Showing papers in "European Journal of Mechanics B-fluids in 1995"

The thermo-acoustic nature of the critical speeding up

Abstract: A slab-like container filled with a near-critical fluid is submitted to a given heat flux at the boundary. Matched asymptotic expansions and multiple-time-scale techniques are applied to the 1-D compressible Navier-Stokes equations written for a Van der Waals gas, in order to describe the thermomechanically-driven flow appearing in the fluid and its coupling with the acoustics. A two-time-scale analytical solution is obtained under the form of a uniformly valid approximation, which shows that the response of the fluid is a system of linear compression waves occurring on a short time-scale, driving a slower variation of the basic thermodynamic properties. This solution clearly highlights the leading role of the acoustics in the rapid thermalisation witnessed in near-critical fluids, and commonly called 'Critical Speeding Up'

Double-diffusive convection in an inclined slot filled with porous medium

Abstract: The Darcy model with the Boussinesq approximation is used to study double-diffusive natural convection in an inclined porous layer subject to transverse gradients of heat and solute. Results are presented for 0.1 ≤ R T ≤ 10 4 , -10 4 ≤ N ≤ 10 4 , 10 -3 ≤ Le ≤ 10 3 , 2 ≤ A ≤ 15 and -180° ≤ Φ ≤ 180°. An analytical solution is obtained by assuming parallel flow in the core region of the cavity and integral forms of the energy and constituent equations. Approximate solutions are derived, for the case of a vertical cavity, that extend the range of validity of the results available in literature. For opposing flows (N < 0) the existence of multiple steady states is demonstrated. Critical Rayleigh numbers for the onset of convection are predicted for the case of a horizontal system. For super critical convection, it is found that multiple steady and unsteady convective modes are possible for a given set of the governing equations. Numerical solutions for the flow fields, temperature and concentration distributions and heat and mass transfer rates are obtained for a wide range of the governing parameters.

The stability of vertical thermal boundary layer flow in a porous medium

Abstract: We consider the linearised stability characteristics of the thermal boundary layer induced by the uniform heating of a semi-infinite vertical surface embedded in a fluid - saturated porous medium. In this paper attention is restricted to two-dimensional disturbances far from the leading edge. This analysis complements and extends the direct numerical simulation of Rees [1993] which shows that the flow is stable at locations sufficiently close to the leading edge. In this asymptotic regime we also find that wave disturbances decay. However, the rate of decay decreases as the distance downstream of the leading edge increases.

New families of steep solitary waves in water of finite depth with constant vorticity

Abstract: Solitary waves with constant vorticity in water of finite depth are considered. Previous calculations showed that there are branches of solutions characterized by a limiting configuration with a 120° angle at the crest of the wave and others which ultimately approach closed regions of constant vorticity in contact with the bottom of the channel. Here it is shown that there are additional families of solutions. As the acceleration of gravity approaches zero, these new solutions approach configurations consisting of a wave with an arbitrary number of circular regions of fluid in rigid body rotation on top of its crest.

On anisotropic subgrid modeling

Abstract: A modification of Smagorinsky's subgrid model is proposed to account for the effects of anisotropic filtering. No new empirical parameters are introduced by the modification. Numerical experiments for a low Reynolds number turbulent channel flow have been carried out. The results are in good agreement with results from direct numerical simulations. The effects of spatial resolution on the results of large eddy simulations are considered in some detail.

Flow induced around a sphere with a non-uniform surface temperature in a rarefied gas, with application to the drag and thermal force problems of a spherical particle with an arbitrary thermal conductivity

Abstract: A flow induced around a sphere with a non-uniform surface temperature in a rarefied gas is investigated using the linearized Boltzmann equation for hard-sphere molecules and the diffuse reflection condition. With the aid of the accurate and efficient numerical method developed by the authors with Aoki, the behaviour of the gas (the velocity distribution function as well as macroscopic variables and force on the sphere) is clarified for the whole range of the Knudsen number. In addition, the solutions of the drag and thermal force (thermophoresis) problems of a spherical particle with an arbitrary thermal conductivity are obtained by appropriate superpositions of the present solution and those of a sphere with infinite thermal conductivity, obtained by the authors with Aoki. The resulting thermal force is compared with various experimental data.

Volume viscosity of dilute polyatomic gas mixtures

Abstract: We present two linear systems with which to evaluate the rotational volume viscosity of dilute polyatomic gas mixtures. These systems are given in their naturally symmetric constrained singular form. In the translational-and-rotational-energy approach, the linear system of Monchick, Yun, and Mason can be recovered if one misprint is corrected in their expressions. In the rotational-energy approach, a new linear system is obtained, thereby yielding a new approximation for the volume viscosity. We also discuss an extension of the present theory to the vibrational volume viscosity. Using iterative methods, we then derive explicit expressions for the rotational volume viscosity that can be implemented at a low computational cost in practical applications. The accuracy of these approximate expressions is illustrated with numerical examples. These expressions are relevant to several compressible flow applications, such as flames, chemical reactors, and high-speed entry into planetary atmospheres.

Asymptotic analysis of laminar boundary-layer flow over finely grooved surfaces

Abstract: A set of matched asymptotic expansions is developed for laminar flow over grooved surfaces, which gives a formal mathematical justification and provides higher-order corrections to the separate study of the viscous sublayer pervading the grooves and of the essentially two-dimensional boundary layer far above. The question of whether, under various conditions, laminar drag is reduced or increased by grooves is answered with the aid of theoretical bounds concerning the protrusion height. The three-dimensional effect of the presence of grooves is reduced to an equivalent wall condition for the two-dimensional boundary layer equations

Convective flows under the influence of high-frequency vibrations

Abstract: Convective flows under the influence of high-frequency vibrations, i.e. the flows induced by periodic oscillations of a container or of a solid body immersed in a fluid are considered. Inconsistency of the Boussinesq approximation is demonstrated for the case in which the orientation of the container may vary over the period of vibrations, for the flows induced by oscillations of a solid body immersed in a fluid and for vibrations in a fluid with free surface. General equations for the description of the time-averaged convective flow under arbitrary vibrations are derived, and within this framework the generalized Boussinesq approximation is formulated. The boundary conditions on rigid and free surfaces are analyzed. The relation to the conventional equations for the high-frequency vibrational convection is discussed.

Spatially localized two-dimensional finite-amplitude states in plane Couette flow

Abstract: The objective of this investigation is to search for two-dimensional finite-amplitude waves in plane Couette flow. The starting point for our computations are two-dimensional travelling waves in plane Poiseuille flow which we extend numerically through the Poiseuille-Couette family to the plane Couette flow limit. Interestingly, the nonlinear states for plane Couette flow take the form of spatially localized (solitary-like) stationary waves. This gives some explanation why previous attempts to compute 2D waves in plane Couette flow failed. The lowest (critical) Reynolds number for the existence of these states, based on half the velocity difference between the walls and channel half-width, is close to 1500. The existence of spatially localized perturbed states corresponds to the subcritical aspect of transition observed in plane Couette flow experiments and the computed nonlinear equilibrium solutions hopefully represent a new basic state for secondary instabilities.

On rotational effects in the modulations of weakly nonlinear water waves over finite depth

Abstract: The modulational stability of Stokes' waves has been investigated in the context of potential Euler (free-surface) equations. In this paper, the amplitude equations for three-dimensional rotational flows are derived. It is shown that there are indeed rotational effects. Moreover, except for the classical ansatz on the expansion of the solutions, we derive the set of amplitude equations without making any extra assumption.

A note on the scattering of obliquely incident surface gravity waves by cylindrical obstacles in waters of finite depth

Abstract: The scattering of obliquely incident surface gravity waves by cylindrical obstacles is investigated using linearized potential theory. The numerical method is then applied to the scattering of obliquely incident waves on periodic sinusoidal bottoms, a surface obstacle or a submerged plate, since these configurations are of practical importance in oceanography and coastal engineering. The influence of incident wave angles on the wave reflection when considering surface or submerged obstacles is discussed

Polymorphism of shocked water

Abstract: Phase transition phenomena in water under shock compression have been investigated on the basis of the shock-particle velocity correlation obtained by treatment of experimental data. The correlation is split up into three linear parts. The lower and higher pressure parts are identified as liquid phases, while the middle part is identified as the mixture of solid and liquid phases. The calculated values of the liquid phase temperature make it possible to compare a shock adiabat with the melting curve of Ice-VII in the pressure-temperature coordinates. The shock adiabat breaks in the shock-particle velocity correlation corresponding to the points of intersection of the shock water adiabat with the phase equilibrium of water-Ice-VII. Comparison of these data with those of other authors allows one to conclude that the shock adiabat of water is changing into the solid phase field of Ice-VII within the pressure region of 2-16 GPa. On the other hand, the value of the weight fraction of Ice-VII varies, it depends upon the pressure and changes from 0 to 0.25 in the pressure range (2.10) GPa.

Contribution to the instability of laminar separating flows along axisymmetric bodies. II: Experiment and comparison with theory

Abstract: A wind-tunnel study for the instability of an axisymmetric backward-facing step flow was carried out using disturbances excited by sound. The data, which were obtained, indicate that the axisymmetry of the separated boundary layer results in a decrease of the instability, compared to that in plane two-dimensional separating layers. The comparison of the data with theoretical results show that calculations of the instability of the axisymmetric flow with the parallel flow approximation predict fairly well the stability characteristics, determined in the experiment ; however, the distributions of the u-fluctuations show differences.

Numerical Simulation of the Stationary One-Dimensional Boltzmann Equation by Particle Methods

Abstract: The paper presents a numerical simulation technique - based on the well-known particle methods - for the stationary, one-dimensional Boltzmann equation for Maxwellian molecules. In contrast to the standard splitting methods, where one works with the instationary equation, the current approach simulates the direct solution of the stationary problem. The model problem investigated is the heat transfer between two parallel plates in the rarefied gas regime. An iteration process is introduced which leads to the stationary solution of the exact - space discretized - Boltzmann equation, in the sense of weak convergence.

Transient properties of a developping laminar disturbance in pipe Poiseuille flow

Abstract: Hot-wire measurements of the velocity disturbance from point-like disturbances in a fully developed laminar pipe Poiseuille flow are performed. Two jets are induced radially into the pipe by diametrically opposed loud speakers. The resulting streamwise disturbance velocity component is investigated over the Reynolds number range 1550-2000. Close to the position of the initial disturbance, the disturbance amplitudes and gradients are large. After a few pipe radii the disturbance is reduced and consists of two small regions of positive disturbance with a larger region of negative disturbance in between. A downstream interval then follows in which the amplitudes of the regions with positive disturbance exhibit an amplification followed by a decay. The peaks of the two amplified regions are located at 0.6 radii and 0.4 radii, respectively, and propagate with velocities of 0.65 times the centreline velocity (U cl ) and 0.88 U cl , respectively. Subsequently, the disturbance obtains an almost constant level, while it becomes elongated in the streamwise direction. An integrated disturbance quantity is defined by integrating the square of the disturbance amplitude over the radius and time in a downstream position.

Contribution to the instability of laminar separating flows along axisymmetric bodies. I: Theory

Abstract: The instability of wall-bounded velocity profiles close to separation in an axisymmetric flow has been investigated by using linearized stability theory. The basic parallel flow is modelled by a modified tanh-profile which has a profile parameter denoting the ratio of the wall-distance of the inflexion point to the displacement boundary layer thickness. The nondimensional spatial growth rates and phase velocities of the axisymmetric and first helical disturbances depend on the normalized frequency, the Reynolds number and on a curvature parameter denoting the ratio of the displacement thickness to the radius of the cylindrical wall. As in the case of plane parallel flow, the instability of a basic velocity profile is strongly increased, if its inflexion point is far from the wall. It is found that an increase of the curvature parameter leads to a reduction of the instability to axisymmetric disturbances, at least for higher frequencies. However, this is not necessarily true for the first helical mode, which can become more unstable than the axisymmetric one. Concerning the profiles of the axial velocity fluctuation, it is found that the profiles can have three peaks for basic velocity profiles close to separation, as in the plane case. For axisymmetric disturbances, the influence of the curvature parameter is modest, but can be strong for the first helical disturbance.

Natural convection beneath a downward facing heated plate in a porous medium

Abstract: The boundary layer singularity appearing at the edge of a downward facing heated plate buried in a fluid-saturated porous medium is analyzed, and a boundary condition at the edge is deduced. Both constant temperature and constant heat flux conditions on the downward facing surface of an infinite strip and a circular disk are considered. The boundary layer equations are shown to possess a similarity solution for the constant temperature boundary condition and results for both the infinite strip and circular plate geometries are obtained. In the case of constant heat flux no similarity solution exists and this problem is solved by numerical integration of the governing partial differential equation. Solutions are also given for a slightly inclined plate maintained at constant temperature

An experimental study of the transition region of the boundary layer along a concave wall

Abstract: An experimental study on the transition of the boundary layer along a concave wall with curvature radius of 1 m was performed by using multichannels of hotwirte anemometers and flow visualization. With a free stream velocity of 2 m/s, three velocity components were measured for the detailed behaviours of the mean velocity field, including the Gortler vortices and the fluctuations. Three types of fluctuations were observed; the meandering motion of the Gortler vortices, horseshoe vortices as the secondary instability of the Gortler vortices, and wall turbulence in the downstream turbulent region with a similar coherent structure as turbulent spots. The respective roles leading the boundary layer to turbulence are discussed

The role of Ekman pumping in confined, electromagnetically-driven flows

Abstract: Our primary thesis is that Ekman pumping is an essential component of many confined, MHD flows. It occurs whenever the axis of a forced, columnar vortex intersects a solid boundary. The weak recirculation associated with Ekman pumping is important for two reasons. First, the recirculation provides an efficient mechanism of removing the energy supplied by the Lorentz force, by flushing all streamlines through a boundary layer. Second, the Coriolis acceleration associated with the secondary flow can be used to balance the azimuthal component of the Lorentz force. We illustrate these points by looking at both axisymmetric and three-dimensional flows. We start with forced swirl in an axisymmetric cavity. Here we extend Davidson's [1992] model and compare its predictions with laboratory and numerical experiments. The experiments were performed in both cones and hemispheres and broadly support the model's predictions. In particular, they show the dominance of Ekman pumping and the resulting independence of angular momentum with depth. Next we note that axial symmetry, although mathematically convenient, is not a physical prerequisite for Ekman pumping.

Nonlinear analysis of two-dimensional compressible liquid-liquid impact

Abstract: Compressibility effects during high-speed collisions between two liquid masses are analyzed and discussed. Particular emphasis is given to the geometry of the colliding liquid surfaces and to the importance of systems of oblique shock waves. After impact an expanding contact zone is formed between the liquids. Initially, shocks that propagate into both liquids adhere to the edge of this zone fully enclosing the compressed liquids. At a later time the conditions for the shocks to adhere to the contact edge break down. Then the shocks move ahead of the contact edge and lateral jetting of the high pressure fluid begins. These processes will be explained in terms of a reversed wedge flow. The maximum impact pressures obtained in this manner are compared with results based on a one-dimensional approximation. Furthermore, the dependence of the impact pressure on impact velocity and impact angle will be discussed. It is found that the geometry of the colliding surfaces is of greatest importance at small impact velocities. When the absolute impact velocity is constant maximum pressures are obtained for oblique impacts. Finally, the occurrence of strong oblique shock waves caused by the upstream flow conditions is discussed.

Reaction of condensed matter to extremely short-duration and intense loading. Strength of solids and liquids under dynamic damage

Abstract: The results of spall damage investigations of low-melting-point metals and water are presented. These,substances occur in either the solid or liquid state under fracture. A hypothesis is suggested here that under conditions of extremely short-duration external action, a substance behaves in only one way, its initial reaction being essentially the same, independent of its overall state. Some examples are considered to confirm this hypothesis

Marangoni instability in a liquid layer with two free surfaces

Abstract: We study the onset of the Marangoni instability in a liquid layer with two free nearly insulating surfaces heated from below. Linear stability analysis yields a condition for the emergence of a longwave (as usual for most convective phenomena in the limit of nearly insulating boundaries) or a finite wavelength instability from the quiescent equilibrium state. Using the method of asymptotic expansions we derive a weakly nonlinear evolution equation describing the spatiotemporal behavior of the velocity and temperature fields at the onset of the longwave instability. The latter is given by ΔM = 24, ΔM being the difference between the upper and the lower Marangoni numbers. It is shown that in some parametric range one convective cell forms across the layer, while in other parametric domains two superimposed convective cells emerge between the two free surfaces.

Pressure diffusion in unsteady non-Darcian flows through porous media

Abstract: The pressure diffusion in unsteady non-Darcian flows through a porous medium is studied analytically. The exact similarity solutions for the pressure and velocity distributions for the Cauchy problem, (i.e. the case of source type solution) are presented and graphically illustrated. Two classes on non-Darcian flows are investigated. The class of unsteady turbulent gas flows with polytropic thermodynamic evolution, and the class of non-Newtonian fluid flows of power law behavior. The derived governing pressure-diffusion equations belong to a class of nonlinear degenerate parabolic equations having solutions with compact support. It is shown that due to the nonlinear effects associated with non-Darcian flows, the pressure and velocity distributions exhibit traveling wave characteristics. The conditions for the existence of these diffusive waves are found, and expressed in terms of the properties of the fluid and the porous medium. (authors). 11 refs., 5 figs.

Receptivity of axisymmetric boundary layers due to excitation by a Dirac point source at the wall

Abstract: The receptivity of an axisymmetric boundary layer excited by a Dirac point source at the wall of a cylindrical body has been investigated on the basis of a parallel-flow approximation. The unstable part of the disturbed flow field has been extracted and discussed. As a measure of the receptivity, the production integral and its axial derivative immediately downstream of the source position is used. For two different mean velocity profiles with inflexion points these quantities have been calculated. Furthermore, the axial variation of the production integral is presented for two different sets of flow parameter values and the development of the RMS-values for the unstable axial velocity fluctuation is shown.

Bifurcation of self-sustained magnetic fields in planar convective flows

Abstract: bifurcation theory and group theoretical methods are applied to the problem of the onset of a convectively driven magnetic field in an electrically conducting fluid heated from below (dynamo effect). We assume periodic boundary conditions in the horizontal directions. Therefore the problem reduces to a fundamental domain, the symmetry of which depends on the kind of periodic lattice chosen for the horizontal periodicity. The case of a square lattice was considered by [Iooss & Lozi], who put the problem in the frame of fully square invariant flows. Our approach consists in generalizing this study by allowing more general symmetries, in the spirit of bifurcation theory with symmetry and with the support of computer assisted algebraic as well as numerical calculations. As an application, we show how a magnetic field bifurcates from the purely convective flow having the symmetry of an hexagonal lattice. We also consider the case when the system rotates about a vertical axis

On short-wavelength instabilities in three-dimensional classical boundary layers

Abstract: Instabilities governed by the classical boundary-layer equations are considered theoretically for a fully three-dimensional incompressible steady or unsteady flow. All boundary layers with nondegenerate cross flows are found to be susceptible to short-wavelength time-growing viscous instabilities. It is shown that, depending on relative spatial scales of disturbances, the temporal mode acquires the off-wall critical-layer, near-wall critical-layer or marginal form. A more restricted class of three-dimensional steady flows proves to be unstable to stationary cross-flow vortex modes. Sufficient conditions for the stationary instability are formulated and properties of the off-wall/near-wall/marginal vortices are studied. Effects of the curvature of the basic flow on both temporal and spatial modes are considered in detail.

The instability of density stratified vortices

Abstract: The instability of a solitary vortex whose core has a lower density than the rest of the liquid is investigated in an approximation of an ideal liquid in the absence of gravity. It is found that such a vortex is unstable to excitation of the modes propagating along the vortex axis. Emergence of the instability is attributed to the interaction of positive and negative energy waves. Results of theoretical calculations are used for explanation of the experiment on investigation of the vortex structure behind a heated cylinder. It is shown that flexural oscillations of vortices in the street that are observed in a definite temperature interval of a streamlined cylinder may result from the instability of a solitary vortex with a heated core.

On the nonlinear development of disturbances in boundary layers assumed as parallel

Abstract: The initial boundary value problem describing the nonlinear development of disturbances in a locally parallel, two or three-dimensional boundary layer is investigated. An asymptotic analysis of spatially periodic solutions with respect to weak temporal stability or instability is performed. The result is a Landau equation, which is coupled with an inhomogeneous heat equation, for determining the amplitude of the disturbance and the mean deformation of the boundary-layer profile. The limit of solutions for long times is calculated under the assumption that such a limit exists. It can be interpreted as a temporally and spatially periodic bifurcating solution of the nonlinear disturbance differential equation in the case of weak temporal instability. The three-dimensional flow over an infinite yawed wedge and Blasius flow over a flat plate are considered as numerical examples. The analysis also shows that the assumption of a locally parallel boundary layer has an important mathematical consequence. While the time-dependent mean-flow distortion decays far from the wall, its limit as time goes to infinity defines a constant vector at the outer edge of the boundary layer, which in general is not equal to zero.

Vortex shedding from a ring in turbulent flow

Abstract: Vortex shedding from a bluff ring in turbulent flow has been investigated experimentally. The shedding frequency, measured using a hot wire placed within the near wake of the ring, was found to be only weakly dependent on the characteristics of the upstream turbulence. For turbulent length scales of the same order as the cross-stream width of the annular section of the ring, the shedding frequency increases monotonically with turbulence intensity (u'/U) to a value, at u'/U =0.14, some 5% greater than in uniform flow. In contrast, for much larger length scales, the increase in shedding frequency is much smaller, although the circumferential coherence of the shedding process is very much weaker than in smooth flow or in turbulence with much smaller length scales. The implication of these results is that vortex flowmeters constructed using a ring as the shedding body, rather than the more usual body shapes which span the pipe diameter, may be relatively unaffected by changes in the turbulence structure of the upstream flow.