Showing papers on "Turbulence published in 1993"

Turbulence in open-channel flows

Abstract: A review of open channel turbulence, focusing especially on certain features stemming from the presence of the free surface and the bed of a river. Part one presents the statistical theory of turbulence; Part two addresses the coherent structures in open-channel flows and boundary layers.

Settling velocity and concentration distribution of heavy particles in homogeneous isotropic turbulence

Abstract: The average settling velocity in homogeneous turbulence of a small rigid spherical particle, subject to a Stokes drag force, has been shown to differ from that in still fluid owing to a bias from the particle inertia (Maxey 1987). Previous numerical results for particles in a random flow field, where the flow dynamics were not considered, showed an increase in the average settling velocity. Direct numerical simulations of the motion of heavy particles in isotropic homogeneous turbulence have been performed where the flow dynamics are included. These show that a significant increase in the average settling velocity can occur for particles with inertial response time and still-fluid terminal velocity comparable to the Kolmogorov scales of the turbulence. This increase may be as much as 50% of the terminal velocity, which is much larger than was previously found. The concentration field of the heavy particles, obtained from direct numerical simulations, shows the importance of the inertial bias with particles tending to collect in elongated sheets on the peripheries of local vortical structures. This is coupled then to a preferential sweeping of the particles in downward moving fluid. Again the importance of Kolmogorov scaling to these processes is demonstrated. Finally, some consideration is given to larger particles that are subject to a nonlinear drag force where it is found that the nonlinearity reduces the net increase in settling velocity.

The structure of intense vorticity in isotropic turbulence

Abstract: The structure of the intense-vorticity regions is studied in numerically simulated homogeneous, isotropic, equilibrium turbulent flow fields at four different Reynolds numbers, in the range Re, = 35-170. In accordance with previous investigators this vorticity is found to be organized in coherent, cylindrical or ribbon-like, vortices (‘worms’). A statistical study suggests that they are simply especially intense features of the background, O(o’), vorticity. Their radii scale with the Kolmogorov microscale and their lengths with the integral scale of the flow. An interesting observation is that the Reynolds number y/v, based on the circulation of the intense vortices, increases monotonically with ReA, raising the question of the stability of the structures in the limit of Re, --z co. Conversely, the average rate of stretching of these vortices increases only slowly with their peak vorticity, suggesting that self-stretching is not important in their evolution. One- and two-dimensional statistics of vorticity and strain are presented; they are non-Gaussian and the behaviour of their tails depends strongly on the Reynolds number. There is no evidence of convergence to a limiting distribution in this range of Re,, even though the energy spectra and the energy dissipation rate show good asymptotic properties in the higher-Reynolds-number cases. Evidence is presented to show that worms are natural features of the flow and that they do not depend on the particular forcing scheme.

Extended self-similarity in turbulent flows

Abstract: We report on the existence of a hitherto undetected form of self-similarity, which we call extended self-similarity (ESS). ESS holds at high as well as at low Reynolds number, and it is characterized by the same scaling exponents of the velocity differences of fully developed turbulence.

A dynamic mixed subgrid‐scale model and its application to turbulent recirculating flows

Abstract: The dynamic subgrid‐scale eddy viscosity model of Germano et al. [Phys. Fluids A 3, 1760 (1991)] (DSM) is modified by employing the mixed model of Bardina et al. [Ph.D dissertation, Stanford University (1983)] as the base model. The new dynamic mixed model explicitly calculates the modified Leonard term and only models the cross term and the SGS Reynolds stress. It retains the favorable features of DSM and, at the same time, does not require that the principal axes of the stress tensor be aligned with those of the strain rate tensor. The model coefficient is computed using local flow variables. The new model is incorporated in a finite‐volume solution method and large‐eddy simulations of flows in a lid‐driven cavity at Reynolds numbers of 3200, 7500, and 10 000 show excellent agreement with the experimental data. Better agreement is achieved by using the new model compared to the DSM. The magnitude of the dynamically computed model coefficient of the new model is significantly smaller than that from DSM.

Variability of the Tropical Atlantic Ocean Simulated by a General Circulation Model with Two Different Mixed-Layer Physics

Abstract: The embedment of a 1.5 turbulence closure model in an ocean general circulation model of the equatorial Atlantic is presented. The eddy viscosity and diffusivity involved in the vertical mixing are defined as the product of a characteristic turbulent velocity—the root square of the turbulent kinetic energy—and a characteristic mixing length. The turbulent kinetic energy is defined through a prognostic equation while the turbulent length scales are defined by a diagnostic formulation. The results of an experiment that includes this closure scheme are compared to the results issued from another experiment that includes a Richardson number-dependent parameterization of the mixing coefficients. The two simulations were performed over the tropical Atlantic during the 1982–1984 period, which allows direct comparisons with data from the FOCAL and SEQUAL experiments. Obvious contrasts between the two experiments on the sea surface temperature and on the dynamics indicate that the turbulent vertical diffu...

Direct numerical simulation of turbulent flow over riblets

Abstract: Direct numerical simulations of turbulent flows over riblet-mounted surfaces are performed to educe the mechanism of drag reduction by riblets. The computed drag on the riblet surfaces is in good agreement with the existing experimental data. The mean-velocity profiles show upward and downward shifts in the log–law for drag-decreasing and drag-increasing cases, respectively. Turbulence statistics above the riblets are computed and compared with those above a flat plate. Differences in the mean-velocity profile and turbulence quantities are found to be limited to the inner region of the boundary layer. Velocity and vorticity fluctuations as well as the Reynolds shear stresses above the riblets are reduced in drag-reducing configurations. Quadrant analysis indicates that riblets mitigate the positive Reynolds-shear-stress-producing events in drag-reducing configurations. From examination of the instantaneous flow fields, a drag reduction mechanism by riblets is proposed: riblets with small spacings reduce viscous drag by restricting the location of the streamwise vortices above the wetted surface such that only a limited area of the riblets is exposed to the downwash of high-speed fluid that the vortices induce.

On the two-way interaction between homogeneous turbulence and dispersed solid particles. I: Turbulence modification

Abstract: The modification of decaying homogeneous turbulence due to its interaction with dispersed small solid particles (d/η<1), at a volumetric loading ratio φv≤5×10−4, is studied using direct numerical simulation. The results show that the particles increase the fluid turbulence energy at high wave numbers. This increase of energy is accompanied by an increase of the viscous dissipation rate, and, hence, an increase in the rate of energy transfer T(k) from the large‐scale motion. Thus, depending on the conditions at particle injection, the fluid turbulence kinetic energy may increase initially. But, in the absence of external sources (shear or buoyancy), the turbulence energy eventually decays faster than in the particle‐free turbulence. In gravitational environment, particles transfer their momentum to the small‐scale motion but in an anisotropic manner. The pressure‐strain correlation acts to remove this anisotropy by transferring energy from the direction of gravity to the other two directions, but at the sa...

Conditional moment closure for turbulent reacting flow

Abstract: Equations governing the variation through the flow field of averages of quantities such as species mass fractions, conditional on mixture fraction, are derived and modeled. The conditioning variable adds to the independent dimensions of the problem, but it is found that this is offset in some cases by reduction in the spatial dimensionality needed. Predictions are made for the reacting scalar mixing layer, and these show good agreement with experiment. The methodology effectively decouples the kinetics from the large inhomogeneity or macromixing aspects of the flow while preserving the input from the scalar dissipation or micromixing. Arbitrarily complex kinetics may be used within reasonable computational cost.

Large-Eddy Simulation of Turbulent Flow Over and Around a Cube in a Plate Channel

Abstract: The solution concept of large-eddy simulation (LES) has been applied to simulate turbulent flow over and around a single cube mounted on the bottom of a plate channel for a Reynolds number of 50000 (based on the incoming mean bulk velocity and obstacle height). Here we present, as a first part of the evaluation of the data, a few interesting views of the time-dependent fields and results for the three-dimensional mean fields (velocity, vorticity, Reynolds stress, enstrophy, helicity). Having engineering application in mind, this flow problem represents an ideal case, which is very well suited for testing and validating numerical simulation techniques and turbulence models.

A Reynolds stress model for near-wall turbulence

Abstract: A tensorially consistent near-wall second-order closure model is formulated. Redistributive terms in the Reynolds stress equations are modelled by an elliptic relaxation equation in order to represent strongly non-homogeneous effects produced by the presence of walls; this replaces the quasi-homogeneous algebraic models that are usually employed, and avoids the need for ad hoc damping functions. A quasi-homogeneous model appears as the source term in the elliptic relaxation equation-here we use the simple Rotta return to isotropy and isotropization of production formulae. The formulation of the model equations enables appropriate boundary conditions to be satisfied. The model is solved for channel flow and boundary layers with zero and adverse pressure gradients. Good predictions of Reynolds stress components, mean flow, skin friction and displacement thickness are obtained in various comparisons to experimental and direct numerical simulation data. The model is also applied to a boundary layer flowing along a wall with a 90°, constant-radius, convex bend. Because the model is of a general, tensorially invariant form, special modifications for curvature effects are not needed; the equations are simply transformed to curvilinear coordinates. The model predicts many important features of this flow. These include: the abrupt drop of skin friction and Stanton number at the start of the curve, and their more gradual recovery after the bend; the suppression of turbulent intensity in the outer part of the boundary layer; a region of negative (counter-gradient) Reynolds shear stress; and recovery from curvature in the form of a Reynolds stress ‘bore’ propagating out from the surface. A shortcoming of the present model is that it overpredicts the rate of this recovery. A heat flux model is developed. It is shown that curvature effects on heat transfer can also be accounted for automatically by a tensorially invariant formulation.

Generation of Mean Flows and Jets on a Beta Plane and over Topography

Abstract: This paper proposes and discusses mechanisms whereby mean flows and jets are produced by differential rotation and by topographic effects. It is shown that, in general, a mean gradient of potential vorticity not only inhibits the cascade of energy to large scales but directly produces anisotropic structures. Scalings for this are examined on the β plane using ideas from classical phenomenology. The scalings are naturally anisotropic and predict the formation of zonal flows directly through a turbulent cascade. Numerical simulations and two-point closure calculations qualitatively confirm the predictions. Also, simulations of barotropic flow on the β plane can produce zonal jet structures of exceptional persistence over many eddy turnover times. Unsteady flow over topography generally produces a mean flow with a correlation between streamfunction and topography, with anticyclonic motion over humps. If the topography is shallow (or the flow sufficiently energetic) the mean streamfunction will be of...

Experimental and numerical study of a turbulent boundary layer with pressure gradients

Abstract: Results are presented of an experimental and numerical study of a turbulent boundary layer with pressure gradients conducted using the recent 'fringe method' with its numerical advantages and good inflow quality. After an inflow transient good agreement is observed; the differences, of up to 13 percent, are discussed. Moderate deviations from the law of the wall are found in the velocity profiles of the simulation. They are fully correlated with the pressure gradient, are in fair quantitative agreement with the experimental results of Nagano et al. (1992), and are roughly the opposite of uncorrected mixing-length-model predictions. Large deviations from the wall scaling are observed for other quantities, notably for the turbulence dissipation rate. The a(1) structure parameter drops mildly in the upper layer with adverse pressure gradient.

Wavelet transforms and atmopsheric turbulence.

Abstract: Wavelet cross spectra and cross scalograms are used to analyze the time-scale structure of bivariate turbulence data from the boundary layer over the ocean. The cross scalogram for the streamwise and vertical turbulent velocity components shows a highly intermittent pattern with significant contributions of opposite signs appearing at two specific scales, ∼60 m and ∼2 km, believed to be related to small-scale turbulent mixing and large-scale secondary flow in the boundary layer

Direct simulations of low-Reynolds-number turbulent flow in a rotating channel

Abstract: Direct numerical simulations of fully developed pressure-driven turbulent flow in a rotating channel have been performed The unsteady Navier–Stokes equations were written for flow in a constantly rotating frame of reference and solved numerically by means of a finite-difference technique on a 128 × 128 × 128 computational mesh The Reynolds number, based on the bulk mean velocity Um and the channel half-width h, was about 2900, while the rotation number Ro = 2|Ω|h/Um varied from 0 to 05 Without system rotation, results of the simulation were in good agreement with the accurate reference simulation of Kim, Moin & Moser (1987) and available experimental data The simulated flow fields subject to rotation revealed fascinating effects exerted by the Coriolis force on channel flow turbulence With weak rotation (Ro = 001) the turbulence statistics across the channel varied only slightly compared with the nonrotating case, and opposite effects were observed near the pressure and suction sides of the channel With increasing rotation the augmentation and damping of the turbulence along the pressure and suction sides, respectively, became more significant, resulting in highly asymmetric profiles of mean velocity and turbulent Reynolds stresses In accordance with the experimental observations of Johnston, Halleen & Lezius (1972), the mean velocity profile exhibited an appreciable region with slope 2Ω At Ro = 050 the Reynolds stresses vanished in the vicinity of the stabilized side, and the nearly complete suppression of the turbulent agitation was confirmed by marker particle trackings and two-point velocity correlations Rotational-induced Taylor-Gortler-like counter-rotating streamwise vortices have been identified, and the simulations suggest that the vortices are shifted slightly towards the pressure side with increasing rotation rates, and the number of vortex pairs therefore tend to increase with Ro

High Reynolds number calculations using the dynamic subgrid‐scale stress model

Abstract: The dynamic subgrid-scale eddy viscosity model was used in the large-eddy simulation of the turbulent flow in a plane channel for Reynolds numbers based on friction velocity and channel half-width ranging between 200 and 2000, a range including values significantly higher than in previous simulations. The computed wall stress, mean velocity, and Reynolds stress profiles compare very well with experimental and direct simulation data. Comparison of higher moments is also satisfactory. Although the grid in the near-wall region is fairly coarse, the results are quite accurate: the turbulent kinetic energy peaks at y(+) of about 12, and the near-wall behavior of the resolved stresses is captured accurately. The model coefficient is o(0.001) in the buffer layer and beyond, where the cutoff wave numbers are in the decaying region of the spectra; in the near-wall region, the cutoff wave numbers are nearer the energy-containing range, and the resolved turbulent stresses become a constant fraction of the resolved stresses. This feature is responsible for the correct near-wall behavior of the model coefficient.

Particle-driven gravity currents.

Abstract: Gravity currents created by the release of a fixed volume of a suspension into a lighter ambient fluid are studied theoretically and experimentally. The greater density of the current and the buoyancy force driving its motion arise primarily from dense particles suspended in the interstitial fluid of the current. The dynamics of the current are assumed to be dominated by a balance between inertial and buoyancy forces; viscous forces are assumed negligible. The currents considered are two-dimensional and flow over a rigid horizontal surface. The flow is modelled by either the single- or the twolayer shallow-water equations, the two-layer equations being necessary to include the effects of the overlying fluid, which are important when the depth of the current is comparable to the depth of the overlying fluid. Because the local density of the gravity current depends on the concentration of particles, the buoyancy contribution to the momentum balance depends on the variation of the particle concentration. A transport equation for the particle concentration is derived by assuming that the particles are vertically well-mixed by the turbulence in the current, are advected by the mean flow and settle out through the viscous sublayer at the bottom of the current. The boundary condition at the moving front of the current relates the velocity and the pressure head at that point. The resulting equations are solved numerically, which reveals that two types of shock can occur in the current. In the late stages of all particle-driven gravity currents, an internal bore develops that separates a particle-free jet-like flow in the rear from a dense gravity-current flow near the front. The second type of bore occurs if the initial height of the current is comparable to the depth of the ambient fluid. This bore develops during the early lock-exchange flow between the two fluids and strongly changes the structure of the current and its transport of particles from those of a current in very deep surroundings. To test the theory, several experiments were performed to measure the length of particle-driven gravity currents as a function of time and their deposition patterns for a variety of particle sizes and initial masses of sediment. The comparison between the theoretical predictions, which have no adjustable parameters, and the experimental results are very good.

Scaling laws for fully developed turbulent shear flows. Part 1. Basic hypotheses and analysis

Abstract: The present work consists of two parts. Here in Part 1, a scaling law (incomplete similarity with respect to local Reynolds number based on distance from the wall) is proposed for the mean velocity distribution in developed turbulent shear flow. The proposed scaling law involves a special dependence of the power exponent and multiplicative factor on the flow Reynolds number. It emerges that the universal logarithmic law is closely related to the envelope of a family of power-type curves, each corresponding to a fixed Reynolds number. A skin-friction law, corresponding to the proposed scaling law for the mean velocity distribution, is derived.In Part 2 (Barenblatt & Prostokishin 1993), both the scaling law for the velocity distribution and the corresponding friction law are compared with experimental data.

Direct numerical simulation of turbulent flow in a square duct

Abstract: A direct numerical simulation of a fully developed, low-Reynolds-number turbulent flow in a square duct is presented. The numerical scheme employs a time-splitting method to integrate the three-dimensional, incompressible Navier-Stokes equations using spectral/high-order finite-difference discretization on a staggered mesh ; the nonlinear terms are represented by fifth-order upwind-biased finite differences. The unsteady flow field was simulated at a Reynolds number of 600 based on the mean friction velocity and the duct width, using 96 x 101 x 101 grid points. Turbulence statistics from the fully developed turbulent field are compared with existing experimental and numerical square duct data, providing good qualitative agreement. Results from the present study furnish the details of the corner effects and near-wall effects in this complex turbulent flow field; also included is a detailed description of the terms in the Reynolds-averaged streamwise momentum and vorticity equations. Mechanisms responsible for the generation of the stress-driven secondary flow are studied by quadrant analysis and by analysing the instantaneous turbulence structures. It is demonstrated that the mean secondary flow pattern, the distorted isotachs and the anisotropic Reynolds stress distribution can be explained by the preferred location of an ejection structure near the corner and the interaction between bursts from the two intersecting walls. Corner effects are also manifested in the behaviour of the pressure-strain and velocity-pressure gradient correlations.

Velocity profiles measured for airflow through a large-scale model of the human nasal cavity

Abstract: An anatomically accurate, x20 enlarged scale model of a healthy right human adult nasal cavity was constructed from computerized axial tomography scans for the study of nasal airflow patterns. Detailed velocity profiles for inspiratory and expiratory flow through the model and turbulence intensity were measured with a hot-film anemometer probe with 1 mm spatial resolution. Steady flow rates equivalent to 1,100, 560, and 180 ml/s through one side of the real human nose were studied. Airflows were determined to be moderately turbulent, but changes in the velocity profiles between the highest and lowest flow rates suggest that for normal breathing laminar flow may be present in much of the nasal cavity. The velocity measurements closest to the model wall were estimated to be inside the laminar sublayer, such that the slopes of the velocity profiles are reasonably good estimates of the velocity gradients at the walls. The overall longitudinal pressure drop inside the nasal cavity for the three inspiratory flow rates was estimated from the average total shear stress measured at the central nasal wall and showed good agreement with literature values measured in human subjects.

The three-dimensional evolution of a plane mixing layer: pairing and transition to turbulence

Abstract: The evolution of three-dimensional temporally evolving plane mixing layers through as many as three pairings has been simulated numerically. All simulations were begun from a few low-wavenumber disturbances, usually derived from linear stability theory, in addition to the mean velocity. Three-dimensional perturbations were used with amplitudes ranging from infinitesimal to large enough to trigger a rapid transition to turbulence. Pairing is found to inhibit the growth of infinitesimal three-dimensional disturbances, and to trigger the transition to turbulence in highly three-dimensional flows. The mechanisms responsible for the growth of three-dimensionality and onset of transition to turbulence are described. The transition to turbulence is accompanied by the formation of thin sheets of spanwise vorticity, which undergo secondary rollups. The post-transitional simulated flow fields exhibit many properties characteristic of turbulent flows.

Mean flow and turbulence fields over two‐dimensional bed forms

Abstract: Detailed laser-Doppler velocity and Reynolds stress measurements over fixed two-dimensional bed forms are used to investigate the coupling between the mean flow and turbulence and to examine effects that play a role in producing the bed form instability and finite amplitude stability. The coupling between the mean flow and the turbulence is explored in both a spatially averaged sense, by determining the structure of spatially averaged velocity and Reynolds stress profiles, and a local sense, through computation of eddy viscosities and length scales. The measurements show that there is significant interaction between the internal boundary layer and the overlying wake turbulence produced by separation at the bed form crest. The interaction produces relatively low correlation coefficients in the internal boundary layer, which suggests that using local bottom stress to predict bed load flux may not only be erroneous, it may also disregard the essence of the bed form instability mechanism. The measurements also indicate that topographically induced acceleration over the bed form stoss slope has a more significant effect in damping the turbulence over bed forms than was previously supposed, which is hypothesized to play a role in the stabilization of fully developed bed forms.

Developments in the gyrofluid approach to Tokamak turbulence simulations

Abstract: A status report is given on developments in the gyrofluid approach to simulating tokamak turbulence. 'Gyrofluid' (r 'gyro-Landau fluid') equations attempt to extend the range of validity of fluid equations to a more collisionless regime typical of tokamaks, by developing fluid models of important kinetic effects such as Landau-damping and gyro-orbit averaging. The fluid moments approach should converge if enough moments are kept, though this may require a large number of moments for some processes. Toroidal gyrofluid equations have been extended from 4 to 6 moments, and to include the mu Del B magnetic mirroring force. An efficient field-line coordinate system for toroidal turbulence simulations (useful for both particle and fluid simulations) is presented. Nonlinear 3-D simulations of toroidal ITG-driven turbulence indicate that turbulence-generated sheared flows play an important role in the development and saturation of the turbulence. There is a strong enhancement of the flows when the electrons are assumed adiabatic on each flux surface, which is partially offset by toroidal drift effects which reduce the flows.

New time scale based k-epsilon model for near-wall turbulence

Abstract: A k-epsilon model is proposed for wall bonded turbulent flows. In this model, the eddy viscosity is characterized by a turbulent velocity scale and a turbulent time scale. The time scale is bounded from below by the Kolmogorov time scale. The dissipation equation is reformulated using this time scale and no singularity exists at the wall. The damping function used in the eddy viscosity is chosen to be a function of R(sub y) = (k(sup 1/2)y)/v instead of y(+). Hence, the model could be used for flows with separation. The model constants used are the same as in the high Reynolds number standard k-epsilon model. Thus, the proposed model will be also suitable for flows far from the wall. Turbulent channel flows at different Reynolds numbers and turbulent boundary layer flows with and without pressure gradient are calculated. Results show that the model predictions are in good agreement with direct numerical simulation and experimental data.