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1.
A weakly nonlinear stability analysis of wave propagation in two superposed dielectric fluids streaming through porous media
in the presence of vertical electric field producing surface charges is investigated in three dimensions. The method of multiple
scales is used to obtain a dispersion relation for the linear problem and a nonlinear Klein–Gordon equation with complex coefficients
describing the behavior of the perturbed system at the critical point of the neutral curve. In the linear case, we found that
the system is always unstable for all physical quantities (including the dimension l), even in the presence of electric fields
and porous medium, in the nonlinear case, novel stability conditions are obtained, and the effects of various parameters on
the stability of the system are discussed numerically in detail. 相似文献
2.
Using the fact that for simple fluids the most general constitutive equation in constant stretch history flows for the extra
stress tensor τ is known in an explicit form, the Giesekus fluid model is cast into this (ω–D) form for two-dimensional flows. The three material functions needed to characterize τ are listed. The explicit results for
simple shear and planar elongation reveal that the parameter α should be restricted to values less than 0.5. It is demonstrated
that in this explicit form the constitutive equation is free from thermodynamic objections and can thus be used as a starting
point for numerical calculations of general, but steady, two-dimensional flows.
Received: 9 November 1998 Accepted: 20 May 1999 相似文献
3.
4.
An analytical theory is presented for the low-frequency behavior of dilatational waves propagating through a homogeneous elastic
porous medium containing two immiscible fluids. The theory is based on the Berryman–Thigpen–Chin (BTC) model, in which capillary
pressure effects are neglected. We show that the BTC model equations in the frequency domain can be transformed, at sufficiently
low frequencies, into a dissipative wave equation (telegraph equation) and a propagating wave equation in the time domain.
These partial differential equations describe two independent modes of dilatational wave motion that are analogous to the
Biot fast and slow compressional waves in a single-fluid system. The equations can be solved analytically under a variety
of initial and boundary conditions. The stipulation of “low frequency” underlying the derivation of our equations in the time
domain is shown to require that the excitation frequency of wave motions be much smaller than a critical frequency. This frequency
is shown to be the inverse of an intrinsic time scale that depends on an effective kinematic shear viscosity of the interstitial
fluids and the intrinsic permeability of the porous medium. Numerical calculations indicate that the critical frequency in
both unconsolidated and consolidated materials containing water and a nonaqueous phase liquid ranges typically from kHz to
MHz. Thus engineering problems involving the dynamic response of an unsaturated porous medium to low excitation frequencies
(e.g., seismic wave stimulation) should be accurately modeled by our equations after suitable initial and boundary conditions
are imposed. 相似文献
5.
This paper presents isosteric-based adsorption equilibrium tests of three activated carbon samples with methanol as an adsorbate.
Experimental data was fitted into Langmuir equation, Freundlich equation and Dubinin-Astakov (D–A) equation, respectively.
The fitted adsorption equations were compared in terms of agreement with experimental data. Moreover, equation format’s impacts
on calculation of the coefficient of performance (COP) and refrigeration capacity of an adsorption refrigeration system was
analyzed. In addition, the sensitivity of each parameter in each adsorption equation format to the estimation of cycle’s COP
and refrigeration capacity was investigated. It was found that the D–A equation is the best form for presenting the adsorptive
property of a carbon-methanol working pair. The D–A equation is recommended for estimating thermal performance of an adsorption
refrigeration system because simulation results obtained using the D–A equation are less sensitive to errors of experimentally
determined D–A equation’s parameters. 相似文献
6.
The Bouc–Wen model for smooth hysteresis has received an increasing interest in the last few years due to the ease of its
numerical implementation and its ability to represent a wide range of hysteresis loop shapes. This model consists of a first-order
nonlinear differential equation that contains some parameters that can be chosen, using identification procedures, to approximate
the behavior of given physical hysteretic system. Despite a large body of literature dedicated to the Bouc–Wen model, the
relationship between the parameters that appear in the differential equation and the shape of the obtained hysteresis loop
is little understood. The objective of this paper is to fill this gap by analytically exploring this relationship using a
new form of the model called the normalized one. The mathematical framework introduced in this study formalizes the vague
notion of “loop shape" into precise quantities whose variation with the Bouc–Wen model parameters is analyzed. In light of
this analysis, the parameters of Bouc–Wen model are re-interpreted. 相似文献
7.
Mohammadhossein Heidari Sureshjani Shahab Gerami Mohammad Ali Emadi 《Transport in Porous Media》2012,93(1):147-169
One of the widely used methods for modeling matrix–fracture fluid exchange in naturally fractured reservoirs is dual porosity
approach. In this type of modeling, matrix blocks are regarded as sources/sinks in the fracture network medium. The rate of
fluid transfer from matrix blocks into fracture medium may be modeled using shape factor concept (Warren and Root, SPEJ 3:245–255,
1963); or the rate–time solution is directly derived for the specific matrix geometry (de Swaan, SPEJ 16:117–122, 1976). Numerous works have been conducted to study matrix–fracture fluid exchange for slightly compressible fluids (e.g. oil).
However, little attention has been taken to systems containing gas (compressible fluid). The objective of this work is to
develop explicit rate–time solutions for matrix–fracture fluid transfer in systems containing single phase gas. For this purpose,
the governing equation describing flow of gas from matrix block into fracture system is linearized using pseudopressure and
pseudotime functions. Then, the governing equation is solved under specific boundary conditions to obtain an implicit relation
between rate and time. Since rate calculations using such an implicit relation need iterations, which may be computationally
inconvenient, an explicit rate–time relation is developed with the aid of material balance equation and several specific assumptions.
Also, expressions are derived for average pseudopressure in matrix block. Furthermore, simplified solutions (originated from
the complex general solutions) are introduced applicable in infinite and finite acting flow periods in matrix. Based on the
derived solutions, expressions are developed for shape factor. An important observation is that the shape factor for gas systems
is the same as that of oil bearing matrix blocks. Subsequently, a multiplier is introduced which relates rate to matrix pressure
instead of matrix pseudopressure. Finally, the introduced equations are verified using a numerical simulator. 相似文献
8.
The apparent viscosities of purely viscous non-Newtonian fluids are shear rate dependent. At low shear rates, many of such
fluids exhibit Newtonian behaviour while at higher shear rates non-Newtonian, power law characteristics exist. Between these
two ranges, the fluid's viscous properties are neither Newtonian or power law. Utilizing an apparent viscosity constitutive
equation called the “Modified Power Law” which accounts for the above behavior, solutions have been obtained for forced convection
flows. A shear rate similarity parameter is identified which specifies both the shear rate range for a given fluid and set
of operating conditions and the appropriate solution for that range. The results of numerical solutions for the friction factor–Reynolds
number product and for the Nusselt number as a function of a dimensionless shear rate parameter have been presented for forced
fully developed laminer duct flows of different cross-sections with modified power law fluids. Experimental data is also presented
showing the suitability of the “Modified Power Law” constitutive equation to represent the apparent viscosity of various polymer
solutions.
Received on 21 August 2000 相似文献
9.
D. G. Arkhipov G. A. Khabakhpashev 《Journal of Applied Mechanics and Technical Physics》2007,48(4):508-518
The dynamics of disturbances of the interface between two layers of incompressible immiscible fluids of different densities
in the presence of a steady flow between the horizontal bottom and lid is studied analytically and numerically. A model integrodifferential
equation is derived, which takes into account long-wave contributions of inertial layers and surface tension of the fluids,
small but finite amplitude of disturbances, and unsteady shear stresses on all boundaries. Numerical solutions of this equation
are given for the most typical nonlinear problems of transformation of both plane waves of different lengths and solitary
waves.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 49–61, July–August, 2007. 相似文献
10.
The generalized second-grade fluids, which have been used for modeling the creep of ice and the flow of coal-water and coal-oil
slurries, are among the simplest non-Newtonian fluid models that can describe shear-thinning/thickening and exhibit normal
stress effects. In this article, we conduct thermodynamic analysis on a class of generalized second-grade fluids, one distinguishing
feature of which is the existence of a constitutive function Φ that describes frictional heating. We work within the framework
of Serrin’s original formulation of neoclassical thermodynamics, where internal energy and entropy functions, if they exist
for a continuous body at all, are to be derived from the classical First Law and (quantitatively reformulated) Second Law
of thermodynamics for cycles. For the class of generalized second-grade fluids in question, we show from the First Law that
an internal energy density u exists, and we derive the equation of energy balance; from the Second Law, we demonstrate the existence of an entropy density
s and derive the Clausius–Duhem inequality that it satisfies. We obtain explicit expressions for u, s and the frictional heating Φ, and derive thermodynamic restrictions on the material functions of temperature μ, α
1, and α
2 that appear in the constitutive relation for the Cauchy stress. For the special case of second-grade fluids, our expressions
for u and s agree with those which Dunn and Fosdick [6] derived under the theoretical framework of the rational thermodynamics of Coleman
and Noll. 相似文献
11.
A two-scale model of ion transfer in a porous medium is obtained for one-dimensional horizontal flows under the action of
a pressure gradient and an external electric field by the method of homogenization. Steady equations of electroosmotic flows
in flat horizontal nano-sized slits separated by thin dielectric partitions are averaged over a small-scale variable. The
resultant macroequations include Poisson’s equation for the vertical component of the electric field and Onsager’s relations
between flows and forces. The total horizontal flow rate of the fluid is found to depend linearly on the pressure gradient
and external electric field, and the coefficients in this linear relation are calculated with the use of microequations.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 4, pp. 162–173, July–August, 2008. 相似文献
12.
Summary This article is concerned with the application of electrorheological fluids (ERF) to the reduction of vibrations by controlled
damping. Many papers deal with mechanical characteristics of ERF, but only a few articles have been published about the technical
applications of these fluids, although great expectations have been placed into it some years ago. Vibration reduction by
damping control is a difficult task because forces can only be generated when relative velocities exist between both ends
of the damper. The design of a control strategy cannot be investigated by the methods of linear control theory. It is a task
for the dynamic programming. The main objective of this paper is to present different methods for the investigation of suitable
control strategies, and to verify the theoretical results by simulation and experiments. By simulation, it can be shown that
the bang–bang control of damping – that means switching between the highest and the lowest possible damping – is an efficient
way for the reduction of vibrations in special systems. Nearly no additional power is necessary. This switching can be realised
with controlled valves and bypasses or by the ERF. Experiments with the ERF prove the theoretical considerations; still, there
are several side effects making it difficult to perform a useful experiment, for example, leakage in the damper or electric
isolation problems or the dependence on whether the AC or the DC is used.
Received 26 October 1998; accepted for publication 20 October 1999 相似文献
13.
The stability of the interface between two immiscible fluids of different density which occupy a plane horizontal layer performing
harmonic horizontal oscillations is considered. Within the framework of the ideal fluid model a transformation reducing the
problem of small plane perturbations to the Mathieu equation is found. Resonance instability domains associated with the formation
of capillary-gravitational waves are investigated. A model which takes into account dissipation processes due to the presence
of viscous friction is constructed. The role of the viscous dissipation in suppressing resonance instability is discussed.
Perm’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 25–31, May–June, 1998.
The work was carried out with partial support from the Russian Foundation for Basic Research (project No. 95-01-00386). 相似文献
14.
Perturbations of the interface between two immiscible ideal fluids of finite thickness (the lower and upper fluids are the
conductor and the dielectric, respectively) located in the gap between two electrodes are considered. In the cases of the
“shallow” and “deep” upper fluid the dispersion relations of linear waves and their longwave expansions are found. The methods
of determining the space-time evolution of an initial surface perturbation are developed on the basis of the linear approximation.
In the cases of the “shallow” and “deep” upper fluid examples of the development of an initial perturbation of the “step”
type are given. The development of an initial perturbation of the “step” type are also considered in the near-critical electric
fields and in the case of degeneration of cubic dispersion. 相似文献
15.
Heat transfer studies to Newtonian and non-Newtonian fluids are carried out in a stirred vessel fitted with anchor/turbine
impeller and a coil for heating/cooling with an objective of determining experimentally the heat transfer coefficient of few
industrially important systems namely castor oil and its methyl esters, soap solution, CMC and chalk slurries. The effect
of impeller geometry, speed and aeration is investigated. Generalized Reynolds and Prandtl numbers are calculated using an
apparent viscosity for non-Newtonian fluids. The data is correlated using a Sieder–Tate type equation. A trend of increase
in heat transfer coefficient with RPM in presence and absence of solids has been observed. Relatively high values of Nusselt
numbers are obtained for non-Newtonian fluids when aeration is coupled with agitation. The contribution of natural convection
to heat transfer has been accounted for by incorporating the Grashof number. The correlations developed based on these studies
are applied for design of commercial scale soponification reactor. Power per unit volume resulted in reliable design of a
reactor. 相似文献
16.
Davide Catania 《Journal of Mathematical Fluid Mechanics》2012,14(1):95-115
We consider two magnetohydrodynamic-α (MHDα) models with kinematic viscosity and magnetic diffusivity for an incompressible fluid in a three-dimensional periodic box
(torus). More precisely, we consider the Navier–Stokes-α-MHD and the Modified Leray-α-MHD models. Similar models are useful to study the turbulent behavior of fluids in presence of a magnetic field because of
the current impossibility to handle non-regularized systems neither analytically nor via numerical simulations. In both cases,
the global existence of the solution and of a global attractor can be shown. We provide an upper bound for the Hausdorff and
the fractal dimension of the attractor. This bound can be interpreted in terms of degrees of
freedom of the long-time dynamics of the involved system and gives information about the numerical stability of the model.
We get the same bound that holds for the Simplified Bardina-MHD model, considered in a previous paper (this result provides,
in some sense, an intermediate bound between the number of degrees of freedom for the Simplified Bardina model and the Navier–Stokes-α equation in the nonmagnetic case). However, the Navier–Stokes-α-MHD system is preferable since, in the ideal case, it conserves more quadratic invariants derived from the standard MHD model. 相似文献
17.
Hadi Saboorian-Jooybari Siavash Ashoori Gholamhossein Mowazi 《Transport in Porous Media》2012,92(3):687-708
In dual porosity modeling of naturally fractured reservoirs, fluids exchange between the high porous matrix blocks and high
permeable fracture systems is governed by transfer function. Therefore, transfer function, and specially shape factor as the
main part of it, control fluids flow behavior, which certainly have significant effects on development and management plan
of naturally fractured reservoirs. Also several formulations have been proposed for shape factor by a number of researchers,
nearly all of them derived for expansion mechanism. But, shape factor is a phase sensitive parameter that can greatly affect
results of simulation. Moreover, several shortcomings are inherent in the derived expressions of shape factor for imbibition
process. The main aim of this work is to develop a new time-dependent matrix–fracture shape factor specific to countercurrent
imbibition. In this study, fluid saturation distribution within a matrix block is analytically derived by solving capillary–diffusion
equation under different imposed boundary conditions for the process where countercurrent imbibition is the dominant oil drive
mechanism. The validity of the solutions is checked against literature experimental data (Bourbiaux and Kalaydjian, SPERE
5, 361–368, SPE 18283, 1990) and also by performing single porosity fine grid simulations. Then, the concept of analogy between the transport phenomena
is employed to propose a new expression for matrix–fracture transfer function that is used to derive transient shape factor.
It is illustrated in this article that time variation of imbibtion rate and shape factor can be used to diagnose different
states of imbibition process. Although, the displacement process and employed approaches are completely different in this
and other studies (Chang, Technical report, 1993; Kazemi and Gilman (eds.) Flow and contaminant transport in fractured rock. Academic Press, San Dieg, 1993; Zimmerman et al., Water Resour Res, 29, 2127–2137, 1993; Lim and Aziz, J Pet Sci Eng 13, 169–178, 1995), but we arrived at the consistent values of shape factor under limiting condition of pseudo steady state flow. This means
that after establishment of pseudo steady state, shape factor is only controlled by matrix geometry regardless of the displacement
process, i.e., expansion or imbibition mechanism, However, shape factor is completely phase sensitive and process dependent
during unsteady and late-transient states. Finally, boundary condition dependency of shape factor is investigated. 相似文献
18.
An analytical solution to the problem of condensation by natural convection over a thin porous substrate attached to a cooled
impermeable surface has been conducted to determine the velocity and temperature profiles within the porous layer, the dimensionless
thickness film and the local Nusselt number. In the porous region, the Darcy–Brinkman–Forchheimer (DBF) model describes the
flow and the thermal dispersion is taken into account in the energy equation. The classical boundary layer equations without
inertia and enthalpyterms are used in the condensate region. It is found that due to the thermal dispersion effect, the increasing
of heat transfer is significant. The comparison of the DBF model and the Darcy–Brinkman (DB) one is carried out. 相似文献
19.
V. E. Zakhvataev 《Journal of Applied Mechanics and Technical Physics》1998,39(1):78-84
The influence of a constant transverse electric field on the dynamics of longwave, weakly nonlinear flow of a viscous dielectric
liquid film down a vertical wall is studied. An amplitude integrodifferential equation in partial derivatives of the Kuramoto-Sivashinskii
equation type, which describes the behavior of the free surface of the layer, is derived using the method of multiscale stretching.
In the case considered, the potential energy of the electric field is a source of longwave perturbations, but, on the whole,
secondary regimes are apparently nonlinearly steady. Probably, the electric polarization effects studied can be used as a
factor that governs the dynamics of film flow.
Computer Center, Siberian Division, Russian Academy of Sciences, Krasnoyarsk 660036. Translated from Prikladnaya Mekhanika
i Tekhnicheskaya Fizika, Vol. 39, No. 1, pp. 90–97, January–February, 1998. 相似文献
20.
Hydrodynamic analysis of the displacement conditions of formation fluids using an axisymmetric model
I. B. Chernoshchuk 《Journal of Applied Mechanics and Technical Physics》2008,49(2):201-208
The axisymmetric problem of the displacement of formation fluids by a drilling mud filtrate with filter cake formation is
considered. An analysis is made of the distribution and variation of the main parameters of the process: filtrate volume,
filter cake thickness, oil saturation, and pressure. The positions of the water-saturation and salt-concentration fronts are
determined. The results are compared with the geophysical logging data for straight-hole drilling.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 56–64, March–April, 2008. 相似文献