Showing papers on "K-epsilon turbulence model published in 1973"

Effects of Streamline Curvature on Turbulent Flow.

Abstract: : Streamline curvature in the plane of the mean shear produces large changes in the turbulence structure of shear layers, usually an order of magnitude more important than normal pressure gradients and other terms in the mean-motion equations for curved flows. The effects on momentum and heat transfer in boundary layers are noticeable on typical wing sections and are very important on highly-cambered turbomachine blades: turbulence may be nearly eliminated on highly-convex surfaces, while on highly-concave surfaces momentum transfer by quasi-steady longitudinal vortices dominates the ordinary turbulence processes. The greatly enhanced mixing rates of swirling jets and the characteristic non-turbulent cores of trailing vortices are also consequences of the effects of streamline curvature on the turbulence structure. A progress report, comprises a review of current knowledge, a discussion of methods of predicting curvature effects, and a presentation of principles for the guidance of future workers.

Experiments on instability and turbulence in a stratified shear flow

Abstract: This is a study of turbulence which results from Kelvin—Helmholtz instability at the interface between two miscible fluids in a two-dimensional shear flow in the laboratory. The growth of two-dimensional ‘billows’, their disruption by turbulence, and the eventual decay of this turbulence and the re-establishment of a gravitationally and kinematically stable interface are described. Continuous measurements of density and horizontal velocity from both fixed and vertically moving probes have been made, and the records obtained are presented, together with photographs showing the simultaneous appearance of the flow, which serve to identify the physical nature of events seen in the records. The measurements show how the fine-structure of the density field described in earlier experiments is related to velocity fluctuations. The vertical length scales of the final mean velocity and density structure are found to be different, and to depend on the Richardson number at which instability first occurred. The eventual Richardson number at the centre of layer is, however, not dependent on the initial Richardson number and has a value of about one third. The implications of these results to the eddy diffusion coefficients, to the energy exchange, and to turbulence in the ocean and the atmosphere are discussed.

A Preliminary Numerical Study of Atmospheric Turbulent Flows in the Idealized Planetary Boundary Layer

Abstract: A turbulent transport model is developed to study atmospheric turbulence in the planetary boundary layer. A total of nine equations governing the mean motion, mean turbulent stresses, and turbulence length scale are integrated numerically. In this preliminary study, only the ideal case of neutral lapse rate, barotropic, statistically stationary, and horizontally homogeneous conditions is treated. The height of the boundary layer is investigated and found to be about 0.5 u*/f, where u* and f are the friction velocity and Coriolis force parameter, respectively. The computed friction coefficient, the crossisobaric angle, the vertical profiles of mean wind, mean turbulent stresses, the turbulent length scale, and eddy coefficients agree well with observations and with Deardorff's results. Various terms in the turbulent stress equations, which are difficult to measure, are discussed. The direction of the stresses seems to align with the direction of the wind shear. The profiles of the turbulent diffus...

Prediction of free shear flows: A comparison of the performance of six turbulence models

Abstract: The performance is evaluated of three distinct classes of turbulence model. These classes are: (1) Turbulent-viscosity models in which the length scale of turbulence is found by way of algebraic formulas, (2) turbulent-viscosity models in which the length scale of turbulence is found from a partial differential equation of transport, and (3) models in which the shear stress itself is the dependent variable of a partial differential conservation equation. Two models were examined in each class; thus, six different models were tested. A complete mathematical statement of these models is provided and a brief commentary on the models is included.

Effect of anisotropic turbulence on aerodynamic noise

Abstract: A model based on Lighthill's theory for predicting aerodynamic noise from a turbulent shear flow is developed. This model is a generalization of the one developed by Ribner. It does not require that the turbulent correlations factor into space and time-dependent parts. It replaces his assumption of isotropic turbulence by the more realistic one of axisymmetric turbulence. In the course of the analysis, a hierarchy of equations is developed wherein each succeeding equation involves more assumptions than the preceding equation but requires less experimental information for its use. The implications of the model for jet noise are discussed. It is shown that for the particular turbulence data considered anisotropy causes the high-frequency self-noise to be beamed downstream.

Prediction of Inert Turbulent Swirl Flows

Abstract: Numerical finite-difference predictions are made of inert turbulent boundary-layer swirling flows. A variety of turbulence models are considered and a nonisotropic model is found to show more realistically the effects of swirl on jet development. Gross effects may be represented by an extended Prandtl mixing length model but constants appearing do not exhibit universality. This deficit is partially overcome by the use of an algebraically-modeled, nonisotropic energy-length turbulence model. The Richardson number and the local swirl number play important parts in linking the rtf-shear with the rx-viscosity and the nonisotropy of the turbulent viscosity.

Enhancement of stagnation flow heat and mass transfer through interactions of free stream turbulence

Abstract: At the forward stagnation point of a bluff body the laminar flow is influenced by externally generated free-stream turbulence, such as from grids, in such a way that heat and mass transport are significantly enhanced above their normal values. The basis of this enhancement is an unsteady, threedimensional flow pattern formed at the forward stagnation point and triggered or altered by the free-stream turbulence. Such complex flows can be interpreted as roll cells oriented with their axes parallel to streamwise coordinates. Such roll cells have been observed by other investigators using special experimental visualization techniques. This complex flow was introduced into the momentum and transport equations, which were then solved numerically to produce the relationships between Nusselt, Reynolds, and Prandtl numbers and free-stream turbulence. Not only were these relationships nearly identical with earlier established empirical correlations, but they revealed in addition a strong augmentation for high Prandtl number flows. Predictions in slurry flows around bluff bodies were also found to be reasonable.

Coherence of Grid-Generated Turbulence

Abstract: For the purpose of predicting the dynamic response of structures and buildings to turbulent winds, a knowledge of the lateral coherence of the upstream velocity fluctuations is essential. For the special case of isotropic turbulence, the character of the coherence function is deduced from theoretical considerations and a simple method of computing this function from any arbitrary power spectrum is derived. Particular emphasis is placed on the range of validity of simple collapsing parameters, associated with certain spectral models. The theoretical predictions are confirmed by extensive hot-wire measurements taken in grid-generated turbulence. This result facilitates determination of the dynamic response of slender structures to wind loading.

Numerical simulation of turbulence

Abstract: : Turbulent flows play a major role in many problems of great practical interest. In the report the authors consider whether the advent of a new generation of computers (Illiac IV, Star, ASC) makes feasible a numerical attack on turbulence by direct integration of the Navier-Stokes equations.

Calculation of Interacting Turbulent Shear Layers: Duct Flow

Abstract: The boundary-layer calculation method of Bradshaw, Ferriss, and Atwell has been adapted to deal with the interaction between two shear layers with a change of sign of shear stress. Good agreement with experiments in symmetrical duct flow is found, using the same empirical input as in a boundary layer and assuming that the turbulence fields on either side of the duct can be superposed. The restriction to symmetrical flow is temporary and is a numerical rather than a physical simplification. In free jet flows, which have higher turbulence levels than ducts, small changes in empirical input are required to treat the interaction.

Role of the outer scale of turbulence in atmospheric degradation of optical images

Abstract: The atmospheric degradation of optical images is investigated by assuming the refractive-index structure function to be independent of the distance between two correlation points when such distance is larger than the outer scale (Von Karman model). It is found that, in most practical cases, the atmospheric turbulence puts a limit to the resolution as predicted by the 2/3-power law, however, only when the turbulence is sufficiently strong. The parameter distinguishing strong from weak turbulence turns out to be the limit value of the wave structure function Dw (∞) for infinite distance. Weak turbulence, with Dw (∞) ≲ 20, does not put a limit to the resolution of an optical system.

Intermittency in Large-Scale Turbulent Flows

Abstract: Observations show that high levels of fluctuations occur sporadica lly in bursts in flows at high Reynolds number. The bursts of turbulence seem to be bursts of gene ration of turbulence involving a hierarchy of scales within a b urst with in­ tensive excbange of energy between scales of motion. The net transfer of energy through the cascade of scales appears to be almost discontinuous in space and time, with transfers over small ranges in scale being imbedded within regions of larger-scale transport. In recent years, we have come closer to an understanding of the properties of energy cascades and intermittency in turbulence. Here, as in every field of science, ideas are suggested based on varying degrees of complete­ ness of physical insight. Other workers take such suggestions and pursue them further, developing formal approximations and models that predict the structure of certain measures of turbulent flows. In turbulence, we are often torn between a desire for detailed description of the physics and a desire for more elegant and

Turbulence measurements in a compressible boundary layer subjected to a shock-wave-induced adverse pressure gradient.

Abstract: The rms intensities of fluctuating mass flux and total temperature and their correlation coefficients are given for the case of an adiabatic, Mach 4, axisymmetric shock-wave boundary-layer interaction. Data were obtained upstream, within, and downstream of the interaction by the use of constant temperature hot-wire anemometer. Turbulence spectra and quantitative behavior from oscilloscope traces are shown at selected locations. The measurements indicate that certain frequencies of the turbulence are increased as a result of the interaction and that the mass flux and total temperature fluctuations remain highly correlated over most of the boundary layer throughout the interaction. The present data are also transformed to rms intensities of fluctuating static temperature and velocity and compared with existing data obtained in adiabatic flows.

On Burgers' model equations for turbulence

Abstract: Burgers’ (1939) model equations for turbulence are considered analytically using a singular perturbation and nonlinear wave approach. The results indicate that there is an ultimate steady turbulent state. This is in agreement with the numerical results of Lee (1971) but not with Case & Chiu (1969): the last two papers start with a Fourier series approach.A consequence of this model is that small disturbances ultimately grow into a single large domain of relatively smooth flow, accompanied by a vortex sheet in which strong vorticity is concentrated. This makes the results from the model different from those usually expected for turbulent flow fields. The model, as a result of its simplicity, has retained a degree of regularity which is not found in most forms of turbulence.

Turbulence and microstructure in the ocean

Abstract: The possibility of distinguishing between turbulence and wave fluctuations of the hydrodynamic fields is discussed. Possible mechanisms of generation of turbulence in the ocean are considered, and theoretical information as well as experimental data are given concerning the spectra of small-scale turbulence in the upper layer of the ocean. Intermittent turbulence in the main body of the ocean is described. The laws governing the turbulent diffusion in the ocean are briefly considered. A hypothesis is advanced concerning the spectral transport of the mean-squared vorticity in the field of quasi-two-dimensional turbulence. The small-scale convection produced by the difference between the diffusion coefficients of heat and salt in sea water is considered. Experimental data are presented on the vertical thin-layer microstructure of the ocean, and possible mechanisms whereby it is generated are considered, such as shear instability, internal waves, lateral convection, and differences between the diffusion coefficients for momentum, heat, and salt. The distortions produced in the internal-wave spectra by the presence of vertical thin-layer microstructure are analyzed.

Response of a rigid aircraft to nonstationary atmospheric turbulence.

Abstract: The plunging response of an aircraft to a type of nonstationary turbulent excitation is considered. The latter consists of stationary Gaussian noise modulated by a well-defined envelope function. The intent of the investigation is to model the excitation experienced by an airplane flying through turbulence of varying intensity and to examine the influence of intensity variations on exceedance frequencies of the gust velocity and the airplane's plunging velocity and acceleration. One analytical advantage of the proposed model is that the Gaussian assumption for the gust excitation is retained. The analysis described herein is developed in terms of an envelope function of arbitrary form; however, numerical calculations are limited to the case of harmonic modulation.

Development of the concepts of plasma turbulence

Abstract: The review is devoted to exposition of the physical principles on which the current ideas on plasma turbulence are based. A comparison is made of the results obtained in the theory of plasma turbulence and the turbulence of incompressible liquids. The basic physical differences between hydrodynamic and plasma turbulence are pointed out. It is shown how the concepts of turbulent excitations arise in the statistical description of turbulence. The fundamental difference is pointed out between turbulent elementary excitations and elementary excitations describing a state close to thermodynamic equilibrium. Special emphasis is given to explanation of the physical meaning of the concept of effective turbulent collisions. It is shown that inclusion of turbulent collisions does not make possible construction of a theory of weak turbulence on the basis of simple expansions of the interaction in the turbulence energy. Examples are presented which show that effective turbulent collisions can fundamentally change the theoretical predictions which must be compared with existing experiments. It is shown how the inclusion of effective turbulent collisions permits construction of a theory of correlation functions of turbulent plasma fields. In connection with the discussion of new approaches to the theory of weak turbulence, taking into account effective turbulent collisions, an analysis is carried out of the theories of anomalous electrical conductivity of a plasma in an external electric field.

Meteor trails and atmospheric turbulence

Abstract: The application of turbulence theory to atmospheric structure revealed by radio meteor trails clearly demonstrates that Batchelor's and Obhukoff's structure function for isotropic turbulence explains some of the observed relations. From these measurements, parameters such as ϵ (the rate of viscous dissipation), 〈uk′²〉 (the eddy intensity of the scales up to k′ within the equilibrium range), Rek′ (the local eddy Reynolds number describing the turbulence up to a scale k′−1), and νk′ and νb (turbulent viscosity coefficient up to scale k′−1 and the vertical turbulent viscosity up to the buoyancy limited scale lb, respectively) are determined. Also, estimates of the rate at which turbulence extracts wind energy from the vertically propagating diurnal tide are given. The results of the parametric study suggest very strongly that the vertical turbulent spectrum, in the upper atmosphere, contains little or no energy extending into the inertial subrange but lies for the most part near the viscous end (high wave number) of the universal equilibrium subrange, owing to the energy transfer to buoyancy, which limits its low wave number value.

Some problems of the calculation of three-dimensional boundary layer flows on general configurations

Abstract: An accurate solution of the three-dimensional boundary layer equations over general configurations such as those encountered in aircraft and space shuttle design requires a very efficient, fast, and accurate numerical method with suitable turbulence models for the Reynolds stresses. The efficiency, speed, and accuracy of a three-dimensional numerical method together with the turbulence models for the Reynolds stresses are examined. The numerical method is the implicit two-point finite difference approach (Box Method) developed by Keller and applied to the boundary layer equations by Keller and Cebeci. In addition, a study of some of the problems that may arise in the solution of these equations for three-dimensional boundary layer flows over general configurations.