Showing papers on "Reynolds number published in 1976"

Terminal Velocity and Shape of Cloud and Precipitation Drops Aloft

Abstract: The terminal velocity of cloud and precipitation size drops has been analyzed for three physically distinct flow regimes: 1) slip flow about a water drop treated as rigid sphere at negligible Reynolds numbers, 2) continuum flow past a water drop treated as a rigid sphere with a steady wake at low and intermediate Reynolds numbers, and 3) continuum flow around a non-circulating water drop of equilibrium shape with an unsteady wake at moderate to large Reynolds numbers. In the lower regime the effect of slip was given by the first-order Knudsen number correction to Stokes drag. In the middle regime a semiempirical drag relation for a rigid sphere was used to obtain a formula for the Reynolds number in terms of the Davies number. In the upper regime a correlation of wind tunnel measurements on falling drops was used in conjunction with sea level terminal velocities for raindrops to obtain a formula for the Reynolds number in terms of the Bond number and physical property number. The result for the u...

Drag Coefficients of Spheres in Continuum and Rarefied Flows

Abstract: A CCURATE representations of the drag coefficients of -^Vspheres over a wide range of flow conditions are a necessary prerequisite to the calculation of gas-particle flows. For greatest utility these representations should be in a form suitable for computer calculations. Two such correlations, both still used in computer programs, were published prior to the collection of a considerable body of experimental data, and, consequently are outdated. A third representation, published subsequently, requires the use of tabular data, and is inaccurate in some flow regimes of interest. This paper presents a new correlation, suitable for utilization in computer calculations, which simplifies in the limit to certain equations derived from theory, and which offers significantly improved agreement with the experimental data. The flow regimes of interest include continuum, slip, transition, and molecular flow at Mach numbers up to 6, and at Reynolds numbers up to the laminar-turbulent transition. The effect on drag of a temperature difference between the sphere and the gas is incorporated.

Contribution towards a Reynolds-stress closure for low-Reynolds-number turbulence

Abstract: The problem of closing the Reynolds-stress and dissipation-rate equations at low Reynolds numbers is considered, specific forms being suggested for the direct effects of viscosity on the various transport processes. By noting that the correlation coefficient is nearly constant over a considerable portion of the low-Reynolds-number region adjacent to a wall the closure is simplified to one requiring the solution of approximated transport equations for only the turbulent shear stress, the turbulent kinetic energy and the energy dissipation rate. Numerical solutions are presented for turbulent channel flow and sink flows at low Reynolds number as well as a case of a severely accelerated boundary layer in which the turbulent shear stress becomes negligible compared with the viscous stresses. Agreement with experiment is generally encouraging.

The mixing layer at high Reynolds number - Large-structure dynamics and entrainment

Abstract: A turbulent mixing layer in a water channel was observed at Reynolds numbers up to 3 × 10^6. Flow visualization with dyes revealed (once more) large coherent structures and showed their role in the entrainment process; observation of the reaction of a base and an acid indicator injected on the two sides of the layer, respectively, gave some indication of where molecular mixing occurs. Autocorrelations of streamwise velocity fluctuations, using a laser-Doppler velocimeter (LDV) revealed a fundamental periodicity associated with the large structures. The surprisingly long correlation times suggest time scales much longer than had been supposed; it is argued that the mixing-layer dynamics at any point are coupled to the large structure further downstream, and some possible consequences regarding the effects of initial conditions and of the influence of apparatus geometry are discussed.

Spatially decaying turbulence and its relation to mixing across density interfaces

Abstract: The turbulence generated by a vertically oscillating grid in a water tank and the entrainment across a salinity interface caused by this turbulence have been investigated experimentally. Measurements were carried out in a homogeneous layer of fluid as well as a two-layered fluid, which permitted us to determine the decay law of this turbulence and the way in which the structure of the turbulence depends on the mesh size and on the frequency and amplitude of the grid oscillation. It was found that the turbulent kinetic energy decays with distance from the grid according to a power law , the Peclet number being high. While the bearing of these results on the problem of the thermocline or an inversion is clear we wish to emphasize that the spatial decay of turbulence is interesting in itself.

Experiments on transition to turbulence in an oscillatory pipe flow

Abstract: Experiments on transition to turbulence in a purely oscillatory pipe flow were performed for values of the Reynolds number Rδ, defined using the Stokes-layer thickness δ = (2ν/ω)½ and the cross-sectional mean velocity amplitude U, from 19 to 1530 (or for values of the Reynolds number Re, defined using the pipe diameter d and U, from 105 to 5830) and for values of the Stokes parameter λ = ½d(ω/2ν)½ (ν = kinematic viscosity and ω = angular frequency) from 1·35 to 6·19. Three types of turbulent flow regime have been detected: weakly turbulent flow, conditionally turbulent flow and fully turbulent flow. Demarcation of the flow regimes is possible on Rλ, λ or Re, λ diagrams. The critical Reynolds number of the first transition decreases as the Stokes parameter increases. In the conditionally turbulent flow, turbulence is generated suddenly in the decelerating phase and the profile of the velocity distribution changes drastically. In the accelerating phase, the flow recovers to laminar. This type of partially turbulent flow persists even at Reynolds numbers as high as Re = 5830 if the value of the Stokes parameter is high.

On Drag of Evaporating Liquid Droplets

Abstract: —Drag data of water, methanol, heptane and benzene droplets are reported here. This data together with the data of Eisenklam et al. cover the entire range of Reynolds numbers from 1 to 2000 and mass transfer numbers from 0 to 3. The present study shows that the drag coefficients as a function of Reynolds numbers correlate well with the “standard drag” curve provided the characteristic density is the free stream density and the characteristic viscosity coefficient is μ r (Tr ). The basis for the choice of these two characteristic properties is discussed. The present correlation is insensitive to the mass transfer number. This suggests that mass efflux has little effect on drag of evaporating droplets. Present study indicates that for the determination of the drag coefficient of any evaporative droplet at quasisteady state, one needs only to know the wet bulb temperature as a function of free stream temperature. This information is sufficient to calculate μ r (Tr ). The “standard drag” curve can th...

Golf Ball Aerodynamics

Abstract: A wind tunnel technique has been developed to measure the aerodynamic forces acting on golf balls over a wide range of Reynolds number and spin rate. Balls with round dimples and hexagonal dimples have been investigated. The dimples are found to induce a critical Reynolds number behaviour at a lower value of Reynolds number than that experienced by a smooth sphere and beyond this point, unlike the behaviour of a sand-roughened sphere, there is little dependence of the forces on further increases in Reynolds number. A hexagonally-dimpled ball has a higher lift coefficient and a slightly lower drag coefficient than a conventional round-dimpled ball. Trajectories are calculated using the aerodynamic data and the ranges are compared with data obtained from a driving machine on a golf course.

Large scales in the developing mixing layer

Abstract: A new experimental technique is described for the study of the interactions between the large-scale vortical features in the two-dimensional mixing layer. Detector probes above and below the mixing layer are used to monitor the large-scale structure. Conditional sampling is performed in a moderate Reynolds number developing flow, by using phase and amplitude information from these detector probes. It is shown that significant Reynolds-stress production is associated with the pairing interaction in which two vortical structures combine to form a single, larger vortical structure.

Vortex shedding from a cylinder vibrating in line with an incident uniform flow

Abstract: A study has been made of the wake of a cylinder vibrating in line with an incident steady flow. The Reynolds number for the experiments was 190, and the vortex shedding was at all times synchronized with the vibrations of the cylinder, which were in a range of frequencies near twice the Strouhal shedding frequency for the stationary cylinder. Two distinct vortex wake patterns were encountered. The first is a complex regime in which two vortices are shed during each cycle of the vibration and form an alternating pattern of vortex pairs downstream. The second pattern is an alternating street which results from the shedding of a single vortex during each cycle of the cylinder's motion. The street geometry in the latter case shares many basic characteristics with the wake of a cylinder vibrating in cross-flow. These include the effects of vibration amplitude and frequency on the longitudinal and transverse spacing of the vortices. The results obtained from these experiments in air are in agreement with previous findings from free- and forced-vibration experiments in water at both higher and lower Reynolds numbers.

The spatial viscous instability of axisymmetric jets

Abstract: The stability of three axisymmetric jet profiles is reviewed. These profiles represent the development of an incompressible jet from a nearly top-hat profile to a fully developed jet profile. The disturbance equations for arbitrary mode number in a region of zero shear, which provide the boundary conditions for the numerical solution, are solved analytically through use of the disturbance vorticity equations. Numerical solutions for the spatial stability for the axisymmetric (n = 0) disturbance and the asymmetric n = l disturbance are presented. Previously published calculations of least stable modes are shown to be incorrectly interpreted and their actual mode types are given. The critical Reynolds number is found to increase as the profile varies from a top-hat to a fully developed jet form. Closed contours of constant amplification, which are unusual in free shear flows, are shown to exist for the n = 1 disturbance in the fully developed jet region. A fluctuation energy balance is used to justify the occurrence of this destabilizing effect of decreasing Reynolds number.

The locking-on of vortex shedding due to the cross-stream vibration of circular cylinders in uniform and shear flows

Abstract: The frequencies of vortex shedding from circular cylinders forced to oscillate transversely in low-turbulence uniform and shear flows were investigated. The stream velocity in the shear flow varied linearly with spanwise distance.In both flows the vortex shedding frequency locked on to the cylinder frequency and to submultiples of the cylinder frequency. In uniform flow the range of cylinder frequencies for locking-on was dependent on the amplitude of oscillation and Reynolds number. At the boundaries of locking-on at the cylinder frequency locked-on shedding was intermittent with unforced shedding and locking-on was accompanied by a change in wake width. At a particular cylinder frequency near mid-range it is conjectured that the wake width jumped from being greater to being less than that for the stationary cylinder. In shear flow the spanwise extent of locking-on at the cylinder frequency was explained by considering the uniform flow results and the inclination of shed vortices in shear flow. At the spanwise boundaries of this locking-on, locked-on cells were shed intermittently with unforced cells which were more stable in frequency than the corresponding cells for the stationary cylinder.

Vorticity concentration and the dynamics of unstable free shear layers

Abstract: The detailed dynamics of an unstable free shear layer are examined for a gravitationally stable or neutral fluid. This first article focuses on the part of the evolution that precedes the first subharmonic interaction. This consists of the transformation of selectively amplified sinusoidal waves into periodically spaced regions of vorticity concentration (the cores) joined by thin layers (the braids), in which vorticity is also concentrated. The thin layers are the channels along which vorticity is advected into the cores, and the cores provide the strain which creates the braids. For moderately long waves an analysis is given of the braid structure as a function of time. For gravitationally stable shear layers at high Reynolds numbers, the local vorticity reaches such large values as to cause secondary shear instability on a small (length) and short (time) scale. A physical account of the primary instability and its self-limiting mechanism is used as a basis for a computation, which yields growth rates and maximum amplitude as a function of initial layer parameters. The computation supplies the wavelength of waves that grow to achieve the largest (absolute) amplitude. Finally, the model makes it clear that, in the absence of secondary instability, this initial phase of the nonlinear development of the layer contributes only a modicum of additional mixing, especially at high Reynolds numbers.

Roll-cell instabilities in rotating laminar and trubulent channel flows

Abstract: The stability of laminar and turbulent channel flow is examined for cases where Coriolis forces are introduced by steady rotation about an axis perpendicular to the plane of mean flow. Linearized equations of motion are derived for small disturbances of the Taylor type. Conditions for marginal stability in laminar Couette and Poiseuille flow correspond, in part, to the analogous solutions of buoyancy-driven convection instabilities in heated fluid layers, and to those of Taylor instabilities in the flow between rotating cylinders. In plane Poiseuille flow with rotation, the critical disturbance mode occurs at a Reynolds number of Rec = 88.53 and rotation number Ro = 0.5. At higher Reynolds numbers, unstable conditions canexist over the range of rotation numbers given by 0 < Ro < 3, provided the undisturbed flow remains laminar. A two-layer model is devised to investigate the onset of longitudinal instabilities in turbulent flow. The linear disturbance equations are solved essentially in their laminar form, whereby the velocity gradient of laminar flow is replaced by a numerically computed profile for the gradient of the turbulent mean velocity. The turbulent stress levels in the stable and unstable flow regions are represented by integrated averages of the eddy viscosity. Onset of instability for Reynolds numbers between 6000 and 35 000 is predicted to occur at Ro = 0.022, a value in remarkable agreement with the experimentally observed appearance of roll instabilities in rotating turbulent channel flow.

Experiments on a viscous fluid flow between concentric rotating spheres

Abstract: Some experimental results on incompressible viscous fluid flow in the gap between two concentric rotating spheres are discussed. The flow field in the spherical gap has been studied qualitatively by flow visualization (photographs) and quantitatively by measurements by the hot-wire technique. For a wide range of Reynolds numbers, the friction torque was measured for several gap widths and a relatively simple method of determining the torque theoretically is given. At higher Reynolds numbers instabilities appear. Their different behaviour for relatively small and large gap widths is demonstrated. For the larger gap widths, the different appearance of the Taylor–Gortler vortices, the reason for their generation, their regimes of existence as well as their influence on the friction torque are thoroughly treated. Detailed information is given on the new effect of the dependence of the wavelength of the vortices on the Reynolds number.

Solutions of the Navier-Stokes equations for vortex breakdown

Abstract: Steady solutions of the Navier-Stokes equations, in terms of velocity and pressure, for breakdown in an unconfined viscous vortex are obtained numerically using the artificial compressibility technique of Chorin combined with an ADI finite-difference scheme. Axisymmetry is assumed and boundary conditions are carefully applied at the boundaries of a large finite region in an axial plane while resolution near the axis is maintained by a coordinate transformation. The solutions, which are obtained for Reynolds numbers up to 200 based on the free-stream axial velocity and a characteristic core radius, show that breakdown results from the diffusion and convection of vorticity away from the vortex core which, because of the strong coupling between the circumferential and axial velocity fields in strongly swirling flows, can lead to stagnation and reversal of the axial flow near the axis.

Details of a Shock-Separated Turbulent Boundary Layer at a Compression Corner

Abstract: An experimental study is described in which detailed mean-flow measurements are made in a shock waveboundary-layer interaction. The interaction is produced by a 24° compression corner mounted on the wall of the Princeton University high Reynolds number wind tunnel. The experiments are performed at Mach 2.85 and Redo = 1.33 million. A detailed mapping of the flowfield is presented, including separated region shape and location and velocity profiles. Results indicate a relatively straight zero-velocity line, a persistent downstream normal pressure gradient, and reverse velocities up to 16% of u^.

Fluctuating forces on a rigid circular cylinder in confined flow

Abstract: The fluctuating lift and drag acting on a long, rigidly supported circular cylinder placed symmetrically in a narrow rectangular duct were investigated for various blockage percentages over a wide range of Reynolds numbers around the critical value. The data obtained permit a full assessment of the effect of confinement on the mean-drag coefficient, the root-mean-square values of both the drag and the lift fluctuations, the Strouhal number of the dominant vortex shedding, and the Reynolds number marking transition from laminar to turbulent flow separation. Besides experimental information on a subject on which little is known so far, the paper provides a basis for the deduction of better correction procedures concerning the effects of blockage.

Steady wake behind a sphere

Abstract: The characteristics of the steady wake behind a sphere were studied experimentally using dyed water for visualization. This work infers the possibility of the existence of a closed recirculating eddy behind a sphere even at R=10 or lower and shows that the eddy can preserve its steady state up to the case for R=190 (R represents the Reynolds number based on the diameter of the sphere). In addition, a new profile for the variation of the wake separation angle against the steady state Reynolds number is presented.

Pressure and force distributions on a sharp-nosed circular cylinder at large angles of inclination to a uniform subsonic stream

Abstract: This paper reports an experimental investigation of pressure and force distributions on a sharp-nosed circular cylinder inclined to a uniform low-speed air flow under conditions of laminar separation of the boundary layer. The main concern is with the out-of-plane force (i.e. the side force if the body is at incidence). The experimental model consisted of an extensively pressure-tapped cylinder to which four different noses were fitted. The results show that there is an oscillatory distribution of out-of-plane force along the cylinder for most of the inclination range 0-90°. The amplitude of this distribution is strongly affected by nose shape in conditions where the out-of-plane force extends onto the nose. At very high angles of inclination the oscillatory distribution disappears and is replaced by a vortex pattern like that found on an infinite yawed cylinder. The general nature of the out-of-plane force is found to be consistent with the impulsively started flow analogy. Unsteadiness in the flow was found to cause a serious reduction in many of the time-averaged values. The unsteadiness is ascribed to the switching of the flow pattern due to free-stream turbulence. Measurements of the time histories of certain pressures enabled values of the force in the unswitched state to be calculated. The Reynolds number was found to have an important influence at inclinations above 55°. However, it was also found that the range of Reynolds numbers over which this effect occurs can depend on the scale of the model.

Numerical Solutions of Supersonic and Hypersonic Laminar Compression Corner Flows

Abstract: An efficient time-splitting, second-order accurate, numerical scheme is used to solve the complete Navier-Stokes equations for supersonic and hypersonic laminar flow over a two-dimensional compression corner. A fine, exponentially stretched mesh spacing is used in the region near the wall for resolving the viscous layer. Good agreement is obtained between the present computed results and experimental measurement for a Mach number of 14.1 and a Reynolds number of 1.04 x 10(exp 5) with wedge angles of 15 deg, 18 deg, and 24 deg. The details of the pressure variation across the boundary layer are given, and a correlation between the leading edge shock and the peaks in surface pressure and heat transfer is observed.

Flow of inelastic and viscoelastic fluids past a sphere

Abstract: This is essentially an engineering study undertaken with a view to providing drag coefficient correlations for the motion of a solid sphere in inelastic and viscoelastic fluids over a wide range of Reynolds numbers. An approximate closed form analytical solution has been obtained for the motion of a solid sphere in powerlaw fluids and this solution has been verified experimentally. The high Reynolds number flow was analysed theoretically using boundary layer theory; the results were used to separate form and skin friction. Viscoelastic fluids showed “drag reduction” at high Reynolds number. About 300 experimental data points were used to obtain drag coefficient correlations over a wide range of material and flow parameters.