Showing papers on "Reynolds number published in 1993"

Numerical Simulations of Particulate Suspensions via a Discretized Boltzmann Equation Part I. Theoretical Foundation

Abstract: A new and very general technique for simulating solid-fluid suspensions is described; its most important feature is that the computational cost scales linearly with the number of particles. The method combines Newtonian dynamics of the solid particles with a discretized Boltzmann equation for the fluid phase; the many-body hydrodynamic interactions are fully accounted for, both in the creeping-flow regime and at higher Reynolds numbers. Brownian motion of the solid particles arises spontaneously from stochastic fluctuations in the fluid stress tensor, rather than from random forces or displacements applied directly to the particles. In this paper, the theoretical foundations of the technique are laid out, illustrated by simple analytical and numerical examples; in the companion paper, extensive numerical tests of the method, for stationary flows, time-dependent flows, and finite Reynolds number flows, are reported.

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.

Energy growth in viscous channel flows

Abstract: In recent work it has been shown that there can be substantial transient growth in the energy of small perturbations to plane Poiseuille and Couette flows if the Reynolds number is below the critical value predicted by linear stability analysis. This growth, which may be as large as O( lOOO), occurs in the absence of nonlinear effects and can be explained by the non-normality of the governing linear operator - that is, the nonorthogonality of the associated eigenfunctions. In this paper we study various aspects of this energy growth for two- and three-dimensional Poiseuille and Couette flows using energy methods, linear stability analysis, and a direct numerical procedure for computing the transient growth. We examine conditions for no energy growth, the dependence of the growth on the streamwise and spanwise wavenumbers, the time dependence of the growth, and the effects of degenerate eigenvalues. We show that the maximum transient growth behaves like O(R2), where R is the Reynolds number. We derive conditions for no energy growth by applying the Hille-Yosida theorem to the governing linear operator and show that these conditions yield the same results as those derived by energy methods, which can be applied to perturbations of arbitrary amplitude. These results emphasize the fact that subcritical transition can occur for Poiseuille and Couette flows because the governing linear operator is non-normal.

Numerical Simulations of Particulate Suspensions via a Discretized Boltzmann Equation Part II. Numerical Results

Abstract: A new and very general technique for simulating solid-fluid suspensions has been described in a previous paper (Part I); the most important feature of the new method is that the computational cost scales with the number of particles. In this paper (Part II), extensive numerical tests of the method are described; for creeping flows, both with and without Brownian motion, and at finite Reynolds numbers. Hydrodynamic interactions, transport coefficients, and the short-time dynamics of random dispersions of up to 1024 colloidal particles have been simulated.

The Flow Around Surface-Mounted, Prismatic Obstacles Placed in a Fully Developed Channel Flow (Data Bank Contribution)

Abstract: The flow field around surface-mounted, prismatic obstacles with different spanwise dimensions was investigated using the crystal violet, oil-film and laser-sheet visualization techniques as well as by static pressure measurements. The aim of this study is to highlight the fundamental differences between nominally two-dimensional and fully three-dimensional obstacle flows. All experiments were performed in a fully developed channel flow. The Reynolds number, based on the height of the channel, lay between 8 X 10[sup 4] and 1.2 X 10[sup 5]. Results show that the middle region of the wake is nominally two-dimensional for width-to-height ratios (W/H) greater than 6. The separated region in front of wider obstacles is characterized by the appearance of a quasi-regular distribution of saddle and nodal points on the forward face of the obstacles. These three-dimensional effects are considered to be inherent to such separating flows with stagnation.

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.

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.

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.

The instability of the steady flow past spheres and disks

Abstract: We consider the instability of the steady, axisymmetric base flow past a sphere, and a circular disk (oriented broadside-on to the incoming flow). Finite-element methods are used to compute the steady axisymmetric base flows, and to examine their linear instability to three-dimensional modal perturbations. The numerical results show that for the sphere and the circular disk, the first instability of the base flow is through a regular bifurcation, and the critical Reynolds number (based on the body radius) is 105 for the sphere, and 58.25 for the circular disk. In both cases, the unstable mode is non-axisymmetric with azimuthal wavenumber m = 1. These computational results are consistent with previous experimental observations (Magarvey & Bishop 1961 a, b; Nakamura 1976; Willmarth, Hawk & Harvey 1964).

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.

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.

Feedback control of vortex shedding at low Reynolds numbers

Abstract: This paper describes experiments undertaken to study in detail the control of vortex shedding from circular cylinders at low Reynolds numbers by using feedback to stabilize the wake instability. Experiments have been performed both in a wind tunnel and in an open water channel with flow visualization. It has been found that feedback control is able to delay the onset of the wake instability, rendering the wake stable at Reynolds numbers about 20% higher than otherwise. At higher flow rates, however, it was not possible to use single-channel feedback to stabilize the wake - although, deceptively, it was possible to reduce the unsteadiness recorded by a near-wake sensor. When control is applied to a long span only the region near the control sensor is controlled. The results presented in this paper generally support the analytical results of other researchers.

Turbulence in stratified shear flows: implications for interpreting shear-induced mixing in the ocean

Abstract: Direct numerical simulations of the time evolution of homogeneous stably stratified turbulent sheer flows have been performed for several Richardson numbers Ri and Reynolds numbers Rλ. The results show excellent agreement with length scale models developed from laboratory experiments to characterize oceanic turbulence. When the Richardson number Ri is less than the stationary value Ris, the turbulence intensity grows at all scales; the growth rate is a function of Ri. The size of the vertical density inversions also increases. When Ri ≥ Ri, the largest turbulent eddies become vertically constrained by buoyancy when the Ellison (turbulence) scale LEand the Ozmidov (buoyancy) scale LO are equal. At this point the mixing is most efficient and the flux Richardson number or mixing efficiency is Rf ≈ 0.20 for the stationary Richardson number Ris = 0.21. The vertical mass flux becomes countergradient when ϵ ≈ 19vN2, and vertical density overturns are suppressed in few than half of a Brunt-Vaisala period...

Control of circular cylinder flow by the use of dimples

Abstract: Measurements are reported of the drag coefficient and Strouhal number of a dimpled circular cylinder over the Reynolds number range from 2 x 104 to 3 x 10s. The ratio of the depth of the dimples to the diameter of the cylinder is 9xlO~ 3. In common with sand-roughened cylinders, the dimpled cylinder has a lower critical Reynolds number than a smooth cylinder. After the drag coefficient minimum, the CD does not rise to the high values that are typical of cylinders with sand roughness but is found to be closer to that for a smooth cylinder. Over a Reynolds number range from about 4xl04 to 3xl05, a dimpled circular cylinder has a lower drag coefficient than a smooth cylinder.

Short-time motion of colloidal particles: Numerical simulation via a fluctuating lattice-Boltzmann equation.

Abstract: A new and general technique for simulating solid-fluid suspensions, which combines molecular dynamics for the solid particles with a lattice-Boltzmann model for the fluid, is described. The many-body hydrodynamic interactions are fully accounted for, both for small particle velocities and at higher Reynolds numbers. Brownian motion of the solid particles is included by adding a fluctuating component to the fluid stress tensor. Simulations of the dynamics of colloidal particles at short times compare favorably with recent diffusing-wave spectroscopy experiments.

Low Reynolds number k —ε modelling with the aid of direct simulation data

Abstract: The constant C sub mu and the near-wall damping function f sub mu in the eddy-viscosity relation of the k-epsilon model are evaluated from direct numerical simulation (DNS) data for developed channel and boundary layer flow at two Reynolds numbers each. Various existing f sub mu model functions are compared with the DNS data, and a new function is fitted to the high-Reynolds-number channel flow data. The epsilon-budget is computed for the fully developed channel flow. The relative magnitude of the terms in the epsilon-equation is analyzed with the aid of scaling arguments, and the parameter governing this magnitude is established. Models for the sum of all source and sink terms in the epsilon-equation are tested against the DNS data, and an improved model is proposed.

Optimal perturbations and streak spacing in wall‐bounded turbulent shear flow

Abstract: The mean streak spacing of approximately 100 wall units that is observed in wall‐bounded turbulent shear flow is shown to be consistent with near‐wall streamwise vortices optimally configured to gain the most energy over an appropriate turbulent eddy turnover time. The streak spacing arising from the optimal perturbation increases with distance from the wall and is nearly independent of Reynolds number, in agreement with experiment.

The hydrodynamic force on a rigid particle undergoing arbitrary time-dependent motion at small Reynolds number

Abstract: The hydrodynamic force acting on a rigid spherical particle translating with arbitrary time-dependent motion in a time-dependent flowing fluid is calculated to O(Re) for small but finite values of the Reynolds number, Re, based on the particle's slip velocity relative to the uniform flow. The corresponding expression for an arbitrarily shaped rigid particle is evaluated for the case when the timescale of variation of the particle's slip velocity is much greater than the diffusive scale, a^2/v, where a is the characteristic particle dimension and v is the kinematic viscosity of the fluid. It is found that the expression for the hydrodynamic force is not simply an additive combination of the results from unsteady Stokes flow and steady Oseen flow and that the temporal decay to steady state for small but finite Re is always faster than the t^-½ behaviour of unsteady Stokes flow. For example, when the particle accelerates from rest the temporal approach to steady state scales as t^-2.

On statistical correlations between velocity increments and locally averaged dissipation in homogeneous turbulence

Abstract: Kolmogorov postulated in 1962 [J. Fluid Mech. 13, 82 (1962)] that the magnitude of velocity increments δur across an inertial range distance r in high Reynolds number flows is typically (rer)1/3, where er is the locally averaged dissipation rate. This refined similarity hypothesis has been widely used in discussions of anomalous exponents of velocity structure functions in connection with the scaling exponents of er. Recently Hosokawa and Yamamoto [Phys. Fluids A 4, 457 (1992)] have presented numerical evidence from turbulence simulations that δur is uncorrelated with er in moderate Reynolds number flows. In the present paper, results of similar measurements are offered for flow fields with a wide range of Reynolds numbers obtained from high‐resolution numerical simulations of both forced and decaying isotropic turbulence. The present results show clear evidence of correlations between δur and er, irrespective of the Reynolds number. Kolmogorov’s hypothesis is verified for r somewhat larger than the visco...