Channel Of Rectangular Cross-section Research Articles

Integral transforms for three-dimensional steady turbulent dispersion in rivers and channels

A three-dimensional steady-state mathematical model is considered for predicting the fate of dissolved contaminants in rivers and channels under turbulent flow conditions. The model allows for variable velocity fields and non-uniform turbulent diffusivities within channels of rectangular cross sections. Making use of the Generalized Integral Transform Technique (GITT), a hybrid numerical–analytical solution for the concentration fields is then obtained. The solution convergence behavior is investigated and the criterion for reordering the terms in the infinite series is discussed, with the aim of reducing the computational effort associated with the multiple eigenfunction expansions. A test case is presented to illustrate the proposed approach.

Application of the GRP scheme to open channel flow equations

The GRP (generalized Riemann problem) scheme, originally conceived for gasdynamics, is reformulated for the numerical integration of the shallow water equations in channels of rectangular cross-section, variable width and bed profile, including a friction model for the fluid–channel shear stress. This scheme is a second-order analytic extension of the first-order Godunov-scheme, based on time-derivatives of flow variables at cell-interfaces resulting from piecewise-linear data reconstruction in cells. The second-order time-integration is based on solutions to generalized Riemann problems at cell-interfaces, thus accounting for the full governing equations, including source terms. The source term due to variable bed elevation is treated in a well-balanced way so that quiescent flow is exactly replicated; this is done by adopting the Surface Gradient Method (SGM). Several problems of steady or unsteady open channel flow are considered, including the terms corresponding to variable channel width and bed elevation, as well as to shear stress at the fluid–channel interface (using the Manning friction model). In all these examples remarkable agreement is obtained between the numerical integration and the exact or accurate solutions.

Effects of channel geometrical configuration and shoulder width on PEMFC performance at high current density

Computational fluid dynamics analysis was employed to investigate the performance of proton exchange membrane fuel cells (PEMFCs) with different channel geometries at high operating current densities. A 3D, non-isothermal model was used with a single straight channel geometry. Both anode and cathode humidifications were included in the model. In addition, phase transportation was included in the model to obtain the total water management for systems operating at different current densities. The simulation results showed that a rectangular channel cross-section gave higher cell voltages compared with trapezoidal and parallelogram channel cross-sections. However, the trapezoidal channel cross-section facilitated reactant diffusion, leading to more uniform reactant and local current density distributions over the reacting area, and thus to a lower cathode overpotential of the cell. Simulations of the three different channel cross-sections using the same boundary conditions showed that among the cell geometrical parameters, the shoulder width is one of the most influential in terms of its impact on cell performance. Simulations using different channel–shoulder width ratios showed that at high operating current densities, Ohmic losses significantly increase with decreasing shoulder width. In contrast, a smaller shoulder width facilitates the distribution of reactants and helps to reduce concentration losses. The simulations disclosed the existence of an optimum channel–shoulder width ratio that gives the highest cell voltage under high current density operating conditions. Under such conditions, however, the cell performance deteriorated dramatically with decreasing shoulder width, even when higher reactants flow rates and inlet velocities were used.

On the possible formation of a vortex flow in a supersonic inlet with three-dimensional compression

The structure of the flow in an inlet with three-dimensional compression and an adjoining channel of rectangular cross-section is experimentally investigated for the external flow parameters M∞ = 4 and Re ≈ 52 · 106 1/m. The phenomenon of vortex generation in the air-intake and its breakdown at the channel entry, where it encounters an elevated pressure gradient, is studied

Pressure drops for droplet flows in microfluidic channels

Designing on-chip microfluidic pumps requires that the dependence of pressure drop across the device on the fluid flow rate be known. This relationship can be complicated for the case of two-phase droplet type flows. We characterized the flow-pressure relationship for the single-file flow of water drops in oil in microfluidic channels of rectangular cross sections. The pressure for such droplet flows was always larger—sometimes over 50% larger—than that for corresponding single-phase flows of the continuous phase. This is in spite of the fact that the water drops had a substantially lower viscosity than the continuous phase oil. The excess pressure was found to correlate reasonably well with the size of the drops relative to the size of the channels. This correlation for the excess pressure, as well as a correlation presented here for the size of drops in microchannels, should provide convenient guidelines in designing microfluidic devices for two-phase flows.

Effective heights and tangential momentum accommodation coefficients of gaseous slip flows in deep reactive ion etching rectangular microchannels

The behavior of a rarefied, compressible flow in long, constant cross section channels provides an opportunity to study complex gas dynamics in a simple geometry that allows analytical solutions. The problem of a rarefied, compressible flow in near unity aspect ratio rectangular cross section channels has been all but ignored despite it being a common flow geometry. We present analytical expressions for the mass flow rate in long, straight and uniform rectangular cross section microchannels in the slip flow regime. Using these analytical expressions, we extract the tangential momentum accommodation coefficient (TMAC) as well as the effective channel dimensions to account for a slight curvature of one of the walls of the rectangle. These expressions are effective in near unity aspect ratio rectangular microchannels made by deep reactive ion etching. The dependence of the flow behavior on the channel height to width aspect ratio is discussed as is the effect of the slight deviation from a rectangular cross section. The obtained TMAC results are consistent with values found by previous researchers using similar materials. Finally, a method of determining TMACs in channels consisting of non-homogenous materials or processing methods is presented.

Theory of two-layer hydraulic exchange flows with rotation

Two-layer rotating exchange flows through channels of rectangular cross-section are modelled using semi-geostrophic, zero-potential-vorticity theory. For a given channel cross-section the full range of possible flow states is considered. The interface always has a uniform slope across the channel, but may separate from one or both of the sidewalls to attach to the upper or lower boundary. The flow may be subcritical, critical or supercritical. These different states are identified in a pseudo-Froude-number plane analogous to that developed by Armi (1986) for non-rotating flows. If the ratio of the channel width to the Rossby radius is constant along the length of the channel, then the solution may be traced along the entire channel using a single diagram. Several examples of maximal and submaximal exchanges are considered. This graphical method of solution is contrasted with the functional approach of Dalziel (1988, 1990).The exchange flux is determined as a function of the channel geometry, the strength of rotation and the difference in Bernoulli potential between the two layers.

Experimental Investigation of the Transverse Self-Oscillations of Circular Cylinders Mounted with a Narrow Clearance in a Plane Channel

The results of an investigation of the flow past and the behavior of free bluff bodies mounted in pipes and channels with a narrow clearance, conducted in the Institute of Mechanics of Moscow State University, are presented. The drag of circular cylinders of different size and mass in a circulation-free water flow in a plane channel of rectangular cross-section was studied in the transverse self-oscillation regime. The experiments were conducted for Reynolds numbers based on the cylinder diameter 1.7 ⋅ 104 ≤ Re ≤ 7.2 ⋅ 104, relative clearances \(\bar S\) based on a cross-sectional area ranging from 0.76 to 0.9, and cylinder-to-water density ratios ρ c /ρ ranging from 1.29 to 8.2. Only the case of intense transverse self-oscillations accompanied by impact interaction with the channel wall was considered. The dependence of the period-average cylinder drag coefficient C x on the basic dimensionless relevant parameters is obtained. The dependence of the dimensionless self-oscillation frequency determined in [1] is refined. The kinematic and dynamic features of the flows past spheres in cylindrical pipes and cylinders in plane channels are compared in the transverse self-oscillation regime.

The front condition for gravity currents

Self-similar plane solutions for the inertial stage of gravity currents are related to the initial parameters and a coefficient that is determined by the boundary condition at the front. Different relations have been proposed for the boundary condition in terms of a Froude number at the front, none of which have a sound theoretical or experimental basis. This paper focuses on considerations of the appropriate Froude number based on results of lock-exchange experiments in which extended inertial gravity currents are generated in a rectangular cross-section channel. We use ‘top-hat’ vertical density profiles of the currents to obtain an ‘equivalent’ depth, defined by profiles having the same buoyancy at every position as the real profiles. As in previous work, our experimental results show that in the initial constant-velocity phase the Froude number can be defined in terms of the lock depth. However, as the current enters the similarity phase when the initial release conditions are no longer relevant, we find that the Froude number is more appropriately defined in terms of the maximum height of the head. Strictly speaking, the self-similar solution to the shallow-water equations requires a front condition that uses the height at the rear of the head. We find that this rear Froude number is not constant and is a function of the head Reynolds number over the range 400–4500.

Unsteady flows of Oldroyd-B fluids in a channel of rectangular cross-section

The aim of this note is to present the exact solutions corresponding to two types of unsteady flows of an Oldroyd-B fluid in a channel of rectangular cross-section. The solutions that have been obtained satisfy both the associate partial differential equations and all imposed initial and boundary conditions. For λ r or λ → 0 they tend toward similar solutions for a Maxwell or second-grade fluid. If both λ r and λ → 0 , the solutions for Navier–Stokes fluids are recovered.

A Numerical Study of Dean Instability in Non-Newtonian Fluids

We present a numerical study of Dean instability for non-Newtonian fluids in a laminar 180deg curved-channel flow of rectangular cross section. A methodology based on the Papanastasiou model (Papanastasiou, T. C., 1987, J. Rheol., 31(5), pp. 385–404) was developed to take into account the Bingham-type rheological behavior. After validation of the numerical methodology, simulations were carried out (using FLUENT CFD code) for Newtonian and non-Newtonian fluids in curved channels of square or rectangular cross section and for a large aspect and curvature ratios. A criterion based on the axial velocity gradient was defined to detect the instability threshold. This criterion was used to optimize the grid geometry. The effects of curvature and aspect ratio on the Dean instability are studied for all fluids, Newtonian and non-Newtonian. In particular, we show that the critical value of the Dean number decreases with increasing curvature ratio. The variation of the critical Dean number with aspect ratio is less regular. The results are compared to those for Newtonian fluids to emphasize the effect of the power-law index and the Bingham number. The onset of Dean instability is delayed with increasing power-law index. The same delay is observed in Bingham fluids when the Bingham number is increased.

Two-phase frictional pressure gradient of R236ea, R134a and R410A inside multi-port mini-channels

In the present paper the pressure drop characteristics of a 1.4 mm hydraulic diameter multiport minichannel tube during adiabatic two-phase flow of HFC refrigerants are discussed. The tube consists of eleven parallel rectangular cross section channels. Although much experimental research has been devoted to investigate the pressure drop characteristics of R134a inside multiport minichannels in the last years, very little information is available on different refrigerants, such as R236ea (low pressure) and R410A (high pressure), whose behaviour is different from R134a. The experimental runs are carried out at mass velocities ranging from 200 to 1400 kg/(m 2 s), depending on the refrigerant under test, at constant value of vapour quality. The frictional pressure gradient is obtained from the saturation temperature drop measurement. The results presented here cover a wide range of the reduced pressure, from 0.1 up to 0.5. The experimental frictional pressure drop data is compared against models available in the literature for prediction of frictional pressure gradient in channels. The comparison of calculated to experimental values shows that the R134a frictional pressure gradient in the multiport minichannel test tube can be fairly well predicted by available correlations, but not satisfactory agreement is found for R236ea data and even worse in the case of R410A data.

Gas displacing liquids from non-circular tubes: high capillary number flow of a shear-thinning liquid

Transient, three-dimensional finite element analysis has been used to investigate the displacement of a shear thinning liquid from prismatic channels of square, rectangular and trapezoidal cross sections. Inertia, gravity and surface tension effects are neglected and the results therefore apply in the limits of low Reynolds and high capillary numbers. The analysis is carried out in a fixed frame of reference and gas penetration is modelled as the bubble moves down the tube, which is long relative to its transverse dimension. Results are provided for the thickness of the layers left on the channel walls under developed conditions, and the fraction of the cross section occupied by liquid, as a function of the channel cross-sectional geometry and the degree of shear thinning, modelled using the power law. Interface contours on the channel cross sections are displayed. It is found for the Newtonian liquid that the fingering instability arises in the rectangular channel when the aspect ratio reaches about five. Shear thinning delays the onset of the instability to higher aspect ratios. The results are systematized, and insights gained into the influence of channel geometry and shear thinning, by noting a qualitative, inverse relationship between the deposited layer thickness and the shear rate at the wall in the flow ahead of the bubble.

Flow Characteristics in Rectangular Cross-Sectioned Two-Pass Channels with Different Channel Aspect Ratio (Analysis by Means of POD)

The experimental study for flow characteristics in the rectangular channels with a sharp 180-deg turn was conducted. PIV measurements were performed both in symmetry plane and in four cross-section planes after the turn for three aspect ratios, AR=1, 2, and 4, at a Reynolds number of 2.0× 104. Proper orthogonal decomposition (POD), which decomposes a field of a time-dependent variable into an orthogonal set of deterministic functions, was demonstrated on the PIV snapshots to identify coherent structures in the flow. Based on the data, the influence of the channel aspect ratio on flow characteristics in the channel is discussed in detail. The unsteadiness of the longitudinal vortices generated in the cross sectional planes after the turn are also investigated.

811 異なる流路アスペクト比を持つ矩形断面往復流路内の流動・伝熱特性(OS8-3 複雑乱流の計測と制御(計測),OS8 複雑乱流の計測と制御,オーガナイズドセッション)

811 異なる流路アスペクト比を持つ矩形断面往復流路内の流動・伝熱特性(OS8-3 複雑乱流の計測と制御(計測),OS8 複雑乱流の計測と制御,オーガナイズドセッション)

Flow of a binary mixture of incompressible Newtonian fluids in a rectangular channel

The problems concerning some simple steady and unsteady flows of a mixture composed of two incompressible Newtonian fluids in an infinitely long channel of rectangular cross-section are examined. By means of finite Fourier sine transforms, the exact solutions of the field equations are obtained for the following four problems: (i) steady Couette flow in a rectangular channel, (ii) unsteady Couette flow in a rectangular channel, (iii) steady Poiseuille flow in a rectangular channel, (iv) unsteady Poiseuille flow in a rectangular channel.

Axially Tapered Microchannels of High Aspect Ratio for Evaporative Cooling Devices

Analytical solutions are derived for evaporating flow in open rectangular microchannels having a uniform depth and a width that decreases along the channel axis. The flow generally consists of two sequential domains, an entry domain where the meniscus is attached to the top corners of the channel followed by a recession domain where the meniscus retreats along the sidewalls toward the channel bottom. Analytical solutions applicable within each domain are matched at their interface. Results demonstrate that tapered channels provide substantially better cooling capacity than straight channels of rectangular or triangular cross section, particularly under opposing gravitational forces. A multiplicity of arbitrarily tapered channels can be microfabricated in metals using LIGA, a process involving electrodeposition into a lithographically patterned mold.

Oscillatory flow in microchannels

Commonly used, lumped-parameter expressions for the impedance of an incompressible viscous fluid subjected to harmonic oscillations in a channel were compared with exact expressions, based on solutions of the Navier-Stokes equations for slots and channels of circular and rectangular cross-section, and were found to differ by as much as 30% in amplitude. These differences resulted in predicted discrepancies by as much as 400% in frequency response amplitude for simple second-order systems based on size scales and frequencies encountered in microfluidic devices. These predictions were verified experimentally for rectangular microchannels and indicate that underdamped fluidic systems operating near the corner frequency of any included flow channel should be modeled with exact expressions for impedance to avoid potentially large errors in predicted behavior. List of symbols A Channel cross-sectional area (m 2 ) Ac Membrane area (m 2 ) a Rectangular duct and slot half-width or radius (m) b Rectangular duct half-depth and slot depth (m) C Capacitance (m 3 /Pa)

Design, fabrication, and evaluation of microfabricated columns for gas chromatography.

The design, fabrication, and performance of gas chromatography columns etched in silicon substrates are described. Deep reactive-ion etching formed the 3-m-long, 150-microm-wide, 240-microm-deep rectangular cross section channels. A glass cover plate was anodically bonded to the remaining surface of the substrate forming the gastight channel. For some of the columns, the silicon channels were oxidized before the channels were sealed with the glass plates. Fused-silica capillary connecting tubes were sealed into ports on the edge of the 3.2-cm x 3.2-cm substrate chips. Dynamic coating was used to deposit a film of nonpolar dimethyl polysiloxane or moderately polar trifluoropropylmethyl polysiloxane stationary phase. The columns were evaluated in a conventional benchtop GC instrument with split injection and flame ionization detection. Column efficiency was evaluated by the use of plots of height equivalent to a theoretical plate versus average carrier gas velocity using both hydrogen and air as carrier gases. The number of theoretical plates measured at the average carrier gas velocity giving the minimum plate height ranged from 4600 to 8200 plates for the dimethyl polysiloxane columns and from 3500 to 5500 plates for the trifluoropropylmethyl polysiloxane columns. Minimum plate height was significantly smaller with air as carrier gas. For the nonpolar phase, the nonoxidized surface gave approximately 1500 plates more than the oxidized surface for both carrier gases. For the polar phase, the oxidized surface gave approximately 200 plates more than the nonoxidized surface. Isothermal chromatograms of a 20-component multifunctional mixture and temperature-programmed chromatograms of a normal alkane mixture are presented.

Laminar flow in channels with wall suction or injection: a new model to study multi-channel filtration systems

A one-dimensional model to determine the laminar flow of a fluid in a porous channel with wall suction or injection is proposed. The approach is based on the integration of the Navier–Stokes equations using the analytical solutions for the two-dimensional local velocity and pressure fields obtained from the asymptotic developments at low filtration Reynolds number proposed by Berman (J. Appl. Phys. 24 (1953) 1232) and Yuan and Finkelstein (Trans. ASME 74 (1956) 719). It is noticeable that the resulting one-dimensional model preserves the whole flow properties, in particular the inertial terms which can affect the wall suction conditions and the spatial distribution of the growing particle cake layer at the wall encountered in filtration processes. The model is validated in the case of a single porous channel of rectangular or circular cross-section with uniform or variable wall suction. Then the model is applied to a two-dimensional multi-channel system which consists of a great number of adjacent entrance and exit channels connected by a filter porous medium. It is shown that the effect of non-uniform boundary conditions and the influence of heterogeneous geometrical characteristics on the heterogeneity of the fluid flow structure can be studied using such a model.