Showing papers on "Reynolds number published in 1996"

Three-dimensional Floquet stability analysis of the wake of a circular cylinder

Abstract: Results are reported from a highly accurate, global numerical stability analysis of the periodic wake of a circular cylinder for Reynolds numbers between 140 and 300 The analysis shows that the two-dimensional wake becomes (absolutely) linearly unstable to three-dimensional perturbations at a critical Reynolds number of 1885±10 The critical spanwise wavelength is 396 ± 002 diameters and the critical Floquet mode corresponds to a ‘Mode A’ instability At Reynolds number 259 the two-dimensional wake becomes linearly unstable to a second branch of modes with wavelength 0822 diameters at onset Stability spectra and corresponding neutral stability curves are presented for Reynolds numbers up to 300

An experimental study of round jets in cross-flow

Abstract: The structure of round jets in cross-flow was studied using flow visualization techniques and flying-hot-wire measurements. The study was restricted to jet to freestream velocity ratios ranging from 2.0 to 6.0 and Reynolds numbers based on the jet diameter and free-stream velocity in the range of 440 to 6200.Flow visualization studies, together with time-averaged flying-hot-wire measurements in both vertical and horizontal sectional planes, have allowed the mean topological features of the jet in cross-flow to be identified using critical point theory. These features include the horseshoe (or necklace) vortex system originating just upstream of the jet, a separation region inside the pipe upstream of the pipe exit, the roll-up of the jet shear layer which initiates the counter-rotating vortex pair and the separation of the flat-wall boundary layer leading to the formation of the wake vortex system beneath the downstream side of the jet.The topology of the vortex ring roll-up of the jet shear layer was studied in detail using phase-averaged flying-hot-wire measurements of the velocity field when the roll-up was forced. From these data it is possible to examine the evolution of the shear layer topology. These results are supported by the flow visualization studies which also aid in their interpretation.The study also shows that, for velocity ratios ranging from 4.0 to 6.0, the unsteady upright vortices in the wake may form by different mechanisms, depending on the Reynolds number. It is found that at high Reynolds numbers, the upright vortex orientation in the wake may change intermittently from one configuration of vortex street to another. Three mechanisms are proposed to explain these observations.

Delay of Airfoil Stall by Periodic Excitation

Abstract: It was recently demonstrated that oscillatory blowing can delay separation from a symmetrical airfoil much more effectively than the steady blowing used traditionally for this purpose. Experiments carried out on different airfoils revealed that this flow depends on many parameters such as, the location of the blowing slot, the steady and oscillatory momentum coefficients of the jet, the frequency of imposed oscillations, and the shape and incidence of the particular airfoil. In airfoils equipped with slotted flaps, the flow is also dependent on the geometry of the slot and on the Reynolds number in addition to the flap deflection that is considered as a part of the airfoil shape. The incremental improvements in single element airfoil characteristics are generally insensitive to a change in Reynolds number, provided the latter is sufficiently large. The imposed oscillations do not generate large oscillatory lift nor do they cause a periodic meander of the c.p. C* C D = dp Ct =

Use of Mass- and Area-Dimensional Power Laws for Determining Precipitation Particle Terminal Velocities

Abstract: Based on boundary layer theory and a comparison of empirical power laws relating the Reynolds and Best numbers, it was apparent that the primary variables governing a hydrometeor's terminal velocity were its mass, its area projected to the flow, and its maximum dimension. The dependence of terminal velocities on surface roughness appeared secondary, with surface roughness apparently changing significantly only during phase changes (i.e., ice to liquid). In the theoretical analysis, a new, comprehensive expression for the drag force, which is valid for both inertial and viscous-dominated flow, was derived. A hydrometeor's mass and projected area were simply and accurately represented in terms of its maximum dimension by using dimensional power laws. Hydrometeor terminal velocities were calculated by using mass- and area-dimensional power laws to parameterize the Best number, X. Using a theoretical relationship general for all particle types, the Reynolds number, Re, was then calculated from the Be...

Large-eddy simulation of turbulent confined coannular jets

Abstract: Large-eddy simulation (LES) was used to study mixing of turbulent, coannular jets discharging into a sudden expansion. This geometry resembles that of a coaxial jet-combustor, and the goal of the calculation was to gain some insight into the phenomena leading to lean blow-out (LBO) in such combustion devices. This is a first step in a series of calculations, where the focus is on the fluid dynamical aspects of the mixing process in the combustion chamber. The effects of swirl, chemical reactions and heat release were not taken into account. Mixing of fuel and oxidizer was studied by tracking a passive scalar introduced in the central jet. The dynamic subgrid-scale (DM) model was used to model both the subgrid-scale stresses and the subgrid-scale scalar flux. The Reynolds number was 38000, based on the bulk velocity and diameter of the combustion chamber. Mean velocities and Reynolds stresses are in good agreement with experimental data. Animated results clearly show that intermittent pockets of fuel-rich fluid (from the central jet) are able to cross the annular jet, virtually undiluted, into the recirculation zone. Most of the fuel-rich fluid is, however, entrained into the recirculation zone near the instantaneous reattachment point. Fuel trapped in the recirculation zone is, for the most part, entrained back into the step shear layer close to the base of the burner.

On boundary conditions in lattice Boltzmann methods

Abstract: A lattice Boltzmann boundary condition for simulation of fluid flow using simple extrapolation is proposed. Numerical simulations, including two‐dimensional Poiseuille flow, unsteady Couette flow, lid‐driven square cavity flow, and flow over a column of cylinders for a range of Reynolds numbers, are carried out, showing that this scheme is of second order accuracy in space discretization. Applications of the method to other boundary conditions, including pressure condition and flux condition are discussed.

The velocity field of the turbulent very near wake of a circular cylinder

Abstract: Hot-wire measurements were conducted in the very near wake (x/d⩽10) of a circular cylinder at a Reynolds number based on cylinder diameter, Re d of 3900. Measurements of the streamwise velocity component with the use of single sensor hot-wire probes were found to be inaccurate for such flowfields where high flow angles are present. An X-array probe provided detailed streamwise and lateral velocity component statistics. Frequency spectra of these two velocity components are also presented. Measurements with a 4-sensor hot-wire probe confirmed that the very near wake region is dominantly two-dimensional, thus validating the accuracy of the present X-array data.

Large-eddy simulation of transition to turbulence in a boundary layer developing spatially over a flat plate

Abstract: It is well known that subgrid models such as Smagorinsky's cannot be used for the spatially growing simulation of the transition to turbulence of flat-plate boundary layers, unless large-amplitude perturbations are introduced at the upstream boundary: they are over-dissipative, and the flow simulated remains laminar. This is also the case for the structure-function model (SF) of Metais & Lesieur (1992). In the present paper we present a sequel to this model, the filtered-structure-function (FSF) model. It consists of removing the large-scale fluctuations of the field before computing its second-order structure function. Analytical arguments confirm the superiority of the FSF model over the SF model for large-eddy simulations of weakly unstable transitional flows. The FSF model is therefore used for the simulation of a quasi-incompressible (M∞ = 0.5) boundary layer developing spatially over an adiabatic flat plate, with a low level of upstream forcing. With the minimal resolution 650 × 32 × 20 grid points covering a range of streamwise Reynolds numbers Rex1 e [3.4 × 105, 1.1 × 106], transition is obtained for 80 hours of time-processing on a CRAY 2 (whereas DNS of the whole transition takes about ten times longer). Statistics of the LES are found to be in acceptable agreement with experiments and empirical laws, in the laminar, transitional and turbulent parts of the domain. The dynamics of low-pressure and high-vorticity distributions is examined during transition, with particular emphasis on the neighbourhood of the critical layer (defined here as the height of the fluid travelling at a speed equal to the phase speed of the incoming Tollmien–Schlichting waves). Evidence is given that a subharmonic-type secondary instability grows, followed by a purely spanwise (i.e. time-independent) mode which yields peak-and-valley splitting and transition to turbulence. In the turbulent region, flow visualizations and local instantaneous profiles are provided. They confirm the presence of low- and high-speed streaks at the wall, weak hairpins stretched by the flow and bursting events. It is found that most of the vorticity is produced in the spanwise direction, at the wall, below the high-speed streaks. Isosurfaces of eddy viscosity confirm that the FSF model does not perturb transition much, and acts mostly in the vicinity of the hairpins.

Propulsion of Microorganisms by Surface Distortions

Abstract: Swimming strategies of microorganisms must conform to the principles of self-propulsion at low Reynolds numbers. Here we relate the translational and rotational speeds to the surface motions of a swimmer and, for spheres, make evident novel constraints on mechanisms for propulsion. The results are applied to a cyanobacterium, an organism while motile mechanism is unknown, by considering incompressible streaming of the cell surface and oscillatory, tangential surface deformations. Finally, swimming efficiency using tangential motions is related to the surface velocities and a bound on the efficiency is obtained. {copyright} {ital 1996 The American Physical Society.}

A theoretical approach to predict the performance of chevron-type plate heat exchangers

Abstract: Manufacturers of plate and frame heat exchangers nowadays mainly offer plates with chevron (or herringbone) corrugation patterns. The inclination angleof the crests and furrows of that sinusoidal pattern relative to the main flow direction has been shown to be the most important design parameter with respect to fluid friction and heat transfer. Two kinds of flow may exist in the gap between two plates (pressed together with the chevron pattern of the second plate turned into the opposite direction): the crossing flow of small substreams following the furrows of the first and the second plate, respectively, over the whole width of the corrugation pattern, dominating at lower inclination angles (lower pressure drop); and the wavy longitudinal flow between two vertical rows of contact points, prevailing at highangles (high pressure drop). The combined effects of the longer flow paths along the furrows, the crossing of the substreams, flow reversal at the edges of the chevron pattern, and the competition between crossing and longitudinal flow are taken into account to derive a relatively simple but physically reasonable equation for the friction factor ξ as a function of the angleand the Reynolds number Re. Heat-transfer coefficients are then obtained from a theoretical equation for developing thermal boundary layers in fully developed laminar or turbulent channel flow — the generalized Leveque equation — predicting heat-transfer coefficients as being proportional to (ξ·Re2)1/3. It is shown, by comparison, that this prediction is in good agreement with experimental observations quoted in the literature.

Control of laminar vortex shedding behind a circular cylinder using splitter plates

Abstract: Laminar vortex shedding behind a circular cylinder and its control using splitter plates attached to the cylinder are simulated. The vortex shedding behind a circular cylinder completely disappears when the length of the splitter plate is larger than a critical length, and this critical length is found to be proportional to the Reynolds number. The Strouhal number of the vortex shedding is rapidly decreasing with the increased plate length until the plate length (l) is nearly the same as the cylinder diameter (d). On the other hand, at 1

Large eddy simulation of particle‐laden turbulent channel flow

Abstract: Particle transport in fully‐developed turbulent channel flow has been investigated using large eddy simulation (LES) of the incompressible Navier–Stokes equations. Calculations were performed at channel flow Reynolds numbers, Reτ, of 180 and 644 (based on friction velocity and channel half width); subgrid‐scale stresses were parametrized using the Lagrangian dynamic eddy viscosity model. Particle motion was governed by both drag and gravitational forces and the volume fraction of the dispersed phase was small enough such that particle collisions were negligible and properties of the carrier flow were not modified. Material properties of the particles used in the simulations were identical to those in the DNS calculations of Rouson and Eaton [Proceedings of the 7th Workshop on Two‐Phase Flow Predictions (1994)] and experimental measurements of Kulick et al. [J. Fluid Mech. 277, 109 (1994)]. Statistical properties of the dispersed phase in the channel flow at Reτ=180 are in good agreement with the DNS; reas...

Axis switching and spreading of an asymmetric jet: the role of coherent structure dynamics

Abstract: The effects of vortex generators and periodic excitation on vorticity dynamics and the phenomenon of axis switching in a free asymmetric jet are studied experimentally. Most of the data reported are for a 3:1 rectangular jet at a Reynolds number of 450 000 and a Mach number of 0.31. The vortex generators are in the form of ‘delta tabs’, triangular-shaped protrusions into the flow, placed at the nozzle exit. With suitable placement of the tabs, axis switching could be either stopped or augmented. Two mechanisms are identified governing the phenomenon. One, as described by previous researchers, is due to the difference in induced velocities for different segments of a rolled-up azimuthal vortical structure. The other is due to the induced velocities of streamwise vortex pairs in the flow. While the former mechanism, referred to here as the ωθ-dynamics, is responsible for a rapid axis switching in periodically forced jets, e.g. screeching supersonic jets, the effect of the tabs is governed mainly by the latter mechanism, referred to as the ωx-dynamics. Both dynamics can be active in a natural asymmetric jet; the tendency for axis switching caused by the ωθ-dynamics may be, depending on the streamwise vorticity distribution, either resisted or enhanced by the ωx-dynamics. While this simple framework qualitatively explains the various observations made on axis switching, mechanisms actually in play may be much more complex. The two dynamics are not independent as the flow field is replete with both azimuthal and streamwise vortical structures which continually interact. Phase-averaged measurements for a periodically forced case, over a volume of the flow field, are carried out in an effort to gain insight into the dynamics of these vortical structures. The results are used to examine such processes as the reorientation of the azimuthal vortices, the resultant evolution of streamwise vortex pairs, as well as the redistribution of streamwise vortices originating from secondary flow within the nozzle.

Topology of fine-scale motions in turbulent channel flow

Abstract: An investigation of topological features of the velocity gradient field of turbulent channel flow has been carried out using results from a direct numerical simulation for which the Reynolds number based on the channel half-width and the centreline velocity was 7860. Plots of the joint probability density functions of the invariants of the rate of strain and velocity gradient tensors indicated that away from the wall region, the fine-scale motions in the flow have many characteristics in common with a variety of other turbulent and transitional flows: the intermediate principal strain rate tended to be positive at sites of high viscous dissipation of kinetic energy, while the invariants of the velocity gradient tensor showed that a preference existed for stable focus/stretching and unstable node/saddle/saddle topologies. Visualization of regions in the flow with stable focus/stretching topologies revealed arrays of discrete downstream-leaning flow structures which originated near the wall and penetrated into the outer region of the flow. In all regions of the flow, there was a strong preference for the vorticity to be aligned with the intermediate principal strain rate direction, with the effect increasing near the walls in response to boundary conditions.

Control of turbulent separated flow over a backward-facing step by local forcing

Abstract: An experimental study was made of the flow over a backward-facing step. Excitations were given to separated flow by means of a sinusoidally oscillating jet issuing from a thin slit near the separation line. The Reynolds number based on the step height (H) varied 13000 ⩽ Re H ⩽ 33000. Effect of local forcing on the flow structure was scrutinized by altering the forcing amplitude (0 ⩽ A 0 ⩽ 0.07) and forcing frequency (0 ⩽ St H ⩽ 5.0). Small localized forcing near the separation edge enhanced the shear-layer growth rate and produced a large roll-up vortex at the separation edge. A large vortex in the shear layer gave rise to a higher rate of entrainment, which lead to a reduction in reattachment length as compared to the unforced flow. The normalized minimum reattachment length (x r )min/x x0 was obtained at St θ ≅ 0.01. The most effective forcing frequency was found to be comparable to the shedding frequency of the separated shear layer.

The passive scalar spectrum and the Obukhov–Corrsin constant

Abstract: It is pointed out that, for microscale Reynolds numbers less than about 1000, the passive scalar spectrum in turbulent shear flows is less steep than anticipated and that the Obukhov–Corrsin constant can be defined only if the microscale Reynolds number exceeds this value In flows where the large‐scale velocity field is essentially isotropic (as in grid turbulence), the expected 5/3 scaling is observed even at modest Reynolds numbers All known data on the Obukhov–Corrsin constant are collected The support for the notion of a ‘‘universal’’ constant is shown to be reasonable Its value is about 04

The Effect of Periodic Ribs on the Local Aerodynamic and Heat Transfer Performance of a Straight Cooling Channel

Abstract: The local aerodynamic and heat transfer performance were measured in a rib-roughened square duct as a function of the rib pitch to height ratio. The blockage ratio of these square obstacles was 10 or 20 percent depending on whether they were placed on one single (1s) or on two opposite walls (2s). The Reynolds number, based on the channel mean velocity and hydraulic diameter, was fixed at 30,000. The aerodynamic description of the flow field was based on local pressure distributions along the ribbed and adjacent smooth walls as well as on two-dimensional LDV explorations in the channel symmetry plane and in two planes parallel to the ribbed wall(s). Local heat transfer distributions were obtained on the floor, between the ribs, and on the adjacent smooth side wall. Averaged parameters, such as friction factor and averaged heat transfer enhancement factor, were calculated from the local results and compared to correlations given in literature. This contribution showed that simple correlations derived from the law of the wall similarity and from the Reynolds analogy could not be applied for the present rib height-to-channel hydraulic diameter ratio (e/D h = 0.1). The strong secondary flows resulted in a three-dimensional flow field with high gradients in the local heat transfer distributions on the smooth side walls.

Examination of hypotheses in the Kolmogorov refined turbulence theory through high-resolution simulations. Part 1. Velocity field

Abstract: The fundamental hypotheses underlying Kolmogorov-Oboukhov (1962) turbulence theory (K62) are examined directly and quantitutivezy by using high-resolution numerical turbulence fields. With the use of massively parallel Connection Machine-5, we have performed direct Navier-Stokes simulations (DNS) at 5123 resolution with Taylor microscale Reynolds number up to 195. Three very different types of flow are considered : free-decaying turbulence, stationary turbulence forced at a few large scales, and a 2563 large-eddy simulation (LES) flow field. Both the forced DNS and LES flow fields show realistic inertial-subrange dynamics. The Kolmogorov constant for the k-5/3 energy spectrum obtained from the 5123 DNS flow is 1.68 kO.15. The probability distribution of the locally averaged disspation rate E, over a length scale r is nearly log-normal in the inertial subrange, but significant departures are observed for high-order moments. The intermittency parameter p, appearing in Kolmogorov's third hypothesis for the variance of the logarithmic dissipation, is found to be in the range of 0.20 to 0.28. The scaling exponents over both E, and r for the conditionally averaged velocity increments ~,u(E, are quantified, and the direction of their variations conforms with the refined similarity theory. The dimensionless averaged velocity increments (&.PI~,)/(E,~)"/ ~ are found to depend on the local Reynolds number Recr = ~f/~r~/~/v in a manner consistent with the refined similarity hypotheses. In the inertial subrange, the probability distribution of ~5,u/(e,r)'/~ is found to be universal. Because the local Reynolds number of K62, I&, = ~:'~r~/~/v, spans a finite range at a given scale r as compared to a single value for the local Reynolds number R,. = Z1/3r4/3/v in Kolmogorov's (1941a,b) original theory (K41), the inertial range in the K62 context can be better realized than that in K41 for a given turbulence field at moderate Taylor microscale (global) Reynolds number RA. Consequently universal constants in the second refined similarity hypothesis can be determined quite accurately, showing a faster-than-exponential growth of the constants with order n. Finally, some consideration is given to the use of pseudo-dissipation in the context of the K62 theory where it is found that the probability distribution of locally averaged pseudo-dissipation ei deviates more from a log-normal model than the full dissipation

Structure functions in turbulence, in various flow configurations, at Reynolds number between 30 and 5000, using extended self-similarity

Abstract: A summary of experimental results on structure functions obtained using extended self-similarity in various flow configurations (jet, grid, mixing layer, duct flow, cylinder) at Reynolds numbers ranging between 30 and 5000 is presented.

Low-Reynolds-number separation on an airfoil

Abstract: Unsteady boundary-layer separation from an Eppler 387 airfoil at low Reynolds number is studied numerically. Through a series of computations, the effects of Reynolds number and angle of attack are investigated. For all cases, vortex shedding is observed from the separated shear layer. From linear stability analysis, a KelvinHelmholtz instability is identified as causing shear layer unsteadiness. The low-turbulence wind-tunnel tests of the Eppler 387 airfoil are used to compare with the time-averaged results of the present unsteady computations. The favorable comparison between computational and experimental results strongly suggests that the unsteady largescale structure controls the low-Reynolds-number separation bubble reattachment with small-scale turbulence playing a secondary role. Nomenclature C = chord length CD - drag coefficient CL = lift coefficient Cp = pressure coefficient / = shedding frequency Re = chord Reynolds number R P - reattachment point S P = separation point Sr = Strouhal number U = velocity 9 = momentum thickness Subscripts sep = conditions at separation oo = freestream conditions