Showing papers on "K-epsilon turbulence model published in 1975"

Progress in the development of a Reynolds-stress turbulence closure

Abstract: The paper develops proposals for a model of turbulence in which the Reynolds stresses are determined from the solution of transport equations for these variables and for the turbulence energy dissipation rate E. Particular attention is given to the approximation of the pressure-strain correlations; the forms adopted appear to give reasonably satisfactory partitioning of the stresses both near walls and in free shear flows. Numerical solutions of the model equations are presented for a selection of strained homogeneous shear flows and for two-dimensional inhomogeneous shear flows including the jet, the wake, the mixing layer and plane channel flow. In addition, it is shown that the closure does predict a very strong influence of secondary strain terms for flow over curved surfaces.

The Structure of Turbulent Shear Flow

Abstract: Note: Bibliogr. : p. 413-424. Index Reference Record created on 2004-09-07, modified on 2016-08-08

Onset of Turbulence in a Rotating Fluid

Abstract: Light-scattering measurements of the time-dependent local radial velocity in a rotating fluid reveal three distinct transitions as the Reynolds number is increased, each of which adds a new frequency to the velocity spectrum. At a higher, sharply defined Reynolds number all discrete spectral peaks suddenly disappear. Our observations disagree with the Landau picture of the onset of turbulence, but are perhaps consistent with proposals of Ruelle and Takens.

Transition to turbulence in oscillating pipe flow

Abstract: Published results on transition in a Stokes layer indicate a wide range of transition Reynolds numbers. As thermal effects in a resonance tube (Merkli & Thomann 1975) depend on the state of the boundary layer, the transition Reynolds number was determined, and a critical Reynolds number Ac ≈ 400 was found. The observations were made with hot wires and with flow visualization by means of smoke, and provide new details on turbulence in a Stokes layer. With this knowledge an explanation of the large discrepancies between some stability theories and the experiments is suggested. The main point is that turbulence occurs in the form of periodic bursts which are followed by relaminarimtion in the same cycle and do not lead to turbulent flow during the whole cycle.A further, unexpected result of the present investigation is the discovery of vortex patterns superimposed on the normal laminar acoustic motion.

Mixing across an interface due to turbulence generated by an oscillating grid

Abstract: Many experimenters have used oscillating grids to produce turbulence for various laboratory purposes, especially in studies of mixing, but there have been few direct measurements of the properties of the turbulence itself. In the present paper we report experiments which attempt to relate the turbulent velocity and length scales to the external parameters, the frequency and amplitude, for three forms of grid oscillated in a tank of water. Turbulent velocities have been measured in the absence of a mean flow by using a hot film moved through the fluid to provide its own mean velocity. The output is stored and analysed in a small computer, which rapidly evaluates velocity and length scale statistics from an ensemble of records. The spatial variation of these quantities with distance from the stirrer is of special interest. It agrees with results suggested by an inertial-decay theory, and with previous measurements made by Bouvard & Dumas (1967) using a different form of stirrer. A particular purpose of the work has been to ‘calibrate’ the entrainment experiments of Turner (1968), by providing absolute scales of velocity and length in the fluid near a mixing interface, for the same grid as was used in the earlier experiments. Evidence is presented which suggests that other forms of grid may not be calibrated simply by extrapolating these results.

Limitations of Gradient Transport Models in Random Walks and in Turbulence

Abstract: Publisher Summary This chapter identifies the conditions necessary for the validity of a gradient transport model in a simple mean-free-path type of random transport process. A principal shortcoming of the telegraph equation as a turbulent diffusion model is that it possesses no Eulerian statistical properties, whereas Eulerian coordinates are those in which most experimental investigations and theoretical analysis of turbulent motion are conveniently carried out. By qualitative analogy with random walk transport, analyzed without rigor, the chapter presents a collection of conditions that may be necessary for the applicability of simple gradient transport models in turbulence. These conditions stipulate degrees of homogeneity and stationarity of the mean field being transported, and of the turbulence properties central to the transport mechanism. One or more of these conditions appear to be violated in each of the traditional turbulent flow boundary value problems, such as boundary layer and jet. There are many alternative approaches to turbulent transport, which are related to neither a gradient transport approximation, nor to a hypothetical, long-path, radiative transport analogy. Closure schemes for hierarchies of turbulence moment equations have been based on a variety of truncated expansion procedures, which often invoke no explicit physical or phenomenological images, but are more or less ad hoc, based sometimes on the intuitive belief that higher order correlation coefficients tend to be very much smaller than lower order ones. It is possible that one of these more formal closure methods will eventually succeed.

Wave Breakdown and Turbulence

Abstract: Some new ideas on the dynamics of shear flow turbulence are presented. Central to these is the phenomenon of wave breakdown. This is defined as the onset of a violent small-scale secondary instability developing on a large-scale primary disturbance of wave-like traveling type. It is suggested that breakdown together with the ensuing violent mixing process (a turbulent “burst”) constitutes the dominant nonlinear mechanism for the fluctuating velocity field in a turbulent boundary layer. A burst regeneration mechanism is proposed whereby one breakdown can excite large velocity defects in the shear flow which then may trigger a new breakdown, thus leading to self-maintenance of the turbulence.

On turbulence and noise of an axisymmetric shear flow

Abstract: The noise produced by mean flow-turbulence interaction of a circular subsonic jet is investigated theoretically, and expanded in azimuthal constituents of the turbulent pressure fluctuations. It is found that the low-order azimuthal constituents are the most efficient sound sources. On the basis of pressure correlation measurements, the azimuthal constituents are determined in a low Mach number jet. It is found that, in a range of Strouhal numbers between 0·2 and 1, the first three to four azimuthal constituents clearly dominate over the rest of the turbulent source quantity. A strictly axisymmetric ring vortex model for the coherent structure of the turbulence is, however, shown to be inappropriate.

Scaling laws for pipe-flow turbulence

Abstract: Using hot-wire-anemometer dynamic-calibration methods, fully developed pipe-flow turbulence measurements have been taken in the Reynolds-number range 80 × 103 to 260 × 103. Comparisons are made with the results of previous workers, obtained using static-calibration methods. From the dynamic-calibration results, a consistent and systematic correlation for the distribution of turbulence quantities becomes evident, the resulting correlation scheme being similar to that which has previously been established for the mean flow. The correlations reported have been partly conjectured in the past by many workers but convincing experimental evidence has always been masked by the scatter in the results, no doubt caused by the difficulties associated with static-calibration methods, particularly the earlier ones. As for the mean flow, the turbulence intensity measurements appear to collapse to an inner and outer law with a region of overlap, from which deductions can be made using dimensional arguments. The long-suspected similarity of the turbulence structure and its consistency with the established mean-flow similarity appears to be confirmed by the measurements reported here.

New Trends in Experimental Turbulence Research

Abstract: In the past few years some novel statistical techniques and significant observations have been made in the search for a better understanding of the turbulence problem. These efforts have spearheaded what is believed to be a new trend in turbulence research. In this review an attempt is made to describe this new direction in a qualitative way, to place it in a proper historical perspective, and to assess its significance. Taking a brief, rather cursory glance at the manner in which experimental techniques have influenced prevailing ideas on treating turbulent flows over the past fifty years, one may recognize several fairly distinct periods of activity. The twenties and thirties were rich in ideas that tried to rationalize the concept of a turbulent viscosity coefficient. Mcan velocity measurement was the primary experi­ mental method available at the time and was extensively used to establish the advantage of one theory over another. While no conclusion could be reached on this point, the measurements gave some support to phenomenological approaches, including similarity arguments for helping to solve practical problems, but they served essentially as a passive tool. By the forties, the hot-wire technique for the measurement of velocity fluctuations was sufficiently developed that the various components of the Reynolds stress could be obtained with confidence. This development made it possible to test the assumptions of the various phenomenological theories more directly. The result was a complete rejection of these theories. On hindsight, this proved to be a rather ironic turn of events: Later results using more sophisticated statistical techniques developed in the early sixties gave some (although not well understood) support to the turbulent viscosity concept; furthermore, it turned many researchers' attention away from shear-flow turbulence to the "simpler" but more academic problem of homogeneous turbulence. With further improvement of the hot-wire technique and associated electronic instrumentation, subsequent experiments in the fifties concentrated on studying the spectral distribution of the turbulent kinetic energy with a particular emphasis

Prediction of turbulent flow in curved pipes

Abstract: A finite-difference procedure is employed to predict the development of turbulent flow in curved pipes. The turbulence model used involves the solution of two differential equations, one for the kinetic energy of the turbulence and the other for its dissipation rate. The predicted total-velocity contours for the developing flow in a 180° bend are compared with the experimental data. Predictions of fully developed velocity profiles for long helically wound pipes are also presented and compared with experimental measurements.

Computational Modeling of Turbulent Transport

Abstract: A rational closure technique is presented for the first and second moment-equations in a stratified, contaminated turbulent flow, Following the application of high Reynolds/Peclet number approximations, remaining third moments are expanded about the isotropic, homogeneous state. The stratified, uncontaminated case reduces to seventeen equations in seventeen unknowns. Other authors have suggested some of the terms generated, but Some have been using the wrong terms, or the right terms for the wrong reasons. The approximation is kinetic-theoretic (turbulence/mean motion scales assumed small, and turbulence nearly in equilibrium) and results in a relaxation time, and in generalized gradient transport forms; however, gradients of one quantity can produce fluxes of another. The model relates the time scale for return to isotropy to the Lagrangian integral time scale (reducing to K-theory in a homogeneous parallel flow with orthogonal temperature gradient). Some coefficients are estimated, and preliminary computations arc presented of the unstratified 2-D turbulent wake; only component energies near the centerline are not well reproduced, probably due to the omission of a term with which temporary computational difficulties were being experienced. Stratified, contaminated 3-D calculations appear to be practical.

On the prediction of intermittent turbulent flows

Abstract: A theoretical model is presented which permits the conservation equations of fluid dynamics to be conditioned in a fashion analogous to the experimentalist's technique of "conditioned sampling". The detailed analysis refers to the best-known sampling condition, outer-edge intermittency; but the model equation may be applicable to other flow situations, wherein conditioning exposes details of the physical phenomena. The analysis results in predictions of the flow variables within the turbulent flow and of the intermittency. Comparison is made with two sets of experimental results for the two-dimensional mixing layer and with a boundary layer.

Modeling the atmospheric boundary layer

Abstract: Publisher Summary Higher order closure models, which use exact equations for the mean field and approximate ones for the turbulence, can reproduce in remarkable detail, the structure of turbulent shear flows. However, the main differences between models are the closure assumptions used for the turbulence equations. This chapter explains the model for the atmospheric boundary layer. Developing model for the atmospheric boundary layer is in some ways more difficult, because the effects of buoyancy and rotation modify the structural relationships found in shear flows and presumably, buoyant and rotation terms should appear in at least some of the closure assumptions. Another difficulty is the lack of atmospheric turbulence data outside the surface layer. However, the results presented in the chapter suggest that steady-state neutral and unstable model is an attractive approach to the calculation of atmospheric boundary layer structure and it takes relatively little computer time. There is a rational technique for refining the model, but, because the data required for model testing are so difficult to obtain in the atmosphere, it seems to have relied heavily on the simulation of various laboratory flows. However, the model itself needs more attention now, particularly with respect to the higher-order terms in the pressure covariance expansions.

Numerical Computation of Turbulent Shear Flows

Abstract: Publisher Summary This chapter describes the simulations of turbulent shear flows by direct numerical solution of the three-dimensional Navier-Stokes equations, the dynamical equations, and boundary conditions employed with particular emphasis on the momentum less wake model The numerical computation approach provides several advantages over more conventional approaches—the complete flow field is obtained at all times so that detailed flow characteristics may be obtained that would be difficult to measure in the laboratory, and the initial conditions can be accurately controlled so that their effect may be determined The technique of imposing the initial conditions allows arbitrary mean velocity profile, turbulence intensity profile, and local turbulence energy spectrum The present simulations of turbulent shear flows are a first step toward proper understanding of the basic mechanisms and dynamics of these flows Detailed comparisons and tests are presently underway between various turbulence modeling hypotheses, laboratory experiments, and the present simulations As time and the art of numerical simulation progress, simulations like the present ones should be expected to fulfill more and more need of a laboratory workhorse

The Critical Richardson Number and the Ratio of the Eddy Transport Coefficients Obtained from a Turbulence Closure Model

Abstract: A turbulent closure model is analyzed under the condition that the turbulent flow is steady in its ensemble average and both the advection and diffusion terms, i.e., third moments of turbulence, are neglected in the turbulent Reynolds stress and heat flux equations. The critical flux Richardson number is defined as a limiting value beyond which physically correct solutions are no longer possible. All the turbulence moments are suppressed completely when the Richardson number exceeds the critical value. The validity of making such an assumption is tested against the numerical results which were obtained by utilizing a more complete set of equations. The critical flux Richardson numbers of 0.18σ0.27 are obtained from the different proposed empirical constants. The ratio of the eddy transport coefficient of heat to that of momentum have values of 0.5σ1.2 at the critical condition of stability. A review is made to clarity the differences between the present model and the earlier works of Ellison, Tow...

A Note on Favre Averaging in Variable Density Flows

Abstract: (1975). A Note on Favre Averaging in Variable Density Flows. Combustion Science and Technology: Vol. 11, No. 5-6, pp. 215-217.

Prediction of the effect of streamline curvature on turbulence

Abstract: It is shown that the observed effects of small amounts of streamline curvature on turbulence are accounted for by the curvature terms which appear in the Reynolds stress equations and in the turbulence model of Launder, Reece, and Rodi. Because of the smallness of these terms, this is a surprising result, but their effect is shown to appear in a magnified form in the effective eddy viscosity. A comparison is made between computed solutions of the modeled Reynolds stress, mean momentum and dissipation rate equations, and experimental data for curved wall jets, a curved free jet, and curved boundary layers. The curvature effects are well predicted when the curvature terms are included. The turbulence model implies that the turbulence shear stress is relatively insensitive to longitudinal accelaration which seems to be in reasonable agreement with experiment.

The turbulent boundary layer: An experimental study of the transport of momentum and heat with the effect of roughness

Abstract: : The turbulent boundary on a deterministic rough wall has been examined for the cases of isothermal and non-isothermal, zero pressure gradient flows with and without transpiration. The data include temperature and velocity profiles, turbulence intensity profiles, turbulence shear stresses and heat flux profiles and the correlation coefficients of both the fluid dynamic and temperature fields.

Production of Turbulence in the Vicinity of Critical Levels for Internal Gravity Waves

Abstract: Calculations demonstrating that Internal gravity waves become unstable in the vicinity of critical levels are reported in this paper. An analytic linear inviscid model is used to look at the geometry of these unstable regions using parameters appropriate to the atmosphere. A nonlinear model is used to establish the usefulness of our simple analytic model. It is argued that turbulence should occur in regions of instability that are tens to hundreds of meters thick in the vertical. It is shown, in a fluid with a sufficiently large kinematic viscosity, that turbulence should no longer occur near critical levels. This condition indicates that turbulence will no longer be produced at critical levels above the altitude of the turbopause, about 100 km. Observational evidence is cited indicating that this production of turbulence near critical levels might be of importance in the planetary boundary layer, in the upper troposphere and stratosphere, in the mesosphere and lower thermosphere, and even in the...

Structure of the turbulence in pulsating pipe flows

Abstract: An experimental investigation was performed to study the dynamic process of bursting in pulsating turbulent flow. Particular emphasis is placed on the details of the process of turbulence generation and its propagation in the radial direction. The results show that the resonance in pulsating flow affects only the generation of turbulence, and that another important factor which characterizes the dynamic behaviour of turbulence is the coherency of propagation of generated turbulence: changing its frequency, the generated turbulence propagates to the centre-line of the tube with a unique propagation time which scales on the wall parameters. The propagation time in which the turbulence propagates from the position of origin to the centre-line agrees well with the mean burst period. This fact suggests that the entire cycle of the bursting phenomenon is characterized by the propagation of generated turbulence in the radial direction and that the bulk parameter dependence of burst period is attributable to the pipe radius.

Improved form of the low Reynolds number k−ε turbulence model

Abstract: The behavior of the k−e turbulence model at a turbulent/nonturbulent interface is examined to determine the turbulent diffusion coefficients σk and σe The analysis leads to a dilemma caused by the modeling of the generation term in the k and e equations Based on limiting values of σk and σe derived from this analysis, a revised form of the low−Reynolds−number incompressible k−e turbulence model is presented which incorporates a new set of model constants, a linear form of the near wall dissipation term in the k equation, and deletion of a nonphysical term in the e equation The revised model is applied to fully developed flow in a channel and found to give better agreement with experiment than the original form of the model developed by Jones and Launder