Showing papers on "Turbulence published in 1994"

Two-equation eddy-viscosity turbulence models for engineering applications

Abstract: Two new two-equation eddy-viscosity turbulence models will be presented. They combine different elements of existing models that are considered superior to their alternatives. The first model, referred to as the baseline (BSL) model, utilizes the original k-ω model of Wilcox in the inner region of the boundary layer and switches to the standard k-e model in the outer region and in free shear flows. It has a performance similar to the Wilcox model, but avoids that model's strong freestream sensitivity

Toward a theory of interstellar turbulence. 2. Strong Alfvenic turbulence

Abstract: We continue to investigate the possibility that interstellar turbulence is caused by nonlinear interactions among shear Alfven waves. Here, as in Paper I, we restrict attention to the symmetric case where the oppositely directed waves carry equal energy fluxes. This precludes application to the solar wind in which the outward flux significantly exceeds the ingoing one. All our detailed calculations are carried out for an incompressible magnetized fluid. In incompressible magnetohydrodynamics (MHD), nonlinear interactions only occur between oppositely direct waves. Paper I contains a detailed derivation of the inertial range spectrum for the weak turbulence of shear Alfven waves. As energy cascades to high perpendicular wavenumbers, interactions become so strong that the assumption of weakness is no longer valid. Here, we present a theory for the strong turbulence of shear Alfven waves. It has the following main characteristics. (1) The inertial-range energy spectrum exhibits a critical balance beween linear wave periods and nonlinear turnover timescales. (2) The "eddies" are elongated in the direction of the field on small spatial scales; the parallel and perpendicular components of the wave vector, k_z and k_⊥, are related by k_z ≈ k^(2/3) _⊥L^(-1/3), where L is the outer scale of the turbulence. (3) The "one-dimensional" energy spectrum is proportional to k^(-5/3) _⊥-an anisotropic Kolmogorov energy spectrum. Shear Alfvenic turbulence mixes specific entropy as a passive contaminant. This gives rise to an electron density power spectrum whose form mimics the energy spectrum of the turbulence. Radio, wave scattering by these electron density fluctuations produces anisotropic scatter-broadened images. Damping by ion-neutral collisions restricts Alfvenic turbulence to highly ionized regions of the interstellar medium. We expect negligible generation of compressive MHD waves by shear Alfven waves belonging to the critically balanced cascade. Viscous and collisionless damping are also unimportant in the interstellar medium (ISM). Our calculations support the general picture of interstellar turbulence advanced by Higdon.

The Atmospheric Boundary Layer

Abstract: 1. The atmospheric boundary layer 2. Basic equations for mean and fluctuating quantites 3. Scaling laws for mean and turbulent quantites 4. Surface roughness and local advection 5. Energy fluxes at the land surface 6. The thermally stratified ABL 7. The cloud topped boundary layer 8. ABL modelling and parameterisation schemes 9. The impact of the ABL on climate.

A New K-epsilon Eddy Viscosity Model for High Reynolds Number Turbulent Flows: Model Development and Validation

Abstract: A new k-epsilon eddy viscosity model, which consists of a new model dissipation rate equation and a new realizable eddy viscosity formulation, is proposed. The new model dissipation rate equation is based on the dynamic equation of the mean-square vorticity fluctuation at large turbulent Reynolds number. The new eddy viscosity formulation is based on the realizability constraints: the positivity of normal Reynolds stresses and Schwarz' inequality for turbulent shear stresses. We find that the present model with a set of unified model coefficients can perform well for a variety of flows. The flows that are examined include: (1) rotating homogeneous shear flows; (2) boundary-free shear flows including a mixing layer, planar and round jets; (3) a channel flow, and flat plate boundary layers with and without a pressure gradient; and (4) backward facing step separated flows. The model predictions are compared with available experimental data. The results from the standard k-epsilon eddy viscosity model are also included for comparison. It is shown that the present model is a significant improvement over the standard k-epsilon eddy viscosity model.

Velocity measurements in a high-Reynolds-number, momentum-conserving, axisymmetric, turbulent jet

Abstract: The turbulent flow resulting from a top-hat jet exhausting into a large room was investigated The Reynolds number based on exit conditions was approximately 105 Velocity moments to third order were obtained using flying and stationary hot-wire and burst-mode laser-Doppler anemometry (LDA) techniques The entire room was fully seeded for the LDA measurements The measurements are shown to satisfy the differential and integral momentum equations for a round jet in an infinite environmentThe results differ substantially from those reported by some earlier investigators, both in the level and shape of the profiles These differences are attributed to the smaller enclosures used in the earlier works and the recirculation within them Also, the flying hot-wire and burst-mode LDA measurements made here differ from the stationary wire measurements, especially the higher moments and away from the flow centreline These differences are attributed to the cross-flow and rectification errors on the latter at the high turbulence intensities present in this flow (30% minimum at centreline) The measurements are used, together with recent dissipation measurements, to compute the energy balance for the jet, and an attempt is made to estimate the pressure-velocity and pressure-strain rate correlations

Local isotropy in turbulent boundary layers at high Reynolds number

Abstract: To test the local-isotropy predictions of Kolmogorov's universal equilibrium theory, we have taken hot-wire measurements of the velocity fluctuations in the test-section-ceiling boundary layer of the 80×120 foot Full-Scale Aerodynamics Facility at NASA Ames Research Center, the world's largest wind tunnel. The maximum Reynolds numbers based on momentum thickness, R θ , and on Taylor microscale, R λ , were approximately 370 000 and 1450 respectively. These are the largest ever attained in laboratory boundary-layer flows. The boundary layer develops over a rough surface, but the Reynolds-stress profiles agree with canonical data sufficiently well for present purposes

On the properties of similarity subgrid-scale models as deduced from measurements in a turbulent jet

Abstract: The properties of turbulence subgrid-scale stresses are studied using experimental data in the far field of a round jet, at a Reynolds number of Rλ ≈ 310. Measurements are performed using two-dimensional particle displacement velocimetry. Three elements of the subgrid-scale stress tensor are calculated using planar filtering of the data. Using a priori testing, eddy-viscosity closures are shown to display very little correlation with the real stresses, in accord with earlier findings based on direct numerical simulations at lower Reynolds numbers. Detailed analysis of subgrid energy fluxes and of the velocity field decomposed into logarithmic bands leads to a new similarity subgrid-scale model. It is based on the ‘resolved stress’ tensor Lij, which is obtained by filtering products of resolved velocities at a scale equal to twice the grid scale. The correlation coefficient of this model with the real stress is shown to be substantially higher than that of the eddy-viscosity closures. It is shown that mixed models display similar levels of correlation. During the a priori test, care is taken to only employ resolved data in a fashion that is consistent with the information that would be available during large-eddy simulation. The influence of the filter shape on the correlation is documented in detail, and the model is compared to the original similarity model of Bardina et al. (1980). A relationship between Lij and a nonlinear subgrid-scale model is established. In order to control the amount of kinetic energy backscatter, which could potentially lead to numerical instability, an ad hoc weighting function that depends on the alignment between Lij and the strain-rate tensor, is introduced. A ‘dynamic’ version of the model is shown, based on the data, to allow a self-consistent determination of the coefficient. In addition, all tensor elements of the model are shown to display the correct scaling with normal distance near a solid boundary.

Active turbulence control for drag reduction in wall-bounded flows

Abstract: The objective of this study is to explore concepts for active control of turbulent boundary layers leading to skin-friction reduction using the direct numerical simulation technique. Significant drag reduction is achieved when the surface boundary condition is modified to suppress the dynamically significant coherent structures present in the wall region. The drag reduction is accompanied by significant reduction in the intensity of the wall-layer structures and reductions in the magnitude of Reynolds shear stress throughout the flow. The apparent outward shift of turbulence statistics in the controlled flows indicates a displaced virtual origin of the boundary layer and a thickened sublayer. Time sequences of the flow fields show that there are essentially two drag-reduction mechanisms. Firstly, within a short time after the control is applied, drag is reduced mainly by deterring the sweep motion without modifying the primary streamwise vortices above the wall. Consequently, the high-shear-rate regions on the wall are moved to the interior of the channel by the control schemes. Secondly, the active control changes the evolution of the wall vorticity layer by stabilizing and preventing lifting of the spanwise vorticity near the wall, which may suppress a source of new streamwise vortices above the wall.

Fully developed turbulent pipe flow: a comparison between direct numerical simulation and experiment

Abstract: Direct numerical simulations (DNS) and experiments are carried out to study fully developed turbulent pipe flow at Reynolds number Rec ≈ 7000 based on centreline velocity and pipe diameter The agreement between numerical and experimental results is excellent for the lower-order statistics (mean flow and turbulence intensities) and reasonably good for the higher-order statistics (skewness and flatness factors) To investigate the differences between fully developed turbulent flow in an axisymmetric pipe and a plane channel geometry, the present DNS results are compared to those obtained from a channel flow simulation Beside the mean flow properties and turbulence statistics up to fourth order, the energy budgets of the Reynolds-stress components are computed and compared The present results show that the mean velocity profile in the pipe fails to conform to the accepted law of the wall, in contrast to the channel flow This confirms earlier observations reported in the literature The statistics on fluctuating velocities, including the energy budgets of the Reynolds stresses, appear to be less affected by the axisymmetric pipe geometry Only the skewness factor of the normal-to-the-wall velocity fluctuations differs in the pipe flow compared to the channel flow The energy budgets illustrate that the normal-to-the-wall velocity fluctuations in the pipe are altered owing to a different ‘impingement’ or ‘splatting’ mechanism close to the curved wall

Source areas for scalars and scalar fluxes

Abstract: The spatial resolution of meteorological observations of scalars (such as concentrations or temperature) and scalar fluxes (e.g., water-vapour flux, sensible heat flux) above inhomogeneous surfaces is in general not known. It is determined by the surface area of influence orsource area of the sensor, which for sensors of quantities that are subject to turbulent diffusion, depends on the flow and turbulence conditions.

Modeling Wave-Enhanced Turbulence in the Ocean Surface Layer

Abstract: Until recently, measurements below the ocean surface have tended to confirm “law of the wall” behavior, in which the velocity profile is logarithmic, and energy dissipation decays inversely with depth. Recent measurements, however, show a sublayer, within meters of the surface, in which turbulence is enhanced by the action of surface waves. In this layer, dissipation appears to decay with inverse depth raised to a power estimated between 3 and 4.6. The present study shows that a conventional model, employing a “level 2½” turbulence closure scheme predicts near-surface dissipation decaying as inverse depth to the power 3.4. The model shows agreement in detail with measured profiles of dissipation. This is despite the fact that empirical constants in the model are determined for situations very different from this near-surface application. The action of breaking waves is modeled by a turbulent kinetic energy input at the surface. In the wave-enhanced layer, the downward flux of turbulent kinetic en...

High Rayleigh Number Convection

Abstract: Turbulent convection exemplifies many of the startling aspects of turbulent flows that have been uncovered in the past two decades, but frequently exhibits a novel twist. Thus, as in the case of free shear flows, convection can organize into large-scale vortical structures, but these then react back in subtle ways on the boundary layers which ultimately sustain them. Thermal plumes are a coherent mode of heat transport, analogous to boundary layer bursts, yet their overall effect can be surprisingly close to the structureless predictions of mixing length theory. Convection cells are closed, which facilitates their experimental control, but fluctuations never exit and there is a dynamically determined bulk forcing. While the single­ pass mode characteristic of wind tunnel experiments seems simpler, the convection cell is, in ways to be discussed, more constrained. This review aims to familiarize the turbulence researcher with con­ vergent lines of investigation in convection and also to remind those working in convection that turbulence is not a new subject. To situate convection within the gamut of other turbulent flows, let us by way of introduction contrast the directions in which convection has developed with research on the turbulent boundary layer. From the onset of convection up to Rayleigh numbers Ra � 1 0 times critical, there is a great wealth of information about flow structures (which can be visualized from above), and their relative stabilities (Busse 198 1 ) . Turbulence, in the sense of many coupled modes, and not just sensitive dependence on initial conditions, can arise for low Ra in large aspect ratio

An improved mixed layer model for geophysical applications

Abstract: An improved mixed layer model, based on second-moment closure of turbulence and suitable for application to oceanic and atmospheric mixed layers, is described. The model is tested against observational data from different locations in the global oceans, including high latitudes and tropics. The model belongs to the Mellor-Yamada hierarchy but incorporates recent findings from research on large eddy simulations and second-moment closure. The modified expansion of Galperin, Kantha, Hassid and Rosati (1988) that leads to a much simpler and more robust quasi-equilibrium turbulence model is employed instead of the original Mellor and Yamada (1974) model. Findings from ongoing research at the National Center for Atmospheric Research on large eddy simulations of the atmospheric boundary layer are utilized to improve parameterizations of pressure covariance terms in the second-moment closure. Shortwave solar radiation penetration is given careful treatment in the model so that the model is applicable to investigations of biological and photochemical processes in the upper ocean. But by far the major improvement is in the inclusion of the shear instability-induced mixing in the strongly stratified region below the oceanic mixed layer that leads to a more realistic and reliable mixed layer model that is suitable for application to a variety of geophysical mixed layers and circulation problems. The model appears to predict the mixing in the upper ocean well on a variety of time scales, from event scale storm-induced deepening and diurnal scale variability to seasonal time scales. With proper attention to the heat and salt balances in the upper ocean, it should be possible to use it for simulations of interannual variability as well. While the model validation has been primarily against oceanic mixed layer data sets, it is believed that the improvements can be readily incorporated into a model of the atmospheric boundary layer as well.

The spatial structure of neutral atmospheric surface-layer turbulence

Abstract: Modelling of the complete second-order structure of homogeneous, neutrally stratified atmospheric boundary-layer turbulence, including spectra of all velocity components and cross-spectra of any combination of velocity components at two arbitrarily chosen points, is attempted. Two models based on Rapid Distortion Theory (RDT) are investigated. Both models assume the velocity profile in the height interval of interest to be approximately linear. The linearized Navier–Stokes equation together with considerations of ‘eddy’ lifetimes are then used to modify the spatial second-order structure of the turbulence. The second model differs from the first by modelling the blocking by the surface in addition to the shear. The resulting models of the spectral velocity tensor contain only three adjustable parameters: a lengthscale describing the size of the largest energy-containing eddies, a non-dimensional number used in the parametrization of ‘eddy’ lifetime, and the third parameter is a measure of the energy dissipation.Two atmospheric experiments, both designed to investigate the spatial structure of turbulence and both running for approximately one year, are used to test and calibrate the models. Even though the approximations leading to the models are very crude they are capable of predicting well the two-point second-order statistics such as cross-spectra, coherences and phases, on the basis of measurements carried out at one point. The two models give very similar predictions, the largest difference being in the coherences involving vertical velocity fluctuations, where the blocking by the surface seems to have a significant effect.

Particle response and turbulence modification in fully developed channel flow

Abstract: The interactions between small dense particles and fluid turbulence have been investigated in a downflow fully developed channel in air. Particle velocities of, and fluid velocities in the presence of, 50 μm glass, 90 μm glass and 70 μm copper spherical beads were measured by laser Doppler anemometry, at particle mass loadings up to 80%. These particles were smaller than the Kolmogorov lengthscale of the flow and could respond to some but not all of the scales of turbulent motion. Streamwise mean particle velocity profiles were flatter than the mean fluid velocity profile, which was unmodified by particle loading. Particle velocity fluctuation intensities were larger than the unladen-fluid turbulence intensity in the streamwise direction but were smaller in the transverse direction. Fluid turbulence was attenuated by the addition of particles; the degree of attenuation increased with particle Stokes number, particle mass loading and distance from the wall. Turbulence was more strongly attenuated in the transverse than in the streamwise direction, because the turbulence energy is at higher frequencies in the transverse direction. Streamwise turbulence attenuation displayed a range of preferred frequencies where attenuation was strongest.

Simulation of Transition with a Two-Equation Turbulence Model

Abstract: This paper demonstrates how well the A>co turbulence model describes the nonlinear growth of flow instabilities from laminar flow into the turbulent flow regime. Viscous modifications are proposed for the A>co model that yield close agreement with measurements and with direct numerical simulation results for channel and pipe flow. These modifications permit prediction of subtle sublayer details such as maximum dissipation at the surface, k ~ y2 as y —> 0, and the sharp peak value of k near the surface. With two transition specific closure coefficients, the model equations yield a realistic description of a transitional incompressible flat-plate boundary layer. A new concept known as the numerical roughness strip is introduced that permits triggering transition at a desired location. A series of transitional boundary-layer applications, including effects of surface heat transfer, pressure gradient and freestream Mach number, verify that the numerical roughness strip is very effective in triggering transition and that flow in the transitional region is realistically described.

A subgrid-scale model for large-eddy simulation of planetary boundary-layer flows

Abstract: A long-standing problem in large-eddy simulations (LES) of the planetary boundary layer (PBL) is that the mean wind and temperature profiles differ from the Monin-Obukhov similarity forms in the surface layer. This shortcoming of LES has been attributed to poor grid resolution and inadequate sub-grid-scale (SGS) modeling. We study this deficiency in PBL LES solutions calculated over a range of shear and buoyancy forcing conditions. The discrepancy from similarity forms becomes larger with increasing shear and smaller buoyancy forcing, and persists even with substantial horizontal grid refinement. With strong buoyancy forcing, however, the error is negligible. In order to achieve better agreement between LES and similarity forms in the surface layer, a two-part SGS eddy-viscosity model is proposed. The model preserves the usual SGS turbulent kinetic energy formulation for the SGS eddy viscosity, but it explicitly includes a contribution from the mean flow and a reduction of the contributions from the turbulent fluctuations near the surface. Solutions with the new model yield increased fluctuation amplitudes near the surface and better correspondence with similarity forms out to a distance of 0.1-0.2 times the PBL depth, i.e., a typical surface-layer depth. These results are also found to be independent of grid anisotropy. The new model is simple to implement and computationally inexpensive.

Breakage and coalescence models for drops in turbulent dispersions

Abstract: A substantial effort has been made by numerous investigators to describe droplet breakage and coalescence in turbulent dispersions. An attempt is made here to improve these models based on existing frameworks and recent advances described in the literature. Two-step mechanisms are considered for both the breakage and coalescence models. The drop breakage function is structured as the product of the drop-eddy collision frequency and breakage efficiency which reflect the energetics of turbulent liquid-liquid dispersions. The coalescence function retains the former structure of the product of drop-drop collision frequency and coalescence efficiency. The coalescence efficiency model has been modified to account for the effects of film drainage for drops with partially mobile interfaces. These models overcome several inconsistencies observed in previous efforts and are applicable for dense dispersions (about ϕ[0.10–0.30]). For the daughter drops produced by breakage, a probability density is proposed based on the energy requirements for the formation of daughter drops.

Vorticity and turbulence

Abstract: This is an introduction to turbulence in vortex systems, and to turbulence theory for incompressible flow described in terms of the vorticity field. It is the author's hope that by the end of the book the reader will believe that these subjects are identical, and constitute a special case of fairly standard statistical mechanics, with both equilibrium and non-equilibrium aspects. The author's main goal is to relate turbulence to statistical mechanics. The first three chapters of the book constitute a fairly standard introduction to homogeneous turbulence in incompressible flow; a quick review of fluid mechanics; a summary of the appropriate Fourier theory; and a summary of Kolmogorov's theory of the inertial range. The next four chapters present the statistical theory of vortex notion, and the vortex dynamics of turbulence. The book ends with the major conclusion that turbulence can no longer be viewed as incomprehensible.

Direct Simulation of a Self-Similar Turbulent Mixing Layer

Abstract: Three direct numerical simulations of incompressible turbulent plane mixing layers have been performed. All the simulations were initialized with the same two velocity fields obtained from a direct numerical simulation of a turbulent boundary layer with a momentum thickness Reynolds number of 300 computed by Spalart (J. Fluid Mech. 187, 61, 1988). In addition to a baseline case with no additional disturbances, two simulations were begun with two-dimensional disturbances of varying strength in addition to the boundary layer turbulence. After a development stage, the baseline case and the case with weaker additional two-dimensional disturbances evolve self-similarly, reaching visual thickness Reynolds numbers of up to 20 000. This self-similar period is characterized by a lack of large-scale organized pairings, a lack of streamwise vortices in the 'braid' regions, and scalar mixing that is characterized by 'marching' Probability Density Functions (PDFs). The case begun with strong additional two-dimensional disturbances only becomes approximately self-similar, but exhibits sustained organized large-scale pairings, clearly defined braid regions with streamwise vortices that span them, and scalar PDFs that are 'nonmarching.' It is also characterized by much more intense vertical velocity fluctuations than the other two cases. The statistics and structures in several experiments involving turbulent mixing layers are in better agreement with those of the simulations that do not exhibit organized pairings.

Effects of the computational time step on numerical solutions for turbulent flow

Abstract: Effects of large computational time steps on the computed turbulence were investigated using a fully implicit method. In turbulent channel flow computations the largest computational time step in wall units which led to accurate prediction of turbulence statistics was determined. Turbulence fluctuations could not be sustained if the computational time step was near or larger than the Kolmogorov time scale.

Preferential concentration of heavy particles in a turbulent channel flow

Abstract: An investigation of the instantaneous particle concentration at the centerline of a turbulent channel flow has been conducted. The concentration field was obtained by digitizing photographs of particles illuminated by a spanwise laser sheet and identifying individual particles. The resulting distribution was then compared to the expected distribution for the same number of particles randomly distributed throughout the volume. Significant departures from randomness have been found and the differences are strongly dependent on the time constants of the particles. Five different particle classes were investigated and the maximum departure from randomness was found when the ratio of the particle’s aerodynamic response time to the Kolmogorov time scale of the flow was approximately one. The length scales of the particle clusters were found to change with the particle size. The correlation dimension was used to produce a single parameter describing the degree of concentration regardless of the scale on which it occurs. The spacing between particle clusters was also investigated and found to be much larger than the scales on which concentration occurs.

Toroidal gyro‐Landau fluid model turbulence simulations in a nonlinear ballooning mode representation with radial modes

Abstract: The method of Hammett and Perkins [Phys. Rev. Lett. 64, 3019 (1990)] to model Landau damping has been recently applied to the moments of the gyrokinetic equation with curvature drift by Waltz, Dominguez, and Hammett [Phys. Fluids B 4, 3138 (1992)]. The higher moments are truncated in terms of the lower moments (density, parallel velocity, and parallel and perpendicular pressure) by modeling the deviation from a perturbed Maxwellian to fit the kinetic response function at all values of the kinetic parameters: k∥vth/ω, b=(k⊥ρ)2/2, and ωD/ω. Here the resulting gyro‐Landau fluid equations are applied to the simulation of ion temperature gradient (ITG) mode turbulence in toroidal geometry using a novel three‐dimensional (3‐D) nonlinear ballooning mode representation. The representation is a Fourier transform of a field line following basis (ky’,kx’,z’) with periodicity in toroidal and poloidal angles. Particular emphasis is given to the role of nonlinearly generated n=0 (ky’ = 0, kx’ ≠ 0) ‘‘radial modes’’ in s...

Natural convection flow in a square cavity revisited: Laminar and turbulent models with wall functions

Abstract: Numerical simulations have been undertaken for the benchmark problem of natural convection flow in a square cavity. The control volume method is used to solve the conservation equations for laminar and turbulent flows for a series of Rayleigh numbers (Ra) reaching values up to 1010. The k-ϵ model has been used for turbulence modelling with and without logarithmic wall functions. Uniform and non-uniform (stretched) grids have been employed with increasing density to guarantee accurate solutions, especially near the walls for high Ra-values. ADI and SIP solvers are implemented to accelerate convergence. Excellent agreement is obtained with previous numerical solutions, while some discrepancies with others for high Ra-values may be due to a possibly different implementation of the wall functions. Comparisons with experimental data for heat transfer (Nusselt number) clearly demonstrates the limitations of the standard k-ϵ model with logarithmic wall functions, which gives significant overpredictions.