral gradient of the mean velocity and the turbulence shear-stress, showed a very strong non-uniform lateral distribution, also across the outer region of the boundary-layer. More over , the non-dimensional values of the eddy viscosity, using the wall-friction velocity and the boundary-layer thickness as the velocity scale and length scale respectively, were higher than those for the boundary-layer when not disturbed by the wake of the spherical cap. However, when account is taken of an axial memory effect of the streamwise variation of the lateral gradient of the mean-velocity, the values of the non-dimensional eddy viscosity are close to those for the undisturbed boundary-layer.