Unsteady boundary layer flow on a cylinder in a channel

The unsteady laminar incompressible nonsimilar boundary layer flow over a circular cylinder placed symmetrically inside a channel has been studied when the unsteadiness and nonsimilarity are due to the free stream velocity. The nonlinear partial differential equations with three independent variables have been solved numerically using an implicit finite-difference in combination with the quasilinearization technique. It is found that the channel blockage parameter controls the transfer of heat from the cylinder and delays separation. The skin friction and heat transfer are significantly affected by the free stream velocity distributions.

Blade manipulators in turbulent channel flow

We report here the results of a series of careful experiments in turbulent channel flow, using various configurations of blade manipulators suggested as optimal in earlier boundary layer studies. The mass flow in the channel could be held constant to better than 0.1%, and the uncertainties in pressure loss measurements were less than 0.1 mm of water; it was therefore possible to make accurate estimates of the global effects of blade manipulation of a kind that are difficult in boundary layer flows. The flow was fully developed at the station where the blades were mounted, and always relaxed to the same state sufficiently far downstream. It is found that, for a given mass flow, the pressure drop to any station downstream is always higher in the manipulated than in the unmanipulated flow, demonstrating that none of the blade manipulators tried reduces net duct losses. However the net increase in duct losses is less than the drag of the blade even in laminar flow, showing that there is a net reduction in the total skin friction drag experienced by the duct, but this relief is only about 20% of the manipulator drag at most.

An experimental study of reverse transition in two-dimensional channel flow

An experimental investigation on reverse transition from turbulent to laminar flow in a two-dimensional channel was carried out. The reverse transition occurred when Reynolds number of an initially turbulent flow was reduced below a certain value by widening the duct in the lateral direction. The experiments were conducted at Reynolds numbers of 625, 865, 980 and 1250 based on half the height of the channel and the average of the mean velocity. At all these Reynolds numbers the initially turbulent mean velocity profiles tend to become parabolic. The longitudinal and vertical velocity fluctuations ($\overline{u^{\prime 2}}$ and $\overline{v^{\prime 2}}$) averaged over the height of the channel decrease exponentially with distance downstream, but $\overline{u^{\prime}v^{\prime}} $ tends to become zero at a reasonably well-defined point. During reverse transition $\overline{u^{\prime}}\overline{v^{\prime}}/\sqrt{\overline{u^{\prime 2}}}\sqrt{\overline{v^{\prime 2}}}$ also decreases as the flow moves downstream and Lissajous figures taken with u’ and v’ signals confirm this trend. There is approximate similarly between $\overline{u^{\prime 2}} $ profiles if the value of $\overline{u^{\prime 2}_{\max}} $ and the distance from the wall at which it occurs are taken as the reference scales. The spectrum of $\overline{u^{\prime 2}} $ is almost similar at all stations and the non-dimensional spectrum is exponential in wave-number. All the turbulent quantities, when plotted in appropriate co-ordinates, indicate that there is a definite critical Reynolds number of 1400±50 for reverse transition.

Flow of a stratified fluid in a wavy channel

The flow of a stratified fluid in a channel with small and large deformations is investigated. The analogy of this flow with swirling flow in tubes with non-uniform cross-sections is studied. The flow near the wall is blocked when the Froude number takes certain critical values. The possibility of preventing the stagnation zones in the flow field is also discussed

Particle dynamics in the channel flow of a turbulent particle-gas suspension at high Stokes number. Part 1. DNS and fluctuating force model

The fluctuating force model is developed and applied to the turbulent flow of a gas-particle suspension in a channel in the limit of high Stokes number, where the particle relaxation time is large compared to the fluid correlation time, and low particle Reynolds number where the Stokes drag law can be used to describe the interaction between the particles and fluid. In contrast to the Couette flow, the fluid velocity variances in the different directions in the channel are highly non-homogeneous, and they exhibit significant variation across the channel. First, we analyse the fluctuating particle velocity and acceleration distributions at different locations across the channel. The distributions are found to be non-Gaussian near the centre of the channel, and they exhibit significant skewness and flatness. However, acceleration distributions are closer to Gaussian at locations away from the channel centre, especially in regions where the variances of the fluid velocity fluctuations are at a maximum. The time correlations for the fluid velocity fluctuations and particle acceleration fluctuations are evaluated, and it is found that the time correlation of the particle acceleration fluctuations is close to the time correlations of the fluid velocity in a `moving Eulerian' reference, moving with the mean fluid velocity. The variances of the fluctuating force distributions in the Langevin simulations are determined from the time correlations of the fluid velocity fluctuations and the results are compared with direct numerical simulations. Quantitative agreement between the two simulations are obtained provided the particle viscous relaxation time is at least five times larger than the fluid integral time.

Particle dynamics in the channel flow of a turbulent particle-gas suspension at high Stokes number. Part 2. Comparison of fluctuating force simulations and experiments

The particle and fluid velocity fluctuations in a turbulent gas-particle suspension are studied experimentally using two-dimensional particle image velocimetry with the objective of comparing the experiments with the predictions of fluctuating force simulations. Since the fluctuating force simulations employ force distributions which do not incorporate the modification of fluid turbulence due to the particles, it is of importance to quantify the turbulence modification in the experiments. For experiments carried out at a low volume fraction of 9.15 x 10(-5) (mass loading is 0.19), where the viscous relaxation time is small compared with the time between collisions, it is found that the gas-phase turbulence is not significantly modified by the presence of particles. Owing to this, quantitative agreement is obtained between the results of experiments and fluctuating force simulations for the mean velocity and the root mean square of the fluctuating velocity, provided that the polydispersity in the particle size is incorporated in the simulations. This is because the polydispersity results in a variation in the terminal velocity of the particles which could induce collisions and generate fluctuations; this mechanism is absent if all of the particles are of equal size. It is found that there is some variation in the particle mean velocity very close to the wall depending on the wall-collision model used in the simulations, and agreement with experiments is obtained only when the tangential wall-particle coefficient of restitution is 0.7. The mean particle velocity is in quantitative agreement for locations more than 10 wall units from the wall of the channel. However, there are systematic differences between the simulations and theory for the particle concentrations, possibly due to inadequate control over the particle feeding at the entrance. The particle velocity distributions are compared both at the centre of the channel and near the wall, and the shape of the distribution function near the wall obtained in experiments is accurately predicted by the simulations. At the centre, there is some discrepancy between simulations and experiment for the distribution of the fluctuating velocity in the flow direction, where the simulations predict a bi-modal distribution whereas only a single maximum is observed in the experiments, although both distributions are skewed towards negative fluctuating velocities. At a much higher particle mass loading of 1.7, where the time between collisions is smaller than the viscous relaxation time, there is a significant increase in the turbulent velocity fluctuations by similar to 1-2 orders of magnitude. Therefore, it becomes necessary to incorporate the modified fluid-phase intensity in the fluctuating force simulation; with this modification, the mean and mean-square fluctuating velocities are within 20-30% of the experimental values.

THREE-LAYER FLUID FLOW OVER A SMALL OBSTRUCTION ON THE BOTTOM OF A CHANNEL

Many boundary value problems occur in a natural way while studying fluid flow problems in a channel. The solutions of two such boundary value problems are obtained and analysed in the context of flow problems involving three layers of fluids of different constant densities in a channel, associated with an impermeable bottom that has a small undulation. The top surface of the channel is either bounded by a rigid lid or free to the atmosphere. The fluid in each layer is assumed to be inviscid and incompressible, and the flow is irrotational and two-dimensional. Only waves that are stationary with respect to the bottom profile are considered in this paper. The effect of surface tension is neglected. In the process of obtaining solutions for both the problems, regular perturbation analysis along with a Fourier transform technique is employed to derive the first-order corrections of some important physical quantities. Two types of bottom topography, such as concave and convex, are considered to derive the profiles of the interfaces. We observe that the profiles are oscillatory in nature, representing waves of variable amplitude with distinct wave numbers propagating downstream and with no wave upstream. The observations are presented in tabular and graphical forms.

Effect of Channel Confinement on Mixed Convective Flow Past an Equilateral Triangular Cylinder

The present work investigates the mixed convective flow and heat transfer characteristics past a triangular cylinder placed symmetrically in a vertical channel. At a representative Reynolds number, Re = 100, simulations are carried out for the blockage ratios beta = 1/3; 1/4; and 1/6. Effect of aiding and opposing buoyancy is brought about by varying the Richardson number in the range -1.0 <= Ri <= 1.0. At a blockage ratio of 1/3, suppression of vortex shedding is found at Ri = 1, whereas von Karman vortex street is seen both at beta = 1/4 and 1/6, respectively. This is the first time that such behavior of blockage ratio past a triangular cylinder in the present flow configuration is reported. Drag coefficient increases progressively with increasing Ri and a slightly higher value is noticed at beta = 1/3. For all b, heat transfer increases with increasing Ri. Flattening of Nu(avg)-Ri curve beyond Ri > 0: 75 is observed at beta = 1/3.

Effect of a magnetic field on the flow and blood oxygenation in channels of variable cross-section

The effect of a magnetic field on the flow and oxygenation of an incompressible Newtonian conducting fluid in channels with irregular boundaries has been investigated. The geometric parameter δ, which is a ratio of the mean half width of the channel d to the characteristic length λ along the channel over which the significant changes in the flow quantities occur, has been used for perturbing the governing equations. Closed form solutions of the various order equations are presented for the stream function. The equations for oxygen partial pressure remain nonlinear even after perturbation, therefore a numerical solution is presented. The expressions for shear stress at a wall and pressure distributions are derived. Here the separation in the flow occurs at a higher Reynolds number than the corresponding non-magnetic case. It is found that the magnetic field has an effect on local oxygen concentration but has a little effect on the saturation length.

Pulsatile blood flow in a rigid pulmonary alveolar sheet with porous walls

This paper deals with the pulsatile blood flow in the lung alveolar sheets by idealizing each of them as a channel covered by porous media. As the blood flow in the lung is of low Reynolds number, a creeping flow is assumed in the channel. The analytical and numerical results for the velocity and pressure distribution in the porous medium are presented. The effect of an imposed slip condition is also studied. Comparisons with the corresponding results for the steady-state case are made at the end.

Metamodeling approach to predict friction factor of alluvial channel

The flow resistance of an alluvial channel flow is not only affected by the Reynolds number and the roughness conditions but also the Froude number. Froude number is the most basic parameter in the case of the alluvial channel, thus effect of Froude number on resistance to flow should be considered in the formulation of the friction factor, which is not in the case of present available resistance equations. At present, no generally acceptable quantitative description of the effects of the Froude number on hydraulic resistance has been developed. Metamodeling technique, which is particularly useful in modeling a complex processes or where knowledge of the physics is limited, is presented as a tool complimentary to modeling friction factor in alluvial channels. Present work uses, a radial basis metamodel, which is a type of neural network modeling, to find the effect of Froude number on the flow resistance. Based on the experimental data taken from different sources, it has been found that the predicting capability of the present model is on acceptable level. Present work also tries in formulating an empirical equation for resistance in alluvial channel comprising all the three majorm, parameters, namely, roughness parameter, Froude number and Reynolds number. (C) 2009 Elsevier B.V. All rights reserved.

Analysis of gradually and spatially varied flow in sand-bed channels

Seepage through a sand bed affects the channel hydrodynamics, which in turn alters channel stability. Thus, the effect of seepage on its hydrodynamic parameters needs to be ascertained. The present work analyses spatially varied flow of a sand-bed channel subjected to seepage in the downward direction through a sand bed. Numerically calculated flow profiles affected by seepage have been verified using experimental observations. The present work also analyses the friction slope, velocity and bed shear stress variations along the channel for both seepage and no-seepage conditions. It was found that the downward seepage-induced channel flow has larger friction slope and bed shear stress than that of no-seepage.

Stability and transition in the flow of polymer solutions

The linear stability analysis of a plane Couette flow of viscoelastic fluid have been studied with the emphasis on two dimensional disturbances with wave number k similar to Re-1/2, where Re is Reynolds number based on maximum velocity and channel width. We employ three models to represent the dilute polymer solution: the classical Oldroyd-B model, the Oldroyd-B model with artificial diffusivity and the non-homogeneous polymer model. The result of the linear stability analysis is found to be sensitive to the polymer model used. While the plane Couette flow is found to be stable to infinitesimal disturbances for the first two models, the last one exhibits a linear instability.

A numerical study of division of flow in open channels

A two-dimensional numerical model which employs the depth-averaged forms of continuity and momentum equations along with k-e turbulence closure scheme is used to simulate the flow at the open channel divisions. The model is generalised to flows of arbitrary geometries and MacCormack finite volume method is used for solving governing equations. Application of cartesian version of the model to analyse the flow at right-angled junction is presented. The numerical predictions are compared with experimental data of earlier investigators and measurements made as part of the present study. Performance of the model in predicting discharge distribution, surface profiles, separation zone parameters and energy losses is evaluated and discussed in detail. To illustrate the application of the numerical model to analyse the flow in acute angled offtakes and streamlined branch entries, a few computational results are presented.