Showing papers on "K-epsilon turbulence model published in 1970"
TL;DR: Turbulence transport equations, describing the dynamics of transient flow of an incompressible fluid in arbitrary geometry, have been derived in such a manner as to incorporate the principles of invariance (tensor and Galilean) and universality as discussed by the authors.
Abstract: Turbulence transport equations, describing the dynamics of transient flow of an incompressible fluid in arbitrary geometry, have been derived in such a manner as to incorporate the principles of invariance (tensor and Galilean) and universality. The equations are described in detail and their applicability is demonstrated by comparison of solutions with experiments on turbulence distortion and on the turbulence in the flow between flat plates.
1,265 citations
TL;DR: A survey of the current state of analytical attempts at a theory of turbulence can be found in this article, where the difficulty posed by the closure problem is examined in detail using the quasinormal approximation as an example.
Abstract: This paper surveys the current state of analytical attempts at a theory of turbulence. The formulation of the problem in terms of moments is discussed. The difficulty posed by the closure problem is examined in detail using the quasinormal approximation as an example. The notion of dynamical relaxation by non-linear scrambling leads to the introduction of eddy relaxation times and the direct-interaction approximation. The properties of the direct-interaction approximation are indicated. Finally, a comparison is made between numerical solution of the equations of turbulence their and direct numerical simulation of the Navier–Stokes equations.
740 citations
TL;DR: In this article, the decay time of low Reynolds number weak turbulence generated by single and multistage grids, considering three dimensional energy spectrum, was investigated for single and multi-stage grids.
Abstract: Decay time of low Reynolds number weak turbulence generated by single and multistage grids, considering three dimensional energy spectrum
73 citations
TL;DR: In this article, free shear layer turbulence in the atmosphere (clear air turbulence) is considered as a mechanism for relieving the formation of discontinuities of wind and temperature in the vertical plane by shearing and stretching deformation.
Abstract: This paper considers free shear layer turbulence in the atmosphere (clear air turbulence) as a mechanism for relieving the formation of discontinuities of wind and temperature in the vertical plane by shearing and stretching deformation.
An expression for the rate of change of the logarithm of the gradient Richardson number following the air motion is derived and the assumption is made that turbulence counteracts the dynamical processes which are reducing the Richardson number, maintaining it at a limiting value. The rate of working required to do this is equated to the turbulent energy dissipation rate and in the model used is given by Φ (ΔV)2/24 (where the logarithmic rate of reduction of Ri which would take place in the absence of turbulence, and ΔV is the velocity difference across the turbulent layer).
Two preliminary tests of the theory as a forecasting tool using the Bushby-Timpson 10-level numerical model show that the dynamical processes changing Ri are largest in areas where clear air turbulence might be expected from synoptic experience.
67 citations
TL;DR: In this article, the mean velocities, turbulence intensities, scales and energy spectra measured in this flow indicate two regions of appreciably different characteristics: a wall region near the plane surfaces is found to occur with flow characteristics close to those found near walls of other turbulent shear flows when these are expressed in terms of the wall similarity parameters.
Abstract: Turbulent flow between two plane surfaces in relative shearing motion has been studied with air in a belt-type apparatus with one fixed surface. Mean velocities, turbulence intensities, scales and energy spectra measured in this flow indicate two regions of appreciably different characteristics. A wall region near the plane surfaces is found to occur with flow characteristics close to those found near walls of other turbulent shear flows when these are expressed in terms of the wall similarity parameters. A core region, of width at least three-eights the distance between the planes, appears away from these evidencing the characteristics of the homogeneous turbulence predicted by von Karman. The mean velocity has a linear gradient in this region and the turbulence intensity and scales are essentially constant; in fact, homogeneity is strongly suggested. For a more than two-fold range in flow Reynolds numbers (center line velocity 15 fps to 35 fps) the microscale is found to be constant, the macroscale increases linearly and the relative intensity is constant.
67 citations
53 citations
01 May 1970
TL;DR: In this paper, the behavior of controlled wave disturbances in turbulent channel flow was studied experimentally and theoretically, and it was shown that the interaction between the organized waves and the turbulence must be considered in such a theory.
Abstract: : The behavior of controlled wave disturbances in turbulent channel flow was studied experimentally and theoretically The work is relevant to Landahl's waveguide theory of shear turbulence It is shown that the interaction between the organized waves and the turbulence must be considered in such a theory (Author)
42 citations
TL;DR: In this paper, the authors measured the turbulence characteristics of the high speed stream issuing from a turbine type impeller in a fully baffled tank using a constant-temperature hotwire anemometer with air as the fluid within the tank.
Abstract: tirred tanks are widely used in the chemical indusS try for effecting mixing, but their design has so far been empirical. A theoretical treatment of the flow within a stirred tank is rendered intractable by the inherent randomness and three-dimensionality of the flow and non-linearity of the governing equations of motion. Experimental studies of the large- and small-scale turbulence characteristics in stirred vessels may be expected to lead to formulation of realistic models of the flow. These models can then be used to predict such quantities of engineering interest as the mixing efficiency, pumping capacity, power requirements, etc. It was the objective of this work to measure the turbulence characteristics of the high speed stream issuing from a turbine type impeller in a fully baffled tank. Turbulence parameters were measured using a constant-temperature hot-wire anemometer with air as the fluid within the tank. The hot-wire technique was chosen because of the ease of operation and extremely good frequency response. Use of mr as working fluid Cooper‘” recently showed that the temporal mean velocity distribution in the impeller stream is the same with air and water as the fluid in the tank. We have assumed that the small-scale turbulence characteristics would also be similar at equal Reynolds numbers irrespective of the fluid in the tank. There exists sufficient confirmation in the literature for air and water flows in circular pipes and circular jets, and also grid-generated turbulent flows in wind and water tunnels. Chuang and Cermak“’ have compared their measurements of turbulent intensities, shear stress and energy spectra in the pipe flow of distilled water for a Reynolds number of 5 x lo4 with those of Sandborn‘J) and Laufer“) who studied the flow of air in a pipe at the same Reynolds number. The agreement between the air and water data is remarkable
42 citations
TL;DR: In this article, the effect of initial disturbance length-scale on turbulence developed in the presence of a uniform mean shear was explored and it was concluded that the imposed length scale fixes the energy level of the resulting turbulence, provided the scale is sufficiently large.
Abstract: Experiments to explore the effect of initial disturbance length-scale on turbulence developed in the presence of a uniform mean shear are the subject of this paper.Flows with nearly the same mean shear (8·6 sec−1) and initially different turbulent scales are generated in a wind tunnel test-section by placing grids just downstream of a honeycomb of uniform cell diameter (¼ in.) and non-uniform cell length. Both round-rod grids of uniform square mesh and parallel-rod construction with roughly equal solidity (0.34) are used. Grid mesh sizes range from in. to 2 in.From the results it is concluded that for a given value of mean shear the imposed length scale fixes the energy level of the resulting turbulence, provided the scale is sufficiently large. When it is reduced below some minimum value the turbulence decays. Also, it is found that two-dimensional flow-generator geometries are more effective than three-dimensional geometries in producing a roughly homogeneous turbulent field with a higher fluctuation level in a shorter distance.
39 citations
TL;DR: Sheer generated atmospheric clear air turbulence growth and dependence on atmospheric instabilities calculated numerically by invariant model is discussed in this article, where the authors show that the model can be used to predict the growth of clear air turbolifts.
Abstract: Sheer generated atmospheric clear air turbulence growth and dependence on atmospheric instabilities calculated numerically by invariant model
39 citations
TL;DR: In this article, the results of a heuristic model of the fine scale structure of homogeneous turbulence are presented, and predictions are made about the way in which flatness and skewness factors of arbitrary order depend upon the Reynolds number of the turbulence.
Abstract: The results of a heuristic model of the fine scale structure of homogeneous turbulence are presented. Predictions are made about the way in which flatness and skewness factors of arbitrary order depend upon the Reynolds number of the turbulence.
TL;DR: In this paper, structural turbulence has been detected in dilute aqueous solutions of polyox coagulant (PCA) and it has been demonstrated that the same molecular oscillations or segmental motions responsible for structural turbulence are now operative in drag reduction.
Abstract: Structural turbulence has been detected in dilute aqueous solutions of Polyox Coagulant (also known to be a highly effective drag-reducing agent). The flow line which characterizes structural turbulence from its onset in the laminar region passes well into the fully turbulent region (Reynolds turbulence) with virtually no change in slope, implying that the same molecular oscillations or segmental motions responsible for structural turbulence are now operative in drag reduction. The persistence of structural turbulence at very low concentrations is rationalized on the basis of Busses explanation of the role of polymer entanglements in viscosity and elastic turbulence.
TL;DR: In this article, it was shown that the log-normal distribution of local energy dissipation in high-Reynolds number turbulence implies that the evolution of turbulence is not determined by specification of initial values for moments of all orders.
Abstract: It is shown that the log‐normal distribution of local energy dissipation in high‐Reynolds‐number turbulence implies that the evolution of turbulence is not determined by specification of initial values for moments of all orders. The consequence of this indeterminacy for theories of turbulence is discussed.
TL;DR: In this paper, an explanation for a phenomenon observed e.g. in a wall jet in a small region near the maximum velocity is given, where the turbulence shear stress is expressed as the sum of two terms, proportional to the first and second derivative of the mean velocity, respectively.
Abstract: An explanation is given for a phenomenon observed e.g. in a wall jet in a small region near the maximum velocity. The turbulence shear stress is expressed as the sum of two terms, proportional to the first and the second derivative of the mean velocity, respectively. Use is made of the nonsymmetric flow pattern around the maximum velocity, and of the nonuniform distribution of the intensity of the lateral turbulence velocity component. The coefficient of the second derivative of the mean velocity is shown to contain the first derivative of this turbulence velocity component. Since the second derivative of the mean velocity is negative around its maximum, a positive turbulence intensity gradient as observed in the region concerned in the wall jet, results in a negative contribution to the shear stress. Hence, in this region the shear stress can have a sign opposite to the positive — though very small — gradient of the mean velocity. Consequences with respect to the mechanical energy balance of the mean flow and of the turbulence are discussed.
TL;DR: In this article, a simplified statistical theory is developed which describes the chemically reacting, turbulent shear flows in a tractable manner, which is completely self-containing provided that the molecular Schmidt number is of order one and that the local turbulence Reynolds number is sufficiently large.
Abstract: A simplified statistical theory is developed which describes the chemically reacting, turbulent shear flows in a tractable manner. This theory, which is based on the concept of the generalized Brownian motion, instead of Navier‐Stokes equation, is completely self‐containing provided that the molecular Schmidt number is of order one and that the local turbulence Reynolds number is sufficiently large. The latter requirement restricts the theory to the flow region outside of the laminar sublayers. The homologous flow and concentration fields are first analyzed for the chemically frozen case. From the analyses, the relationships between the mean velocity and concentration gradients, and the Reynolds stress, turbulence energy, turbulent transport of chemical species, and the mean square fluctuation of the species concentration are established. Comparison of the present results with the available experimental data is made, which shows a satisfactory agreement. The nonequilibrium chemical reaction is then analyzed and is found to create an inhomogeneity in the concentration field which, among other things, causes the mean square fluctuation to vary nonuniformly with respect to the Damkohler number and the flow region.
TL;DR: In this article, the deficiencies of the conventional power laws for the decay of grid turbulence, i.e., the discontinuous change from an initial to a final zone and the undefined range of validity, were successfully overcome by analyzing grid flow as the plane-source counterpart of flows past point and line sources of turbulence energy.
Abstract: The deficiencies of the conventional power laws for the decay of grid turbulence, i.e., the discontinuous change from an initial to a final zone and the undefined range of validity, have been successfully overcome by analyzing grid flow as the plane-source counterpart of flows past point and line sources of turbulence energy. A comparison of the analytical results with experimental data on turbulence intensity, dissipation length, and integral scale for a great variety of grid geometries and Reynolds numbers reveals good agreement for all down-stream zones. The data used include those of Baines and Peterson, Batchelor and Townsend, Comte-Bellot and Corrsin, Dryden, Stewart and Townsend, Uberoi, van der Hegge-Zijnen, von Karman, and Wyatt. Functional relationships between the constants of the resulting analytical expressions, including the position of the virtual origin, and the grid-flow parameters have been deduced to facilitate prediction of turbulence characteristics and their downstream development for any given grid flow.
01 Jun 1970
TL;DR: The effects of gas rarefaction, compressibility, and turbulence on free stream sphere drag coefficient were studied in this article, where the authors found that the effects varied with the density of the free-stream sphere.
Abstract: Effects of gas rarefaction, compressibility, and turbulence on free stream sphere drag coefficient
TL;DR: In this paper, a new electrolytic turbulence transducer has been developed in order to measure the turbulent velocity fluctuation superposed on the oscillatory flow velocity, which is induced by ripples which appear on the movable bed of wave flume and the correlation between the turbulence intensity and the characteristics of sediment particles at the same level such as their fall velocity and sediment concentration.
Abstract: A new electrolytic turbulence transducer has been developed in order to measure the turbulent velocity fluctuation superposed on the oscillatory flow velocity The aim of the present paper is firstly to describe the outline of this transducer and secondly to introduce some of the experimental results The main items of the results are, l) the vertical distribution of turbulence intensity averaged over one wave cycle, where the turbulence is induced by ripples which appear on the movable bed of wave flume, and 2) the correlation between the turbulence intensity and the characteristics of sediment particles at the same level such as their fall velocity and sediment concentration.
TL;DR: In this paper, the authors consider the mathematical difficulties associated with converting this knowledge into practical aeronautical design procedures and present challenges including resolution of the relation between probabilistic structure of turbulence and response exceedance statistics, determination of the structure of the largest gusts, and the combined problem of developing mathematical methods for representing turbulent velocities for both simulation and the study of nonlinear effects.
TL;DR: In this paper, the authors apply the Cameron-Martin-Wiener (formerly known as the Wiener-Hermite) expansion of a random velocity field to the analytical study of turbulence.
Abstract: We apply the Cameron—Martin—Wiener (formerly ‘Wiener—Hermite’) expansion of a random velocity field to the analytical study of turbulence. The kernels of this expansion contain all statistical information about the ensemble. Complete expressions are derived for constructing statistical quantities in terms of the kernels, and for the equations of motion of the kernels. We rigorously prove the Gaussian trend of the velocity field of the Navier—Stokes equation in the very late stage when the non-linear term is neglected. The n-dependence (n is the order of derivative) of the flatness factor, minus three for derivatives of the velocity field, shows a rapid increase with n in this stage.The late decay problem of the Burgers model of turbulence is studied analytically with a view to obtaining suggestive guidelines for fitting the non-linear aspects of the model turbulence. We can divide the energy spectrum density into two parts, the larger of which is a kind of steady solution, which we call the ‘equilibrium state’, which remains self-similar in time in terms of an appropriate variable. The deviation from this ‘equilibrium solution’ satisfies the Karman—Howarth equation. As initial velocity field, we take two particular cases: (a) a pure Gaussian, and (b) a non-Gaussian velocity field. With these two cases a detailed spectral analysis has been obtained. The energy spectrum deviation from ‘equilibrium’ declines exponentially to zero for all wave-numbers. The Gaussian case shows that the flatness factor minus three increases rapidly with n, while the non-Gaussian case does not show any marked dependence on n.
TL;DR: In this article, the initial condition for a previous analysis of turbulence with shear was modified to give a finite initial energy, and the total energy increases for finite periods, during which turbulence production exceeds dissipation.
Abstract: The initial condition for a previous analysis of turbulence with shear is modified to give a finite initial energy. The total energy increases for finite periods, during which turbulence production exceeds dissipation. For large times the turbulence decays.
01 Mar 1970
TL;DR: In this paper, the effect of high intensity turbulence with the flow past a rigid circular cylinder was studied experimentally at subcritical Reynolds numbers, and it was shown that even severe large-scale turbulence can be considered equivalent to an increase in the effective Reynolds Number.
Abstract: : The interaction of high intensity turbulence with the flow past a rigid circular cylinder was studied experimentally at subcritical Reynolds numbers. Grids were used to produce homogeneous turbulence fields with longitudinal scales ranging from 0.36D to 4.40D, and with longitudinal intensities greater than 10%. Power and cross-spectra of the turbulence components (the 'system input') were measured in order to carefully define the turbulence characterists. In particular, lateral coherences of the longitudinal component were found to collapse well when plotted versus zeta/lambda (lateral separation/wavelength) as suggested by Davenport. A model with which measurement of arbitrary two-point pressure correlations could be made was used in the response experiments. Subsequent integrations yielded the spectral properties of the unsteady drag and lift. Measurement of mean drag and Strouhal frequency indicate that to some extent even severe large-scale turbulence can be considered equivalent to an increase in the effective Reynolds Number. Vortex shedding is not disrupted drastically by severe turbulence, but is affected more by that at low frequency than at high. The unsteady lift response is still dominated by the vortex shedding, whereas the unsteady drag is primarily a response to turbulence. The cross-spectra of the drag collapse well when plotted versus zeta/lambda, and were used, for one grid, to derive a 'describing function' for the drag 'response' to turbulence. This describing function is the central element needed for the calculation of structural response in the drag direction. (Author)
TL;DR: In this paper, a unified heuristic model of fluid turbulence is proposed which supplements the basic equations of motion and continuity so as to define determinate solutions at high Reynolds number under a wide range of conditions.
01 Jan 1970
TL;DR: In this article, strongly accelerated turbulent boundary layer, investigating free stream turbulence effect on heat transfer, is used for heat transfer in a free stream environment, where the boundary layer is composed of two layers.
Abstract: Strongly accelerated turbulent boundary layer, investigating free stream turbulence effect on heat transfer
26 Oct 1970
TL;DR: In this article, a model of Kelvin-Helmholtz waves has been developed which predicts their maximum amplitude, the mode of breaking, and the resulting turbulent kinetic energy The model is internally consistent and is in reasonable accord with available observations.
Abstract: : In this paper a model of Kelvin-Helmholtz waves has been developed which predicts their maximum amplitude, the mode of breaking, and the resulting turbulent kinetic energy The model is internally consistent and is in reasonable accord with available observations (Author)
TL;DR: In this article, a criterion for the instability of shearing gravitational waves on the discontinuous interface between a two-isothermal-layer is derived from the result of Bjerkness et al.
Abstract: A criterion for the instability of shearing gravitational waves on the discontinuous interface between a two-isothermal-layer is derived from the result of Bjerkness et al. Comparison of this criterion with the Richardson number gives the results that in the present model the critical Richardson number is ½ and the vertical extent of the turbulent layer is estimated to reach 1/2(π) of the wavelength. Various observed data in actual clear air turbulence are used to evaluate these two constants.