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Showing papers on "Reynolds number published in 2004"


Journal ArticleDOI
TL;DR: In this article, the authors review the experimental evidence on turbulent flows over rough walls and discuss some ideas on how rough walls can be modeled without the detailed computation of the flow around the roughness element.
Abstract: ▪ AbstractWe review the experimental evidence on turbulent flows over rough walls. Two parameters are important: the roughness Reynolds number ks+, which measures the effect of the roughness on the buffer layer, and the ratio of the boundary layer thickness to the roughness height, which determines whether a logarithmic layer survives. The behavior of transitionally rough surfaces with low ks+ depends a lot on their geometry. Riblets and other drag-reducing cases belong to this regime. In flows with δ/k ≲ 50, the effect of the roughness extends across the boundary layer, and is also variable. There is little left of the original wall-flow dynamics in these flows, which can perhaps be better described as flows over obstacles. We also review the evidence for the phenomenon of d-roughness. The theoretical arguments are sound, but the experimental evidence is inconclusive. Finally, we discuss some ideas on how rough walls can be modeled without the detailed computation of the flow around the roughness element...

1,389 citations


Journal ArticleDOI
TL;DR: In this paper, the spectra and correlations of the velocity fluctuations in turbulent channels, especially above the buffer layer, were analyzed using direct numerical simulations with friction Reynolds numbers up to Re at very large ones.
Abstract: The spectra and correlations of the velocity fluctuations in turbulent channels, especially above the buffer layer, are analysed using new direct numerical simulations with friction Reynolds numbers up to Re at very large ones.

717 citations


Journal ArticleDOI
TL;DR: A very simple one-dimensional swimmer consisting of three spheres that are linked by rigid rods whose lengths can change between two values can be used in constructing molecular-sized machines.
Abstract: We propose a very simple one-dimensional swimmer consisting of three spheres that are linked by rigid rods whose lengths can change between two values. With a periodic motion in a nonreciprocal fashion, which breaks the time-reversal symmetry as well as the translational symmetry, we show that the model device can swim at low Reynolds number. This model system could be used in constructing molecular-sized machines.

519 citations


Journal ArticleDOI
TL;DR: In this article, an experimental study of the migration of dilute suspensions of particles in Poiseuille flow at Reynolds numbers from the entrance, changes from one centred at the annulus predicted by the theory to one with the particles primarily on the inner annulus.
Abstract: An experimental study of the migration of dilute suspensions of particles in Poiseuille flow at Reynolds numbers from the entrance, changes from one centred at the annulus predicted by the theory to one with the particles primarily on the inner annulus. The case of slightly non-neutrally buoyant particles was also investigated. A particle trajectory simulation based on asymptotic theory was performed to facilitate the comparison of theory and the experimental observations.

463 citations


Journal ArticleDOI
TL;DR: The results suggest that the transport of vorticity from the leading edge to the wake that permits prolonged vortex attachment takes different forms at different Re, analogous to the flow structure generated by delta wing aircraft.
Abstract: The elevated aerodynamic performance of insects has been attributed in part to the generation and maintenance of a stable region of vorticity known as the leading edge vortex (LEV). One explanation for the stability of the LEV is that spiraling axial flow within the vortex core drains energy into the tip vortex, forming a leading-edge spiral vortex analogous to the flow structure generated by delta wing aircraft. However, whereas spiral flow is a conspicuous feature of flapping wings at Reynolds numbers (Re) of 5000, similar experiments at Re=100 failed to identify a comparable structure. We used a dynamically scaled robot to investigate both the forces and the flows created by a wing undergoing identical motion at Re of ~120 and ~1400. In both cases, motion at constant angular velocity and fixed angle of attack generated a stable LEV with no evidence of shedding. At Re=1400, flow visualization indicated an intense narrow region of spanwise flow within the core of the LEV, a feature conspicuously absent at Re=120. The results suggest that the transport of vorticity from the leading edge to the wake that permits prolonged vortex attachment takes different forms at different Re.

442 citations


Journal ArticleDOI
TL;DR: In this paper, three-dimensional travelling wave solutions for pressure-driven fluid flow through a circular pipe are found for wall-bounded shear flows using a constructive continuation procedure based on key physical mechanisms.
Abstract: Three-dimensional travelling wave solutions are found for pressure-driven fluid flow through a circular pipe. They consist of three well-defined flow features – streamwise rolls and streaks which dominate and streamwise-dependent wavy structures. The travelling waves can be classified by the and traceable down to a Reynolds number (based on the mean velocity) of 1251. The new solutions are found using a constructive continuation procedure based upon key physical mechanisms thought generic to wall-bounded shear flows. It is believed that the appearance of these new alternative solutions to the governing equations as the Reynolds number is increased is a necessary precursor to the turbulent transition observed in experiments.

436 citations


Journal ArticleDOI
TL;DR: In this paper, it was shown that dissipation is not important at high Reynolds number, and provided an alternative theory that predicts the current speed and depth based on energy-conserving flow that is in good agreement with experiments.
Abstract: The dynamics of gravity currents are believed to be strongly influenced by dissipation due to turbulence and mixing between the current and the surrounding ambient fluid. This paper describes new theory and experiments on gravity currents produced by lock exchange which suggest that dissipation is unimportant when the Reynolds number is sufficiently high. Although there is mixing, the amount of energy dissipated is small, reducing the current speed by a few percent from the energy-conserving value. Benjamin (J. Fluid Mech. vol. 31, 1968, p. 209) suggests that dissipation is an essential ingredient in gravity current dynamics. We show that dissipation is not important at high Reynolds number, and provide an alternative theory that predicts the current speed and depth based on energy-conserving flow that is in good agreement with experiments. We predict that in a deep ambient the front Froude number is 1, rather than the previously accepted value of √ 2. New experiments are reported for this case that support the new theoretical value. This paper provides an analysis of the motion of a gravity current produced by lock exchange. In a lock exchange experiment, fluids of different densities initially at rest are separated by a vertical barrier – the lock gate – in a tank. When the gate is removed, differences in the hydrostatic pressure cause the denser fluid to flow in one direction along the bottom boundary of the tank, while the lighter fluid flows in the opposite direction along the top boundary of the tank. Figure 1 shows the initial configurations for lock exchange flows: a full-depth release when the depths of heavy and light fluid on both sides of the gate are equal is shown in (a )a nd apartial-depth release when the dense fluid occupies only a fraction of the full depth is shown in (b). Figure 2 shows the flow resulting from a full-depth lock release experiment. In this case the densities on the two sides of the lock gate are very similar (the density ratio γ = ρ1/ρ2 < 1 is close to unity). A dense gravity current travels to the right along the lower boundary and a buoyant current travels to the left along the upper boundary. Visually the flows are very nearly symmetric, and the dense and light fronts travel at almost the same speeds (figure 2b). The currents occupy about half the channel depth in each case, although they may be shallower immediately behind the head where there is mixing. The speeds of the two currents are constant within experimental resolution. Previous similar observations led Benjamin (1968) to develop a theory for the propagation of a steadily advancing current. He considered one half of the flow shown in figure 2(a), say the dense current only. In a frame of reference moving with the current, the front

407 citations


Journal ArticleDOI
TL;DR: In this paper, the conditions required to form nanoliter-sized droplets (plugs) of viscous aqueous reagents in flows of inuniscible carrier fluid within microfluidic channels were characterized.

388 citations


Journal ArticleDOI
TL;DR: In this paper, micro T-mixers are fabricated and tested to investigate their feasibility as a rapid mixing micromixer and their corresponding mixing performances are observed with an optical microscope.
Abstract: In this paper, micro T-mixers are fabricated and tested to investigate their feasibility as a rapid mixing micromixer. The micro T-mixers are fabricated out of a silicon substrate and bonded to a Pyrex glass plate to enable their mixing performances be observed and characterized. The mixing is characterized using a blue dye and a colourless liquid, the results are further verified by the hydrolysis reaction of dichloroacetyl phenol red. Different pressures are applied onto the inlets of the micro T-mixers and their corresponding mixing performances are observed with an optical microscope. Liquid streams break up into striations at progressively higher Reynolds number of flow and there exists a Reynolds number, between 400 and 500, when these striations disappear into uniform concentration across the mixing channel. The observations are further supported by computer simulations, which enable the fast mixing to be explained by the asymmetrical flow conditions at the inlets, in addition to the generation of vortices and secondary flow at the junction. It is shown that for a micro T-mixer with a mixing channel having a hydraulic diameter of 67 μm, an applied pressure of 5.5 bar is sufficient to cause complete mixing within less than a millisecond after the two liquids make contact.

382 citations


Journal ArticleDOI
TL;DR: In this article, the effect of high levels of free-stream turbulence on the transition in a Blasius boundary layer is studied by means of direct numerical simulations, where a synthetic turbulent inflow is obtained as superposition of modes of the continuous spectrum of the Orr-Sommerfeld and Squire operators.
Abstract: The effect of high levels of free-stream turbulence on the transition in a Blasius boundary layer is studied by means of direct numerical simulations, where a synthetic turbulent inflow is obtained as superposition of modes of the continuous spectrum of the Orr–Sommerfeld and Squire operators. In the present bypass scenario the flow in the boundary layer develops streamwise elongated regions of high and low streamwise velocity and it is suggested that the breakdown into turbulent spots is related to local instabilities of the strong shear layers associated with these streaks. Flow structures typical of the spot precursors are presented and these show important similarities with the flow structures observed in previous studies on the secondary instability and breakdown of steady symmetric streaks.Numerical experiments are performed by varying the energy spectrum of the incoming perturbation. It is shown that the transition location moves to lower Reynolds numbers by increasing the integral length scale of the free-stream turbulence. The receptivity to free-stream turbulence is also analysed and it is found that two distinct physical mechanisms are active depending on the energy content of the external disturbance. If low-frequency modes diffuse into the boundary layer, presumably at the leading edge, the streaks are induced by streamwise vorticity through the linear lift-up effect. If, conversely, the free-stream perturbations are mainly located above the boundary layer a nonlinear process is needed to create streamwise vortices inside the shear layer. The relevance of the two mechanisms is discussed.

373 citations


Journal ArticleDOI
TL;DR: In this paper, high-resolution Navier-Stokes simulations and laboratory measurements of fluid flow in a natural sandstone fracture were conducted, where epoxy casts were made of the two opposing fracture surfaces, and the surface profiles were then measured at a vertical resolution of ±2 μm, every 20 μm in the x and y-directions, over 2 cm × 2 cm regions of the fracture.

Journal ArticleDOI
TL;DR: In this article, entropy production in incompressible turbulent shear flows of Newtonian fluids is analyzed systematically and incorporated into a CFD code, based on asymptotic considerations wall functions for the four production terms are developed.

Journal ArticleDOI
TL;DR: The bottleneck effect is shown to be equally strong both for magnetic and nonmagnetic turbulence, but it is far weaker in one-dimensional spectra that are normally studied in laboratory turbulence.
Abstract: Nonhelical hydromagnetic forced turbulence is investigated using large scale simulations on up to $256$ processors and ${1024}^{3}$ mesh points. The magnetic Prandtl number is varied between 1∕8 and 30, although in most cases it is unity. When the magnetic Reynolds number is based on the inverse forcing wave number, the critical value for dynamo action is shown to be around 35 for magnetic Prandtl number of unity. For small magnetic Prandtl numbers we find the critical magnetic Reynolds number to increase with decreasing magnetic Prandtl number. The Kazantsev ${k}^{3∕2}$ spectrum for magnetic energy is confirmed for the kinematic regime, i.e., when nonlinear effects are still unimportant and when the magnetic Prandtl number is unity. In the nonlinear regime, the energy budget converges for large Reynolds numbers (around 1000) such that for our parameters about $70%$ is in kinetic energy and about $30%$ is in magnetic energy. The energy dissipation rates are converged to $30%$ viscous dissipation and $70%$ resistive dissipation. Second-order structure functions of the Elsasser variables give evidence for a ${k}^{\ensuremath{-}5∕3}$ spectrum. Nevertheless, the three-dimensional spectrum is close to ${k}^{\ensuremath{-}3∕2}$, but we argue that this is due to the bottleneck effect. The bottleneck effect is shown to be equally strong both for magnetic and nonmagnetic turbulence, but it is far weaker in one-dimensional spectra that are normally studied in laboratory turbulence. Structure function exponents for other orders are well described by the She-Leveque formula, but the velocity field is significantly less intermittent and the magnetic field is more intermittent than the Elsasser variables.

Journal ArticleDOI
TL;DR: In this article, an empirical model of the surface pressure spectrum beneath a two-dimensional, zero-pressure-gradient boundary layer is presented that is based on the experimental surface pressure spectra measured by seven research groups.
Abstract: An empirical model of the surface pressure spectrum beneath a two-dimensional, zero-pressure-gradient boundary layer is presented that is based on the experimental surface pressure spectra measured by seven research groups. The measurements cover a large range of Reynolds number, 1.4 × 10 3 < Reθ < 2.34 × × 10 4 . The model is a simple function of the ratio of the timescales of the outer to inner boundary layer. It incorporates the effect of Reynolds number through the timescale ratio and compares well to experimental data. It is proposed that the effect of Reynolds number is more aptly described as the effect of the range of relevant scales. Spectral features of the experimental data and the scaling behavior of the surface pressure spectrum are also discussed.

Journal ArticleDOI
TL;DR: A second generation micro-mixer, being a further optimised version of a first prototype, relying on the consequent utilisation of the split-and-recombine principle is presented, and it is shown that the mixing can be characterized by a positive finite-time Lyapunov exponent although being highly regular and uniform.
Abstract: A second generation micro-mixer, being a further optimised version of a first prototype, relying on the consequent utilisation of the split-and-recombine principle is presented. We show that the mixing can be characterized by a positive finite-time Lyapunov exponent although being highly regular and uniform. Using computational fluid dynamics (CFD) we investigate the mixing performance for Reynolds numbers in the range of about 1 to about 100. In particular for low Reynolds numbers (Re < 15) the CFD results predict an almost ideal multi-lamination. Thus, the developed mixer is especially suited for efficient mixing of highly viscous fluids. Furthermore, the numerical results are experimentally validated by investigations of mixing of water–glycerol solutions. The experimental results are found to be in excellent agreement with the numerical data and prove the high mixing efficiency.

Journal ArticleDOI
TL;DR: In this paper, the flow structure and heat transfer characteristics of an isolated square cylinder in cross flow are investigated numerically for both steady and unsteady periodic laminar flow in the two-dimensional regime, for Reynolds numbers of 1 to 160 and a Prandtl number of 0.7.
Abstract: The flow structure and heat transfer characteristics of an isolated square cylinder in cross flow are investigated numerically for both steady and unsteady periodic laminar flow in the two-dimensional regime, for Reynolds numbers of 1 to 160 and a Prandtl number of 0.7. The effect of vortex shedding on the isotherm patterns and heat transfer from the cylinder is discussed. Heat transfer correlations between Nusselt number and Reynolds number are presented for uniform heat flux and constant cylinder temperature boundary conditions.

Journal ArticleDOI
TL;DR: In this article, the effects of viscous dissipation on the temperature field and ultimately on the friction factor have been investigated using dimensional analysis and experimentally validated computer simulations using three common working fluids, i.e., water, methanol and iso-propanol, in different conduit geometries.

Journal ArticleDOI
TL;DR: In this article, the effect of jet temperature on the noise radiated by subsonic jets was quantified and it was concluded that the change in spectral shape at high jet temperatures, normally attributed to the contribution from dipoles, is due to Reynolds number effects and not dipoles.
Abstract: A systematic study has been undertaken to quantify the effect of jet temperature on the noise radiated by subsonic jets. Nozzles of different diameters were tested to uncover the effects of Reynolds number. All the tests were carried out at Boeing's Low Speed Aeroacoustic Facility, with simultaneous measurement of thrust and noise. It is concluded that the change in spectral shape at high jet temperatures, normally attributed to the contribution from dipoles, is due to Reynolds number effects and not dipoles. This effect has not been identified before. A critical value of the Reynolds number that would need to be maintained to avoid the effects associated with low Reynolds number has been estimated to be 400 000. It is well-known that large-scale structures are the dominant generators of noise in the peak radiation direction for high-speed jets. Experimental evidence is presented that shows the spectral shape at angles close to the jet axis from unheated low subsonic jets to be the same as from heated supersonic jets. A possible mechanism for the observed trend is proposed. When a subsonic jet is heated with the Mach number held constant, there is a broadening of the angular sector in which peak radiation occurs. Furthermore, there is a broadening of the spectral peak. Similar trends have been observed at supersonic Mach numbers. The spectral shapes in the forward quadrant and in the near-normal angles from unheated and heated subsonic jets also conform to the universal shape obtained from supersonic jet data. Just as for unheated jets, the peak frequency at angles close to the jet axis is independent of jet velocity as long as the acoustic Mach number is less than unity. The extensive database generated in the current test programme is intended to provide test cases with high-quality data that could be used for the evaluation of theoretical/semi-theoretical jet noise prediction methodologies.

Journal ArticleDOI
TL;DR: In this paper, a non-dimensional number quantifying the part of axial conduction in walls of a mini-micro counter-flow heat exchanger is proposed, which is shown to be a good approximation of the heat transfer coefficient.

Journal ArticleDOI
TL;DR: In this article, the authors present detailed wind tunnel tests data taken on six airfoils having application to small wind turbines, including the E387, FX 63-137, S 822, S834, SD2030, and SH3055.
Abstract: This paper presents detailed wind tunnel tests data taken on six airfoils having application to small wind turbines. In particular, lift, drag and moment measurements were taken at Reynolds numbers of 100,000, 200,000, 350,000 and 500,000 for both clean and rough conditions. In some cases, data was also taken at a Reynolds number of 150,000. The airfoils included the E387, FX 63-137, S822, S834, SD2030, and SH3055. Prior to carrying out the tests, wind tunnel flow quality measurements were taken to document the low Reynolds number test environment, and also oil flow visualization data and performance data were taken on the E387 for comparison with measurements taken at NASA Langley in the Low Turbulence Pressure Tunnel. The new results compare favorably with the benchmark NASA data. Highlights of the performance characteristics of the six airfoils are then discussed.

Journal ArticleDOI
TL;DR: In this article, a study of the lift, drag, and pitching moment characteristics of low aspect ratio operating at low Reynolds numbers is presented, which includes comparison of lift-curve slope, nonlinear equation approximations, maximum lift coefficient, and center of lift.
Abstract: The recent interest in the development of small unmanned aerial vehicles (UAVs) and micro air vehicles has revealed a need for a more thorough understanding of the aerodynamics of small airplanes flying at low speeds. In response to this need, a study of the lift, drag, and pitching moment characteristics of wings of low aspect ratio operating at low Reynolds numbers are presented. Wind-tunnel tests of wings with aspect ratios between 0.5 and 2.0, four distinct planforms, thickness-to-chord ratios of ≈ 2%, and 5-to-1 elliptical leading edges have been conducted as part of this research. The Reynolds numbers considered were in the range of 7 × × 10 4 to 2 × × 10 5 . Analysis of the data includes comparison of lift-curve slope, nonlinear equation approximations, maximum lift coefficient, and center of lift.

Journal ArticleDOI
TL;DR: In this paper, a simulation of turbulent heat transfer in a channel flow has been carried out in order to investigate the characteristics of surface heat-flux fluctuations, and the effect of large-scale structures extends even to the surface heatfluctuations, and increases with increasing Reynolds number.

Journal ArticleDOI
TL;DR: In this article, the transition to turbulent flow is studied for liquids of different polarities in glass microtubes having diameters between 50 and 247 µm, and the onset of transition occurs at Reynolds numbers of ~1,800-2,000, as indicated by greater thanlaminar pressure drop and micro-PIV measurements of mean velocity and rms velocity fluctuations at the centerline.
Abstract: The transition to turbulent flow is studied for liquids of different polarities in glass microtubes having diameters between 50 and 247 µm. The onset of transition occurs at Reynolds numbers of ~1,800–2,000, as indicated by greater-than-laminar pressure drop and micro-PIV measurements of mean velocity and rms velocity fluctuations at the centerline. Transition at anomalously low values of Reynolds number was never observed. Additionally, the results of more than 1,500 measurements of pressure drop versus flow rate confirm the macroscopic Poiseuille flow result for laminar flow resistance to within −1% systematic and ±2.5% rms random error for Reynolds numbers less than 1,800.

Journal ArticleDOI
TL;DR: In this article, a detailed analysis of the dependence of drag reduction on the oscillatory parameters allows us to address conflicting results hitherto reported in the literature, and we assess the possibility for the power saved to be higher than the power spent for the movement of the walls (when mechanical losses are neglected).
Abstract: Direct numerical simulations of the incompressible Navier–Stokes equations are employed to study the turbulent wall-shear stress in a turbulent channel flow forced by lateral sinusoidal oscillations of the walls. The objective is to produce a documented database of numerically computed friction reductions. To this aim, the particular numerical requirements for such simulations, owing for example to the time-varying direction of the skin-friction vector, are considered and appropriately accounted for. A detailed analysis of the dependence of drag reduction on the oscillatory parameters allows us to address conflicting results hitherto reported in the literature. At the Reynolds number of the present simulations, we compute a maximum drag reduction of 44.7%, and we assess the possibility for the power saved to be higher than the power spent for the movement of the walls (when mechanical losses are neglected). A maximum net energy saving of 7.3% is computed. Furthermore, the scaling of the amount of drag reduction is addressed. A parameter, which depends on both the maximum wall velocity and the period of the oscillation, is found to be linearly related to drag reduction, as long as the half-period of the oscillation is shorter than a typical lifetime of the turbulent near-wall structures. For longer periods of oscillation, the scaling parameter predicts that drag reduction will decrease to zero more slowly than the numerical data. The same parameter also describes well the optimum period of oscillation for fixed maximum wall displacement, which is smaller than the optimum period for fixed maximum wall velocity, and depends on the maximum displacement itself.

Journal ArticleDOI
TL;DR: Groisman and Steinberg as discussed by the authors presented an extended account of experimental observations of elasticity-induced turbulence in three different systems: a swirling flow between two plates, a Couette-Taylor (CT), and a flow in a curvilinear channel.
Abstract: Following our first report (A Groisman and V Steinberg 2000 Nature 405 53), we present an extended account of experimental observations of elasticity-induced turbulence in three different systems: a swirling flow between two plates, a Couette–Taylor (CT) flow between two cylinders, and a flow in a curvilinear channel (Dean flow). All three set-ups had a high ratio of the width of the region available for flow to the radius of curvature of the streamlines. The experiments were carried out with dilute solutions of high-molecular-weight polyacrylamide in concentrated sugar syrups. High polymer relaxation time and solution viscosity ensured prevalence of non-linear elastic effects over inertial non-linearity, and development of purely elastic instabilities at low Reynolds number (Re) in all three flows. Above the elastic instability threshold, flows in all three systems exhibit features of developed turbulence. They include: (i) randomly fluctuating fluid motion excited in a broad range of spatial and temporal scales and (ii) significant increase in the rates of momentum and mass transfer (compared with those expected for a steady flow with a smooth velocity profile). Phenomenology, driving mechanisms and parameter dependence of the elastic turbulence are compared with those of the conventional high-Re hydrodynamic turbulence in Newtonian fluids. Some similarities as well as multiple principal differences were found. In two out of three systems (swirling flow between two plates and flow in the curvilinear channel), power spectra of velocity fluctuations decayed rather quickly, following power laws with exponents of about −3.5. It suggests that, being random in time, the flow is rather smooth in space, in the sense that the main contribution to deformation and mixing (and, possibly, elastic energy) is coming from flow at the largest scale of the system. This situation, random in time and smooth in space, is analogous to flows at small scales (below the Kolmogorov dissipation scale) in high-Re turbulence.

Journal ArticleDOI
TL;DR: In this article, the wake structures and the lift and thrust of the airfoil are shown to be strongly dependent on both the Strouhal number and the reduced frequency k of the plunge oscillation at this Reynolds number.
Abstract: The flow over a NACA 0012 airfoil, oscillated sinusoidally in plunge, is simulated numerically using a compressible two-dimensional Navier-Stokes solver at a Reynolds number of 2 ×10 4 . The wake of the airfoil is visualized using a numerical particle tracing method. Close agreement is obtained between numerically simulated wake structures and experimental wake visualizations in the literature, when the flow is assumed to be fully laminar. The wake structures, and the lift and thrust of the airfoil, are shown to be strongly dependent on both the Strouhal number and the reduced frequency k of the plunge oscillation at this Reynolds number. Leading-edge separation appears to dominate the generation of aerodynamic forces for reduced frequencies below approximately k = 4 but becomes secondary for higher frequencies. Wake structures appear to be controlled primarily by trailing-edge effects at all frequencies tested up to k=20. Aerodynamic force results obtained at this Reynolds number show marked differences from those predicted by potential flow analyses at low plunge frequency and high amplitude but are similar at high frequency and low amplitude, consistent with the effect of leading-edge separation.

Journal ArticleDOI
TL;DR: In this article, the behavior of flows over a backward-facing step geometry for various expansion ratios H/h=1.9423, 2.5 and 3.0 was investigated.
Abstract: This paper is concerned with the behavior of flows over a backward-facing step geometry for various expansion ratios H/h=1.9423, 2.5 and 3.0. A literature survey was carried out and it was found that the flow shows a strong two-dimensional behavior, on the plane of symmetry, for Reynolds numbers ReD=ρUbD/μ below approximately 400 (Ub= bulk velocity and D= hydraulic diameter). In this Reynolds number range, two-dimensional predictions were carried out to provide information on the general integral properties of backward-facing step flows, on mean velocity distributions and streamlines. Information on characteristic flow patterns is provided for a wide Reynolds number range, 10−4≤ReD≤800. In the limiting case of ReD→0, a sequence of Moffatt eddies of decreasing size and intensity is verified to exist in the concave corner also at ReD=1. The irreversible pressure losses are determined for various Reynolds numbers as a function of the expansion ratio. The two-dimensional simulations are known to underpredict the primary reattachment length for Reynolds numbers beyond which the actual flow is observed to be three-dimensional. The spatial evolution of jet-like flows in both the streamwise and the spanwise direction and transition to three-dimensionality were studied at a Reynolds number ReD=648. This three-dimensional analysis with the same geometry and flow conditions as reported by Armaly et al. (1983) reveals the formation of wall jets at the side wall within the separating shear layer. The wall jets formed by the spanwise component of the velocity move towards the symmetry plane of the channel. A self-similar wall-jet profile emerges at different spanwise locations starting with the vicinity of the side wall. These results complement information on backward-facing step flows that is available in the literature.

Journal ArticleDOI
TL;DR: The effect of a magnetic field on peristaltic transport of blood in a non-uniform two-dimensional channels has been investigated under zero Reynolds number with long wavelength approximation and it is found that the pressure rise decreases as the couple-stress fluid parameter @c increases and increases as the Hartmann number M increases.

Journal ArticleDOI
TL;DR: In this paper, a systematic numerical study of flow past an impulsively started circular cylinder at low and moderate Reynolds numbers using a lattice-Boltzmann algorithmic approach is presented together with an extended volumetric boundary scheme.
Abstract: In this paper a systematic numerical study of flow past an impulsively started circular cylinder at low and moderate Reynolds numbers using a lattice-Boltzmann algorithmic approach is presented together with an extended volumetric boundary scheme. Results agree well with some well-known previous works. It is demonstrated that in the nearly incompressible limit, this approach is able to provide accurate direct numerical simulations of unsteady flows with curved geometry.

Journal ArticleDOI
TL;DR: In this paper, the authors examined the streamwise velocity component in fully developed pipe flow for Reynolds numbers in the range 5.5 x 10^4 ≤ ReD ≤ 5.7 × 10^6.
Abstract: Statistics of the streamwise velocity component in fully developed pipe flow are examined for Reynolds numbers in the range 5.5 x 10^4 ≤ ReD ≤ 5.7 x 10^6. Probability density functions and their moments (up to sixth order) are presented and their scaling with Reynolds number is assessed. The second moment exhibits two maxima: the one in the viscous sublayer is Reynolds-number dependent while the other, near the lower edge of the log region, follows approximately the peak in Reynolds shear stress. Its locus has an approximate (R^+)^{0.5} dependence. This peak shows no sign of ‘saturation’, increasing indefinitely with Reynolds number. Scalings of the moments with wall friction velocity and $(U_{cl}-\overline{U})$ are examined and the latter is shown to be a better velocity scale for the outer region, y/R > 0.35, but in two distinct Reynolds-number ranges, one when ReD 7 x 10^4. Probability density functions do not show any universal behaviour, their higher moments showing small variations with distance from the wall outside the viscous sublayer. They are most nearly Gaussian in the overlap region. Their departures from Gaussian are assessed by examining the behaviour of the higher moments as functions of the lower ones. Spectra and the second moment are compared with empirical and theoretical scaling laws and some anomalies are apparent. In particular, even at the highest Reynolds number, the spectrum does not show a self-similar range of wavenumbers in which the spectral density is proportional to the inverse streamwise wavenumber. Thus such a range does not attract any special significance and does not involve a universal constant.