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Showing papers on "Reynolds number published in 1995"


Journal ArticleDOI
TL;DR: In this article, a new k -ϵ eddy viscosity model, which consists of a new model dissipation rate equation and a new realizable eddy viscous formulation, is proposed.

4,648 citations


01 Jun 1995
TL;DR: In this article, a level set method for capturing the interface between two fluids is combined with a variable density projection method to allow for computation of two-phase flow where the interface can merge/break and the flow can have a high Reynolds number.
Abstract: A level set method for capturing the interface between two fluids is combined with a variable density projection method to allow for computation of two-phase flow where the interface can merge/break and the flow can have a high Reynolds number. A distance function formulation of the level set method enables one to compute flows with large density ratios (1000/1) and flows that are surface tension driven; with no emotional involvement. Recent work has improved the accuracy of the distance function formulation and the accuracy of the advection scheme. We compute flows involving air bubbles and water drops, to name a few. We validate our code against experiments and theory.

3,556 citations


Journal ArticleDOI
TL;DR: In this article, a model of the deposition-splashing boundary in terms of Reynolds number and Ohnesorge number is presented, which is only achieved if the normal velocity component of the impinging droplets is used in these dimensionless numbers.

1,073 citations


Journal ArticleDOI
TL;DR: For large enough microscale Reynolds numbers, the data (despite much scatter) support the notion of a "universal" constant that is independent of the flow as well as the Reynolds number, with a numerical value of about 0.5.
Abstract: All known data are collected on the Kolmogorov constant in one‐dimensional spectral formula for the inertial range. For large enough microscale Reynolds numbers, the data (despite much scatter) support the notion of a ‘‘universal’’ constant that is independent of the flow as well as the Reynolds number, with a numerical value of about 0.5. In particular, it is difficult to discern support for a recent claim that the constant is Reynolds number dependent even at high Reynolds numbers.

678 citations


Journal ArticleDOI
TL;DR: In this article, an ensemble-averaged statistics at constant phase of the turbulent near-wake flow (Reynolds number ≈ 21400 around a square cylinder) were obtained from two-component laser-Doppler measurements.
Abstract: Ensemble-averaged statistics at constant phase of the turbulent near-wake flow (Reynolds number ≈ 21400 around a square cylinder have been obtained from two-component laser-Doppler measurements. Phase was defined with reference to a signal taken from a pressure sensor located at the midpoint of a cylinder sidewall. The distinction is drawn between the near wake where the shed vortices are ‘mature’ and distinct and a base region where the vortices grow to maturity and are then shed. Differences in length and velocity scales and vortex celerities between the flow around a square cylinder and the more frequently studied flow around a circular cylinder are discussed. Scaling arguments based on the circulation discharged into the near wake are proposed to explain the differences. The relationship between flow topology and turbulence is also considered with vorticity saddles and streamline saddles being distinguished. While general agreement with previous studies of flow around a circular cylinder is found with regard to essential flow features in the near wake, some previously overlooked details are highlighted, e.g. the possibility of high Reynolds shear stresses in regions of peak vorticity, or asymmetries near the streamline saddle. The base region is examined in more detail than in previous studies, and vorticity saddles, zero-vorticity points, and streamline saddles are observed to differ in importance at different stages of the shedding process.

649 citations


Journal ArticleDOI
TL;DR: In this article, a detailed analysis is presented to demonstrate the capabilities of the lattice Boltzmann method for the two-dimensional, driven cavity flow, and thorough comparisons with other numerical solutions for the 2D cavity flow give accurate results over a wide range of Reynolds numbers.

547 citations


Journal ArticleDOI
TL;DR: In this article, an experimental and theoretical investigation of low Reynolds number, high subsonic Mach number, compressible gas flow in channels was presented, and the measured friction factor was in good agreement with theoretical predictions assuming isothermal, locally fully developed, first-order slip flow.
Abstract: An experimental and theoretical investigation of low Reynolds number, high subsonic Mach number, compressible gas flow in channels is presented. Nitrogen, helium, and argon gases were used. The channels were microfabricated on silicon wafers and were typically 100 μm wide, 104 μm long, and ranged in depth from 0.5 to 20 μm. The Knudsen number ranged from 10-3 to 0.4. The measured friction factor was in good agreement with theoretical predictions assuming isothermal, locally fully developed, first-order, slip flow.

493 citations


Journal ArticleDOI
TL;DR: In this article, a study of compressible supersonic turbulent flow in a plane channel with isothermal walls has been performed using direct numerical simulation Mach numbers, based on the bulk velocity and sound speed at the walls, of 15 and 3 are considered; Reynolds numbers, defined in terms of the centreline velocity and channel halfwidth, are of the order of 3000.
Abstract: A study of compressible supersonic turbulent flow in a plane channel with isothermal walls has been performed using direct numerical simulation Mach numbers, based on the bulk velocity and sound speed at the walls, of 15 and 3 are considered; Reynolds numbers, defined in terms of the centreline velocity and channel half-width, are of the order of 3000 Because of the relatively low Reynolds number, all of the relevant scales of motion can be captured, and no subgrid-scale or turbulence model is needed The isothermal boundary conditions give rise to a flow that is strongly influenced by wall-normal gradients of mean density and temperature These gradients are found to cause an enhanced streamwise coherence of the near-wall streaks, but not to seriously invalidate Morkovin's hypothesis : the magnitude of fluctuations of total temperature and especially pressure are much less than their mean values, and consequently the dominant compressibility effect is that due to mean property variations The Van Driest transformation is found to be very successful at both Mach numbers, and when properly scaled, statistics are found to agree well with data from incompressible channel flow results

402 citations


Journal ArticleDOI
TL;DR: In this article, the transition of the cylinder wake is investigated experimentally in a water channel and is computed numerically using a finite-difference scheme, and four physically different instabilities are observed: a local vortex-adhesion mode, three near-wake instabilities associated with three different spanwise wavelengths of approximately 1, 2, and 4 diam.
Abstract: The transition of the cylinder wake is investigated experimentally in a water channel and is computed numerically using a finite‐difference scheme. Four physically different instabilities are observed: a local ‘‘vortex‐adhesion mode,’’ and three near‐wake instabilities, which are associated with three different spanwise wavelengths of approximately 1, 2, and 4 diam. All four instability processes can originate in a narrow Reynolds‐number interval between 160 and 230, and may give rise to different transition scenarios. Thus, Williamson’s [Phys. Fluids 31, 3165 (1988)] experimental observation of a hard transition is for the first time numerically reproduced, and is found to be induced by the vortex‐adhesion mode. Without vortex adhesion, a soft onset of three‐dimensionality is numerically and experimentally obtained. A control‐wire technique is proposed, which suppresses transition up to a Reynolds number of 230.

400 citations


Journal ArticleDOI
TL;DR: In this paper, the development of a viscous incompressible flow generated from a circular cylinder impulsively started into rectilinear motion is studied computationally, and an adaptative numerical scheme based on vortex methods is used to integrate the vorticity/velocity formulation of the Navier-Stokes equations for a wide range of Reynolds numbers (Re = 40 to 9500).
Abstract: The development of a two-dimensional viscous incompressible flow generated from a circular cylinder impulsively started into rectilinear motion is studied computationally. An adaptative numerical scheme, based on vortex methods, is used to integrate the vorticity/velocity formulation of the Navier–Stokes equations for a wide range of Reynolds numbers (Re = 40 to 9500). A novel technique is implemented to resolve diffusion effects and enforce the no-slip boundary condition. The Biot–Savart law is employed to compute the velocities, thus eliminating the need for imposing the far-field boundary conditions. An efficient fast summation algorithm was implemented that allows a large number of computational elements, thus producing unprecedented high-resolution simulations. Results are compared to those from other theoretical, experimental and computational works and the relation between the unsteady vorticity field and the forces experienced by the body is discussed.

391 citations


Journal ArticleDOI
TL;DR: In this paper, a series of numerical simulations were carried out in order to improve knowledge of the forces acting on a sphere embedded in accelerated flows at finite Reynolds number, Re. 1 ≤ Re ≤ 300 for flows around both a rigid sphere and an inviscid spherical bubble.
Abstract: This work reports the first part of a series of numerical simulations carried out in order to improve knowledge of the forces acting on a sphere embedded in accelerated flows at finite Reynolds number, Re. Among these forces added mass and history effects are particularly important in order to determine accurately particle and bubble trajectories in real flows. To compute these hydrodynamic forces and more generally to study spatially or temporally accelerated flows around a sphere, the full Navier–Stokes equations expressed in velocity–pressure variables are solved by using a finite-volume approach. Computations are carried out over the range 0.1 ≤ Re ≤ 300 for flows around both a rigid sphere and an inviscid spherical bubble, and a systematic comparison of the flows around these two kinds of bodies is presented.Steady uniform flow is first considered in order to test the accuracy of the simulations and to serve as a reference case for comparing with accelerated situations. Axisymmetric straining flow which constitutes the simplest spatially accelerated flow in which a sphere can be embedded is then studied. It is shown that owing to the viscous boundary condition on the body as well as to vorticity transport properties, the presence of the strain modifies deeply the distribution of vorticity around the sphere. This modification has spectacular consequences in the case of a rigid sphere because it influences strongly the conditions under which separation occurs as well as the characteristics of the separated region. Another very original feature of the axisymmetric straining flow lies in the vortex-stretching mechanism existing in this situation. In a converging flow this mechanism acts to reduce vorticity in the wake of the sphere. In contrast when the flow is divergent, vorticity produced at the surface of the sphere tends to grow indefinitely as it is transported downstream. It is shown that in the case where such a diverging flow extends to infinity a Kelvin–Helmholtz instability may occur in the wake.Computations of the hydrodynamic force show that the effects of the strain increase rapidly with the Reynolds number. At high Reynolds numbers the total drag is dramatically modified and the evaluation of the pressure contribution shows that the sphere undergoes an added mass force whose coefficient remains the same as in inviscid flow or in creeping flow, i.e. CM = ½, whatever the Reynolds number. Changes found in vorticity distribution around the rigid sphere also affect the viscous drag, which is markedly increased (resp. decreased) in converging (resp. diverging) flows at high Reynolds numbers.

Journal ArticleDOI
TL;DR: In this article, a variety of jet and suction devices were used to create repeatable disturbances, which were then used to test the stability of developed Poiseuille flow.
Abstract: We report the results of an experimental study of the transition to turbulence in a pipe under the condition of constant mass flux. The transition behaviour and structures observed in this experiment were qualitatively the same as those described in previous reported studies performed in pressure-driven systems. A variety of jet and suction devices were used to create repeatable disturbances which were then used to test the stability of developed Poiseuille flow. The Reynolds number ( Re ) and the parameters governing the disturbances were varied and the outcome, whether or not transition occurred some distance downstream of the injection point, was recorded. It was found that a critical amplitude of disturbance was required to cause transition at a given Re and that this amplitude varied in a systematic way with Re . This finite, critical level was found to be a robust feature, and was relatively insensitive to the form of disturbance. We interpret this as evidence for disconnected solutions which may provide a pointer for making progress in this fundamental, and as yet unresolved, problem in fluid mechanics.

Journal ArticleDOI
TL;DR: In this paper, the velocity and shape of rising bubbles, with an equivalent radius of 0.33-1.00 mm, in "hyper clean" water, have been experimentally determined.
Abstract: The velocity and shape of rising bubbles, with an equivalent radius of 0.33–1.00 mm, in ‘hyper clean’ water, have been experimentally determined. For the small bubbles there is perfect agreement with theory, proving that this water can be considered as pure (no surfactants). For the larger bubbles there is a small discrepancy due to an overestimation in the theory.

Journal ArticleDOI
TL;DR: In this paper, the inviscid stability of the boundary-layer flow over a disk rotating in otherwise still fluid is analyzed and it is suggested that absolute instability may cause the onset of transition from laminar to turbulent flow.
Abstract: This paper is concerned with the theoretical behaviour of the boundary-layer flow over a disk rotating in otherwise still fluid. The flow is excited impulsively at a certain radius at time t = 0. This paper analyses the inviscid stability of the flow and the stability with viscous, Coriolis and streamline curvature effects included. In both cases, within a specific range of the parameter space, it is shown that the flow is absolutely unstable, i.e. disturbances grow in time at every fixed point in space. Outside this range, the flow is convectively unstable or stable. The absolute or convective nature of the instabilities is determined by examining the branch-point singularities of the dispersion relation. Absolute instability is found for Reynolds numbers above 510. Experimentally observed values for the onset of transition from laminar to turbulent flow have an average value of 513. It is suggested that absolute instability may cause the onset of transition to turbulent flow. The results from the inviscid analysis show that the absolute instability is not caused by Coriolis effects nor by streamline curvature effects. This indicates that this mechanism may be possible on swept wings, where Coriolis effects are not present but the boundary layers are otherwise similar.

Journal ArticleDOI
TL;DR: In this article, results of two-dimensional and three-dimensional simulations of flow past elliptic and circular cylinders have been systematically compared in an effort to pinpoint the exact cause for the inaccurate prediction of the lift and drag by 2D simulations.
Abstract: It has been known for some time that two‐dimensional numerical simulations of flow over nominally two‐dimensional bluff bodies at Reynolds numbers for which the flow is intrinsically three dimensional, lead to inaccurate prediction of the lift and drag forces. In particular, for flow past a normal flat plate (International Symposium on Nonsteady Fluid Dynamics, edited by J. A. Miller and D. P. Telionis, 1990, pp. 455–464) and circular cylinders [J. Wind Eng. Indus. Aerodyn. 35, 275 (1990)], it has been noted that the drag coefficient computed from two‐dimensional simulations is significantly higher than what is obtained from experiments. Furthermore, it has been found that three‐dimensional simulations of flows lead to accurate prediction of drag [J. Wind Eng. Indus. Aerodyn. 35, 275 (1990)]. The underlying cause for this discrepancy is that the surface pressure distribution obtained from two‐dimensional simulations does not match up with that obtained from experiments and three‐dimensional simulations and a number of reasons have been put forward to explain this discrepancy. However, the details of the physical mechanisms that ultimately lead to the inaccurate prediction of surface pressure and consequently the lift and drag, are still not clear. In the present study, results of two‐dimensional and three‐dimensional simulations of flow past elliptic and circular cylinders have been systematically compared in an effort to pinpoint the exact cause for the inaccurate prediction of the lift and drag by two‐dimensional simulations. The overprediction of mean drag force in two‐dimensional simulations is directly traced to higher Reynolds stresses in the wake. It is also found that the discrepancy in the drag between two‐dimensional and three‐dimensional simulations is more pronounced for bluffer cylinders. Finally, the current study also provides a detailed view of how the fluctuation, which are associated with the Karman vortex shedding in the wake, affect the mean pressure distribution and the aerodynamic forces on the body.

Journal ArticleDOI
TL;DR: In this paper, the authors investigated the shallow two-dimensional turbulent wake flows on a large water table, where cylinders and flat solid and porous plates oriented transversely to the ambient flow were inserted into the base flow.

Journal ArticleDOI
TL;DR: In this article, the local heat transfer from a small heat source to a normally impinging, axisymmetric, and submerged liquid jet, in confined and unconfined configurations, was experimentally investigated.
Abstract: The local heat transfer from a small heat source to a normally impinging, axisymmetric, and submerged liquid jet, in confined and unconfined configurations, was experimentally investigated. A single jet of FC-77 issuing from a round nozzle impinged onto a square foil heater, which dissipated a constant heat flux. The nozzle and the heat source were both mounted in large round plates to ensure axisymmetric radial outflow of the spent fluid. The local surface temperature of the heat source was measured at different radial locations (r/d) from the center of the jet in fine increments. Results for the local heat transfer coefficient distribution at the heat source are presented as functions of nozzle diameter (0.79 ≤ d ≤ 6.35 mm), Reynolds number (4000 to 23,000), and nozzle-to-heat source spacing (1 ≤ Z/d ≤ 14). Secondary peaks in the local heat transfer observed at r/d 2 were more pronounced at the smaller (confined) spacings and larger nozzle diameters for a given Reynolds number, and shifted radially outward from the stagnation point as the spacing increased. The secondary-peak magnitude increased with Reynolds number, and was higher than the stagnation value in some instances.

Journal ArticleDOI
TL;DR: In this article, a class of wing-type vortex generators, which can easily be incorporated into heat transfer surfaces, is considered in fully developed and developing channel flows with respect to heat transfer enhancement and pressure loss penalty.

Journal ArticleDOI
TL;DR: In this article, the Navier-Stokes equations were approximated to fourth-order accuracy with stencils extending only over a 3 x 3 square of points, and the key advantage of the new compact 4-order scheme is that it allows direct iteration for low-to-mediwn Reynolds numbers.
Abstract: SUMMARY We note in this study that the Navier-Stokes equations, when expressed in streamfunction-vorticity fonn, can be approximated to fourth--order accuracy with stencils extending only over a 3 x 3 square of points. The key advantage of the new compact fourth-order scheme is that it allows direct iteration for low~to-mediwn Reynolds numbers. Numerical solutions are obtained for the model problem of the driven cavity and compared with solutions available in the literature. For Re $1500 point-SOR iteration is used and the convergence is fast.

Journal ArticleDOI
TL;DR: In this paper, the authors measured the instantaneous velocity fields in the x −y plane of a zero pressure gradient turbulent boundary layer using particle image velocimetry and found that there exist random, time-varying zones in the u −ν fields in which the streamwise momentum is remarkably uniform.
Abstract: Instantaneous velocity fields in the x‐y plane of a zero pressure gradient turbulent boundary layer are measured using particle image velocimetry. It is found that there exist random, time‐varying zones in the u‐ν fields in which the streamwise momentum is remarkably uniform. The largest dimension of a typical zone is proportional to the boundary layer thickness. The zone closest to the wall contains viscous‐inertial inclined structures similar to those found in low Reynolds number wall turbulence. A second zone is located above the wall zone in a region that coincides roughly with the logarithmic layer. The wake region of the boundary layer contains a complicated, time‐varying pattern of several nearly‐constant‐momentum zones. The zones are separated from each other and from the free stream by thin viscous shear layers that contain concentrations of spanwise vorticity.

Journal ArticleDOI
TL;DR: In this paper, the mean velocity and statistical moments of turbulent velocity fluctuations in the near-wall region of a fully developed pipe flow at low Reynolds numbers were measured using laser-Doppler measurements.
Abstract: This paper presents laser-Doppler measurements of the mean velocity and statistical moments of turbulent velocity fluctuations in the near-wall region of a fully developed pipe flow at low Reynolds numbers. A refractive-index-matched fluid was used in a Duran-glass test section to permit access to the near-wall region without distortion of the laser beams. All measurements were corrected for the influence of the finite size of measuring control volume. Measurements of long-time statistical averages of all three fluctuating velocity components in the near-wall region are presented. It is shown that the turbulence intensities in the wall region do not scale with inner variables. However, the limiting behaviour of the intensity components very close to the wall show only small variations with the Reynolds number. Measurements of higher-order statistical moments, the skewness and flatness factors, of axial and tangential velocity components confirm the limiting behaviour of these quantities obtained from direct numerical simulations of turbulent channel flow. The comparison of measured data with those obtained from direct numerical simulations reveals that noticeable discrepancies exist between them only with regard to the flatness factor of the radial velocity component near the wall. The measured v’ flatness factor does not show the steep rise close to the wall indicated by numerical simulations. Analysis of the measured data in the near-wall region reveals significant discrepancies between the present LDA measurements and experimental results obtained using the hot-wire anemometry.

Journal ArticleDOI
TL;DR: In this article, the effect of various sources on convective instabilities in a boundary layer is found by using the solution of an inhomogeneous adjoint problem, and the results are compared with the asymptotic solutions obtained from triple-deck theory, and agree with previous finite-Reynolds-number calculations.
Abstract: The effectiveness with which various sources excite convective instabilities in a boundary layer is found by a simple method. Chosen field values of the adjoint to the Tollmien–Schlichting eigensolution, normalized appropriately, indicate the amplitude of the unstable disturbance which will result for direct time-harmonic forcing by sources of momentum, mass and vorticity, as well as by boundary motions. For the Blasius boundary layer, forcing in the vicinity of the critical layer induces the largest response. At this position, the response to forcing in the wall-normal direction is typically 5% of that resulting from streamwise forcing of the same magnitude. At the wall, normal motions elicit a much stronger response than streamwise motions. Forcing close to the lower branch of the neutral stability curve leads to the largest response. The adjoint field values are equivalent to the residues of Fourier-inversion integrals. This equivalence is discussed for two problems; the vibrating ribbon problem and excitation of an inviscid free shear layer by a vorticity source. The efficiency factor is calculated for the scattering of ‘acoustic’ waves into Tollmien–Schlichting waves in the presence of small surface roughness, at a finite Reynolds number, based on the Orr–Sommerfeld operator. This is achieved by using the solution of an inhomogeneous adjoint problem. The results are compared with the asymptotic solutions obtained from triple-deck theory, and agree with previous finite-Reynolds-number calculations.

Journal ArticleDOI
TL;DR: In this article, the authors investigated the scaling properties of three-dimensional isotropic and homogeneous turbulence and found that anomalous scaling of the velocity structure functions is clearly detectable even at a moderate and low Reynolds number and it extends over a much wider range of scales with respect to the inertial range.

Journal ArticleDOI
TL;DR: In this article, smoke-wire and surface oil-flow techniques are employed to visualize the flow patterns and evolution of vortex shedding and shear-layer instability of a NACA 0012 cantilever wing.
Abstract: Flow patterns and characteristics of vortex shedding and shear-layer instability of a NACA 0012 cantilever wing are experimentally studied. Smoke-wire and surface oil-flow techniques are employed to visualize the flow patterns and evolution of vortex shedding. Hot-wire anemometers are used to characterize the frequency domain of the unsteady flow structures. Several characteristic flow modes are classified in the domain of chord Reynolds number and root angle of attack. Effects of the juncture and wing tip are discussed. Vortex shedding can be classified into four characteristic modes. Vortex shedding at low and high angles of attack are found to have different dominant mechanisms. Effects of the juncture and wing tip on the vortex shedding are discussed. Shear-layer instabilities are found to be closely related to the behaviors of the vortex shedding. Behaviors of the shear-layer instabilities can be traced back to the characteristics of the boundary layer on the suction surface of the airfoil.

Journal ArticleDOI
TL;DR: In this paper, a weighting function model of transient friction is developed for flows in smooth pipes by assuming the turbulent viscosity to vary linearly within a thick shear layer surrounding a core of uniform velocity and is thus applicable to flows at high Reynolds number.
Abstract: Two of the most promising analytical models of unsteady friction in turbulent pipe flows are based on sharply contrasting hypotheses. One uses the history of the flow; the other uses instantaneous conditions. The purposes of this paper are to present an analysis using the former approach and to indicate how to determine which of the two methods is appropriate. A weighting function model of transient friction is developed for flows in smooth pipes by assuming the turbulent viscosity to vary linearly within a thick shear layer surrounding a core of uniform velocity and is thus applicable to flows at high Reynolds number. In the case of low Reynolds number turbulent flows and short time intervals, the predicted skin friction is identical to an earlier model developed by Vardy et al (1993). In the case of laminar flows, it gives results equivalent to those of Zielke (1966, 1968). The predictions are compared with analytical results for the special case of flows with uniform acceleration. It is this case that ...

Journal ArticleDOI
TL;DR: In this paper, the authors reviewed the state of the art of aerosol resuspension research and compared the advantages and limitations of the existing models of particle reentrainment by means of a comparison between theory and experiments, recast in terms of dimensionless groups.

Journal ArticleDOI
TL;DR: In this paper, the turbulent structure in plane Couette flow at low Reynolds numbers is studied using data obtained both from numerical simulation and physical experiments, and it is shown that the near-wall turbulence structure is quite similar to what has earlier been found in plane Poiseuille flow; however, there are also some large differences especially regarding Reynolds stress production.
Abstract: The turbulent structure in plane Couette flow at low Reynolds numbers is studied using data obtained both from numerical simulation and physical experiments. It is shown that the near-wall turbulence structure is quite similar to what has earlier been found in plane Poiseuille flow; however, there are also some large differences especially regarding Reynolds stress production. The commonly held view that the maximum in Reynolds stress close to the wall in Poiseuille and boundary layer flows is due to the turbulence-generating events must be modified as plane Couette flow does not exhibit such a maximum, although the near-wall coherent structures are quite similar. For two-dimensional mean flow, turbulence production occurs only for the streamwise fluctuations, and the present study shows the importance of the pressure—strain redistribution in connection with the near-wall coherent events.

Journal ArticleDOI
TL;DR: In this paper, experimental data on the heat transfer performance of a periodically baffled tube subject to both steady (net) flow and oscillatory flow was reported. But the authors did not consider the effect of the superposition of fluid oscillations.

Journal ArticleDOI
TL;DR: In this article, the Strouhal numbers of the observed oscillating and coalescing systems agree reasonably well with those appearing in the literature for wall-mounted circular cylinders, and the relationship between the unsteady horseshoe vortex motions in the wake is studied for a velocity ratio of 4.
Abstract: The horseshoe vortex system resulting from the interaction between a laminar boundary layer and a round transverse jet was studied over a range of Reynolds numbers and velocity ratios using hydrogen bubble wire visualization in a water channel. The study shows that the horseshoe vortex system can be steady, oscillating, or coalescing, depending on the flow conditions. Topological concepts are used to interpret the observed flow patterns and compare these patterns with those observed and computed upstream of wall‐mounted circular cylinders. The Strouhal numbers of the observed oscillating and coalescing systems agree reasonably well with those appearing in the literature for wall‐mounted circular cylinders. The relationship between the unsteady horseshoe vortex motions and the unsteady vortex motions in the wake is studied for a velocity ratio of 4. Here it is shown that the oscillating regime occurs at the same frequency as the wake and the coalescing regime occurs at approximately double the frequency of...

Book
01 Feb 1995
TL;DR: The boundary integral equations for low Reynolds number flow: Greens' identities hydrodynamic single and double-layer potentials indirect formulation Lyapunov-Tauber theorem as discussed by the authors.
Abstract: Part 1 Introduction to fluid mechanics: basic conservation laws approximate forms of the governing equations special forms of the governing equations. Part 2 Integral equation theory: classification of integral equations method of successive approximations integral equations with degenerate kernels general case of Fredholm's equation systems of integral equations. Part 3 Potential theory: basic concepts of potential theory indirect formulation regularity conditions for exterior problems. Part 4 Numerical solution of potential flow problems: boundary integral equation formulation and numerical solution of selected problems. Part 5 Boundary integral equations for low Reynolds number flow: Greens' identities hydrodynamic single- and double-layer potentials indirect formulation Lyapunov-Tauber theorem for Stokes double-layer potential dynamic properties of the singularities and their distributions. Part 6 The low Reynolds number deformation of viscous drops and gas bubbles: viscous drop deformation compound drop deformation gas bubble deformation. Part 7 Navier-Stokes equations: velocity-pressure formulation velocity-vorticity formulation.