Showing papers on "K-epsilon turbulence model published in 1972"
Book•
01 Jan 1972
TL;DR: In this paper, the authors present a reference record created on 2005-11-18, modified on 2016-08-08 and used for the analysis of turbulence and transport in the context of energie.
Abstract: Keywords: turbulence ; transport ; contraintes ; transport ; couche : limite ; ecoulement ; tourbillon ; energie Reference Record created on 2005-11-18, modified on 2016-08-08
8,276 citations
TL;DR: In this article, the local turbulent viscosity is determined from the solution of transport equations for the turbulence kinetic energy and the energy dissipation rate, and the predicted hydrodynamic and heat-transfer development of the boundary layers is in close agreement with the measured behaviour.
3,999 citations
TL;DR: In this paper, the authors provided a model of turbulence which effects closure through approximated transport equations for the Reynolds stress tensor the turbulence energy κ and e.g., the turbulent shear stress does not vanish where the mean rate of strain goes to zero.
Abstract: The paper provides a model of turbulence which effects closure through approximated transport equations for the Reynolds stress tensor the turbulence energy κ and e. This model has been incorporated in the numerical solution procedure of Patankar & Spalding (1970) and applied to the prediction of a number of boundary-layer flows including examples of flow remote from walls, those developing along one wall and those confined within ducts. Three of the flows are strongly asymmetric with respect to the surface of zero shear stress and here the turbulent shear stress does not vanish where the mean rate of strain goes to zero. In most cases the predicted profiles and other quantities accord with the data within the probable accuracy of the measurements.
1,026 citations
TL;DR: In this paper, a new boundary condition, motivated by an analogy with phenomenological theories of turbulence, is proposed for plane or axisymmetric stagnation point flow of a micropolar fluid over a flat plate.
183 citations
TL;DR: In this article, a hot-film probe was developed for use within arteries and operated with a commercial constant-temperature anemometer and linearizcr. The performance of the system in the recording of arterial velocity wave forms is described, and instantaneous and time-averaged velocity profiles constructed from measurements in the thoracic aorta of dogs are presented.
Abstract: The development and evaluation of a hot-film probe, suitable for use within arteries and operated with a commercial constant-temperature anemometer and linearizcr, is described. The performance of the system in the recording of arterial velocity wave forms is described, and instantaneous and time-averaged velocity profiles constructed from measurements in the thoracic aorta of dogs are presented. The profiles were blunt, with boundary layers estimated to be less than 2 mm thick throughout the cycle, and significant skews were observed, the explanation for which appears to lie in the influence of local geometry on the flow. A preliminary study of flow disturbances in the aorta based on visual observation of instantaneous velocity wave forms and frequency spectrum analysis is reported. The occurrence of flow disturbances and turbulence is shown to be related to peak Reynolds number and the frequency parameter α. The possible roles of free-stream disturbances and boundary-layer transition in generating these disturbances are discussed.
164 citations
01 Jan 1972
TL;DR: In this article, numerical simulations of three-dimensional homogeneous, isotropic turbulence at windtunnel Reynolds numbers (Rλ 20−40) are reported. And the results of the simulations are compared with the predictions of turbulence theories.
Abstract: Numerical simulations of three-dimensional homogeneous, isotropic turbulence at windtunnel Reynolds numbers (Rλ 20–40) are reported. The results of the simulations are compared with the predictions of turbulence theories.
129 citations
Journal Article•
TL;DR: In this paper, integral and transport differential equations are discussed as aids in analyzing turbulence in fluid dynamics studies and the mechanism of turbulence and physics of shear layers are evaluated as preliminary steps, and typical calculation methods for turbulence models presented.
Abstract: Mathematical methods, such as integral and transport differential equations, are discussed as aids in analyzing turbulence in fluid dynamics studies. The mechanism of turbulence and physics of shear layers are evaluated as preliminary steps, and typical calculation methods for turbulence models presented.
115 citations
TL;DR: In this article, a turbulence model is proposed for the prediction of boundary-layer flows near walls, and four cases of self-similar flow are predicted with the model and found to compare favorably with the relevant experimental data.
Abstract: A turbulence model is proposed for the prediction of boundary‐layer flows near walls. Two differential equations are solved: one for the kinetic energy of turbulence, and one for its length scale. The local effective viscosity in the flow is taken as proportional to the product of the length and the square root of the energy. The constants appearing in the equations are determined by reference to experimental data. Four cases of self‐similar flow are predicted with the model and found to compare favorably with the relevant experimental data. Satisfactory predictions for more general flows are also reported.
115 citations
83 citations
TL;DR: In the absence of large linear-momentum wakes the energy of turbulence relaxes very quickly into a stable self-preserving structure, which decays at different constant inverse powers of time as mentioned in this paper.
Abstract: Experimental study of weak isotropic turbulence, created by a mechanically agitated grid, has indicated that in the absence of large linear‐momentum wakes the energy of turbulence relaxes very quickly into a stable self‐preserving structure, which, depending on the initial Reynolds number of turbulence, decays at different constant inverse powers of time. Both the longitudinal correlation coefficients and the corresponding spectral distributions, except for the difference in the parametric constants, are of the same functional type as those found previously for a passive grid.
80 citations
TL;DR: In this paper, the test field model for isotropic turbulence is restated in a form which is independent of the choice of orthogonal basis functions for representing the velocity field, which greatly simplifies computations when the co-variance matrix and related statistical matrices are non-diagonal.
Abstract: The test-field model for isotropic turbulence is restated in a form which is independent of the choice of orthogonal basis functions for representing the velocity field. The model is then extended to non-stationary inhomogeneous turbulence with a mean shearing velocity, contained by boundaries of arbitrary shape. A modification of the model is introduced which makes negligible changes in the numerical predictions but which greatly simplifies computations when the co-variance matrix and related statistical matrices are non-diagonal. The altered model may be regarded as a kind of generalization of Orszag's eddy-damped Markovian model, with the damping factors determined systematically, in representation-independent form, from dynamical equations. The final equations of the test-field model are presented in a sufficiently explicit form to serve as a starting point for numerical work. To facilitate comparison, the corresponding direct-interaction equations for inhomogeneous turbulence with mean shear are presented also, in a uniform notation. The test-field model is much faster to compute than the direct-interaction approximation because, in the former, only single-time statistical functions need be computed. This advantage is at the cost of a less rich and less faithful representation of the dynamics.
01 Sep 1972
TL;DR: In this paper, the effects of various passive devices (screens, perforated plates, porous foam, and honeycomb-like matrices formed with closely packed plastic drinking straws) on free-stream turbulence and mean velocity profiles are studied in air with hot-wire anemonetry and in water using hydrogen-bubbles visualization.
Abstract: : The effects of various passive devices (screens, perforated plates, porous foam, and honeycomb-like matrices formed with closely packed plastic drinking straws) on free-stream turbulence and mean velocity profiles are studied in air with hot-wire anemonetry and in water using hydrogen-bubbles visualization. These 'turbulence manipulators' are viewed as operators which suppress the level of the incoming turbulence and generate, primarily through documented instabilities, new turbulences with scales characteristic of the device and its shear layers. In this sense these manipulators can be used to control, manage and/or modify the incoming turbulence flow to yield the one appropriate to the application.
TL;DR: In this paper, the velocity field of the Burgers one-dimensional model of turbulence at extremely large Reynolds numbers is expressed as a train of random triangular shock waves, and the distributions of the intensity and the interval of the shock fronts are defined.
Abstract: The velocity field of the Burgers one-dimensional model of turbulence at extremely large Reynolds numbers is expressed as a train of random triangular shock waves. For describing this field statistically the distributions of the intensity and the interval of the shock fronts are defined. The equations governing the distributions are derived taking into account the laws of motion of the shock fronts, and the self-preserving solutions are obtained. The number of shock fronts is found to decrease with time t as t−α, where α (0 [les ] α < 1) is the rate of collision, and consequently the mean interval increases as tα. The distribution of the intensity is shown to be the exponential distribution. The distribution of the interval varies with α, but it is proved that the maximum entropy is attained by the exponential distribution which corresponds to α = ½. For α = ½, the turbulent energy is shown to decay with time as t−1, in good agreement with the numerical result of Crow & Canavan (1970).
TL;DR: In this paper, it is demonstrated by numerical simulation that the addition of a linear drag term on the forced viscous vorticity equation allows the development of statistically steady-state two-dimensional turbulence, which then can be considered an analog of the large scale atmosphere.
Abstract: It is demonstrated by numerical simulation that the addition of a linear drag term on the forced viscous vorticity equation allows the development of statistically steady-state two-dimensional turbulence, which then can be considered an analog of the large scale atmosphere. Two different types and two scales of forcing are applied, and the results are interpreted in terms of a Kovasznay-type closure theory. The energy spectrum is similar to that predicted by Kraichnan for forced two-dimensional turbulence but the drag term produces some significant modifications. Certain results are extrapolated to make predictions of the energy distribution in the large scale atmosphere. The predicted scale of maximum atmospheric energy is not easily tested, but seems somewhat too small. The relationships between two-dimensional turbulence and Charney's model of geostrophic turbulence are discussed.
TL;DR: The importance of fluctuating turbulent Reynolds stresses in the flow over a wave is examined in this article, where it is shown that anisotropic stresses are essential to the process of energy flow to the wave.
Abstract: The importance of fluctuating turbulent stresses in the flow over a wave is examined. It is shown that anisotropic stresses, which are most likely to be turbulent Reynolds stresses, are essential to the process of energy flow to the wave. Two fundamentally different methods of predicting fluctuating turbulent Reynolds stresses are examined. One method makes use of a phenomenological closure of the conservation equation for the turbulent Reynolds stresses and is similar to the turbulent boundary-layer calculation scheme of Bradshaw, Ferriss & Atwell (1967). The second method is based on the assumption that the turbulent stresses are determined by the recent history of velocity shear experienced by a fluid parcel and results in a viscoelastic constitutive relation for the turbulence; in the limit of shortest’ memory’ this relation becomes the eddy viscosity model proposed by Hussain & Reynolds (1970). Comparison of predicted and measured values of surface pressure indicates that the eddy viscoelasticity model can explain measured pressure distributions but the comparison is not conclusive. Suggestions for further measurements are made.
TL;DR: In this article, the effect of turbulence on the structure of weak shock waves is investigated and the equilibrium structure is shown to be governed by a balance between nonlinear steepening and the turbulent scattering of acoustic energy out of the main wave direction.
Abstract: The effect of turbulence on the structure of weak shock waves is investigated. The equilibrium structure is shown to be governed by a balance between nonlinear steepening and the turbulent scattering of acoustic energy out of the main wave direction. The scattered energy appears as perturbations behind the shock front. For conditions typical of sonic booms in atmospheric turbulence the wave structure is governed by a Burgers equation similar to that describing viscous shocks, except that parameters related to the turbulence appear instead of the viscosity coefficient. The magnitude of the perturbations following a shock is estimated from first-order scattering applied to a thickened shock. Predictions of shock thicknesses and perturbations compare favourably with available experimental data.
TL;DR: In this paper, a general expression for the diffusion coefficient D(V) was derived for the particle propagator for a broad-band spectrum, allowing statistical spreading of trajectories in both position and velocity.
Abstract: To obtain convergent series in plasma turbulence theory, it is necessary to include the effects of the turbulent fields in the particle propagator. The assumptions and different approaches of previous workers, notably Dupree, Rudakov and Tsytovich, and Weinstock, are clarified. Their results may be obtained by a simple assumption: that particles in phase space diffuse in a Markovian way under the action of the stochastic turbulent fields. From statistical arguments similar to those of Weinstock, a quite general expression for the diffusion coefficient D(V) emerges. This result holds without assuming weak turbulence if the wave spectrum is sufficiently broad. From the Markovian view above there follows immediately, without involved calculation, the familar expression for D(V) found by Dupree. Using probabilistic arguments, the particle propagator for a broad‐band spectrum is calculated, allowing statistical spreading of trajectories in both position and velocity. This is identical to the usual method of obtaining a Green's function from a differential equation, but simpler. This new approach is valid whenever the turbulence is sufficiently broad‐banded.
TL;DR: In this article, a laser velocimeter capable of measuring these turbulence parameters has been utilized and described in detail, showing that the turbulent shearing stress is reduced in the turbulent core by an amount proportional to the observed decrease in pressure gradient at the wall, and that the wall value in agreement with calculated local wall shear.
Abstract: Measurements of Reynolds stress and axial and transverse
turbulence intensities have been made in drag-reducing
turbulent pipe flow of a dilute solution of high molecular
weight polymer and compared to measurements made with pure
water. A newly developed laser velocimeter capable of
measuring these turbulence parameters has been utilized and
is described in detail.
Axial turbulence intensities measured in polymer solution
are consistent with previous polymer results and
viscous sublayer thickening is observed. New results include
demonstration that the turbulent shearing stress is
reduced in the turbulent core by an amount proportional to
the observed decrease in pressure gradient at the wall, and
extrapolates to a wall value in agreement with calculated
local wall shear. Near the wall polymer solution Reynolds
stress is reduced below that measured for water consistent
with observed velocity profiles. Polymer radial turbulence
intensities are comparable with those for water in the
turbulent core, but exhibit similar dramatic suppression
near the wall. These and other recent results strongly
suggest that dilute polymer solution drag reduction is
primarily a wall phenomenon. Polymers appear to have little
or no effect on turbulent flow away from a solid boundary
where turbulent velocities scale with u_τ, the shear
velocity based on the observed wall shear.
TL;DR: In this paper, the equations governing two-dimensional turbulence are written as an infinite system of ordinary differential equations, in which the dependent variables are the coefficients in the expansion of the vorticity field in a double Fourier series.
Abstract: The equations governing two-dimensional turbulence are written as an infinite system of ordinary differential equations, in which the dependent variables are the coefficients in the expansion of the vorticity field in a double Fourier series. The variables are sorted into sets which correspond to consecutive bands in the wavenumber spectrum; within each set it is supposed that the separate variables will exhibit statistically similar behaviour. A low order model is then constructed by retaining only a few variables within each set. Multiplicative factors are introduced into the equations to compensate for the reduced number of terms in the summations. Like the original equations, the low order equations conserve kinetic energy and enstrophy, apart from the effects of external forcing and viscous dissipation. A special case is presented in which the bands are half octaves and there is effectively only one dependent variable per set. Solutions of these equations are compared with conventional numerical simulations of turbulence, and agree reasonably well, although the nonlinear effects are somewhat underestimated.
TL;DR: In this paper, the effects of free-stream turbulence on the drag coefficient of a circular cylinder were investigated experimentally in an air duct and the experiments were performed over a range of Reynolds number, based on mean velocity and cylinder diameter.
Abstract: The effects of free-stream turbulence on the drag coefficient of a circular cylinder were investigated experimentally in an air duct. The experiments were performed over a range of Reynolds number, based on mean velocity and cylinder diameter, from 1,350 < Re < 8,000. A constant temperature hot-film anemometer was used to determine the turbulence intensity which was between 1.2% < u′ < 21%. The range of the dimensionless turbulence scale was from 0.5 < ∂/D < 3.3, in which ∂ = the turbulence scale defined through the integral of auto-correlation function and D = the diameter of the cylinder. Two smooth circular cylinders were used. They were 1/4 in. and 1/2 in. 6.35 mm and 12.7 mm shell fraction. Quantitative results were obtained. Equations describing the relationship between the drag coefficient and turbulence characteristics were also obtained.
TL;DR: It is shown that equivalent models of turbulence may give rise to substantially different structure functions of a wave parameter, although such models turn out not to be equivalent.
Abstract: The concept of equivalent models of turbulence is introduced in order to investigate how the theoretical behavior of the structure function of an electromagnetic wave propagating in a given turbulent medium depends on the turbulence model. It is shown that equivalent models may give rise to substantially different structure functions of a wave parameter. On the other hand, the experimental structure function of the phase of a plane wave can be well fitted by the theoretical curves derived from different models, with suitable choices of the turbulence parameters appearing in the models. However, such models turn out not to be equivalent. When experimental data on the turbulence are not available, simultaneous measurements of the structure functions of more than one wave parameter are suggested, for the choice of the model.
TL;DR: One of the possible models of statistical description of momentum and scalar property (temperature, conservative mass concentration) transfer in a non-homogeneous turbulent incompressible flow is considered in this paper.
TL;DR: In this paper, the importance of turbulence intensity in energy and mass transfer between plant surfaces and the air within crops is demonstrated, and the role of within-crop eddies in energy transfer is discussed.
TL;DR: In this article, the effect of mainstream turbulence on heat transfer from a cylinder was investigated and the results showed that in the Reynolds number range 5000-35 000 increases in freestream turbulence intensity of 10 per cent result in improvements of heat transfer at the rear of the cylinder of up to 100 per cent.
TL;DR: In this article, the authors measured the structure of wind at a site in Melbourne, Australia using an 18.5 m tower and found that the turbulence is predominantly of mechanical origin, and thus dependent on terrain roughness.
Abstract: The increasing requirement for data about turbulence in a city environment, particularly in relation to building design and the imminent operation of aircraft from this environment, has prompted the measurement of the structure of wind at a site in Melbourne, Australia. Fast response propellor-type anemometers located at three heights on an 18.5 m tower were used. Data on the frequency distribution of gusts, the intensity of turbulence, the surface drag coefficient, and the spectra of turbulence are presented. It is concluded that the turbulence is predominantly of mechanical origin, and thus dependent on terrain roughness. The spectra are found to be best described in wavenumber space and scaled by variance.
01 Jan 1972
01 Jun 1972
TL;DR: In this article, an invariant model designed expressly for the computation of shear flows is discussed. But the complexity of the analysis is restrained by limiting the consideration to a flat plate boundary layer where the mean pressure can be taken to be constant.
Abstract: The development of an invariant model designed expressly for the computation of shear flows is discussed. The model for incompressible layers seeks a second-order closure of the equations for the mean and fluctuating fields. The development of a method for computing the behavior of shear layers in compressible forces is described. The complexity of the analysis is restrained by limiting the consideration to a flat plate boundary layer where the mean pressure can be taken to be constant.