Showing papers on "K-epsilon turbulence model published in 1979"
TL;DR: In this article, periodic homogeneous isotropic turbulence is used to simulate the experimental decay of grid turbulence and the computed flow field is then treated as a realization of a physical turbulent flow.
Abstract: A calculation of periodic homogeneous isotropic turbulence is used to simulate the experimental decay of grid turbulence. The calculation is found to match the experiment in a number of important aspects and the computed flow field is then treated as a realization of a physical turbulent flow. From this flow, a calculation is conducted of the large eddy field and the various averages of the subgrid-scale turbulence that occur in the large eddy simulation equations. These quantities are compared with the predictions of the models that are usually applied in large eddy simulation. The results show that the terms which involve the large-scale field are accurately modeled but the subgrid-scale Reynolds stresses are only moderately well modeled. It is also possible to use the method to predict the constants of the models without reference to experiment. Attempts to find improved models have not met with success.
833 citations
TL;DR: The turbulence structure observed in seven early evening runs of the 1973 Minnesota experiments is presented and discussed in this article, where Spectral shapes and the vertical profiles of turbulence variances and covariances, dissipation rates for turbulent kinetic energy and temperature variance, and energy-containing range length scales are analyzed.
Abstract: The turbulence structure observed in seven early evening runs of the 1973 Minnesota experiments is presented and discussed. Wind and temperature sensors mounted on a 32 m tower and on the tethering cable of a large balloon spanned the entire depth of the rapidly evolving nocturnal boundary layer. Spectral shapes and the vertical profiles of turbulence variances and covariances, dissipation rates for turbulent kinetic energy and temperature variance, and energy-containing range length scales show remarkable order when plotted in dimensionless coordinates, even though properties varied widely among the runs. Observed dissipation rates and boundary layer depth agree well with predictions of the Brost-Wyngaard (1978) model. It is shown that the slight (0.0014) terrain slope and possibly baroclinity affected the boundary-layer evolution, and that although the turbulence structure was probably in equilibrium with the wind and temperature fields, these were strongly evolving during the runs.
327 citations
TL;DR: In this article, the mechanisms of the relaminarization of turbulent flows are investigated with a view to establishing any general principles that might govern them, and three basic archetypes of reverting flows are considered: the dissipative type, the absorptive type, and the Richardson type exemplified by a turbulent boundary layer subjected to severe acceleration.
Abstract: The mechanisms of the relaminarization of turbulent flows are investigated with a view to establishing any general principles that might govern them. Three basic archetypes of reverting flows are considered: the dissipative type, the absorptive type, and the Richardson type exemplified by a turbulent boundary layer subjected to severe acceleration. A number of other different reverting flows are then considered in the light of the analysis of these archetypes, including radial Poiseuille flow, convex boundary layers, flows reverting by rotation, injection, and suction, as well as heated horizontal and vertical gas flows. Magnetohydrodynamic duct flows are also examined. Applications of flow reversion for turbulence control are discussed.
274 citations
TL;DR: In this article, the effect of filter shape, grid-scale spectrum and gridscale anisotropy on the effective eddy viscosity was investigated and the validity of using these viscosities in an open calculation was considered.
Abstract: The problem of subgrid modelling, that is, of representing energy transfers from large to small eddies in terms of the large eddies only, must arise in any large eddy simulation, whether the equations of motion are open or direct (unaveraged) or closed (averaged). Models for closed calculations are derived from classical closures, and these are used to determine the effect of filter shape, grid-scale spectrum and grid-scale anisotropy on the effective eddy viscosity: the Leonard or resolvable-scale stress is calculated separately and is found to account for 14% of the total drain in a typical high Reynolds number case.The validity of using these eddy viscosities in an open calculation is considered. It is concluded that this is not unreasonable, but that the simulation would be much improved if the gross drain could be separated into net drain and backscatter.
256 citations
240 citations
TL;DR: In this paper, a general theory for the fluctuation spectrum of the onset of turbulence is developed, applying to systems that approach turbulence through a cascade of subharmonic bifurcations applied to Rayleigh-Benard flow.
215 citations
TL;DR: In this article, the authors proposed the optimum theory for the understanding of turbulent flows without the introduction of heuristic assumptions that are commonly used in other theories of turbulence, which is an alternative approach in which the lack of information about properties of the fluctuating velocity field is reflected by the theoretical results.
Abstract: Publisher Summary This chapter discusses that the optimum theory represents an approach toward the understanding of turbulent flows without the introduction of heuristic assumptions that are commonly used in other theories of turbulence. As there does not seem to be a generally accepted definition of turbulence, this chapter shall regard, for the present purpose, a fluid flow as turbulent if the details of the velocity field are too complex to be of interest and only the information about certain average properties is needed. The chapter highlights that the optimum theory is hardly appropriate for all turbulent systems of this general nature and a more suitable mathematical definition of turbulence will be required later. The main point is that turbulent fluid systems are characterized by an information gap that is neither possible nor desirable to fill. The optimum theory represents an alternative approach in which the lack of information about properties of the fluctuating velocity field is reflected by the theoretical results. Instead of a theoretical prediction of the physically realized average properties, bounds on those properties are obtained. The idea of the optimum theory is to consider not the manifold of solutions of the basic equations for a particular problem, but a larger manifold of vector fields, which includes the actual solutions. This manifold of fields shares with the solutions kinematic relationships such as boundary conditions and the energy balance.
140 citations
130 citations
TL;DR: In this paper, a model of the two-phase turbulent jet is presented and a set of model differential equations is developed for cases in which the mean velocities of the phases are sensibly equal.
123 citations
TL;DR: In this article, a statistical model of turbulence in fully developed two-dimensional incompressible turbulent mixing layers is proposed, which is based on the proposition that the turbulence of a fully developed 2D mixing layer is in a state of quasi-equilibrium and used to predict the second-order turbulence statistics of the flow including single-point turbulent Reynolds stress distribution, intensity of turbulent velocity components, rms turbulent pressure fluctuations, power spectra and two-point space-time correlation functions.
Abstract: A statistical model of turbulence in fully developed two-dimensional incompressible turbulent mixing layers is proposed. The development of this model is largely motivated by the recent experimental observations of Brown and Roshko (1974). The model is based on the proposition that the turbulence of a fully developed two-dimensional incompressible mixing layer is in a state of quasi-equilibrium. The model is used to predict the second-order turbulence statistics of the flow including single-point turbulent Reynolds stress distribution, intensity of turbulent velocity components, rms turbulent pressure fluctuations, power spectra and two-point space-time correlation functions. It is shown that numerical results compare favorably with available experimental measurements.
117 citations
TL;DR: Several multiequation eddy viscosity models of turbulence are used with the Navier-Stokes equations to compute three classes of experimentally documented shock-separated turbulent boundary-layer flows as mentioned in this paper.
Abstract: Several multiequation eddy viscosity models of turbulence are used with the Navier-Stokes equations to compute three classes of experimentally documented shock-separated turbulent boundary-layer flows. The types of flow studied are: (1) a normal shock at transonic speeds in both a circular duct and a two-dimensional channel; (2) an incident oblique shock at supersonic speeds on a flat surface; and (3) a two-dimensional compression corner at supersonic speeds. Established zero-equation (algebraic), one-equation (kinetic energy), and two-equation (kinetic energy plus length scale) turbulence models are each utilized to describe the Reynolds shear stress for the three classes of flows. These models are assessed by comparing the calculated values of skin friction, wall pressure distribution, velocity, Mach number, and turbulent kinetic energy profiles with experimental measurements. Of the models tested the two-equation model results gave the best overall agreement with the data.
TL;DR: In this article, the effect of thermal fluctuations on a turbulent flow is estimated, and it is argued that these fluctuations are important in selecting the stationary measure on phase space which describes turbulence.
01 Jan 1979
TL;DR: In this article, Fourier transforms were used for evaluating spatial derivatives to improve the accuracy of the large eddy simulation of homogeneous isotropic turbulence; in particular, the treatment of certain terms that arise in filtering the equations is considerably improved in both speed and accuracy.
Abstract: By using Fourier transforms for evaluating spatial derivatives, we are able to improve the accuracy of the large eddy simulation of homogeneous isotropic turbulence; in particular, the treatment of certain terms that arise in filtering the equations is considerably improved in both speed and accuracy. Use of vorticity as the principal variable is shown to be a viable and potentially useful alternative to the primitive variables. A method of deriving conservation properties of numerical schemes is given which is much simpler than previous methods and is widely applicable. The methods are applied to the computation of homogeneous isotropic turbulence, and it is found that the subgrid scale model is improved by using finite differences in place of “exact” derivatives.
TL;DR: In this article, a special measuring system has been developed with which investigation of undisturbed suspension pipe flow is possible, even close to the wall, based on laser-Doppler anemometry.
01 Jan 1979
TL;DR: In this article, numerical predictions for seven different two-dimensional turbulent "elliptic" flows are presented for TEACH, which is embodied in the TEACH computer program and numerical tests reported.
Abstract: Numerical predictions are presented for seven different two-dimensional turbulent “elliptic” flows. The solution procedure, which is embodied in the TEACH computer program, is described and numerical tests reported. The calculated properties of the seven flows are compared with experimental results and demonstrate that the procedure, with a two-equation turbulence model, provides adequate precision for many engineering applications. The two-equation model is shown, however, to be deficient in detail.
TL;DR: In this paper, the intensity covariance resulting from the assumed source propagating through atmospheric turbulence is calculated using a formalism developed previously, and the resultant eightfold intergral is evaluated in closed form retaining all phase, log-amplitude, and cross-phaselog-AMplitude structure functions by employing the quadratic approximation for the complex phase.
Abstract: A source having a deterministic beam-wave amplitude distribution with a spatially random phase variation is assumed. The source distibution simulates laser reflectance from (or transmission through) a rough surface with arbitrary height deviation and a correlation yielding a Gaussian intensity covariance. The intensity covariance resulting from the assumed source propagating through atmospheric turbulence is calculated using a formalism developed previously. The resultant eight-fold intergral is evaluated in closed form retaining all phase, log-amplitude, and cross phaselog-amplitude structure functions by employing the quadratic approximation for the complex phase. Limiting case conditions of (i) a field from a partially coherent source propagating in vacuo (speckle) and (ii) a coherent beam-wave propagating through turbulence are examined. Speckle contrast calculations replicate published data using less restrictive assumptions than formerly employed, while turbulent atmosphere beam-wave calculations appear more physically reasonable than results of Ishimaru. General-case calculations show that the normalized intensity variance (contrast or fluctuation parameter) increases less rapidly with increasing turbulence as the phase variance of the source increases. A saturation phenomenon is observed at high turbulence levels as the coherence decreases. The inability to sustain high spatial frequency speckle in turbulence is reflected in the calculated intensity covariance function.
TL;DR: In this article, the invariance of second moment turbulent closure under a change of frame is examined and it is shown that the Reynolds stresses and the higher turbulence correlations based on an ensemble mean are frame-indifferent while the Reynolds stress transport equations are frame dependent.
Abstract: The invariance of second moment turbulent closure under a change of frame is examined. It is shown that the Reynolds stresses and the higher turbulence correlations based on an ensemble mean are frame‐indifferent while the Reynolds stress transport equations are frame dependent. As a result of this incompatibility, second moment closure cannot form a general foundation for the study of turbulence. Alternative approaches that are properly invariant are discussed.
TL;DR: In this article, a simplified second-moment turbulence closure model was used to simulate BOMEX (Barbados Oceanographic and Meteorological Experiment) data, and partial differential equations for the turbulence energy and a master length scale were solved.
Abstract: A one-dimensional version of a simplified second-moment turbulence closure model, coupled with a recently developed cloud model, is used to simulate BOMEX (Barbados Oceanographic and Meteorological Experiment) data. Partial differential equations for the turbulence energy and a master length scale are solved. Simulated mixing ratios of water vapour, virtual temperatures and horizontal wind speeds are compared with observations. Horizontal wind speeds agree quite well; however, simulated temperature and mixing ratio of water vapour at the end of the fourth day are about 2K and 1.5 g kg−1 higher, respectively, than corresponding observations; possibly this is due to the fact that the surface temperature used in the simulation is too high. Mean liquid water, cloud volume, liquid water variance, turbulence energy and eddy viscosity coefficients are presented, but data for these variables are not available for comparison. Surface momentum, heat and moisture fluxes are also presented and are compared with data. Sensitivity studies indicate that the simulated mixing ratios of water vapour agree best with observations when both vertical wind and horizontal advection obtained from the data are included.
The present study is encouraging, although further research is required to improve the model and to develop confidence in its predictive capability.
TL;DR: In this article, a finite-difference procedure is employed to predict the turbulent flow and heat transfer in horizontal, inclined and vertical pipes when influenced by buoyancy, where the flow is treated as parabolic; and the turbulence model used involves the solution of two differential equations, one for the kinetic energy of turbulence and the other for its dissipation rate.
Abstract: A finite-difference procedure, is employed to predict the turbulent flow and heat transfer in horizontal, inclined and vertical pipes when influenced by buoyancy. The flow is treated as parabolic; and the turbulence model used involves the solution of two differential equations, one for the kinetic energy of turbulence and the other for its dissipation rate. Results are presented for the velocity and temperature fields, and the associated flow-resistance and heat-transfer coefficients. The predictions for horizontal and vertical pipes have been compared with the available experimental results, and the agreement obtained is good.
TL;DR: In this paper, the effect of large but finite values of the two dominant characteristic numbers, a turbulence Reynolds number providing a measure of the intensity of the turbulence and a Damkohler number relating a turbulence time to a chemical time, was investigated for planar, oblique, and normal flames.
TL;DR: In this paper, spatial correlation functions of phaseexpansion coefficients are derived for phase fluctuations of a wave that has propagated through a layer of atmospheric turbulence, and some of the correlations are integrated over the Hufnagel 1974 structure constant model to obtain results applicable to ground-to-space propagation.
Abstract: Spatial correlation functions of phase-expansion coefficients are derived for phase fluctuations of a wave that has propagated through a layer of atmospheric turbulence. First, a general expression is derived giving the correlation of the coefficients of phase-expansion functions orthogonal over an arbitrary circularly symmetric weighting function for an isotropic turbulence spectrum. Second, the correlations are evaluated analytically for a Gaussian weight and numerically for a uniform circular weight. Finally, some of the correlations for a layer are integrated over the Hufnagel 1974 structure constant model to obtain results applicable to ground-to-space propagation.
TL;DR: In this article, the authors analyzed the turbulence generated by random entropy fluctuations in an accelerating stream and showed that the energy of the entropy-generated turbulence increases more rapidly with the contraction ratio of a subsonic flow than that of any imposed upstream turbulence.
Abstract: The turbulence generated by random entropy fluctuations in an accelerating stream is analyzed. The results are obtained by using rapid distortion theory together with a high frequency solution of a previously developed wave equation that governs the small-amplitude unsteady vortical and entropic motion on steady potential flows (Goldstein, 1978). Simple results are obtained for the case of symmetric contraction, expansion or combination of the two. It is shown that the energy of the entropy-generated turbulence increases more rapidly with the contraction ratio of a subsonic flow than that of any imposed upstream turbulence. This result indicates that the entropy-generated turbulence may be more significant than the hydrodynamically generated turbulence in the turbine stages of aircraft engines.
TL;DR: In this article, an extension of the k-means model to rotating flows is derived and tested, and a suitably chosen constant eddy viscosity is adequate for predicting the velocity and shear stress distributions in the Ekman layer.
Abstract: A mathematical model is employed for analysing the structure of the homogeneous ocean surface layer. The model is verified against laboratory measurements of the fully developed channel flow and the wind-induced channel flow. Turbulence models of different complexities are used and discussed. An extension of the k — e turbulence model to rotating flows is derived and tested. The study indicates that a suitably chosen constant eddy viscosity is adequate for predicting the velocity and shear stress distributions in the Ekman layer. For transport of different chemical and biological species it is, however, necessary to know the detailed transport properties of the layer. Non-dimensional vertical distributions of different turbulence quantities, characterizing the Ekman layer, are therefore predicted and analysed. Rotational effects in the turbulence model are found to somewhat change the shear stress distribution in the deeper parts of the boundary layer. DOI: 10.1111/j.2153-3490.1979.tb00913.x
TL;DR: In this article, the authors present a second-moment approximation to turbulent convection in which the turbulent heat fluxes themselves form the subject of a set of transport equations Closure at this level avoids the need to prescribe the turbulent Prandtl number which is the principal empirical uncertainty in simpler treatments.
TL;DR: In this paper, a grid-generated turbulence is subjected to a pure plane strain and the principal axes of the Reynolds stress tensor become those of the strain, which is associated with a forced decay of the anisotropy of the motion.
Abstract: A grid-generated turbulence is subjected to a pure plane strain and the principal axes of the Reynolds stress tensor become those of the strain. This ‘oriented’ homogeneous turbulence is then submitted to a new strain the principal axes of which have a different orientation. We show that in such a situation it is possible to observe a transfer of energy from the fluctuating motion to the mean one. Such transfer is necessarily associated with a forced decay of the anisotropy of the motion. A detailed analysis of the reorientation of the principal axes of the Reynolds stress tensor in the frame of those of the second strain gives an explanation of the evolution of the principal axes of the Reynolds stress tensor in a shear flow.
TL;DR: In this paper, a double backward facing step was investigated in a closed loop flow system with a Reynolds number of 30,210 and significant changes of flow patterns, increases in turbulence kinetic energy, velocity fluctuations, and shear stresses were observed downstream of the step expansion.
Abstract: Turbulent flow with separation and recirculation over a double backward facing step has been investigated experimentally. Time mean streamwise, transverse and cross-stream components of the velocity fluctuations, together with turbulence kinetic energy and Reynolds shear stresses, were measured using a laser Doppler anemometer, operating in the differential Doppler mode with forward scattering. Ordinary tap water was used in a closed loop flow system with a Reynolds number of 30,210 and significant changes of flow patterns, increases in turbulence kinetic energy, velocity fluctuations, and shear stresses were observed downstream of the step expansion.
TL;DR: In this paper, the authors apply the test field model developed by Kraichnan to the study of an isotropic, passive scalar contaminant convected by decaying isotropics turbulence.
Abstract: This paper applies the test field model developed by Kraichnan to the study of an isotropic, passive scalar contaminant convected by decaying isotropic turbulence. Test field model predictions of scalar and velocity dissipation spectra at large Reynolds and Peclet numbers are shown to be in excellent agreement with atmospheric data, after intrinsic scale constants in the model are adjusted to give valid inertial range coefficients. Theoretical values for the inertial range coefficients are obtained for large and small Prandtl numbers. Simulation results for velocity and scalar energy, dissipation and transfer spectra and second- and third-order velocity, scalar and velocity–scalar correlations at moderate Reynolds and Peclet numbers are shown to agree moderately well with heated grid turbulence data. Simulation results are presented for the normalized decay rates of the scalar and velocity dissipation rates and for the ratio of the velocity to scalar decay time scales; these quantities are employed in second-order modelling. In the self-similar decay mode the simulations yield unity levels of the normalized decay rates and of the ratio of decay time scales over the moderate range of Reynolds and Prandtl numbers investigated. These results are compared with data from heated grid turbulence experiments and are discussed in the light of asymptotic decay of concomitant scalar and velocity fields.