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1.
This article deals with the onset of thermosolutal natural convection in horizontal superposed fluid and porous layers. A
linear stability analysis is performed using the one-domain approach. As in the thermal convection case, the results show
a bimodal nature of the marginal stability curves where each mode corresponds to a different convective instability. At small
wave numbers, the convective flow occurs in the whole cavity (“porous mode”) while perturbations of large wave numbers lead
to a convective flow mainly confined in the fluid layer (“fluid mode”). Furthermore, it is shown that the onset of thermosolutal
natural convection is characterized by a multi-cellular flow in the fluid region for negative thermal Rayleigh numbers. For
positive thermal Rayleigh numbers, the convective flow takes place both in the fluid and porous regions. The influence of
the depth ratio and thermal diffusivity ratio is also investigated for a wide range of the thermal Rayleigh numbers. 相似文献
2.
A numerical study of mixed convection in a vertical channel filled with a porous medium including the effect of inertial forces
is studied by taking into account the effect of viscous and Darcy dissipations. The flow is modeled using the Brinkman–Forchheimer-extended
Darcy equations. The two boundaries are considered as isothermal–isothermal, isoflux–isothermal and isothermal–isoflux for
the left and right walls of the channel and kept either at equal or at different temperatures. The governing equations are
solved numerically by finite difference method with Southwell–Over–Relaxation technique for extended Darcy model and analytically
using perturbation series method for Darcian model. The velocity and temperature fields are obtained for various porous parameter,
inertia effect, product of Brinkman number and Grashof number and the ratio of Grashof number and Reynolds number for equal
and different wall temperatures. Nusselt number at the walls is also determined for three types of thermal boundary conditions.
The viscous dissipation enhances the flow reversal in the case of downward flow while it counters the flow in the case of
upward flow. The Darcy and inertial drag terms suppress the flow. It is found that analytical and numerical solutions agree
very well for the Darcian model.
An erratum to this article is available at . 相似文献
3.
Parametric convective instability of a horizontal layer of a homogeneous ferrofluid under the action of an alternating magnetic
field is studied. A case with rigid boundaries is considered. Convection thresholds are found. In an alternating magnetic
field with a zero mean value, perturbations are found to have a synchronous character. These perturbations, however, can belong
to different classes, because they depend on the temperature difference on the layer boundaries, the layer thickness, the
frequency and amplitude of the alternating external field, and the physical properties of the ferrofluid.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 18–27, July–August, 2009. 相似文献
4.
In this second part of our analysis of the destabilization of transverse modes in an extended horizontal layer of a saturated
porous medium with inclined temperature gradient and vertical throughflow, we apply the mathematical formalism of absolute
and convective instabilities to studying the nature of the transition to instability of such modes by assuming on physical
grounds that the transition is triggered by growing localized wavepackets. It is revealed that in most of the parameter cases
treated in the first part of the analysis (Brevdo and Ruderman 2009), at the transition point the evolving instability is
convective. Only in the cases of zero horizontal thermal gradient, and in the cases of zero vertical throughflow and the horizontal
Rayleigh number R
h < 49, the instability is absolute implying that, as the vertical Rayleigh number, R
v, increases passing through its critical value, R
vc, the destabilization tends to affect the base state throughout and eventually destroys it at every point in space. For the
parameter values considered, for which the destabilization has the nature of convective instability, we found that, as R
v, increases beyond the critical value, while the horizontal Rayleigh number, R
h, and the Péclet number, Q
v, are kept fixed, the flow experiences a transition from convective to absolute instability. The values of the vertical Rayleigh
number, R
v, at the transition from convective to absolute instability are computed. For convectively unstable, but absolutely stable
cases, the spatially amplifying responses to localized oscillatory perturbations, i.e., signaling, are treated and it is found
that the amplification is always in the direction of the applied horizontal thermal gradient. 相似文献
5.
M. Turkyilmazoglu J.W. Cole J.S.B. Gajjar 《Theoretical and Computational Fluid Dynamics》2000,14(1):21-37
A numerical study has been undertaken to investigate the nature of inviscid instability of the three-dimensional compressible
boundary layer flow due to a rotating disk. The compressible Rayleigh equation is integrated using a spectral Chebyshev-collocation
method together with a fourth-order Runge–Kutta integrator. In the context of spatio-temporal stability analysis, the singularities
of the resulting dispersion relation are determined and the ones that satisfy the Briggs–Bers pinching criterion have been
selected. In certain finite parameter regions of eigenvalues (wave numbers and wave angles, for instance) it is found that
by varying the Mach number, absolute instability occurs in the compressible boundary layer on a rotating disk. The range corresponding
to the incompressible flow case given in Lingwood (1995) (ε between 14.615° and 38.114°) is verified. The results of Cole
(1995) are also verified. The overall effect of compressibility is to reduce the extent of absolute instability at higher
Mach numbers. The effect of heating the wall is to enhance the absolute instability properties, however, cooling the wall
is found to decrease greatly the region of absolute instability regime for the range of Mach numbers studied. It is also shown
in this study that for non-insulated walls a direct spatial resonance of the eigenmodes is possible and this raises the possibility
of large local algebraic growth of perturbations being important in some instances.
Received 15 October 1999 and accepted 10 December 1999 相似文献
6.
M.S. Mughal 《Theoretical and Computational Fluid Dynamics》1998,12(4):195-217
In many fluid flows of practical importance transition is caused by the linear growth of wave instabilities, such as Tollmien–Schlichting
waves, which eventually grow to a finite size at which stage secondary instabilities come into play. If transition is to be
delayed or even avoided in such flows, then the linear growth of the disturbances must be prevented since control in the nonlinear
regime would be a considerably more difficult task. Here a strategy for active control of two-dimensional incompressible and
compressible Tollmien–Schlichting waves and its use in controlling the more practically relevant problem of crossflow instability
which arises in swept-wing flows is discussed. The control is through an active suction/blowing distribution at the wall though
the same result could be achieved by variable wall heating. In order to control the instability it is assumed that the wall
shear stress and pressure are known from measurements. It is shown that, certainly at finite Reynolds numbers, it is sufficient
to know the flow properties at a finite number of points along the wall. The cases of high and finite Reynolds numbers are
discussed using asymptotic and numerical methods respectively. It is shown that a control strategy can be developed to stop
the growth of all two-dimensional Tollmien–Schlichting waves at finite and large Reynolds numbers. Some discussion of nonlinear
effects in the presence of active control is given and the possible control of other instability mechanisms investigated.
Received 1 May 1998 and accepted 24 September 1998 相似文献
7.
《European Journal of Mechanics - B/Fluids》2001,20(1):127-144
The question of absolute instabilities occuring in a boundary-layer flow with compliant coatings is reassessed. Compliant coatings of the Kramer's type are considered. Performing a local, linear absolute/convective stability analysis, a family of spring-backed elastic plates with damping is shown to be absolutely unstable for sufficiently thin plates. The absolute instability arises from the coalescence between an upstream propagating evanescent mode and the Tollmien–Schlichting wave. To reinforce the local, linear stability results the global stability behaviour of the system is investigated, integrating numerically the full nonparallel and nonlinear two-dimensional Navier–Stokes system coupled to the dynamical model. Injecting Gaussian-type, spatially localized flow disturbances as initial conditions, the spatio-temporal evolution of wave packets is computed. The absolute stability behaviour is retrieved in the global system, for a compliant panel of finite length. It is demonstrated numerically that the global stability behaviour of the wall, triggered by finite-end-effects, may be independent of the disturbance propagation in the flow. 相似文献
8.
This paper describes the three-dimensional flow structure in grooved channels with different cavity lengths at intermediate
Reynolds numbers. For steady flow, the three-dimensional effects are dominant near the side walls of the channel. However,
after the onset of self-sustained oscillatory flow due to Tollmien–Schlichting waves as the primary instability, a secondary
instability produces a three-dimensional flow with Taylor–Geortler-like vortical structure, at the bottom of the groove. This
trend becomes more significant as the cavity length increases. Furthermore, the reason for three-dimensional flow is discussed
using additional numerical analysis, and it is confirmed that the source of three-dimensional instability is the groove vortices
due to the presence of side walls, rather than the channel traveling wave.
Received: 7 September 1999/Accepted: 11 November 2000 相似文献
9.
《Journal of Fluids and Structures》1999,13(6):663-680
The effect of internal plug flow on the lateral stability of fluid conveying pipes is investigated by determining the absolute or convective nature of the instability from the analytically derived linear dispersion relation. The fluid–structure interaction is modelled by following the work of Gregory & Paı̈doussis. The formulation of the fluid-conveying pipe problem is shown to be related to previous studies of a flat plate in the presence of uniform flow by Brazier-Smith & Scott and Crigthon & Oswell. The different domains of stability, convective instability, and absolute instability are explicitly derived in control parameter space. The effects of flow velocity, fluid–structure mass ratio, stiffness of the elastic foundation, bending rigidity and axial tension are considered. Absolute instability in flexural pipes prevails over a wide range of parameters. Convective instability is mostly found in tensioned pipes, which are modelled by a generalized linear Klein–Gordon equation. The impulse response is given in closed form or as an integral approximation and its behaviour confirms the results found directly from the dispersion equation. 相似文献
10.
V. P. Reutov A. B. Ezersky G. V. Rybushkina V. V. Chernov 《Journal of Applied Mechanics and Technical Physics》2007,48(4):469-478
Evolution of convective structures in a thin layer of an evaporating liquid (ethanol) located under a turbulent boundary layer
of an airflow is studied experimentally and theoretically. Evolution of the structures is examined under conditions of an
increased flow velocity. A transition is found from convective cells formed in the absence of the flow to convective rolls
elongated in the streamwise direction. The theoretical analysis is performed within a two-dimensional model of the flow in
the liquid layer. The boundary conditions on the liquid surface are obtained with the use of self-similar solutions for mean
fields in the airflow. The onset and evolution of a periodic system of rolls are simulated numerically. Theoretical conclusions
are compared with experimental data.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 3–14, July–August, 2007. 相似文献
11.
J.C. Umavathi 《International Journal of Non》2005,40(1):91-101
The problem of combined free and forced convective magnetohydrodynamic flow in a vertical channel is analysed by taking into account the effect of viscous and ohmic dissipations. The channel walls are maintained at equal or at different constant temperatures. The velocity field and the temperature field are obtained analytically by perturbation series method and numerically by finite difference technique. The results are presented for various values of the Brinkman number and the ratio of Grashof number to the Reynolds number for both equal and different wall temperatures. Nusselt number at the walls is determined. It is found that the viscous dissipation enhances the flow reversal in the case of downward flow while it counters the flow in the case of upward flow. It is also found that the analytical and numerical solutions agree very well for small values of ε. 相似文献
12.
A. N. Golovanov 《Journal of Applied Mechanics and Technical Physics》2006,47(5):637-642
A gas-dynamic flow in an axisymmetric convective jet is studied experimentally. It is demonstrated that the jet flow with
Grashof numbers Gr = (0.4–2.0) · 106 is self-similar. Acoustic oscillations directed perpendicular to the axis of symmetry transform the profiles of the gas-flow
parameters; two temperature maximums located outside the axis can appear. The results obtained indicate that flow instability
is generated in high-gradient regions.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 5, pp. 27–33, September–October, 2006. 相似文献
13.
Leonid Brevdo 《Journal of Elasticity》1997,49(3):201-237
We solve the initial-boundary-value linear stability problem for small localised disturbances in a homogeneous elastic waveguide
formally by applying a combined Laplace – Fourier transform. An asymptotic evaluation of the solution, expressed as an inverse
Laplace – Fourier integral, is carried out by means of the mathematical formalism of absolute and convective instabilities.
Wave packets, triggered by perturbations localised in space and finite in time, as well as responses to sources localised
in space, with the time dependence satisfying e−iωt
+ O(e−ɛt
), for t → ∞, where Im ω0 = 0 and ω > 0 , that is, the signaling problem, are treated. For this purpose, we analyse the dispersion relation of the
problem analytically, and by solving numerically the eigenvalue stability problem. It is shown that due to double roots in
a wavenumber k of the dispersion relation function D(k, ω), for real frequencies ω, that satisfy a collision criterion, wave packets with an algebraic temporal decay and signaling
with an algebraic temporal growth, that is, temporal resonances, are present in a neutrally stable homogeneous waveguide.
Moreover, for any admissible combination of the physical parameters, a homogeneous waveguide possesses a countable set of
temporally resonant frequencies. Consequences of these results for modelling in seismology are discussed.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
14.
A system of two stratified layers at a free surface, consisting of distilled water above a layer of salty water separated
by an interface, is studied under laboratory conditions involving uniform temperature heating from below. Shadowgraph and
particle images have been used with temperature and salt concentration measurements to investigate the interface instability
induced by convection when it is developing in the upper and lower layer. It is found that the interface is governed by local
shear flow that induces a Kelvin–Helmholtz instability. Moreover, the entrainment interface is subject to a combination of
two closely related effects: (1) double diffusion and convective motion and (2) double diffusion and Kelvin–Helmholtz instability.
Received: 22 December 1999/Accepted: 31 October 2000 相似文献
15.
J. Prathap Kumar J. C. Umavathi I. Pop Basavaraj M. Biradar 《Transport in Porous Media》2009,80(1):117-135
An analysis of fully developed combined free and forced convective flow in a fluid saturated porous medium channel bounded
by two vertical parallel plates is presented. The flow is modeled using Brinkman equation model. The viscous and Darcy dissipation
terms are also included in the energy equation. Three types of thermal boundary conditions such as isothermal–isothermal,
isoflux–isothermal, and isothermal–isoflux for the left–right walls of the channel are considered. Analytical solutions for
the governing ordinary differential equations are obtained by perturbation series method. In addition, closed form expressions
for the Nusselt number at both the left and right channel walls are derived. Results have been presented for a wide range
of governing parameters such as porous parameter, ratio of Grashof number and Reynolds number, viscosity ratio, width ratio,
and conductivity ratio on velocity, and temperature fields. It is found that the presence of porous matrix in one of the region
reduces the velocity and temperature. 相似文献
16.
This paper is concerned with a liquid metal flow driven by a rotating magnetic field inside a stationary cylinder. We consider
especially the secondary meridional flow during the time when the fluid spins up from rest. The developing flow is investigated
experimentally and by direct numerical simulations. The vertical profiles of the axial velocity are measured by means of the
ultrasound Doppler velocimetry. Evolving instabilities in the form of Taylor–G?rtler vortices have been observed just above
the instability threshold (Ta ≥ 1.5· Ta
cr). The rotational symmetry may survive over a distinct time even if a first Taylor–G?rtler vortex pair has been formed as
closed rings along the cylinder perimeter. The transition to a three-dimensional flow in the side layers results from the
advection or a precession and splitting of the Taylor–G?rtler vortex rings. The predictable behaviour of the Taylor–G?rtler
vortices disappears with increasing magnetic field strength. The numerical simulations agree very well with the flow measurements. 相似文献
17.
A theoretical model for the instability of turbulent boundary layer over compliant surfaces is described. The investigation
of instability is carried out from a time-asymptotic space-time perspective that classifies instabilities as either convective
or absolute. Results are compared against experimental observations of surface waves on elastic and viscoelastic compliant
layers. 相似文献
18.
The two-phase flow in a short horizontal channel of a rectangular cross-section with the height of 100–500 µm and width of 9–40 mm was studied experimentally. The use of the Schliren and fluorescent methods made it possible to reveal the flow of liquid in the channel and to determine its characteristics quantitatively. The features of the churn, jet and drop flow patterns were studied in details. Two particular regimes that can be distinguished represent formation of immobile drops on the channel walls because of the liquid film or liquid bridges breakage and appearance of mobile drops due to the two-phase flow instabilities. It is found out that formation of various two-phase flow patterns and transitions between them are determined by instabilities of the liquid–gas flow in the side parts of a channel. Frontal instability has been observed during the liquid–gas interaction in the region of liquid output from the nozzle. It is shown that a change in the height and width of the horizontal channels has a substantial effect on the boundaries between the flow regimes. One of the results is that the region of the churn regime increases significantly with decreasing thickness of the channel. 相似文献
19.
Yih Nen Jeng Jiann Lin Chen
Win Aung
《International Journal of Heat and Fluid Flow》1992,13(4):329-339The problem of mixed convection in a vertical channel with asymmetric wall temperatures including situations of flow reversal is studied numerically. The SIMPLER algorithm with a staggered grid system is employed to solve the corresponding numerical equations formulated by the finite-volume method. A second-order upwind scheme is used to model the convective term, and a suitable grid distribution is introduced. The ranges of the parameters studied are 0 rt 1, 1 Re 1000, and 0 Gr/Re 500.
The numerical results, with the streamwise coordinate scaled by the Reynolds number (Re), show that solutions for the velocity and temperature fields are independent of the Reynolds number when Re 50, even in the presence of flow reversal. These solutions, however, are dependent on rt and Gr/Re. Subsequently, correlations are proposed for the bulk temperature distribution and the local Nusselt numbers along the hot wall and the cold wall. 相似文献
20.
Arturo F. Méndez-Sánchez M. Rosario López-González V. Hugo Rolón-Garrido José Pérez-González Lourdes de Vargas 《Rheologica Acta》2003,42(1-2):56-63
The rheological behavior of a cetylpyridinium chloride 100 mmol l–1/sodium salicylate 60 mmol l–1 aqueous solution was studied in this work under homogeneous (cone and plate) and non-homogeneous flow conditions (vane-bob
and capillary rheometers), respectively. Instabilities consistent with non-monotonic flow curves were observed in all cases
and the solution exhibited similar behavior under the different flow conditions. Hysteresis and the sigmoidal flow curve suggested
as characteristic of systems that show constitutive instabilities were observed when running cycles of increasing and decreasing
stress or shear rate, respectively. This information, together with a detailed determination of steady states at shear stresses
close to the onset of the instabilities, allowed one to show unequivocally that "top and bottom jumping" are the mechanisms
to trigger the instabilities in this micellar system. It is shown in addition that there is not a true plateau region in between
the "top and bottom jumping". Finally, the flow behavior beyond the upturn seemed to be unstable and was found accompanied
by an apparent violation of the no-slip boundary condition. 相似文献