Showing papers on "K-epsilon turbulence model published in 1987"

Turbulence statistics in fully developed channel flow at low reynolds number

Abstract: A direct numerical simulation of a turbulent channel flow is performed. The unsteady Navier-Stokes equations are solved numerically at a Reynolds number of 3300, based on the mean centerline velocity and channel half-width, with about 4 million grid points. All essential turbulence scales are resolved on the computational grid and no subgrid model is used. A large number of turbulence statistics are computed and compared with the existing experimental data at comparable Reynolds numbers. Agreements as well as discrepancies are discussed in detail. Particular attention is given to the behavior of turbulence correlations near the wall. A number of statistical correlations which are complementary to the existing experimental data are reported for the first time.

On nonlinear K-l and K-ε models of turbulence

Abstract: The commonly used linear K-l and K-e models of turbulence are shown to be incapable of accurately predicting turbulent flows where the normal Reynolds stresses play an important role. By means of an asymptotic expansion, nonlinear K-l and K-e models are obtained which, unlike all such previous nonlinear models, satisfy both realizability and the necessary invariance requirements. Calculations are presented which demonstrate that this nonlinear model is able to predict the normal Reynolds stresses in turbulent channel flow much more accurately than the linear model. Furthermore, the nonlinear model is shown to be capable of predicting turbulent secondary flows in non-circular ducts - a phenomenon which the linear models are fundamentally unable to describe. An additional application of this model to the improved prediction of separated flows is discussed briefly along with other possible avenues of future research.

Examples of calculation methods for flow and mixing in stratified fluids

Abstract: Certain mathematical models for predicting the flow and mixing processes in stratified fluids are reviewed, with particular focus on stratified lakes and reservoirs. The various types of prediction methods are introduced briefly, from one-dimensional integral methods to direct simulations of the Navier-Stokes equations. The paper concentrates on turbulence models for simulating the turbulent momentum, heat, and mass transport terms appearing in the statistical methods employing averaged equations. Models ranging from the simple Prandtl mixing length theory to second-order-closure schemes are discussed. To illustrate the predictive capabilities of the methods, examples are presented of applications of the method covered to a variety of stratified flow situations.

Turbulence in stratified fluids: A review

Abstract: Buoyancy length scale and internal disturbance Froude number criteria for turbulence collapse in stratified fluid are examined in the light of recent laboratory experiments, oceanographie observations, and numerical simulations. From these it emerges that the onset of collapse occurs when the turbulence integral length scale is of the order of the buoyancy length scale, giving a disturbance Froude number close to 1. Complete collapse of three-dimensional turbulence, characterized by nearly zero vertical mass flux, occurs at a lower value of the disturbance Froude number. In particular, a spatially inhomogeneous turbulence undergoes a drastic change in structure at a value of the disturbance Froude number of 0.2–0.3. In the collapsed state, internal wave motion and quasi two-dimensional turbulence coexist on different time scales, results supported also by the rotating turbulence analogy. Vertical diffusion coefficients and mixing efficiency, which are of direct practical importance, are also examined.

Fundamentals of Turbulence for Turbulence Modeling and Simulation

Abstract: : Topics include: Fundamentals of fluid motion -- Kinematics of motion, Constitutive equations, and Vorticity dynamics; Turbulence equations; Statistical descriptions of homogeneous turbulence; Rapid distortion of homogeneous turbulence; Modeling scale evolution in homogeneous turbulence; Modeling anisotropy in homogeneous turbulence; and Numerical simulations of turbulence.

Log-normal Rician probability-density function of optical scintillations in the turbulent atmosphere

Abstract: The log-normal Rician probability-density function is based on the following paradigm for the optical field after propagation through atmospheric turbulence: a field with reduced coherence that obeys Rice–Nakagami statistics is modulated by a multiplicative factor that obeys log-normal statistics. The larger eddies in the turbulent medium produce the log-normal statistics, and the smaller ones produce the Gaussian statistics. On the basis of this model all the parameters required by the density function can be calculated by using physical parameters such as turbulence strength, inner scale, and propagation configuration. The heuristic density function is consistent with available data at low and at high turbulence levels.

Turbulent channel and Couette flows using an anisotropic k-epsilon model

Abstract: Turbulent channel and Couette flows are studied numerically by using an anisotropic A>e model. A feature of this model lies in an anisotropic expression for the Reynolds stress and the deviation of the Reynolds stress from an isotropic eddy-viscosity representation is incorporated. Only one kind of wall damping function is introduced to impose the no-slip boundary condition on solid walls. The results obtained show that turbulence quantities of channel and Couette flows are in good agreement with experimental data and numerical results from large-eddy simulation. The anisotropy of turbulent intensities, which the usual A:-e model cannot predict, is well reproduced.

Computation of turbulent flows using an extended k-epsilon turbulence closure model

Abstract: An extended kappa-epsilon turbulence model is proposed and tested with successful results. An improved transport equation for the rate of dissipation of the turbulent kinetic energy, epsilon, is proposed. The proposed model gives more effective response to the energy production rate than does the standard kappa-epsilon turbulence model. An extra time scale of the production range is included in the dissipation rate equation. This enables the present model to perform equally well for several turbulent flows with different characteristics, e.g., plane and axisymmetric jets, turbulent boundary layer flow, turbulent flow over a backward-facing step, and a confined turbulent swirling flow. A second-order accurate finite difference boundary layer code and a nearly second-order accurate finite difference elliptic flow solver are used for the present numerical computations.

Interaction of radiation with turbulence - application to a combustion system

Abstract: Turbulence/radiation interaction is examined in order to provide better fundamental understanding of temporal aspects of radiative transfer in combustion systems. Two aspects of radiative transfer in a turbulent medium are considered in this paper. In the first, transfer of radiation along a path with turbulent concentration and temperature fluctuations is calculated for the time-mean irradiance at a combustion chamber wall due to random concentration of absorbing species and emission with Gaussian probability density functions. In the second, turbulence/radiation interaction and the effect of radiation transfer on the fully coupled structure and mean properties are assessed for an industrial natural gas-fired furnace. The results of calculations based on the approximate formulation utilized here show that the effects of turbulence/radiation interaction on combustion and flow properties is relatively small for a preheated methane-air mixture. The interaction is greater when the oxidant is cold and the flame is relatively long. 24 references.

Turbulence Modeling for Gust Loading

Abstract: This paper presents the analytical models most in use at present for the description of the structure of turbulence in the surface atmospheric boundary layer. The study gives maximum prominence to the degree of uncertainty involved in these models, showing that a detailed forecast of the configuration of turbulence is very often fallacious. In the light of this consideration, two straightforward expressions of the power spectrum and of the coherence function are proposed that are particularly apt for the evaluation of the actions of wind on constructions such as buildings, towers, and chimneys. The use of each of these equations calls for the assignment of only one parameter, the best choice and the variability field of which are discussed.

Consistency conditions for random‐walk models of turbulent dispersion

Abstract: Random‐walk models have long been used to calculate the dispersion of passive contaminants in turbulence. When applied to nonstationary and inhomogeneous turbulence, the model coefficients are functions of the Eulerian turbulence statistics. More recently the same random‐walk models have been used as turbulence closures in the evolution equation for the Eulerian joint probability density function (pdf) of velocity. There are, therefore, consistency conditions relating the coefficients specified in a random‐walk model of dispersion and the Eulerian pdf calculated using the same random‐walk model. It is shown that even if these conditions are not satisfied, the dispersion model does not violate the second law of thermodynamics: all that is required to avoid a second‐law violation is that the mean pressure gradient be properly incorporated. It is also shown that for homogeneous turbulence the consistency conditions are satisfied by a linear Gaussian model; and that for inhomogeneous turbulence they are satisfied by a nonlinear Gaussian model.

Near-wall k-epsilon turbulence modeling

Abstract: The flow fields from a turbulent channel simulation are used to compute the budgets for the turbulent kinetic energy (k) and its dissipation rate (epsilon). Data from boundary layer simulations are used to analyze the dependence of the eddy-viscosity damping-function on the Reynolds number and the distance from the wall. The computed budgets are used to test existing near-wall turbulence models of the k-epsilon type. It was found that the turbulent transport models should be modified in the vicinity of the wall. It was also found that existing models for the different terms in the epsilon-budget are adequate in the region from the wall, but need modification near the wall. The channel flow is computed using a k-epsilon model with an eddy-viscosity damping function from the data and no damping functions in the epsilon-equation. These computations show that the k-profile can be adequately predicted, but to correctly predict the epsilon-profile, damping functions in the epsilon-equation are needed.

Calculating Rotordynamic Coefficients of Seals by Finite-Difference Techniques

Abstract: For modelling the turbulent flow in a seal the Navier-Stokes equations in connection with a turbulence (kappa-epsilon) model are solved by a finite-difference method. A motion of the shaft round the centered position is assumed. After calculating the corresponding flow field and the pressure distribution, the rotor-dynamic coefficients of the seal can be determined. These coefficients are compared with results obtained by using the bulk flow theory of Childs and with experimental results.

Fossil turbulence and intermittency in sampling oceanic mixing processes

Abstract: Oceanic mixing must be sampled at the length and time scales of the mixing processes to evaluate the rates and mechanisms of the mixing with minimum ambiguity. Sampling is complicated by the wide range of scales and extreme intermittency of planetary turbulence, and the interpretation of microstructure data is subject to wide deviations between current theories of stratified turbulent mixing. The statistical and hydrodynamic issues are connected, but may be treated separately. Estimation of the mean mixing rate χ– in a “layer” requires only that the probability density function of the local mixing rate χ be known from measurements, whatever the processes leading to the mixing may be. The mixing may be either uniform or intermittent within the layer space-time control volume, and the flow may be turbulent or nonturbulent. Hydrodynamic questions arise because oceanic microstructure data sets from most layers indicate undersampling: the data generally do not include regions of strong active turbulence suggested by the large intermittency factors of the measured probability distribution functions. However, the data sets do include fossil-turbulence remnants of such events which confirm the undersampling hypothesis. Baker and Gibson [1987] find that viscous and diffusive dissipation rates e and χ in most data sets have distributions indistinguishable from lognormal, with large intermittency factors σlne,χ2 in the range 3–7, where σ is the variance about the mean. In a fossil-turbulence-mixing model, Gibson (1980–1987) shows that the microstructure measured is generally in a mixed fossil-and-active turbulence state, with previous active turbulence e and χ values large enough to be consistent with the measured intermittent log-normal distributions. Previous e and χ values are inferred from fossil parameters of microstructure such as vertical overturn scales of the density fluctuations, or from the Cox number. Primary active turbulent events start the mixing process, fossilize, and are eroded back toward the initial uniform-density-gradient nonturbulent state by parasitic secondary-active-turbulent events which complete the mixing. Comparisons are presented between laboratory, lake, ocean, and fjord data sets and the Gibson (1980–1987) fossil-turbulence model.

Turbulence in Oscillatory Boundary Layers

Abstract: This paper reports the results of an experimental investigation on the turbulent oscillatory boundary layer flows which occur over both the smooth and rough walls, the rough wall case having a roughness parameter, the amplitude-to-roughness-height ratio of 1800. The boundary layer properties are found to be strongly dependent on the phase as well as on the wall category.

Energetics of Daytime Sea Breeze Circulation as Determined from a Two-Dimensional, Third-Order Turbulence Closure Model

Abstract: A two-dimensional, third-order turbulence closure model is developed to study the atmospheric boundary layer with one horizontal direction of inhomogeneity. Use of the Flux Corrected Transport scheme leads to numerical stability with low nonphysical diffusion. The case of a sea breeze circulation is simulated. The turbulence structure of the flow is described. The turbulent kinetic energy is included in the energetics of the circulation. The relations between convection and the dynamics of the sea breeze, including the velocity of the inland penetration of the front, are studied.

Turbulence intensity and spatial integral scale during compression and expansion strokes in a four-cycle reciprocating engine

Abstract: A laser homodyne technique is applied to measure turbulence intensities and spatial scales during compression and expansion strokes in a non-fired engine. By using this technique, relative fluid motion in a turbulent flow is detected directly without cyclic variation biases caused by fluctuation in the main flow. Experiments are performed at different engine speeds, compression ratios, and induction swirl ratios. In no-swirl cases the turbulence field near the compression end is almost uniform, whereas in swirled cases both the turbulence intensity and the scale near the cylinder axis are higher than those in the periphery. In addition, based on the measured results, the k-epsilon two-equation turbulence model under the influence of compression is discussed.

Contributions of numerical simulation data bases to the physics, modeling and measurement of turbulence

Abstract: The use of simulation data bases for the examination of turbulent flows is an effective research tool. Studies of the structure of turbulence have been hampered by the limited number of probes and the impossibility of measuring all desired quantities. Also, flow visualization is confined to the observation of passive markers with limited field of view and contamination caused by time-history effects. Computer flow fields are a new resource for turbulence research, providing all the instantaneous flow variables in three-dimensional space. Simulation data bases also provide much-needed information for phenomenological turbulence modeling. Three dimensional velocity and pressure fields from direct simulations can be used to compute all the terms in the transport equations for the Reynolds stresses and the dissipation rate. However, only a few, geometrically simple flows have been computed by direct numerical simulation, and the inventory of simulation does not fully address the current modeling needs in complex turbulent flows. The availability of three-dimensional flow fields also poses challenges in developing new techniques for their analysis, techniques based on experimental methods, some of which are used here for the analysis of direct-simulation data bases in studies of the mechanics of turbulent flows.

Modified k-.EPSILON. model for turbulent swirling flow in a straight pipe.

Abstract: On propose trois modeles k-e. Le modele k-e modifie avec une representation anisotrope de la turbulence donne une bonne precision du champ d'ecoulement complexe

Modified k-ε Model for Turbulent Swirling Flow in a Straight Pipe : Fluids Engineering

Abstract: Turbulence models applicable to turbulent swirling flow in a straight pipe have been developed. Two models, the standard k-e model with higher order terms in Reynolds stress equation are applied, and a modified k-e model with an anisotropic representation of turbulence is proposed. The comparisons between the computed flow distributions and the experimental data show that the modified k-e model predicts complex flow fields successfully. The magnitudes of the viscosity tensor components in the modified k-e model are discussed in detail.

Observations of Turbulence in Stratified Flow.

Abstract: Various theoretical properties of the structure function are evaluated. Additional functions are constructed to describe the overall influence of stratification, the anisotropy and intermittency of the turbulence, and the asymmetry of the main drafts. These functions and the usual spectral decomposition are computed from aircraft-measured turbulence data collected in nocturnal boundary layers and in turbulence over mountainous terrain. Certain features of the turbulence are found to depend more on stability than on the external situation. Three general types of turbulence are found: 1) intermittent turbulence driven by shear-driven overturning; 2) continuous turbulence where strong drafts in the presence of shear are characterized by sharp boundaries or microfronts, particularly on their upstream sides; and 3) weaker continuous turbulence. The costructure fields are generally consistent with vertical gradient transfer. However, the bora turbulence on larger scales is dominated by horizontal motio...

A Study of the Relationship Between Free-Stream Turbulence and Stagnation Region Heat Transfer

Abstract: A study has been conducted at the NASA Lewis Research Center to investigate the mechanism that causes free-stream turbulence to increase heat transfer in the stagnation region of turbine vanes and blades. The work was conducted in a wind tunnel at atmospheric conditions to facilitate measurements of turbulence and heat transfer. The model size was scaled up to simulate Reynolds numbers (based on leading edge diameter) that are to be expected on a turbine blade leading edge. Reynolds numbers from 13,000 to 177,000 were run in the present tests. Spanwise averaged heat transfer measurements with high and low turbulence have been made with “rough” and smooth surface stagnation regions. Results of these measurements show that, at the Reynolds numbers tested, the boundary layer remained laminar in character even in the presence of free-stream turbulence. If roughness was added the boundary layer became transitional as evidenced by the heat transfer increase with increasing distance from the stagnation line. Hot-wire measurements near the stagnation region downstream of an array of parallel wires has shown that vorticity in the form of mean velocity gradients is amplified as flow approaches the stagnation region. Finally smoke wire flow visualization and liquid crystal surface heat transfer visualization were combined to show that, in the wake of an array of parallel wires, heat transfer was a minimum in the wire wakes where the fluctuating component of velocity (local turbulence) was the highest. Heat transfer was found to be the highest between pairs of vortices where the induced velocity was toward the cylinder surface.