Showing papers on "Reynolds number published in 1988"

Direct simulation of a turbulent boundary layer up to R sub theta = 1410

Abstract: The turbulent boundary layer on a flat plate, with zero pressure gradient, is simulated numerically at four stations between R sub theta = 225 and R sub theta = 1410. The three-dimensional time-dependent Navier-Stokes equations are solved using a spectra method with up to about 10 to the 7th power grid points. Periodic spanwise and stream-wise conditions are applied, and a multiple-scale procedure is applied to approximate the slow streamwise growth of the boundary layer. The flow is studied, primarily, from a statistical point of view. The solutions are compared with experimental results. The scaling of the mean and turbulent quantities with Reynolds number is examined and compared with accepted laws, and the significant deviations are documented. The turbulence at the highest Reynolds number is studied in detail. The spectra are compared with various theoretical models. Reynolds-stress budget data are provided for turbulence-model testing.

The Existence of Two Stages in the Transition to Three-Dimensionality of a Cylinder Wake

Abstract: The transition to three‐dimensionality in the near wake of a circular cylinder involves two successive transitions, each of which corresponds with a discontinuity in the Strouhal–Reynolds number relationship. The first discontinuity [between Reynolds numbers (Re) of 170 to 180] is associated with the inception of vortex loops, and it is hysteretic. The second discontinuity (between Re=230 to 260) corresponds with a change to a finer‐scale streamwise vortex structure. At this discontinuity there is no hysteresis, and it is suggested that two modes of vortex shedding alternate in time.

Creeping flow of dilute polymer solutions past cylinders and spheres

Abstract: A dilute polymer solution is modelled as a suspension of dumbbells with finite extensibility. Time-dependent numerical calculations are performed of flow part cylindrical and spherical surfaces at low Reynolds number. A finite-difference scheme is employed in which the evolution in time of the dumbbells is followed from an initially unstretched equilibrium. Results are calculated with (i) a no-slip, and (ii) a zero-tangential-stress boundary condition at the body surface. At large Deborah number, D , the polymer is most highly stretched in thin regions of fluid close to and downstream of stagnation points of the flow. The most important region dynamically is found to be at the rear of the obstacle. Numerical refinements in space and time are included in order properly to resolve this fine-scale structure. Numerically stable results are obtained for values of D up to 16, and show that the flow field and drag force on the obstacle tend toward finite values at large D . Experimental measurements of the drag on a falling rigid sphere, and the velocity distribution around it, are compared with the numerical results for the no-slip boundary. Observations of bubble behaviour are discussed in the light of the results for the slip boundary.

Defining a universal and continuous Strouhal–Reynolds number relationship for the laminar vortex shedding of a circular cylinder

Abstract: The existence of a discontinuity in the Strouhal–Reynolds number relationship for the laminar vortex shedding of a cylinder is found to be caused by a change in the mode of oblique shedding. By ‘‘inducing’’ parallel shedding (from manipulating end conditions) the resulting Strouhal curve becomes completely continuous and agrees very well with the oblique‐shedding data, if it is transformed by S0=Sθ/cos θ (where Sθ is the Strouhal number corresponding with the oblique‐shedding angle θ). The curve also agrees with data from a completely different facility. This provides evidence that this Strouhal curve (S0) is universal (for a circular cylinder).

Heat transfer and friction characteristics in rectangular channels with rib turbulators

Abstract: The effect of the channel aspect ratio on the distribution of the local heat transfer coefficient in rectangular channels with two opposite ribbed walls (to simulate turbine airfoil cooling passages) was determined for a Reynolds number range of 10,000 to 60,000. The channel width-to-height ratios (W/H, ribs on side W) were 1/4, 1/2, 1, 2, and 4. The test channels were heated by passing current through thin, stainless steel foils instrumented with thermocouples. The local heat transfer coefficients on the ribbed side wall and on the smooth side wall of each test channel from the channel entrance to the fully developed regions were measured for two rib spacings (P/e = 10 and 20). The rib angle-of-attack was kept at 90 deg. The local data in the fully developed region were averaged and correlated, based on the heat transfer and friction similarity laws developed for ribbed channels, to cover the ranges of channel aspect ratio, rib spacing, rib height, and Reynolds number. The results compare well with the published data for flow in a square channel with two opposite ribbed walls. The correlations can be used in the design of turbine airfoil cooling passages.

A new theory of the instability of a uniform fluidized bed

Abstract: The form of the momentum equation for one-dimensional (vertical) unsteady mean motion of solid particles in a fluidized bed or a sedimenting dispersion is established from physical arguments In the case of a fluidized bed that is slightly non-uniform this equation contains two dependent variables, the local mean particle velocity V and the local concentration ϕ, and several statistical parameters of the particle motion in a uniform bed All these parameters are functions of ϕ with clear physical meanings, and the important ones are measurable It is a novel feature of the equation that it contains two explicit contributions to the bulk modulus of elasticity of the particle configuration, one arising from the transfer of particle momentum by velocity fluctuations and one arising from the effective repulsive force exerted between particles in random motion This latter contribution, which proves to be the more important of the two, is related to the gradient diffusivity of the particles, a key quantity in the new theoryThe equation of mean motion of the particles and the equation of particle conservation are sufficient to determine the behaviour of a small disturbance with sinusoidal variation of V and ϕ in the vertical direction Particle inertia forces in such a propagating wavy disturbance may promote amplitude growth, whereas particle diffusion tends to suppress it, and instability occurs when the particle Froude number exceeds a critical value Rough estimates of the relevant parameters allow the criterion for instability to be put in approximate numerical from for both gas-fluidized beds (for which the flow Reynolds number at marginal stability is small) and liquid-fluidized beds of solid spherical particles (for which the Reynolds number is well above unity), although more information about the particle diffusivity in particular is needed The predictions of the theory appear to be in qualitative accord with the available observational data on instability of gas- and liquid-fluidized beds

Instability mechanisms in shear-flow transition

Abstract: Developing an understanding of turbulent shear flow at high Reynolds numbers has been a central problem in the theory of fluid motion for over a century Like all turbulent flows, turbulent shear flow is a fluid motion of complex and irregular character whose exact behavior is very sensitive to small changes in initial or boundary conditions Turbulent shear flows are further characterized by a large range of length and time scales, with energy and momentum transfer predominantly affected by nonlinear (iner­ tial) processes between eddies of different scales In many situations of interest, the external conditions are geometrically and temporally simple, and the flow equations admit a correspondingly simple solution: one example is Hagen-Poiseuille flow in a pipe with a constant pressure gradi­ ent Simple, or laminar, flow is generally preferred at low or moderate Reynolds numbers, while turbulent flow is preferred at high Reynolds

Viscous flow with large free surface motion

Abstract: An arbitrary Lagrangian-Eulerian (ALE) Petrov-Galerkin finite element technique is developed to study nonlinear viscous fluids under large free surface wave motion. A review of the kinematics and field equations from an arbitrary reference is presented and since the major challenge of the ALE description lies in the mesh rezoning algorithm, various methods, including a new mixed formulation, are developed to update the mesh and map the moving domain in a more rational manner. Moreover, the streamline-upwind/Petrov-Galerkin formulation is implemented to accurately describe highly convective free surface flows. The effectiveness of the algorithm is demonstrated on a tsunami problem, the dam-break problem where the Reynolds number is taken as high as 3000, and a large-amplitude sloshing problem.

Linear stability of plane Poiseuille flow of two superposed fluids

Abstract: Stability of two superposed fluids of different viscosity in plane Poiseuille flow is studied numerically. Conditions for the growth of an interfacial wave are identified. The analysis extends Yih’s results [J. Fluid Mech. 27, 337 (1967)] for small wavenumbers to large wavenumbers and accounts for differences in density and thickness ratios, as well as the effects of interfacial tension and gravity. Neutral stability diagrams for the interfacial mode are reported for a wide range of the physical parameters describing the flow. The analysis shows also that the flow is linearly unstable to a shear mode instability. The dependence of the critical Reynolds number for the shear mode on the viscosity ratio is reported. Theoretical predictions of critical Reynolds numbers for both modes of instability are compared with available experimental data.

The absolute and convective nature of instability in two-dimensional wakes at low Reynolds numbers

Abstract: The linear parallel and incompressible stability of a family of bluff‐body wake profiles is studied at Reynolds numbers close to the onset of Karman vortex shedding The family of mean flow profiles allows for the variation of the wake depth as well as for a variable ratio of wake width to mixing layer thickness The absolute or convective nature of the sinuous instability is determined as a function of the profile parameters and Reynolds number A comparison of this survey with experimental data shows that in bluff‐body near wakes a region of local absolute instability begins to form at a Reynolds number of approximately one‐half the critical value for Karman vortex shedding Hence, at the onset of the global response (Karman vortex shedding), a substantial region of local absolute instability already exists in the wake This confirms the qualitative model prediction of Chomaz, Huerre, and Redekopp [submitted to Phys Rev Lett] and also shows that the prediction of vortex shedding frequencies, when based on local stability properties alone, is somewhat arbitrary even at the critical Reynolds number

On vortex formation from a cylinder. part 1: the initial instability

Abstract: Vortex shedding from a circular cylinder is examined over a tenfold range of Reynolds number, 440 ≤ Re ≤ 5040. The shear layer separating from the cylinder shows, to varying degrees, an exponential variation of fluctuating kinetic energy with distance downstream of the cylinder. The characteristics of this unsteady shear layer are interpreted within the context of an absolute instability of the near wake. At the trailing-end of the cylinder, the fluctuation amplitude of the instability correlates well with previously measured values of mean base pressure. Moreover, this amplitude follows the visualized vortex formation length as Reynolds number varies. There is a drastic decrease in this near-wake fluctuation amplitude in the lower range of Reynolds number and a rapid increase at higher Reynolds number. These trends are addressed relative to the present, as well as previous, observations.

Fluid flow due to a stretching cylinder

Abstract: The fluid flow outside of a stretching cylinder is studied. The problem is governed by a third‐order nonlinear ordinary differential equation that leads to exact similarity solutions of the Navier–Stokes equations. Because of algebraic decay, an exponential transform is used to facilitate numerical integration. Asymptotic solutions for large Reynolds numbers compare well with numerical results. The heat transfer is determined.

Closure of the Reynolds stress and scalar flux equations

Abstract: A second‐order, single‐point closure model for calculating the transport of momentum and passive scalar quantities in turbulent flows is described. Of the unknown terms that appear in the Reynolds stress and scalar flux balance equations, it is those which involve the fluctuating pressure that exert a dominant influence in the majority of turbulent flows. A closure approximation (linear in the Reynolds stress) has been formulated for the velocity‐pressure gradient correlation appearing in the Reynolds stress equation. When this is used in conjunction with previous proposals for the other unknown terms in the stress equation, the proposed model closely simulates most of the data on high Reynolds number homogeneous turbulent flows. For the fluctuating scalar‐pressure gradient correlation appearing in the scalar flux equation, an approximation has been devised that satisfies the linear transformation properties of the exact equation. Additional characteristics of the fluctuating scalar field are obtained from the solution of modeled balance equations for the scalar variance and its ‘‘dissipation’’ rate. The resulting complete scalar field model is capable of reproducing measured data in decaying scalar grid turbulence and strongly sheared, nearly homogeneous flow in the presence of a mean scalar gradient. In addition, applications to the thermal mixing layer developing downstream from a partially heated grid and to a slightly heated plane jet issuing into stagnant surrounds result in calculated profiles in close agreement with those measured.

Observations of the frequencies in a sphere wake and of drag increase by acoustic excitation

Abstract: Vortex shedding and instability wave frequencies have been measured in the wakes of spheres in the Reynolds number range 500

On vortex formation from a cylinder. Part 2. Control by splitter-plate interference

Abstract: Control of vortex formation from a circular cylinder by a long plate in its wake is examined over the Reynolds number range 140 < Re < 3600. There are two basic flow regimes: a pre-vortex formation regime, in which the plate precludes formation of a large-scale vortex upstream of the tip of the plate; and a post-vortex formation regime in which one or more large-scale vortices are formed upstream of the edge. The unsteady pressure loading at the tip of the plate increases by over an order of magnitude during transition from the pre- to post-vortex formation regime. If the plate is located near the cylinder, it is possible to more than double the vortex formation length, relative to the case of the free wake. Moreover, these observations suggest that: there is a minimum streamwise lengthscale for development of the absolute instability of the near wake and thereby the large-scale vortex; and the vortex formation length may also be influenced by the downstream vorticity dynamics. When the plate is located downstream of the initially formed vortex, effective control is possible when the near-wake fluctuation level and mean base pressure of the corresponding free (non-impinging) wake are sufficiently small. This occurs in the low and moderate subcritical regimes; the substantial control by the wake-plate interaction in this range of Reynolds number implies low strength of the absolute instability of the near wake. However, in the pure von Karman regime, selfcontrol of the near wake dominates that imposed by the wake-edge interaction, suggesting a strong absolute instability of the near wake.

Peristaltic pumping in circular cylindrical tubes: a numerical study of fluid transport and its efficiency

Abstract: A numerical method employing an upwind finite-difference technique is adopted for an investigation of peristaltic pumping in circular cylindrical tubes. such as some organs in the living body. Various peristaltic flows are calculated under conditions of finite wave amplitudes, finite wavelengths and finite Reynolds numbers, and the influence of the magnitude of these quantities on the flow is investigated. The fluid mechanics of peristaltic mixing and transport are studied in detail by analysing the reflux and the trapping phenomena. The mechanical efficiency of peristaltic pumping is also discussed, with reference to engineering and physiological applications. It is shown that quantitative differences are observed between the results obtained for flows in a circular cylindrical tube and a two-dimensional plane channel. However, for both cases the appearance of peristaltic reflux depends upon the Reynolds number and the wavenumber (mean tube radius/wavelength). Much greater peristaltic mixing and transport are realized in a circular tube than in a plane channel.

Effects of independent variation of Mach and Reynolds numbers on the low-speed aerodynamic characteristics of the NACA 0012 airfoil section

Abstract: A comprehensive data base is given for the low speed aerodynamic characteristics of the NACA 0012 airfoil section. The Langley low-turbulence pressure tunnel is the facility used to obtain the data. Included in the report are the effects of Mach number and Reynolds number and transition fixing on the aerodynamic characteristics. Presented are also comparisons of some of the results with previously published data and with theoretical estimates. The Mach number varied from 0.05 to 0.36. The Reynolds number, based on model chord, varied from 3 x 10 to the 6th to 12 x 10 to the 6th power.

Steady viscous flow past a sphere at high Reynolds numbers

Abstract: Numerical solutions are presented for steady incompressible flow past a sphere At high Reynolds numbers (results are presented up to R = 5000), the wake is found to resemble a Hill's spherical vortex

An experimental study of the wake of gas slugs rising in liquids

Abstract: A photographic study of the wakes of slugs rising in tubes of 19 mm and 52 mm internal diameter is presented. The dependence of the flow pattern in the wake upon the Reynolds number of the rising slug, R, is established for different slug lengths. Values of R covered in this study are in the range 25 to 1.3 × 104. For low values of R the flow pattern in the wake is laminar and axisymmetric and values of wake length and wake volume could be determined from the photographs: these values were correlated with the other variables in the system by means of dimensional analysis.

Peristaltic transport of a power-law fluid: Application to the ductus efferentes of the reproductive tract

Abstract: The problem of peristaltic transport of a non-Newtonian (power-law) fluid in uniform and non-uniform two-dimensional channels has been investigated under zero Reynolds number with long wavelength approximation. A comparison of the results with those for a Newtonian fluid model shows that the magnitude of pressure rise, under a given set of conditions, is smaller in the case of the non-Newtonian fluid (power-law indexn < 1) at zero flow rate. Further, the pressure rise is smaller asn decreases from 1 at zero flow rate, is independent ofn at a certain value of flow rate and becomes greater if flow rate increases further. Also, at a given flow rate, an increase in wavelength leads to a decrease in pressure rise and increase in the influence of non-Newtonian behaviour. Pressure rise in the case of non-uniform geometry, is found to be much smaller than the corresponding value in the case of uniform geometry. Finally, the analysis is applied and compared with observed flow rates in the ductus efferentes of the male reproductive tract.

Turbulent structure in low-concentration drag-reducing channel flows

Abstract: A two-component laser-Doppler velocimeter was used to obtain simultaneous measurements of the velocity components parallel and normal to the wall in two fully developed well-mixed low-concentration drag-reducing channel flows and one turbulent channel flow. For the drag-reducing flows, the average time between bursts was found to increase. Although the basic structure of the fundamental momentum transport event is shown to be the same in these drag-reducing flows, the lower-threshold Reynolds-stress-producing motions were found to be damped, while the higher-threshold motions were not. It is suggested that some strong turbulent motions are needed to maintain extended polymer molecules, which produce a solution with properties that can damp lower threshold turbulence and thereby reduce viscous drag.

Velocity measurements in a plane turbulent air jet at moderate Reynolds numbers

Abstract: An experimental investigation of the moderate Reynolds number plane air jets was undertaken and the effect of the jet Reynolds number on the turbulent flow structure was determined. The Reynolds number, which was defined by the jet exit conditions, was varied between 1000 and 7000. Other initial conditions, such as the initial turbulence intensity, were kept constant throughout the experiments. Both hot-wire and laser Doppler anemometry were used for the velocity measurements. In the moderate Reynolds number regime, the turbulent flow structure is in transition. The average size and the number of the large scale of turbulence (per unit length of jet) was unaffected by the Reynolds number. A broadening of the turbulent spectra with increasing Reynolds number was observed. This indicated that there is a decrease in the strength of the large eddies resulting from a reduction of the relative energy available to them. This diminished the jet mixing with the ambient as the Reynolds number increased. Higher Reynolds numbers led to lower jet dilution and spread rates. On the other hand, at higher Reynolds numbers the dependence of jet mixing on Reynolds number became less significant as the turbulent flow structure developed into a self-preserving state.

Boundary-layer measurements on an airfoil at low Reynolds numbers

Abstract: Etude experimentale des caracteristiques des bulles de decollement de transition par anemometrie laser et a fil chaud

Minimum-dissipation transport enhancement by flow destabilization: Reynolds’ analogy revisited

Abstract: A classical transport enhancement problem is concerned with increasing the heat transfer in a system while minimizing penalties associated with shear stress, pressure drop, and viscous dissipation. It is shown by Reynolds' analogy that viscous dissipation in a wide class of flows scales linearly with the Nusselt number and quadratically with the Reynolds number. It thus follows that transport enhancement optimization is equivalent to a problem in hydrodynamic stability theory; a more unstable flow will achieve the same Nusselt number at a lower Reynolds number, and therefore at a fraction of the dissipative cost. This transport-stability theory is illustrated in a numerical study of supercritical (unsteady) two-dimensional flow in an eddy-promoter channel comprising a plane channel with an infinite periodic array of cylindrical obstructions.It is shown that the addition of small cylinders to a plane channel results in stability modes that are little changed in form or frequency from plane-channel Tollmien-Schlichting waves. However, eddy-promoter flows are dramatically less stable than their plane-channel counterparts owing to cylinder-induced shear-layer instability (with critical Reynolds numbers on the order of hundreds rather than thousands), and thus these flows yield heat transfer rates commensurate with those of a plane-channel turbulent flow but at much lower Reynolds number. Small-cylinder supercritical eddy-promoter flows are shown to roughly preserve the convective-diffusive Reynolds analogy, and it thus follows from the transport-stability theory that eddy-promoter flows achieve the same heat transfer rates as plane-channel turbulent flows while incurring significantly less dissipation.