Showing papers on "Reynolds number published in 2002"

Chaotic Mixer for Microchannels

Abstract: It is difficult to mix solutions in microchannels. Under typical operating conditions, flows in these channels are laminar—the spontaneous fluctuations of velocity that tend to homogenize fluids in turbulent flows are absent, and molecular diffusion across the channels is slow. We present a passive method for mixing streams of steady pressure-driven flows in microchannels at low Reynolds number. Using this method, the length of the channel required for mixing grows only logarithmically with the Pe «clet number, and hydrodynamic dispersion along the channel is reduced relative to that in a simple, smooth channel. This method uses bas-relief structures on the floor of the channel that are easily fabricated with commonly used methods of planar lithography.

Wall-layer models for large-eddy simulations

Abstract: The numerical simulation of high Reynolds number flows is hampered by model accuracy if the Reynolds-averaged Navier–Stokes (RANS) equations are used, and by computational cost if direct or large-eddy simulations (LES) that resolve the near-wall layer are employed. The cost of a calculation scales like the Reynolds number to the power 3 for direct numerical simulations, or 2.4 for LES, making the resolution of the wall layer at high Reynolds number infeasible even with the most advanced computers. In LES, an attractive alternative to compute high-Re flows is the use of wall-layer models, in which only the outer layer is resolved, while the near-wall region is modeled. Three broad classes of approaches are presently used: bypassing this region altogether using wall functions, solving a separate set of equations in the near-wall region, weakly coupled to the outer flow, or simulating the near-wall region in a global, Reynolds-averaged, sense. These approaches are discussed and their ranges of applicability are highlighted. Various unresolved issues in wall-layer modeling are presented.

On self-sustained oscillations in two-dimensional compressible flow over rectangular cavities

Abstract: Numerical simulations are used to investigate the resonant instabilities in two-dimensional flow past an open cavity. The compressible Navier–Stokes equations are solved directly (no turbulence model) for cavities with laminar boundary layers upstream. The computational domain is large enough to directly resolve a portion of the radiated acoustic field, which is shown to be in good visual agreement with schlieren photographs from experiments at several different Mach numbers. The results show a transition from a shear-layer mode, primarily for shorter cavities and lower Mach numbers, to a wake mode for longer cavities and higher Mach numbers. The shear-layer mode is characterized well by the acoustic feedback process described by Rossiter (1964), and disturbances in the shear layer compare well with predictions based on linear stability analysis of the Kelvin–Helmholtz mode. The wake mode is characterized instead by a large-scale vortex shedding with Strouhal number independent of Mach number. The wake mode oscillation is similar in many ways to that reported by Gharib & Roshko (1987) for incompressible flow with a laminar upstream boundary layer. Transition to wake mode occurs as the length and/or depth of the cavity becomes large compared to the upstream boundary-layer thickness, or as the Mach and/or Reynolds numbers are raised. Under these conditions, it is shown that the Kelvin–Helmholtz instability grows to sufficient strength that a strong recirculating flow is induced in the cavity. The resulting mean flow is similar to wake profiles that are absolutely unstable, and absolute instability may provide an explanation of the hydrodynamic feedback mechanism that leads to wake mode. Predictive criteria for the onset of shear-layer oscillations (from steady flow) and for the transition to wake mode are developed based on linear theory for amplification rates in the shear layer, and a simple model for the acoustic efficiency of edge scattering.

Measurement of particle accelerations in fully developed turbulence

Abstract: We use silicon strip detectors (originally developed for the CLEO III high-energy particle physics experiment) to measure fluid particle trajectories in turbulence with temporal resolution of up to 70000 frames per second. This high frame rate allows the Kolmogorov time scale of a turbulent water flow to be fully resolved for 140 [ges ] Rλ [ges ] 970. Particle trajectories exhibiting accelerations up to 16000 m s −2 (40 times the r.m.s. value) are routinely observed. The probability density function of the acceleration is found to have Reynolds-number-dependent stretched exponential tails. The moments of the acceleration distribution are calculated. The scaling of the acceleration component variance with the energy dissipation is found to be consistent with the results for low-Reynolds-number direct numerical simulations, and with the K41-based Heisenberg–Yaglom prediction for Rλ [ges ] 500. The acceleration flatness is found to increase with Reynolds number, and to exceed 60 at Rλ = 970. The coupling of the acceleration to the large-scale anisotropy is found to be large at low Reynolds number and to decrease as the Reynolds number increases, but to persist at all Reynolds numbers measured. The dependence of the acceleration variance on the size and density of the tracer particles is measured. The autocorrelation function of an acceleration component is measured, and is found to scale with the Kolmogorov time τη.

Mixing processes in a zigzag microchannel: finite element simulations and optical study

Abstract: A finite element model has been used in order to study the mixing process of species in a 100-μm-wide zigzag microchannel integrating a “Y” inlet junction. The distribution of the concentration was obtained by solving successively the Navier−Stokes equation and the diffusion−convection equation in the steady state form. Because of the large range of Reynolds numbers studied (1 < Re < 800), the 2D diffusion−convection simulations are carried out with high diffusion coefficients. The results illustrated the effects of both flow rate and channel geometry on hydrodynamics and mixing efficiency. Below a critical Reynolds number of ∼80, the mixing is entirely ensured by molecular diffusion. For higher Reynolds numbers, simulations revealed the mixing contribution of laminar flow recirculations. This effect increases for lower values of diffusion coefficients. Experimental studies on the mixing of species at different flow rates are reported showing the same hydrodynamic tendency.

Velocity field statistics in homogeneous steady turbulence obtained using a high-resolution direct numerical simulation

Abstract: Velocity field statistics in the inertial to dissipation range of three-dimensional homogeneous steady turbulent flow are studied using a high-resolution DNS with up to N=10243 grid points. The range of the Taylor microscale Reynolds number is between 38 and 460. Isotropy at the small scales of motion is well satisfied from half the integral scale (L) down to the Kolmogorov scale (η). The Kolmogorov constant is 1.64±0.04, which is close to experimentally determined values. The third order moment of the longitudinal velocity difference scales as the separation distance r, and its coefficient is close to 4/5. A clear inertial range is observed for moments of the velocity difference up to the tenth order, between 2λ≈100η and L/2≈300η, where λ is the Taylor microscale. The scaling exponents are measured directly from the structure functions; the transverse scaling exponents are smaller than the longitudinal exponents when the order is greater than four. The crossover length of the longitudinal velocity struct...

Mechanisms for particle transfer and segregation in a turbulent boundary layer

Abstract: Particle transfer in the wall region of turbulent boundary layers is dominated by the coherent structures which control the turbulence regeneration cycle. Coherent structures bring particles toward and away from the wall and favour particle segregation in the viscous region, giving rise to non-uniform particle distribution proles which peak close to the wall. The object of this work is to understand the reasons for higher particle concentration in the wall region by examining turbulent transfer of heavy particles to and away from the wall in connection with the coherent structures of the boundary layer. We will examine the behaviour of a dilute dispersion of heavy particles { flyashes in air { in a vertical channel flow, using pseudo-spectral direct numerical simulation to calculate the turbulent flow eld at a shear Reynolds number Re = 150, and Lagrangian tracking to describe the dynamics of particles. Drag force, gravity and Saman lift are used in the equation of motion for the particles, which are assumed to have no influence on the flow eld. Particle interaction with the wall is fully elastic. As reported in several previous investigations, we found that particles are transferred by sweeps { Q2 type events { in the wall region, where they preferentially accumulate in the low-speed streak environments, whereas ejections { Q4 type events { transfer particles from the wall region to the outer flow. We quantify the eciency of the instantaneous realizations of the Reynolds stresses events in transferring different size particles to the wall and away from the wall, respectively. Our ndings conrm that sweeps and ejections are ecient transfer mechanisms for particles. In particular, we nd that only those sweep and ejection events with substantial spatial coherence are eective in transferring particles. However, the eciency of the transfer mechanisms is conditioned by the presence of particles to be transferred. In the case of ejections, particles are more rarely available since, when in the viscous wall layer, they are concentrated under the low-speed streaks. Even though the low-speed streaks are ejection-like environments, particles remain trapped for a long time. This phenomenon, which causes accumulation of particles in the near-wall region, can be interpreted in terms of overall fluxes toward and away from the wall by the theory of turbophoresis. This theory, proposed initially by Caporaloni et al. (1975) and re-examined later by Reeks (1983), can help to explain the existence of net particle fluxes toward the wall as a manifestation of the skewness in the velocity distribution of the particles (Reeks 1983). To understand the local and instantaneous mechanisms which give rise to the phenomenon of turbophoresis, we focus on the near-wall region of the turbulent boundary layer. We examine the role of the rear-end of a quasistreamwise vortex very near to the wall in preventing particles in the proximity of the wall from being re-entrained by the pumping action of the large, farther from the wall, forward-end of a following quasi-streamwise vortex. We examine several mechanisms

Bouncing motion of spherical particles in fluids

Abstract: We investigate experimentally the bouncing motion of solid spheres onto a solid plate in an ambient fluid which is either a gas or a liquid. In particular, we measure the coefficient of restitution e as a function of the Stokes number, St, ratio of the particle inertia to the viscous forces. The coefficient e is zero at small St, increases monotonically with St above the critical value Stc and reaches an asymptotic value at high St corresponding to the classical “dry” value emax measured in air or vacuum. This behavior is observed for a large range of materials and a master curve e/emax=f(St) is obtained. If gravity is sufficient to describe the rebound trajectory (after the collision) in a gas, this is not the case in a liquid where drag and added-mass effect are important but not sufficient: History forces are shown to be non-negligible even at large Reynolds number.

Slip flow past a stretching surface

Abstract: The slip-flow of a Newtonian fluid past a linearly stretching sheet is considered. The partial slip is controlled by a dimensionless slip factor, which varies between zero (total adhesion) and infinity (full slip). An exact analytical solution of the governing Navier-Stokes equation is found, which is formally valid for all Reynolds numbers.

Particle imaging velocimetry experiments and lattice-Boltzmann simulations on a single sphere settling under gravity

Abstract: A comparison is made between experiments and simulations on a single sphere settling in silicon oil in a box. Cross-correlation particle imaging velocimetry measurements were carried out at particle Reynolds numbers ranging from 1.5 to 31.9. The particle Stokes number varied from 0.2 to 4 and at bottom impact no rebound was observed. Detailed data of the flow field induced by the settling sphere were obtained, along with time series of the sphere’s trajectory and velocity during acceleration, steady fall and deceleration at bottom approach. Lattice–Boltzmann simulations prove to capture the full transient behavior of both the sphere motion and the fluid motion. The experimental data were used to assess the effect of spatial resolution in the simulations over a range of 2–8 grid nodes per sphere radius. The quality of the flow field predictions depends on the Reynolds number. When the sphere is very close to the bottom of the container, lubrication theory has been applied to compensate for the lack of spatial resolution in the simulations.

Large Eddy Simulation of Flow Around an Airfoil Near Stall

Abstract: A large eddy simulation (LES) of a turbulent flow past an airfoil near stall at a chord Reynolds number of 2.1 x 10 6 is performed and compared with wind-tunnel experiments. This configuration still constitutes a challenging test case for Reynolds-averaged Navier-Stokes (RANS) simulation and LES as a result of the complexity of the suction side boundary layer: an adverse pressure gradient creates successively a laminar separation bubble, a turbulent reattachment, and a turbulent separation near the trailing edge. To handle this high-Reynolds-number flow with LES on available supercomputers, a local mesh-refinement technique and a discretization of the convective fluxes are developed in a block-structured finite volume code to reduce the total number of grid points and the numerical dissipation acting on the small scales, respectively. Influence of subgrid scale modeling (SGS) is assessed through the comparisons of explicit selective mixed scale model (SMSM) and implicit monotone-integrated LES model results. Moreover, the solution sensitiveness to grid refinement and spanwise extent is investigated

Three-dimensional instability in flow over a backward-facing step

Abstract: Results are reported from a three-dimensional computational stability analysis of flow over a backward-facing step with an expansion ratio (outlet to inlet height) of 2 at Reynolds numbers between 450 and 1050. The analysis shows that the first absolute linear instability of the steady two-dimensional flow is a steady three-dimensional bifurcation at a critical Reynolds number of 748. The critical eigenmode is localized to the primary separation bubble and has a flat roll structure with a spanwise wavelength of 6.9 step heights. The system is further shown to be absolutely stable to two-dimensional perturbations up to a Reynolds number of 1500. Stability spectra and visualizations of the global modes of the system are presented for representative Reynolds numbers.

The Effects of Compression and Pore Size Variations on the Liquid Flow Characteristics in Metal Foams

Abstract: Open-cell aluminum foams were investigated using water to determine their hydraulic characteristics. Maximum fluid flow velocities achieved were 1.042 m/s. The permeability and form coefficient varied from 2.46×10 -10 m 2 and 8701 m -1 to 3529 × 10 -10 m 2 and 120 m -1 , respectively. It was determined that the flowrate range influenced these calculated parameters, especially in the transitional regime where the permeability based Reynolds number varied between unity and 26.5. Beyond the transition regime where Re K ≥30, the permeability and form coefficient monotonically approached values which were reported as being calculated at the maximum flow velocities attained. The results obtained in this study are relevant to engineering applications employing metal foams ranging from convection heat sinks to filters and flow straightening devices

Prandtl and Rayleigh number dependence of the Reynolds number in turbulent thermal convection

Abstract: The Prandtl and Rayleigh number dependences of the Reynolds number in turbulent thermal convection following from the unifying theory by Grossmann and Lohse [J. Fluid Mech. 407, 27 (2000); Phys. Rev. Lett. 86, 3316 (2001)] are presented and compared with various recent experimental findings. This dependence Re(Ra,Pr) is more complicated than a simple global power law. For Pr=5.5 and 108

Effect of different initial conditions on a turbulent round free jet

Abstract: Velocity measurements were made in two jet flows, the first exiting from a smooth contraction nozzle and the second from a long pipe with a fully developed pipe flow profile. The Reynolds number, based on nozzle diameter and exit bulk velocity, was the same (≃86,000) in each flow. The smooth contraction jet flow developed much more rapidly and approached self-preservation more rapidly than the pipe jet. These differences were associated with differences in the turbulence structure in both the near and far fields between the two jets. Throughout the shear layer for x<3d, the peak in the v spectrum occurred at a lower frequency in the pipe jet than in the contraction jet. For x≥3d, the peaks in the two jets appeared to be nearly at the same frequency. In the pipe jet, the near-field distributions of f(r) and g(r), the longitudinal and transverse velocity correlation functions, differed significantly from the contraction jet. The integral length scale Lu was greater in the pipe jet, whereas Lv was smaller. In the far field, the distributions of f(r) and g(r) were nearly similar in the two flows. The larger initial shear layer thickness of the pipe jet produced a dimensionally lower frequency instability, resulting in longer wavelength structures, which developed and paired at larger downstream distances. The regular vortex formation and pairing were disrupted in the shear layer of the pipe jet. The streamwise vortices, which enhance entrainment and turbulent mixing, were absent in the shear layer of the pipe jet. The formation of large-scale structures should occur much farther downstream in the pipe jet than in the contraction jet.

Measurement of interstitial convective heat transfer and frictional drag for flow across metal foams

Abstract: Convective heat transfer and friction drag in a duct inserted with aluminum foams have been studied experimentally. The combined effects of foam porosity (e=0.7, 0.8, and 0.95) and flow Reynolds number (1900≤Re≤7800) are examined. Frictional drags for flow across the aluminum foam are measured by pressure taps, while interstitial heat transfer coefficients in the aluminum foam are determined using a transient single-blow technique with a thermal non-equilibrium two-equation model. Solid material temperature distribution is further measured for double check of the heat transfer results. To understand the frictional drag mechanisms, smoke-wire flow visualization is conducted in the aluminum-foam ducts. Results show that both the friction factor and the volumetric heat transfer coefficient increase with decreasing the foam porosity at a fixed Reynolds number. In addition, the aluminum foam of e=0.8 has the best thermal performance under the same pumping power constraint among the three aluminum foams investigated. Finally, empirical correlations for pore Nusselt number are developed in terms of pore Reynolds number under various foam porosities

Elliptic blending model: A new near-wall Reynolds-stress turbulence closure

Abstract: A new approach to modeling the effects of a solid wall in one-point second-moment (Reynolds-stress) turbulence closures is presented. The model is based on the relaxation of an inhomogeneous (near-wall) formulation of the pressure–strain tensor towards the chosen conventional homogeneous (far-from-a-wall) form using the blending function ?, for which an elliptic equation is solved. The approach preserves the main features of Durbin’s Reynolds-stress model, but instead of six elliptic equations (for each stress component), it involves only one, scalar elliptic equation. The model, called “the elliptic blending model,” offers significant simplification, while still complying with the basic physical rationale for the elliptic relaxation concept. In addition to model validation against direct numerical simulation in a plane channel for Re? = 590, the model was applied in the computation of the channel flow at a “real-life” Reynolds number of 106, showing a good prediction of the logarithmic profile of the mean velocity.

Computation of Flow Noise Using Source Terms in Linearized Euler's Equations

Abstract: An acoustic analogy using linearized Euler’ s equations (LEE) forced with aerodynamic source terms is investigated to computetheacousticfare eld. Thishybridmethod isappliedto threemodelproblemssimulatedby solving Navier‐Stokes equations. In this way, its validity is estimated by comparing the predicted acoustic e eld with the reference solution given directly by the Navier ‐Stokes equations. The noise radiated by two corotating vortices is studied: e rst, in a medium at rest and, second, in a mean sheared e ow with no convection velocity. Then the sound e eld generated by vortex pairings in a subsonic mixing layer is investigated. In this case, a simplie ed formulation of LEE is proposed to prevent the exponential growth of instability waves. The acoustic e elds obtained by solving LEE are in good agreement with the reference solution. This study shows that the source terms introduced into the LEE are appropriate for free sheared e ows and that acoustic ‐mean e ow interactions are properly taken into account in the wave operator. Nomenclature b = half-width of the monopolar source c = sound velocity E;F;H = vectors in linearized Euler’ s equations (LEE) f = frequency f0 = fundamental frequency of the mixing layer k = complex wave number, kr Ciki M = Mach number p = pressure Re = Reynolds number rc = vortex core radius r0 = initial half distance between the two vortices S = sound source vector in LEE Si = source terms in the momentum equations T = period Tij = Lighthill’ s tensor t = time U = unknown vector in LEE U1 = slow stream velocity of the mixing layer U2 = rapid stream velocity of the mixing layer u = velocity vector, .u1;u2/ Vµ = initial tangential velocity of vortices