Stream power criterion and design of sand bed channels at incipient motion

The critical stream power criterion may be used to describe the incipient motion of cohesionless particles of plane sediment beds. The governing equation relating ``critical stream power'' to ``shear Reynolds number'' is developed by using the present experimental data as well as the data from several other sources. Simultaneously, a resistance equation, relating the ``particle Reynolds number'' to the``shear Reynolds number'' is developed for plane sediment beds in wide channels with little or no transport. By making use of these relations, a procedure is developed to design plane sediment beds such that any two of the four design variables, including particle size, energy/friction slope, flow depth, and discharge per unit width in the channel should be known to predict the remaining two variables. Finally, a straightforward design procedure using design tables/design curves and analytical methods is presented to solve six possible design problems.

The effects of slip velocity at a membrane surface on blood flow in the microcirculation

Closed-form solutions are presented for blood flow in the microcirculation by taking into account the influence of slip velocity at the membrane surface. In this study, the convective inertia force is neglected in comparison with that of blood viscosity on the basis of the smallness of the Reynolds number of the flow in microcirculation. The permeability property of the blood vessel is based on the well known Starling's hypothesis [11]. The effects of slip coefficient on the velocity and pressure fields are clearly depicted.

Oscillatory flow in an elastic tube of variable cross-section

An oscillatory flow of a viscous incompressible fluid in an elastic tube of variable cross section has been investigated at low Reynolds number. The equations governing, the flow are derived under the assumption that the variation of the cross-section is slow in the axial direction for a tethered tube. The problem is then reduced to that of solving for the excess pressure from a second order ordinary differential equation with complex valued Bessel functions as the coefficients. This equation has been solved numerically for geometries of physiological interest and a comparison is made with some of the known theoretical and experimental results.

Unsteady flow of a dilute suspension in a semi-infinite contracting or expanding pipe

In the present paper an exact similar solution of the Navier-Stokes equation for unsteady flow of a dilute suspension in a semi-infinite contracting or expanding circular pipe is presented. The effects of the Schmidt number (Sc), Reynolds number (|ε|), the volume fraction (α) and the relaxation time (τ) of the particulate phase on the flow characteristics are examined. The presence of the solid particles has been observed to influence the flow behaviour significantly. These solutions are valid down to the state of a completely collapsed pipe, since the nonlinearity is retained fully. The results may help understanding the flow near the heart and certain forced contractions or expansions of valved veins.

A couple stress model of blood flow in the microcirculation

A simple mathematical model depicting blood flow in the capillary is developed with an emphasis on the permeability property of the blood vessel based on Starling's hypothesis. In this study the effect of inertia has been neglected in comparison with the viscosity on the basis of the smallness of the Reynolds number of the flow in the capillary. The capillary blood vessel is approximated by a circular cylindrical tube with a permeable wall. The blood is represented by a couple stress fluid. With such an ideal model the velocity and pressure fields are determined. It is shown that an increase in the couple stress parameter increases the resistance to the flow and thereby decreases the volume rate flow. A comparison of the results with those of the Newtonian case has also been made.

A numerical study of thermocapillary flow in a rectangular cavity during laser melting

The surface tension gradient driven flow that occurs during laser melting has been studied. The vorticity-streamfunction form of the Navier-Stokes equations and the energy equation has been solved by the ‘Alternative Direction Implicit’ method. It has been shown that the inertia forces in the melt strongly influence the flow pattern in the melt. The convection in the melt modifies the isotherms in the melt at high surface tension Reynolds number and high Prandtl number. The buoyancy driven flow has been shown to be negligible compared to the surface tension gradient driven flow in laser melting.

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.

Turbulent spot growth in favorable pressure gradients

Experimental results are presented on the lateral growth of turbulent spots in a series of flows with favorable pressure gradients. It is shown that the wedge angle increases slowly with the Reynolds number and that a favorable pressure gradient inhibits the growth of turbulent spots and, in general, results in a nonlinear turbulent wedge. As soon as the pressure gradient decreases to the point where the flow becomes supercritical, however, spot growth increases rapidly and the associated turbulent wedge becomes linear.

Mechanics of transition in an axisymmetric laminar boundary layer on a circular cylinder

Measurements of the growth of artificially generated turbulent spots and intermittency distribution in the transition region on a circular cylinder in axial flow show that the instability Reynolds number of 11,000 has a marked effect on the properties. In particular, it is found that the spot production in the initial region when a single turbulent spot has not yet wrapped around the cylinder and the propagation is essentially two-dimensional, is significantly altered. But the transition in the downstream or latter region, where most of the turbulent spots propagate onedimensionally (like the turbulent plugs in a pipe), is not affected. When the radius Reynolds number is more than 11,000, the intermittency law in the initial region is essentially the same as in twodimensional flow on a flat plate and in the latter region it is the one-dimensional flow in a pipe, the demarcation between the two regions being quite sharp.

Zero-crossings in turbulent signals

A primary motivation for this work arises from the contradictory results obtained in some recent measurements of the zero-crossing frequency of turbulent fluctuations in shear flows. A systematic study of the various factors involved in zero-crossing measurements shows that the dynamic range of the signal, the discriminator characteristics, filter frequency and noise contamination have a strong bearing on the results obtained. These effects are analysed, and explicit corrections for noise contamination have been worked out. New measurements of the zero-crossing frequency N0 have been made for the longitudinal velocity fluctuation in boundary layers and a wake, for wall shear stress in a channel, and for temperature derivatives in a heated boundary layer. All these measurements show that a zero-crossing microscale, defined as Λ = (2πN0)−1, is always nearly equal to the well-known Taylor microscale λ (in time). These measurements, as well as a brief analysis, show that even strong departures from Gaussianity do not necessarily yield values appreciably different from unity for the ratio Λ/λ. Further, the variation of N0/N0 max across the boundary layer is found to correlate with the familiar wall and outer coordinates; the outer scaling for N0 max is totally inappropriate, and the inner scaling shows only a weak Reynolds-number dependence. It is also found that the distribution of the interval between successive zero-crossings can be approximated by a combination of a lognormal and an exponential, or (if the shortest intervals are ignored) even of two exponentials, one of which characterizes crossings whose duration is of the order of the wall-variable timescale ν/U2*, while the other characterizes crossings whose duration is of the order of the large-eddy timescale δ/U[infty infinity]. The significance of these results is discussed, and it is particularly argued that the pulse frequency of Rao, Narasimha & Badri Narayanan (1971) is appreciably less than the zero-crossing rate.

Peristaltic motion of a micropolar fluid

Peristaltic motion of a micropolar fluid is studied for small amplitudes of peristalic waves under low Reynolds number analysis. The effect of pressure gradient on the secondary motion reveals many interesting and useful results. The critical value of the pressure gradient ensuing the reversal effect in both velocity field and microrotation is evaluated and discussed.

Evaluation of k-epsilon and RNG turbulence models for confined swirling and non-swirling flow

In a very recent study [1] the Renormalisation Group (RNG) turbulence model was used to obtain flow predictions in a strongly swirling quarl burner, and was found to perform well in predicting certain features that are not well captured using less sophisticated models of turbulence. The implication is that the RNG approach should provide an economical and reliable tool for the prediction of swirling flows in combustor and furnace geometries commonly encountered in technological applications. To test this hypothesis the present work considers flow in a model furnace for which experimental data is available [2]. The essential features of the flow which differentiate it from the previous study [1] are that the annular air jet entry is relatively narrow and the base wall of the cylindrical furnace is at 90 degrees to the inlet pipe. For swirl numbers of order 1 the resulting flow is highly complex with significant inner and outer recirculation regions. The RNG and standard k-epsilon models are used to model the flow for both swirling and non-swirling entry jets and the results compared with experimental data [2]. Near wall viscous effects are accounted for in both models via the standard wall function formulation [3]. For the RNG model, additional computations with grid placement extending well inside the near wall viscous-affected sublayer are performed in order to assess the low Reynolds number capabilities of the model.

Experiments on the fine structure of turbulence

Investigations have been carried out of some aspects of the fine-scale structure of turbulence in grid flows, in boundary layers in a zero pressure gradient and in a boundary layer in a strong favourable pressure gradient leading to relaminarization. Using a narrow-band filter with suitable mid-band frequencies, the properties of the fine-scale structure (appearing as high frequency pulses in the filtered signal) were analysed using the variable discriminator level technique employed earlier by Rao, Narasimha & Badri Narayanan (1971). It was found that, irrespective of the type of flow, the characteristic pulse frequency (say Np) defined by Rao et al. was about 0·6 times the frequency of the zero crossings. It was also found that, over the small range of Reynolds numbers tested, the ratio of the width of the fine-scale regions to the Kolmogorov scale increased linearly with Reynolds number in grid turbulence as well as in flat-plate boundarylayer flow. Nearly lognormal distributions were exhibited by this ratio as well as by the interval between successive zero crossings. The values of Np and of the zero-crossing rate were found to be nearly constant across the boundary layer, except towards its outer edge and very near the wall. In the zero-pressure-gradient boundary-layer flow, very near the wall the high frequency pulses were found to occur mostly when the longitudinal velocity fluctuation u was positive (i.e. above the mean), whereas in the outer part of the boundary layer the pulses more often occurred when u was negative. During acceleration this correlation between the fine-scale motion and the sign of u was less marked.

Simulation of laminar flow in a three-dimensional lid-driven cavity by lattice Boltzmann method

Purpose - The purpose of this paper is to apply lattice Boltzmann equation method (LBM) with multiple relaxation time (MRT) model, to investigate lid-driven flow in a three-dimensional (3D), rectangular cavity, and compare the results with flow in an equivalent two-dimensional (2D) cavity. Design/methodology/approach - The second-order MRT model is implemented in a 3D LBM code. The flow structure in cavities of different aspect ratios (0.25-4) and Reynolds numbers (0.01-1000) is investigated. The LBM simulation results are compared with those from numerical solution of Navier-Stokes (NS) equations and with available experimental data. Findings - The 3D simulations demonstrate that 2D models may predict the flow structure reasonably well at low Reynolds numbers, but significant differences with experimental data appear at high Reynolds numbers. Such discrepancy between 2D and 3D results are attributed to the effect of boundary layers near the side-walls in transverse direction (in 3D), due to which the vorticity in the core-region is weakened in general. Secondly, owing to the vortex stretching effect present in 3D flow, the vorticity in the transverse plane intensifies whereas that in the lateral plane decays, with increase in Reynolds number. However, on the symmetry-plane, the flow structure variation with respect to cavity aspect ratio is found to be qualitatively consistent with results of 2D simulations. Secondary flow vortices whose axis is in the direction of the lid-motion are observed; these are weak at low. Reynolds numbers, but become quite strong at high Reynolds numbers. Originality/value - The findings will be useful in the study of variety of enclosed fluid flows.

Numerical Study of Heat Transfer From Pin-Fin Heat Sink Using Steady and Pulsated Impinging Jets

This paper investigates numerically the heat transfer characteristics of confined slot jet impingement on a pin-fin heat sink. A variety of pin-fin heat sinks is investigated, and the resulting enhancement of heat transfer studied. The distribution of heat transfer coefficient on the top surface of the base plate and that along the fin height are examined. Both steady and pulsated jets are studied. It is observed that for a steady jet impingement on a pin-fin heat sink, the effective heat transfer coefficient increases with fin height, leading to a corresponding decrease in base plate temperature for the same heat flux. In the case of pulsated jets, the influence of pulse frequency and the Reynolds number is examined, and their effect on the effective heat transfer coefficient is studied.