Showing papers on "K-epsilon turbulence model published in 1980"

Theory of Homogeneous Turbulence

Abstract: Publisher Summary This chapter presents an overview of the theory of homogeneous turbulence. Homogeneous isotropic turbulence is an idealized concept of turbulence, assumed to be governed by a statistical law that is invariant under arbitrary translation (homogeneity), rotation, or reflection (isotropy) of the coordinate system. This is an idealization of real turbulent motions, which are observed in nature or produced in a laboratory, and generally have much more complicated structures. This idealization was first introduced by Taylor to the theory of turbulence and used to reduce the formidable complexity of the statistical expression of turbulence, and thus make the subject feasible for theoretical treatment. Turbulence combines the difficulty of a strongly nonlinear dynamical system with that of a nonconservative system. The presence of energy dissipation due to viscosity deprives turbulence of the opportunity of being in a thermal equilibrium state. In this chapter, concepts of quasi-normality of large-scale motions are explained. A brief discussion on zero cumulant approximation and modified zero cumulant approximation is presented. Turbulence of other dimensions is also explained.

Two-dimensional turbulence

Abstract: The theory of two-dimensional turbulence is reviewed and unified, and some hydrodynamic and plasma applications are considered. The topics covered include some equations of incompressible hydrodynamics, absolute statistical equilibrium, spectral transport of energy and enstrophy, turbulence on the surface of a rotating sphere, turbulent diffusion, MHD turbulence, and two-dimensional superflow. Finally, an attempt is made to assess the status and future of the principal research topics which have been discussed.

Fully developed turbulence and intermittency

Abstract: The word “turbulence” refers to a variety of phenomena observed i n high Reynolds number flows. These phenomena are only poorly understood at present; there seems, however, little doubt that they can in principle be analyzed within the framework of purely classical macroscopic physics. The hydrodynamic incompressible turbulence that I want to discuss is governed by a quadratically nonlinear PDE known for over a century, the Navier-Stokes equation

On the calculation of turbulent heat transport downstream from an abrupt pipe expansion

Abstract: A numerical study is reported of flow and heat transfer in the separated flow region created by an abrupt pipe expansion Computations employed an adaptation of the TEACH-2E computer program with the standard model of turbulence Emphasis is given to the simulation, from both a physical and numerical viewpoint, of the region in the immediate vicinity of the wall where turbulent transport gives way to molecular conduction and diffusion Wall resistance laws or wall functions used to bridge this near-wall region are based on the idea that, beyond the viscous sublayer, the turbulent length scale is universal, increasing linearly with distance from the wall Predictions of expermental data for a diameter ratio of 054 show generally encouraging agreement with experiment At a diameter of 043 different trends are discernible between measurement and calculation though this appears to be due to effects unconnected with the wall region studied

A stochastic model of two-particle dispersion and concentration fluctuations in homogeneous turbulence

Abstract: A new definition of concentration fluctuations in turbulent flows is proposed. The definition implicitly incorporates smearing effects of molecular diffusion and instrumental averaging. A stochastic model of two-particle dispersion, consistent with this definition, is formulated. The stochastic model is an extension of Taylor's (1921) model and is consistent with Richardson's represents net destruction of fluctuations by relative dispersion. Only the first term is included in the usual one-particle model (Corrsin 1952).

Baroclinic instability and geostrophic turbulence

Abstract: I examine the geostrophic turbulence field in equilibrium with a horizontally uniform mean zonal flow driven by solar heating. The equilibrium mean vertical shear is highly supercritical, and the turbulence field has its maximum in kinetic energy at wavenumbers smaller than the wavenumbers of fastest growth predicted by linear stability theory. Wavenumber spectra obtained by averaging lengthy numerical integrations of the two-level quasi-geostrophic equations agree well with the predictions of a simple Markovian turbulence model. Analysis of the turbulence model suggests that the most energetic wavenumbers equilibrate from scattering of the temperature perturbations into higher wavenumbers by the barotropic adverting field. In the higher unstable wavenumbers, including the most supercritical, linear instability is offset chiefly by local rotations of the unstable structures by larger, more energetic eddies.

Injection and Mixing in Turbulent Flow

Abstract: Injection and mixing in turbulent flow , Injection and mixing in turbulent flow , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی

Subcritical transition to turbulence in plane channel flows

Abstract: A linear three dimensional mechanism for the transition of plane Poiseuille flows to turbulence is presented which provides good agreement with experimental observations. The mechanism is based on the evolution of states within a band of quasi-equilibria which slowly approach the stable upper branch solutions for the evolution of flow energy but which are strongly unstable to infinitesimal three-dimensional disturbances. Numerical simulation has shown that if two-dimensional flow persists long enough for the three-dimensional perturbations to attain finite amplitude, the resulting three dimensional flow quickly develops a turbulent character with nonperiodic behavior, and thus transition can be predicted from knowledge of the initial two- and three-dimensional energies and time scales. The mechanism predicts transition to turbulence at Reynolds numbers greater than 1000, as observed in experiments, and implies higher threshold three-dimensional energies in plane Couette flow.

Progress in turbulence modeling for complex flow fields including effects of compressibility

Abstract: Two second-order-closure turbulence models were devised that are suitable for predicting properties of complex turbulent flow fields in both incompressible and compressible fluids. One model is of the "two-equation" variety in which closure is accomplished by introducing an eddy viscosity which depends on both a turbulent mixing energy and a dissipation rate per unit energy, that is, a specific dissipation rate. The other model is a "Reynolds stress equation" (RSE) formulation in which all components of the Reynolds stress tensor and turbulent heat-flux vector are computed directly and are scaled by the specific dissipation rate. Computations based on these models are compared with measurements for the following flow fields: (a) low speed, high Reynolds number channel flows with plane strain or uniform shear; (b) equilibrium turbulent boundary layers with and without pressure gradients or effects of compressibility; and (c) flow over a convex surface with and without a pressure gradient.

Mixing across a density interface produced by grid turbulence

Abstract: The mixing produced by dropping a horizontal grid through a sharp density interface is examined experimentally. The fraction of the available kinetic energy used to mix the fluid, the flux Richardson number Rf, is measured as a function of the overall Richardson number Ri0. It is found that Rf increases from zero as Ri0 does, reaches a maximum, and then decreases with further increase in Ri0. The final interface thickness is found to be a decreasing function of Ri0, and the equivalent vertical diffusion coefficient is calculated. Qualitative observations of the flow show that the final stages of the decay of motion in the interface are characterized by pancake-shaped modes with large horizontal and small vertical scales.

Use of Doppler radar for the measurement of atmospheric turbulence parameters from the intensity of clear‐air echoes

Abstract: Doppler radars measure the refractivity turbulence structure constant Cn2 in a straightforward manner. In this paper we explore the relationship between Cn2 and the intensity of atmospheric turbulence as parameterized by the eddy dissipation rate e. We develop some tentative relations between mean Cn2 and mean e within the framework of inertial range turbulence theory, taking into account the intermittent nature of atmospheric turbulence. These relations permit the estimation of mean e from radar observations alone. The analysis is applied to the determination from Sunset radar data of vertical profiles and time-height contours of mean e.

The response of sheared turbulence to additional distortion

Abstract: In unidirectional flows, the ratios of Reynolds shear stress to total intensity (except near positions of zero stress) remain remarkably constant from one flow to another, but curvature or strong divergence of the mean flow causes very considerable changes in the stress ratios. A scheme for calculating the changes is described, based on the rapid-distortion approximation of the equations of motion. The results depend to some extent on the effective history of distortion of the turbulence and on the magnitude of an eddy viscosity that models the effect of nonlinear transfer of energy to smaller eddies of the dissipation sequence, but the correspondence with measured values in a distorted wake and in a curved mixing layer is fairly good. In particular, the curious behaviour of stress ratios in the curved mixing-layer can be reproduced qualitatively without any difficulty. Small perturbations of wall turbulence provide a simple application, and earlier calculations of the energy transfer between wind and water waves have been repeated including the changes in the stress ratios predicted by the scheme. In the latter case, very large changes in the distributions of pressure and shear stress are found, and the rates of energy transfer are much larger and in better agreement with observations.

Further Encounters with Clear Air Turbulence In Research Aircraft

Abstract: A series of aircraft penetrations into clear air turbulence zones within upper level fronts is presented. Heat and momentum diffusivities am estimated with a view toward obtaining more realistic parameterizations for numerical models. Two passes through severe turbulence are discussed in detail.

Modeling the Evolution of the Convective Planetary Boundary Layer

Abstract: The level 3 turbulence closure model proposed by Mellor and Yamada (1974) is modified 1) to incorporate the formulations for the turbulence third-order moments and pressure terms proposed by Zeman and Lumley (1976) and 2) to introduce turbulence length scales which depend upon the stratification of the atmosphere. The vertical heat and moisture fluxes and the temperature-humidity covariance are determined from differential equations. The model includes two other differential equations, one for the turbulence kinetic energy and the other for virtual potential temperature variance. All other turbulence variables are determined from algebraic equations. The model is used to simulate the daytime evolution of the planetary boundary layer observed on day 33 of the Wangara boundary-layer experiment. The calculated vertical profiles of the mean wind, temperature and humidity are found to be in good agreement with the observations. The calculated vertical distributions of turbulence variables, including k...

A subharmonic route to turbulent convection

Abstract: It has recently been discovered that the transition to turbulent convection can occur in a variety of qualitatively distinct ways as the temperature difference across a fluid layer is increased.'-' One common route to turbulence involves a succession of instabilities, which cause the fluid to oscillate quasi-periodically a t two, or sometimes three, incommensurate frequencies. These oscillations can exhibit phase locking and the interactions among them can result in broadband spectral noise in the velocity field.',4 The resulting nonperiodic motion may be defined as the onset of turbulence. A second route to turbulence involves successive subharmonic bifurcations, each of which halves the characteristic frequency of a periodic oscillation.',' I t has been known for some time that a one-parameter family of maps on an interval can show a sequence of subharmonic bifurcations.' Furthermore, maps can be generated from continuous flows by observing the intersections of trajectories with a fixed hyperplane in phase space. Thus, it is not far-fetched to imagine a connection between the properties of maps and the physical behavior of a fluid system. Feigenbaum has recently shown that a wide class of maps with a single extremum exhibit a sequence of subharmonic bifurcations as a parameter X is varied, with the bifurcation points, A,, forming a geometric series in the limit,\

A two-dimensional numerical study of horizontal roll vortices in the neutral atmospheric boundary layer

Abstract: The dynamics of large-scale, horizontal roll vortices in the neutral planetary boundary layer are investigated by means of a two-dimensional numerical model. The rolls are assumed to be two-dimensional and are calculated explicitly, while small-scale turbulence is parametrized by a mixing-length hypothesis. Although buoyancy effects are never negligible in the atmosphere, the assumptions of the turbulence modelling are supported by atmospheric observations of large eddies which are highly elongated in a direction close to that of the geostrophic wind, together with the observed partitioning of turbulence energy between the large eddies and a distinctly smaller scale. The results indicate a strong sensitivity to the roll orientation, and also the presence of a slow variation on the Coriolis timescale.

Influence of Freestream Turbulence on Boundary-Layer Development

Abstract: The influence of the wind-tunnel turbulence on the development of a turbulent boundary was studied. The experiments were carried out in the low-turbulence wind tunnel of the DFVLR-AVA at a freestream velocity of U^ = 20 m/s. The turbulence level (Tut -0.06%) was increased up to Tuj «1% by means of various grids at different positions in the settling chamber or nozzle. For a fixed transition and constant distance from the nozzle throat, the effect of the wind-tunnel turbulence on the wall shear stress was investigated. In particular, an attempt was made to separate the effects which result from the turbulence intensity and from the turbulence structure, which is different in each wind tunnel.

The effect of finite turbulence spatial scale on the amplification of turbulence by a contracting stream

Abstract: The turbulence downstream of a rapid contraction is calculated for the case when the turbulence scale can have the same magnitude as the mean-flow spatial scale. The approach used is based on the formulation of Goldstein (1978) for turbulence downstream of a contraction, with the added assumptions of a parallel mean flow at downstream infinity and turbulence calculated far enough downstream so that the nonuniformity of the mean flow field has decayed, and by treating the inverse contraction ratio as a small parameter. Consideration is given to the large-contraction-ratio and classical rapid-distortion theory limits, and to results at an arbitrary contraction ratio. It is shown that the amplification effect of the contraction is reduced when the spatial scale of the turbulence increases, with the upstream turbulence actually suppressed for a contraction ratio less than five and a turbulence spatial scale greater than three times the transverse dimensions of the downstream channel.

A visual investigation of turbulence in stagnation flow about a circular cylinder

Abstract: A visual investigation of turbulence in stagnation flow around a circular cylinder was carried out in order to gain a physical insight into the model advocated by the corticity-amplification theory. Motion pictures were taken from three different viewpoints, and a frame by frame examination of selected movie strips was conducted. Qualitative and quantitative analyses of the flow events focused on tracing the temporal and spatial evolution of a cross-vortex tube outlined by the entrained smoke filaments. The visualization supplied evidence verifying: (1) the selective stretching of cross-vortex tubes which is responsible for the amplification of cross vorticity and, hence, of streamwise turbulence; (2) the streamwise tilting of stretched cross-vortex tubes; (3) the existence of a coherent array of vortices near the stagnation zone; (4) the interaction of the amplified vorticity with the body laminar boundary layer; and, (5) the growth of a turbulent boundary layer.

Turbulence Measurements in Simulated Tidal Flow

Abstract: Field measurements of tidal flow have shown that there is an increase in turbulent parameters (turbulent intensity, Reynolds stress, coefficient of turbulent diffusivity, and the rate of sediment transport) when the flow is decelerating as compared with when it is accelerating. A series of experiments were conducted to study the effect of unsteady flow on turbulence characteristics. The flow in a long flume was accelerated and then decelerated for the same periods of time. Instantaneous velocity components in three directions, water surface slope, and shear stress at bed were measured. From measured data mean velocity profiles, temporal and spatial Reynolds stress profiles, and energy spectra were determined. The results were compared, wherever possible, with those obtained from field measurements.

Diffusion mixing in grid turbulence without mean shear

Abstract: An experimental examination of the fundamental properties of free turbulent interactions in a mixing flow has been conducted. A turbulent, two-dimensional, incompressible, uniform-density mixing layer was produced by using a parallel bar grid of different bar spacings but the same space to bar diameter ratio M/D = 2. In this unique mixing-flow geometry, two initially parallel flowing streams of air were formed in such a way as to possess the same mean structure but different turbulent kinetic energy. The mixing phenomenon was driven solely by the turbulent kinetic-energy self-diffusion process.The data showed the development of the turbulent properties without the interference caused by turbulence generated by a mean shear flow. A simple diffusion model was constructed by assuming an analogy between the unsteady gradient diffusion process and the transport of turbulent kinetic energy by the fluctuations. An empirical error function least squares curve fit, a diffusional power law and diffusion coefficients were derived. The empirical coefficients of self-diffusion were found to be 10.4 and 68.6 cm2 s−1 for the longitudinal and transverse turbulent energy components, or about a hundred and five hundred times faster than molecular viscous shear diffusion, respectively. This self-diffusion mechanism by microscale size eddies may account for some of the error found by other investigators in balancing the measured terms of the turbulent kinetic-energy equation.

Effects of the motion of dust particles on turbulence transport equations

Abstract: A generalized eddy-viscosity function ν T , is introduced in order to express the Reynolds stress in an incompressible dusty gas as a linear combination of the Kronecker and rate-of-strain tensors. On the basis of Saffman's dusty-gas model a transport equation for the eddy viscosity is derived from the general turbulence energy equations, thereby introducing two additional functions, the specific turbulence kinetic energy E 1 , and a scale variable s . In order to determine the three variables modified Prandtl–Wieghardt relation among them is accepted and a transport equation for s is postulated in the same manner as in the clean-gas turbulence transport model (firstly proposed by Harlow & Nakayama 1967) but with the inclusion of an additional term accounting for the dust particles stabilizing action. We are considering values of loading (mass ratio of particles) of order of unity, with particle/gas density ratios of order of 10 3 and volume concentrations of the order of 10 −3 , so that particle–particle interactions are neglected. Supposing that the particles nearly follow the gas motion, following well at large scales and poorly at small, an application of the theory to problem of numerical calculations of the dusty-gas parameters such as mean velocity profile of turbulent pipe flow is given.

Freestream Turbulence Effects on Galloping

Abstract: Galloping is the term used to describe large amplitude single degree-of-freedom motions of a structure associated with a sectional aerodynamic force characteristic which produces a force in the direction of and in phase with the cross-wind motion. Detailed experimental investigations show that freestream turbulence has profound effects on the galloping behavior of a square tower. It is generally believed that increase in freestream turbulence increases the turbulence mixing in the separated shear layers and the rate of entrainment from the wake, and decreases the radius of curvature of the shear layers. These effects significantly alter the transverse force characteristic and thus the galloping behavior of the tower. It is also shown that the fine-scale turbulence produced by a thin rod upstream of the stagnation streamline of the tower is sufficient to cause these effects.