Showing papers in "Fluid Dynamics Research in 2002"

Flow structure around a finite circular cylinder embedded in various atmospheric boundary layers

Abstract: The flow structure around the free end of a finite circular cylinder (FC) embedded in various atmospheric boundary layers (ABLs) was investigated experimentally. The experiments were carried out in a closed-return type subsonic wind tunnel with various oncoming ABLs. A finite circular cylinder with an aspect ratio (L/D) of 6 was mounted vertically on a flat plate. The Reynolds number based on the cylinder diameter is ~Re = 20,000. The wake structure behind a cylinder located in a uniform flow condition was also measured for comparison. A hot-wire anemometer was employed to measure the wake velocity, and mean pressure distributions on the cylinder surface were also measured. The flow past the FC free end exhibits a complicated three-dimensional wake structure, and the flow structure is quite different from that of a two-dimensional cylinder. The three-dimensional flow structure seems to arise from the strong entrainment of irrotational fluids caused by the downwash counter-rotating vortices separated from the FC free end. The vortex-shedding frequency and vortex-formation length are lower for an FC immersed in ABLs compared with those in a uniform flow. Spectral analysis revealed that a peculiar flow structure with a 24 Hz frequency component closely related to the counter-rotating twin-vortex exists near the FC free end.

On drag, Strouhal number and vortex-street structure

Abstract: A phenomenological model for the vortex-shedding process behind bluff cylindrical bodies is proposed. Relationships between Strouhal frequency St, drag coefficient cD, Reynolds number Re and geometric wake parameters are obtained from mass conservation, momentum conservation in the transverse direction and energy considerations. For the first time, Roshko's (Technical Report TN 3169, NACA, US Government Printing Office, Washington DC, 1954) experimental discovery of vortex-street similarity behind different cylinders is analytically derived. In addition, the empirically obtained Strouhal-frequency laws of Roshko (Technical Report TN1191, NACA, US Government Printing Office, Washington DC, 1954) and Fey (Phys. Fluids A 10 (1998) 1547) are also reproduced. Measurements of St and cD including their Re dependency for flows around cylinders with circular, square, triangular, semi-circular and other cross sections agree favorably with the proposed model.

Laminar flows through a curved rectangular duct over a wide range of the aspect ratio

Abstract: The laminar flow in a curved rectangular duct for a range of the aspect ratio 1 ≤ l ≤ 12 is investigated by use of the spectral method. The steady solutions are obtained using the Newton–Raphson method with the symmetry condition. As a result, five branches of steady solutions are found. Linear stability characteristics are also investigated for all the steady solutions. It is found that one steady solution is linearly stable for most of l, but two linearly stable steady solutions exist for a region of small l and there are several intervals of l where there is no linearly stable steady solution. We performed time-evolution calculations with and without the symmetry condition, and observed periodic oscillations with the symmetry condition and aperiodic time evolutions without the symmetric condition. Finally, the present results numerically suggest that what determines which solution is realizable may be the maximum of the momentum transfer in the cross section.

Visualization of the flow in a helical pipe

Abstract: The secondary flow structure in a helical pipe with large torsion is investigated by using a numerical calculation of a fluid particle trajectory and an experiment using a smoke visualization technique. Good agreement is obtained between the experiment and the numerical calculation. The secondary flow in a cross-section is transformed from a two counter-rotating vortices structure to a one-recirculation structure with increase of the torsion of the pipe at a constant Dean number. The line dividing two vortices varies its direction from horizontal to vertical as the torsion increases.

Surface roughness effects in a short porous journal bearing with a couple stress fluid

Abstract: In this paper, a theoretical study of the effect of surface roughness in hydrodynamic lubrication of a porous journal bearing with couplestress fluid as lubricant is made. The modified Reynolds equations accounting for the couple stresses and randomized surface roughness structure are mathematically derived. The Christensen stochastic theory of hydrodynamic lubrication of rough surfaces is used to study the effects of surface roughness on the static characteristics of a short porous journal bearing with couplestress fluid as lubricant. Further, it is assumed that, the roughness asperity heights are small compared to the film thickness. It is observed that, the effects of surface roughness on the bearing characteristics are more pronounced for couplestress fluids as compared to the Newtonian fluids.

Large eddy simulation of wind flow around parallel buildings with varying configurations

Abstract: The paper presents numerical calculations of turbulent wind flow conditions around two parallel buildings with different wind directions and building arrangements. The numerical simulations are carried out with the RNG sub-grid scale model following an initial test case for a single building configuration with the time averaged and filtered Navier–Stokes equations based turbulence models. A comparison with the experimental data indicates that the present RNG sub-grid scale model gives much better results than other turbulence models tested to predict the time-dependent atmospheric flow field. This model is further extended to analyse the wind effects between buildings by considering different building geometry, wind flow direction and passage width. All numerical simulations are carried out by using the finite volume method (FVM). The simulation results show that the present sub-grid scale model with the FVM is rather promising to study the wind effects on buildings and can overcome the disadvantages of conventional Reynolds averaged Navier–Stokes equations based turbulence models.

Interfacial gravity waves in a two-fluid system

Abstract: In this work a theoretical and experimental investigation is performed on the sloshing of two immiscible liquid layers inside of a closed square-section tank. By applying a variational approach to the potential formulation of the fluid motion, a nonlinear dynamical system is derived applying the Lagrange equations to the Lagrangian of motion defined in terms of suitable generalised coordinates. These coordinates are the time depending coefficients of the modal expansions adopted for the separation surface of the two fluids and for the velocity potentials of the fluid layers. Dissipative effects are taken into account by considering generalised dissipative forces derived by a dissipative model extensively treated in the paper. Numerical integration of the dynamical system furnish solutions which well reproduce the examined experimental configurations.

Mixed convection along a vertical surface: similarity solutions for uniform flow

Abstract: The similarity equations for mixed convection boundary-layer flow over a vertical semi-infinite flat plate in which the free stream velocity is uniform and the wall temperature is inversely proportional to the distance along the plate are considered. The solutions are analysed for both small and large values of the Prandtl number, σ, and for different values of the mixed convection parameter, λ, including forced (λ = 0), free (λ → ∞) and mixed (λ≠0) convection flow regimes. It is found that, for mixed convection, there are qualitative differences in the solution structure for σ σc, (σc0.761). In the former case, solutions exist for all positive λ (aiding flows) but there is only a finite range of negative λ for which solutions exist with two solution branches for λ in this range. For σ > σc solutions exist for all negative λ (opposing flows) with solutions possible for only a finite range of positive λ. The critical role that the Prandtl number plays in the present results is different to previously published results.

Dynamic free-surface deformations in thermocapillary liquid bridges

Abstract: Flow-induced dynamic free-surface deformations in thermocapillary liquid bridges are investigated in the limit of small capillary number. The asymptotic solution in lowest order is calculated numerically. Dynamic deformations caused by steady axisymmetric flows and by time-dependent three-dimensional critical modes are considered for representative Prandtl numbers (Pr=0.02 and 4.38). The magnitude and phase of the dynamic surface-deformation wave relative to the magnitude of the temperature field of a hydrothermal wave are predicted and discussed. It is shown that the total dynamic deformation can be decomposed to elucidate the relative importance of the hydrodynamic pressure, the viscous stress, the change of the volume due to thermal expansion, the temperature-dependence of the surface tension, and the temperature-dependence of the hydrostatic pressure. Since the dynamic deformations are caused by flow fields which arise at lower orders of the capillary number, the leading-order dynamic deformations do not feed back to the leading-order thermocapillary flow. This conclusion holds for steady axisymmetric flows as well as for non-axisymmetric three-dimensional flows close to the critical onset of hydrothermal waves.

Chaotic mixing due to a spatially periodic three-dimensional flow

Abstract: The chaotic mixing of a fluid due to a slow flow in a spatially periodic system called the partitioned-pipe mixer is studied. This system, originally composed of alternate horizontal and vertical plates of the same length in a duct, is generalized so that both the ratio a of the lengths of these plates and the angle between neighboring plates can be changed. Using the Poincare plots of the locations of fluid particles after every period, we find that the mixing performance in many periods can be improved to a considerable extent by choosing appropriate values of a and . Furthermore, it is shown that the mixing performance in a few periods can be estimated from the distribution of the lines of separation, defined as the set of cross-sectional initial locations of fluid particles which move to one of the leading edges of the plates within a specified period. Using this distribution, we find that this mixing performance also can be improved by the above generalization.

Water wave scattering by a submerged circular-arc-shaped plate

Abstract: The problem of water wave scattering by a thin circular-arc-shaped plate submerged in infinitely deep water is investigated by linear theory. The circular-arc is not necessarily symmetric about the vertical through its center. The problem is formulated in terms of a hypersingular integral equation for a discontinuity of the potential function across the plate. The integral equation is solved approximately using a finite series involving Chebyshev polynomials of the second kind. The unknown constants in the finite series are determined numerically by using the collocation and the Galerkin methods. Both the methods ultimately produce very accurate numerical estimates for the reflection coefficient. The numerical results are depicted graphically against the wave number for a variety of configurations of the arc. Some results are compared with known results available in the literature and good agreement is achieved. The suitability of using a circular-arc-shaped plate as an element of a water wave lens has also been discussed on the basis of the present numerical results.

Aluminum dust ignition behind reflected shock wave: two-dimensional simulations

Abstract: In this paper results of parallel computer simulations on aluminum dust ignition behind a reflected shock wave are presented. Computations show the time-evolution of a complicated flow field created due to a shock wave collision with a pile of dust, shock reflection from a wall, and its interaction with vortices. Particles, blown away by the incident shock, are heated mainly behind the reflected shock wave. The estimated ignition delay time is of the order of 80–100 μs and is a strong function of the incident shock wave strength. The simulations show that it may be very difficult to ignite aluminum particles when the incident shock wave Mach number is smaller than about Ms ≈ 3, while for stronger shocks the estimated ignition delay time quickly decreases.

Interfacial instabilities of miscible fluids in a rotating Hele-Shaw cell

Abstract: Numerical simulations of interfacial stability for miscible droplet in a rotating Hele–Shaw cell by means of high-accurate numerical schemes are presented. The interfacial instability is dominated by four control parameters, such as rotating speed, viscosity contrast, diffusion between the species and injecting strength. More vigorous interfacial fingerings are found at higher rotating speed and lower viscosity contrast. The effect of stronger diffusion is not significant to the fingering patterns, but leads only to milder instability. Injection in general reinforces viscous stabilization. For the case of annulus, different mechanisms of instability are observed on the inner and outer fronts. The injecting strength tends to stabilize the outer interface, and perturbs the inner.

Asymptotic analysis of the formation of thin liquid film in spin coating

Abstract: Unsteady thin liquid film flow of non-uniform thickness on a rotating disk is analyzed by asymptotic methods. Short- and long-time-scale solutions for the transient film profile near the rotating axis are independently derived as a function of space and time. Analyses were performed for a case in which the initial film thickness is even in radial distance and the peripheral effects of the liquid film are assumed to be negligible. The result reveals the effects of the gravitational and surface tension forces, coupled with inertial force, on the film planarization and thinning process.

Mixed convection boundary-layer flow past a horizontal permeable flat plate

Abstract: The self-similar mixed convection boundary layer flow over a horizontal flat plate with the temperature distribution Tw(x)~x−1/2 and a lateral suction (γ > 0) of the fluid was considered in this paper Between this problem and "Schneider's problem" of the impermeable plate (γ = 0), essential differences were found Thus: (i) while in the impermeable case the temperature distribution Tw(x)~x−1/2 allows for a non-vanishing heat flow at the leading edge only, in the permeable case heat is transferred through every point x of the plate at a rate '(0) = −Pr γ; (ii) while in the impermeable case unique solutions exist only for aiding flows, in the presence of suction such solutions could also be obtained for opposing flows; (iii) in addition to the dual solutions already encountered in the impermeable case, for γ > 0 and negative values of the mixed convection parameter K (opposing flow) also triple and quadruple solutions have been found; (iv) for the case of strong suction (γ 1) approximate analytical solutions were derived

Low-order dynamical models of thermal convection in high-aspect ratio enclosures

Abstract: Low-dimensional dynamical models for transitional buoyancy-driven flow in differentially heated enclosures are presented. The full governing partial differential equations with the associated boundary conditions are solved by a spectral element method. Proper orthogonal decomposition is applied to the oscillatory solutions obtained from the full model in order to construct empirical eigenfunctions. Using the most energetic empirical eigenfunctions for the velocity and temperature fields as basis functions and applying Galerkin's method, low-order models consisting of few non-linear ordinary differential equations are obtained. For all cases, close to the “design” conditions (Pr0,Gr0), the low-order model (LOM) predictions are in excellent agreement with the predictions of the full model. In particular, the critical Grashof number at the onset of the first temporal flow instability (Hopf bifurcation) as well as the frequency and amplitude of oscillations at slightly supercritical conditions are in excellent agreement with the predictions of the full model. Far from design conditions, the LOMs capture some important characteristic properties of the full model solutions. For example, the low-order model derived for a cavity of A=20 and Gr0=3.2×104, Pr0=0.71, captures the multiplicity of solutions for large values of Grashof number, while it predicts a unique steady solution at small values of Grashof number. In addition, the model predicts that a stationary instability precedes the onset of oscillatory convection. On the other hand, low-order models derived for low-aspect ratio cavities predict that the solution is unique and stable for sufficiently small values of Grashof number and that the primary instability leads to oscillatory time-dependent flow in agreement with experimental and numerical studies based on the full model.

Propagation of cylindrical waves in a rotating fluid

Abstract: Surface and internal wave dynamics in a rotating fluid is considered for axisymmetrical disturbances. The model equation for nonlinear waves (the Ostrovsky equation for axisymmetrical perturbations) is derived from a primitive shallow water Boussinesq equations taking into account the Coriolis force. The evolution of solitary (pulse type) and periodical disturbances is studied theoretically, numerically, and in laboratory experiments. Different regimes of wave decay are described and analysed in detail. The dependencies of wave amplitudes and other wave parameters on distance in a polar co-ordinate system are derived. Some estimates for surface and internal waves in real oceanic conditions under the influence of Earth's rotation are discussed.

Stability of a pair of planar counter-rotating vortices in a rectangular box

Abstract: The stability and transition of a pair of planar counter-rotating vortices in a confined region are investigated numerically. Direct numerical simulations in a rectangular box: D = [0,2kπ] × [0,π], where k is an aspect ratio, are done with symmetric external forcing. A pair of steady symmetric counter-rotating vortices are generated under weak forcing while they become unstable with stronger forcing. Special attention is paid to the effect of the aspect ratio k on the stability and the transition. It is found that a steady asymmetric pattern appears for k > k0 ≈ 0.5 while an oscillating asymmetric pattern for k < k0. In particular, the symmetric vortices become very stable around k = 0.5 (i.e. the square region). Linear stability analysis of a model flow similar to the symmetric vortices generated in the numerical simulations gives the same tendency as the above findings. The results suggest that the singular property of the stability at k = k0 ≈ 0.5 is mainly dependent on the aspect ratio k of the region but rather independent of the superficial difference of the vorticity distribution.

Equatorial magnetic dipole field intensification by convection vortices in a rotating spherical shell

Abstract: Dynamo mechanism by thermal convection of an electrically conducting fluid in a rotating spherical shell is investigated by numerical simulation analysis of the MHD Boussinesq equations. The magnetic field is intensified, by stretching of magnetic field lines, along outgoing streamlines emanating from stagnation points in the convection velocity field so long as the magnetic field is weak. Once the magnetic field grows comparable in magnitude with the velocity field, however, the structure of the latter is deformed and the mechanism of magnetic field intensification is altered. The eastward drift of the convection vortices accelerated through the Lorentz torque creates a wavy zonal flow on which acceleration and deceleration are repeated periodically. The magnetic field is intensified, again through stretching of magnetic field lines, on the accelerating parts of the zonal flow predominantly near the equatorial plane. This establishes the magnetic dipole field with axis on the equatorial plane rotating around the rotation axis of the spherical shell.

Suboptimal control for drag reduction in turbulent pipe flow

Abstract: A suboptimal control law in turbulent pipe flow is derived and tested. Two sensing variables ∂p/∂θ|w and ∂vθ/∂r|w are applied with two actuations φθ and φr. To test the suboptimal control law, direct numerical simulations of turbulent pipe flow at Reτ=150 are performed. When the control law is applied, a 13–23% drag reduction is achieved. The most effective drag reduction is made at the pair of ∂vθ/∂r|w and φr. An impenetrable virtual wall is observed by the controlled wall suction and blowing. The virtual wall concept is useful for analyzing the near-wall behavior of the controlled flow. Comparison of the present suboptimal control with that of turbulent channel flow reveals that the curvature effect is insignificant.

Higher-order asymptotic theory for the velocity field induced by an inviscid vortex ring

Abstract: We explore the flow field around a thin axisymmetric vortex ring steadily translating in an ideal fluid, with vorticity proportional to distance from the axis of symmetry, originally treated by Dyson (Philos. Trans. R. Soc. 184 (1893) 1041). By making a higher-order extension of the method of matched asymptotic expansions in a small parameter e, the ratio of the core radius to the ring radius R0, an explicit form of the streamfunction is derived, to O(e3), both inside and outside the core. The pressure and velocity fields are written out in full to the same order. It is shown that the circle of minimum pressure coincides, to O(e2R0), with the circle of stagnation points viewed from the frame moving with the core.

Curved squeeze film with inertial effects — energy integral approach

Abstract: The laminar squeeze flow of an incompressible viscous fluid between a flat circular disk and a curved circular disk is analysed by taking into account the effects of fluid inertia and curvature, using energy integral method. The shape of the curved plate is assumed to be axisymmetric and the squeeze film characteristics are examined for arbitrary shape of the curved disk. The normal force exerted on the curved disk by the fluid is obtained and the numerical results are presented for the sinusoidal motion of the curved disk. Special shapes for the curved disk are assumed and the results are compared with the available investigations. Further, the equation of the gapwidth for the constant force squeezing state is obtained and is solved numerically. The properties of the squeeze film are investigated through the inertial and curvature effects on the load carrying capacity of the curved squeeze film.

Geometrical theory of fluid flows and dynamical systems

Abstract: Various dynamical systems have often common geometrical structures and can be formulated on the basis of Riemannian geometry and Lie group theory, provided that a dynamical system has a group symmetry, namely it is invariant under group transformations, and further that the group manifold is endowed with a Riemannian metric. The basic ideas and tools are described, and their applications are presented for the following five problems: (a) free rotation of a rigid body, which is a well-known system in mechanics and presented as an illustrative example of the geometrical theory; (b) geodesic equation and KdV equation on the group of diffeomorphisms of a circle and its extended group; (c) a self-gravitating system of a finite number of points masses and a geometrical interpretation of chaos of Henon–Heiles system; (d) geometrical formulation of hydrodynamics of an incompressible ideal fluid on the group of volume preserving diffeomorphisms, where an interpretation of the origin of Riemannian curvatures of the fluid flow is given; (e) geodesic equation on a loop group and the local induction equation for the motion of a vortex filament, where the geodesic equation on its extended group is found to be equivalent to the equation for a vortex filament with an axial flow along it. It is remarkable that the present geometrical formulations are successful for all the problems considered here and give an insight into the deep background common to the diverse physical systems. Furthermore, the geometrical formulation opens a new approach to various dynamical systems, which is rewarded with new results.

Edge wave scattering by a coastal structure

Abstract: The propagation of an incident edge wave on a straight beach with a coastal structure perpendicular to the coastline is analyzed. A simple idealized beach profile with a steep foreshore, a plane slope and a horizontal shelf on an infinitely long straight shoreline is considered. The edge wave is reflected and transmitted at the structure and, by assuming that its width is much smaller than the alongshore wave length, the solution to the problem is obtained by a mode matching method including the head loss at the structure. The existence of the steep foreshore and the shelf modifies the dispersion equation of the trapped modes obtained by Eckart (Wave Report 100, Ref. 51-12, Scripps Institute of Oceanography, University of California, La Jolla, 1951, 99pp). The reflection coefficient, defined by the ratio of the incident and reflected edge wave amplitudes, depends on the friction coefficient at the coastal structure.

The linear instability of a thermal boundary layer with suction in an anisotropic porous medium

Abstract: We consider the combined effects of suction and transverse anisotropy on the instability of the uniform thickness boundary layer which is formed on an inclined heated surface in a porous medium. When the medium is isotropic, the stability characteristics are shown to be very similar to that of the inclined Darcy–Benard problem. In particular, longitudinal rolls are always preferred, and transverse rolls are always stable when the inclination of the surface is greater than approximately 31.9°. Transverse anisotropy has no effect on the identity of the preferred mode of convection whenever the anisotropy parameter, ξ, is less than unity. When ξ > 1, there always exists a range of surface inclinations where transverse rolls are preferred. A detailed set of numerical results are given showing how the critical Rayleigh number and wavenumber vary with both inclination and ξ.

Nonlinear dynamics of a highly viscous and elastic fluid in pipe flow

Abstract: Nonlinear dynamics of the inertialess viscoelastic flow in pipe are studied for a highly elastic polyisobutylene (PIB) based polymer solution (referred to as PIB Boger fluid). It is shown that for flow rates above the criticality the steady pipe flow bifurcates to a time dependent flow. Instantaneous pressure measurements at various axial locations imply that there is a series of flow transitions. The critical conditions for the onset of these elastic instabilities and the temporal structure of the resulting secondary flows are determined for a large range Deborah number.

On the stability of a forced-free boundary layer flow with viscous heating

Abstract: The inviscid instability of an accelerating forced-free convection boundary layer with viscous dissipation is investigated. The boundary layer equations for the flow with free-stream velocity U∞xn admit self-similar solutions for n = 1 only. The "overshooting" of the free-stream value, characteristic of accelerating buoyant boundary layers, is found to increase with increasing viscous heating. The scaled temperature profile is also found to exceed its plate value close to the plate where the viscous dissipation effects are strongest. For Eckert number Ec = 0 only one single inviscid unstable mode exists. For the flow with viscous dissipation, three unstable modes have been identified. The secondary modes may be associated with the combined effect of thermal buoyancy and viscous heating. There is evidence of these modes crossing at relatively higher wavenumbers. The disturbance growth rate is found to increase with increasing buoyancy and viscous heating.

Similarity solution for laser-driven shock waves in a dust-laden gas with internal heat transfer effects

Abstract: The non-adiabatic flow behind a laser-driven strong shock wave propagating in a mixture of gas and small solid particles is the subject of this paper. A similarity solution which accounts for the influence of internal heat fluxes due to high temperatures achieved at the centre has been obtained. The heat fluxes in the blast-wave equations are considered in terms of Fourier's law for conduction and by an expression for thermal radiation of the diffusion type. As for adiabatic flow, it is assumed that the equilibrium-flow condition is maintained and that the variable laser energy is completely absorbed at the shock front according to a time-dependent power law. The formulation results in a two-point boundary-value problem. The effects of a parameter characterising the various energy input of the blast wave on the similarity solution as well as on its limits have been examined. The computations have been performed for various values of mass concentration of the solid particles and for the ratio of density of solid particles to the constant initial density of gas.

Numerical solutions for the liquid-metal flow in a rotating cylinder with a weak transverse magnetic field

Abstract: This paper treats the steady, three-dimensional, laminar flow of an electrically conducting liquid in a finite-length, insulating cylinder which rotates at a constant angular velocity about its axis. A steady, uniform, weak, transverse magnetic field produces a small deviation from a rigid-body rotation with the cylinder. This deviation consists of an axisymmetric flow, which is very similar to the classical Ekman flow for the spin-up of a cylinder, and a nonaxisymmetric flow. This paper presents numerical results for the nonaxisymmetric flow and for the ratio of the magnitude of the nonaxisymmetric flow to that of the axisymmetric flow for various values of the Reynolds number.

Steady streaming and mass transfer due to capillary waves in a two-layer system

Abstract: The work deals with stationary (dc) streaming flows resulting from standing capillary waves at the interface between two immiscible liquid layers, and with their effect on the mass transfer rate of a passive scalar (for example, a protein). Planar layers in a narrow channel are considered. Secondary streaming flows in the Stokes layers near the interfaces are calculated, as well as the corresponding vortical flows arising in the bulk. It is shown that the vortices can significantly enhance the mass transfer rate of a passive scalar which is to be extracted by one liquid from the other. The corresponding Sherwood number is of order [|u int ∗ |λ/ D 1 ] 1/2 , where |u int ∗ | is the magnitude of the interfacial streaming velocity, λ is the wavelength, and D 1 is the diffusion coefficient in liquid 1. This means that the effective diffusion coefficient is of order D 1 [|u int ∗ |λ/ D 1 ] 1/2 , which can be more than an order of magnitude higher than D 1 . The results obtained are discussed in the context of potential novel bioseparator devices for protein extraction.