On the interplay between inertial and viscoelastic effects for the flow in weakly modulated channels

The flow inside a spatially modulated channel is examined for viscoelastic fluids of the Oldroyd‐B type. The lower wall is flat and the upper wall is sinusoidally modulated. The modulation amplitude is assumed to be small. Thus, a regular perturbation expansion of the flow field coupled to a variable‐step finite‐difference scheme is used to solve the problem. Convergence and accuracy assessment against earlier experimental results indicate that there is a significant range of validity of the perturbation approach. The influences of wall geometry, inertia and viscoelasticity on the flow kinematics and stresses are investigated systematically. In particular, the interplay between the flow and fluid parameters effects on the conditions for the onset of backflow, number of vortices, their size and location is revealed. The distance between the flow separation and reattachment locations identifies the vortex size. Non‐monotonic dependence of the vortex size on elasticity is reported. The critical conditions for the onset of negative elasticity effects on vortex size are identified. The critical Reynolds number for the onset of backflow initially decreases then levels off or even increases as elasticity increases. For highly elastic fluid and large enough Reynolds number, more than one vortex appear near the lower wall. Copyright © 2005 John Wiley & Sons, Ltd.     

Shear‐thinning flow in weakly modulated channels

The steady flow inside a spatially modulated channel is examined for shear‐thinning and shear‐thickening fluids. The flow is induced by the translation of the lower plate. The modulation amplitude is assumed to be small. A regular perturbation expansion of the flow field is used, coupled to a variable‐step finite‐difference scheme, to solve the problem. Convergence and accuracy assessment against finite‐volume calculations indicates that there is a significant range of validity of the perturbation approach. The influence of the wall geometry, inertia and non‐Newtonian effects are investigated systematically. In particular, the influence of the flow and fluid parameters is examined on the conditions for the onset of separation, vortex size and location. Copyright © 2005 John Wiley & Sons, Ltd.     

Singular perturbation for the weakly nonlinear reaction diffusion equation with boundary perturbation

In this paper, a class of nonlinear singularly perturbed initial boundary value problems for reaction diffusion equations with boundary perturbation are considered under suitable conditions. Firstly, by dint of the regular perturbation method, the outer solution of the original problem is obtained. Secondly, by using the stretched variable and the expansion theory of power series the initial layer of the solution is constructed. And then, by using the theory of differential inequalities, the asymptotic behavior of the solution for the initial boundary value problems is studied. Finally, using some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation are discussed.     

Freezing in turbulent flow inside tubes and channels

A simple and quite flexible numerical model is presented to predict the steady state ice-layer formation inside a cooled two dimensional channel or a tube containing a turbulent flow. The effects of arbitrary entrance velocity distributions upon the shape of the ice-layers are examined. The presented numerical scheme is verified by comparing the predicted ice-layers with measurements and generally good agreement was found.     

Calculation of three-dimensional weakly expanding flow in jets and channels

The results are given of a calculation of laminar flow in a channel of square section and the motion of a turbulent jet from a cruciform nozzle in an ambient flow. To calculate the secondary flows, the field of the transverse velocity is decomposed into irrotational and solenoidal components. The results of the calculation of the flow in the channel are compared with the calculations of other authors and experimental data. To calculate the flow in the turbulent jet, a one-parameter turbulence model is used, and the influence of the inhomogeneity of the distribution of the longitudinal component of the velocity on the components of the Reynolds stress tensor is taken into account. The results of calculation of the flow in the jet behind a cruciform nozzle are compared with experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 36–44, July–August, 1984.     

Two-phase flow behavior inside a header connected to multiple parallel channels

The main objective of this work is to examine the flow distribution of two-phase mixture to parallel channels and to investigate the flow behavior at header-channel junctions simulating the corresponding parts of compact heat exchangers. The cross-section of the header and the channels were fixed to 14 mm × 14 mm and 12 mm × 1.6 mm, respectively. The mass flux and the mass quality ranges were 70–165 kg/m² s and 0.3–0.7, respectively. Air and water were used as the test fluids. The flow distribution at the fore part of the header (region A) is affected only by the upstream flow configuration and the rate of liquid flow separation decreased a flowing downwards. On the other hand, in the rear part, the downstream effect predominates over the upstream effect due to strong flow recirculation near the end plate. In this part, the liquid separation increased (region B) and then decreased (region C) as the mixture proceeds downwards. The validity of the existing models for branching flows at parallel T-junction was tested, and turned out to be appropriate for region A. However, the models were not applicable to the rear part due to a strong flow recirculation. Moreover, the effect of the membranes in channels was investigated, but that was minor.     

Experiments on two-phase flow distribution inside parallel channels of compact heat exchangers

Uneven distribution in heat exchangers is a cause of reduction in both thermal and fluid-dynamic performances. Many papers have dealt with single-phase flow and both flow distribution data and analytical or numerical models are available for header design. With regard to two-phase flow, phase separation in manifolds with several outlets is so complicated that, to date, there is no general way to predict the distribution of two-phase mixtures at header-channel junctions. The design of headers for new generation compact heat exchangers and multi-microchannel evaporators is still based on an empirical approach, as a number of variables act together: geometrical parameters and orientation of the manifolds and of the channels, operating conditions, fluid physical properties.     

On the stability of non-isothermal flow in channels

Summary We study here stability of non-isothermal flow between two closely spaced, heat conducting, infinite parallel flat plates of lengthl and distanceh apart. Fluid enters uniformly alongx = 0 at temperatureT ₁ >T _w the plate temperature. The flow non-uniformity is assumed to occur due to coupling between the energy equation, which describes the heat transfer mechanism between fluid and channel walls, and the flow equation which includes the temperature dependence of viscosity.The model for the flow assumes that similarity profiles exist for velocity and temperature in the flow direction. The stability of the unidirectional flow by a linearized first order perturbation analysis of the proposed model is examined.Notation b rheological parameter of the fluid defined by eq. [4] - B dimensionless viscosity-temperature parameter defined by eq. [11] - C rheological parameter defined by eq. [4] - h distance between the two parallel plates, ft. - H a thermal transfer coefficient (l/h) - l length of the plates, ft. - p pressure - P inlet pressure - G _z Graetz number defined by eq. [11] - t time, h - T mean temperature as defined by eq. [2] - T ₁ inlet temperature - u velocity vector withu _x ,u _y ,u _z as component velocities - v mean velocity vector as defined by eq. [1] - V mean steady state axial velocity - x, y, z Cartesian coordinate system - w refers to wall condition - thermal diffusivity, ft²/h - A effective thermal diffusivity tensor - dimensionlessx coordinate - wave number iny direction - dimensionless wave number iny direction - µ ₀ viscosity of fluid - density of fluid - dimensionless velocity inx direction - growth rate of disturbances - dimensionless growth rate - proportionality constant for heat generation in eq. [5] With 4 figures     

Low Reynolds number flow inside straight micro channels with irregular cross sections

This paper presents an analysis of the compound effect of finite temperature differences and fluid friction on the existence of an optimum laminar flow regime in singly connected micro channels with complex free flow area cross sections. A widespread conviction has been established that the two competing irreversibility sources in a channel flow with heat transfer lead to the existence of an optimum flow regime. The results presented in this paper clearly shows the opposite. When an objective function is represented by the entropy generation rate per unit heat capacity rate of the fluid stream, the thermodynamic optimum flow regime represents a rather rare occurrence in the laminar region of irregularly shaped ducts. The presence of an extremum is more probable for very small diameters, the ones of an order of magnitude of O(≤10⁻³ m). The analysis is performed for selected ranges of relevant geometric, flow, and thermal parameters of a set of straight micro channels with irregular free flow area cross-sections. The following geometries of the free flow area cross section were investigated: (i) sine duct, (ii) circular duct, (iii) elliptical duct, (iv) moon-shaped ducts, and (v) four-cuspped duct. The range of Reynolds numbers has been established between O(10²) and O(10⁴). The existence of the objective function minimum is confirmed for ducts with an irregular cross section only for very small hydraulic diameters. These minima are relatively weak, and as a general rule, the sets of optimum parameters are close to the onset of turbulence or possibly even in the transitional or turbulent regions. Received on 10 November 1998     

On flow characteristics of liquid-solid mixed-phase nanofluid inside nanochannels

The atomic behavior of liquid-solid mixed-phase nanofluid flows inside nanochannels is investigated by a molecular dynamics simulation （MDS）. The results of visual observation and statistic analysis show that when the nanoparticles reach near each other, the strong interatomic force will make them attach together. This aggrega- tion continues until all nanoparticles make a continuous cluster. The effect of altering the external force magnitude causes changes in the agglomeration rate and system enthalpy. The density and velocity profiles are shown for two systems, i.e., argon （Ar）-copper （Cu） nanofluid and simple Ar fluid between two Cu walls. The results show that using nanopar- ticles changes the base fluid particles ordering along the nanochannel and increases the velocity. Moreover, using nanoparticles in simple fluids can increase the slip length and push the near-wall fluid particles into the main flow in the middle of the nanochannel.     

Two-phase flow distributors for fuel cell flow channels

All existing proton exchange membrane （PEM） fuel cell gas flow fields have been designed on the basis of single-phase gas flow distribution. The presence of liquid water in the flow causes non-uniform gas distribution, leading to poor cell performance. This paper demonstrates that a gas flow restrictor/distributor, as is commonly used in two-phase flow to stabilize multiphase transport lines and multiphase reactors, can improve the gas flow distribution by significantly reducing gas real-distribution caused by either non-uniform water formation in parallel flow channels or flow instability associated with negative-slope pressure drop characteristic of two-phase horizontal flow systems.     

The calculation of eigenvalues for the stationary perturbation of couette-poiseuille flow

The problem considered is that of two-dimensional viscous flow in a straight channel. The decay of a stationary perturbation from the Couette-Poiseuille flow in the downstream is sought. A differential eigenvalue equation resembling the Orr-Sommerfeld equation is solved by using a spectral method and an initial-value method (the compound matrix method) for values of the Reynolds number R between 0 and 2000. The eigenvalues are presented for several of interesting cases with different measures of mass flux. These eigenvalues determine the rate of decay for the purturbation.     

On the problem of oscillatory laminar flow of elastico-viscous liquids in channels

Summary A possibility is shown for an exact solution by means of tabulated functions of the problem about the velocity profile of oscillatory flow of elastico-viscous liquids in channels with annular cross-section.

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Zusammenfassung Es wird gezeigt, wie man mit Hilfe tabulierter Funktionen das Geschwindigkeitsprofil in einem Rohr mit Kreisring-Querschnitt für die oszillierende Strömung einer viskoelastischen Flüssigkeit bestimmen kann.

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On the energy transfer equation for weakly interacting waves

The derivation of the transfer equation based on analysis of the equations for spectral semi-invariant and not invoking equations for realization of the random wave field is presented. Uniformly valid asymptotic expansions for the third and the fourth spectral semi-invariant are constructed using the multiple scale method and the matched asymptotic expansion method. This approach makes it possible to investigate the boundary layer in a neighbourhood of the resonant surface where intensive growth in time of the third spectral semi-invariant occurs. This boundary layer defines the form of the transfer equations. An analogous boundary layer for the fourth spectral semiinvariant and its influence on the second and the third spectral semi-invariants are also investigated.     

Stochastic analysis of two-phase flow in porous media: I. Spectral/perturbation approach

Stochastic analysis of steady-state two-phase (water and oil) flow in heterogeneous porous media is performed using the perturbation theory and spectral representation techniques. The governing equations describing the flow are coupled and nonlinear. The key stochastic input variables are intrinsic permeability,k, and the soil and fluid dependent retention parameter, . Three different stochastic combinations of these two imput parameters were considered. The perturbation/spectral analysis was used to develop closed-form expressions that describe stochastic variability of key output processes, such as capillary and individual phase pressures and specific discharges. The analysis also included the estimation of the effective flow properties. The impact of the spatial variability ofk and on the variances of pressures, effective conductivities, and specific discharges was examined.