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This study aims at investigating two-dimensional laminar flow of power-law fluids around three unconfined side-by-side cylinders.

The numerical study is performed by solving the governing (continuity and momentum) equations using a finite volume-based code ANSYS Fluent. The numerical results have been presented for different combinations of the governing dimensionless parameters (dimensionless spacing, 1.2 = L = 4; Reynolds number, 0.1 = Re = 100; power-law index, 0.2 = n = 1.8). The dependence of the kinematic and macroscopic characteristics of the flow such as streamline patterns, distribution of the surface pressure coefficient, total drag coefficient with its components (pressure and friction) and total lift coefficient on these dimensionless parameters has been discussed in detail.

It is found that the separation of the flow and the apparition of the wake region accelerate as the dimensionless spacing decreases, the number of the cylinder increases and/or the fluid behavior moves from shear-thinning to Newtonian then to shear-thickening behavior. In addition, the distribution of the pressure coefficient on the surface of the cylinders presents a complex dependence on the fluid behavior index and Reynolds number when the dimensionless spacing between two adjacent cylinders is varied. At low Reynolds numbers, the drag coefficient of shear-thinning fluids is stronger than that of Newtonian fluids; this tendency decreases progressively with increasing of Re until a critical value; beyond the critical Re, the opposite trend is observed. The lift coefficient of the middle cylinder is null, whereas, the exterior cylinders experience opposite lift coefficients, which show a complex dependence on the dimensionless spacing, the Reynolds number and the power-law index.

The flow over bluff bodies is a practical engineering problem. In the literature, it can be seen that the previous studies on non-Newtonian fluids are limited to the flow over one or two cylinders (effect of an odd number of cylinders on each other). Besides that, the available results concerning the flow of Newtonian fluids over three cylinders are limited to the high Reynolds numbers region only. However, this work treats the flow of non-Newtonian power-law fluids past three circular cylinders in side-by-side arrangements under a wide range of Re. The outcome of the present study demonstrates that the augmentation of the geometry complexity to three cylinders (effect of pair surrounding cylinders on the surrounded ones in what concerns Von Karman Street phenomenon) causes a drastic change in the flow patterns and in the macroscopic characteristics. The present results may be used to predict the flow behavior around multiple side-by-side cylinders.

This paper aims to analyze the effect of aspect ratio A and aspect velocity ratio a on the bifurcation occurrence phenomena in lid-driven cavity by using finite volume method (FVM) and multigrid acceleration. This study has been performed for certain pertinent parameters; a wide range of the Reynolds number values has been adopted, and aspect ratios ranging from 0.25 to 1 and various velocity ratios from 0.25 to 0.825 have been considered in this investigation. Results show that the transition to the unsteady regime follows the classical scheme of Hopf bifurcation, giving rise to a perfectly periodic state. Flow periodicity has been verified through time history plots for the velocity component and phase-space trajectories as a function of Reynolds number. Velocity profile for special case of a square cavity (A = 1) was found to be in good agreement between current numerical results and published ones. Flow characteristics inside the cavity have been presented and discussed in terms of streamlines and vorticity contours at a fixed Reynolds number (Re = 5,000) for various aspect ratios (a = 0).

The numerical method is based on the FVM and multigrid acceleration.

Computations have been investigated for several Reynolds numbers and aspect ratios A (0.25, 0.5, 0.75, 0.825 and 1). Besides, various velocity ratios (a = 0.25, 0.5, 0.75 and 0.825) at fixed aspect ratios (A = 0.25, 0.5 and 0.75) were considered. It is observed that the transition to the unsteady regime follows the classical scheme of Hopf bifurcation, giving rise to a perfectly periodic state. Flow periodicity is verified through time history plots for velocity components and phase-space trajectories.

The bifurcations between steady and unsteady states are investigated.

The aim of this study is to modify the critical Reynolds number (Re_cr) which is the critical parameter of the transition from laminar to turbulence regime. The transition to turbulence is delayed by increasing the critical Reynolds number.

A method to control the critical Reynolds number of viscous flow between parallel plates with an imposed pressure gradient to infinitesimal harmonic disturbances is introduced. The method consists of introducing harmonic perturbations to the lower plate based on skin friction measurements at the upper plate. The size of the introduced harmonic perturbation is chosen to be proportional to the measured skin friction. The proportionality constant is the control parameter for the manipulation of the critical Reynolds number. The resulting eigenvalue problem, similar to the Orr‐Sommerfeld problem, is solved for various values of the control parameter.

Solution of the eigenvalue problem shows that the critical Reynolds number for the instability with respect to infinitesimal disturbances can be increased from 5,772.22 to 37,900.

The paper demonstrates that it is theoretically possible to increase the critical Reynolds number of parallel plate flow from 5,772.22 to 37,900 by applying a small motion to the bottom plate, the amplitude of the motion being proportional to the skin friction measured at the upper plate.

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.

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.

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.

The findings will be useful in the study of variety of enclosed fluid flows.

This study aims to investigate lattice Boltzmann (LB) simulation of the fluid flow and heat transfer characteristics of a heated porous elliptic cylinder in uniform flow based on the two-domain scheme. In the present research, the effect of axis ratio (1 ≤ AR ≤ 2), Reynolds number (5 ≤ Re ≤ 40) and Darcy number (10⁻⁴ ≤ Da ≤ 10⁻²) are studied.

To perform the LB simulation based on the two-domain scheme, the nonequilibrium extrapolation method is modified to model the heat transfer interfacial conditions required at the curved interface.

The results show that the axis ratio as well as Reynolds and Darcy numbers significantly affect the fluid flow and heat transfer characteristics of the porous elliptic cylinder. It is shown that for AR > 1, the phenomenon of detached recirculating zone occurs at much higher Darcy numbers compared with the case of the porous circular cylinder (AR = 1). The results show that the location of maximum temperature within the cylinder moves downstream when the Reynolds number, Darcy number and axis ratio increase. It is also concluded that the average Nusselt number of a porous elliptic cylinder is always lower than that of a porous circular cylinder.

The LB simulation of forced convection from a porous cylinder in uniform flow with a curved interface based on the two-domain scheme has not been studied yet.

Fluid flows in pipes whose cross-sectional area are increasing in the stream-wise direction are prone to separation of the recirculation region. This paper aims to investigate such fluid flow in expansion pipe systems using direct numerical simulations. The flow in circular diverging pipes with different diverging half angles, namely, 45, 26, 14, 7.2 and 4.7 degrees, are considered. The flow is fed by a fully developed laminar parabolic velocity profile at its inlet and is connected to a long straight circular pipe at its downstream to characterise recirculation zone and skin friction coefficient in the laminar regime. The flow is considered linearly stable for Reynolds numbers sufficiently below natural transition. A perturbation is added to the inlet fully developed laminar velocity profile to test the flow response to finite amplitude disturbances and to characterise sub-critical transition.

Direct numerical simulations of the Navier–Stokes equations have been solved using a spectral element method.

It is found that the onset of disordered motion and the dynamics of the localised turbulence patch are controlled by the Reynolds number, the perturbation amplitude and the half angle of the pipe.

The authors clarify different stages of flow behaviour under the finite amplitude perturbations and shed more light to flow physics such as existence of Kelvin–Helmholtz instabilities as well as mechanism of turbulent puff shedding in diverging pipe flows.

A numerical study is performed to investigate flow instability phenomena in a square channel with steady, laminar throughflow. The channel rotates around an axis perpendicular to the channel longitudinal axis. The flow field extends from the channel entrance to a distance of 120 to 600Dh. The range of Reynolds number is Re = 300−2000. The inlet flow velocity is assumed uniform. Surface vorticity intensity is introduced to indicate the variation of vortices. It is revealed that at intermediate Reynolds numbers (680 > Re > 300), the flow is characterized by three vortex patterns: at slow rotation there is one vortex pair; at intermediate rotation a secondary vortex, in addition to the original vortex, emerges near the trailing wall and then breaks down downstream; and at rapid rotation the secondary vortex does not exist with the flow being restabilized to form a single‐pair vortex pattern. At low Reynolds numbers (Re ≤ 300), the flow exhibits a single‐pair vortex pattern, while at high Reynolds numbers (Re ≥ 680), the flow experiences the emergence and breakdown of a secondary vortex, but no restabilization is found with an increase in the rotational speed. It is also disclosed that the variation of the vortices is related to the distance from the inlet.

The effects of steady fluid flow through double bell‐shaped constrictions in tubes were investigated numerically for the Reynolds number range of 5 to 400. The double constrictions studied were for similar first and second constrictions of 1/3, 1/2 and 2/3. A dimensionless constriction spacing of 1.0 was considered. Study showed that the major part of the mean dimensionless pressure drop in the constricted tube occurs predominantly across the first constriction when flow moves towards the valley region formed by the two constrictions. Minimum pressures along the constricted tubes occurs downstream of each constrictions. When the constriction magnitudes increased, the pressure drop across the same length of the tube increases exponentially. The effect of increasing the Reynolds number for all the constriction values considered here is to increase the spreading of the recirculation region between the valley region of the constrictions. The recirculation region formed between the two constrictions has a deminishing effect on the generation of wall vorticity near the second constriction. The effects are more pronounce when the recirculatory flow from the first constriction has spread over the second constriction. In general, a peak wall vorticity is found slightly upstream of each of the constrictions. When the Reynolds number is increased, the peak wall vorticity increases and its location moved upstream. It is noted for the cases considered here that the peak wall vorticity generated by the first constriction is always greater than the peak wall vorticity generated by the second constriction.

This paper aims to derive a reduced-order model for the heat transfer across the interface between a millimetric thermocapillary liquid bridge from silicone oil and the surrounding ambient gas.

Numerical solutions for the two-fluid model are computed covering a wide parametric space, making a total of 2,800 numerical flow simulations. Based on the computed data, a reduced single-fluid model for the liquid phase is devised, in which the heat transfer between the liquid and the gas is modeled by Newton’s heat transfer law, albeit with a space-dependent Biot function Bi(z), instead of a constant Biot number Bi.

An explicit robust fit of Bi(z) is obtained covering the whole range of parameters considered. The single-fluid model together with the Biot function derived yields very accurate results at much lesser computational cost than the corresponding two-phase fully-coupled simulation required for the two-fluid model.

Using this novel Biot function approach instead of a constant Biot number, the critical Reynolds number can be predicted much more accurately within single-phase linear stability solvers.

The Biot function for thermocapillary liquid bridges is derived from the full multiphase problem by a robust multi-stage fit procedure. The derived Biot function reproduces very well the theoretical boundary layer scalings.

According to very small dimensions of the microchannels, producing a microchannel with smooth surfaces is approximately impossible. The surface roughness can have a specific effect on microchannel performances. This paper aims to investigate the changes in friction and pressure drop in the microchannels by considering the different roughness elements on microchannel wall and changes in elementary geometry and flow conditions. Results show a significant effect of roughness on the pressure drop and friction.

Two-dimensional fluid flow in the rough microchannels is analyzed using FLUENT. Microchannels have a height of 50 µm. Water at room temperature (25°C) has been used as working fluid. The Reynolds numbers are considered in laminar flow range and from 50 to 300.

The results show that the value of friction factor reduces nonlinearly with an increase in Reynolds number. But, the pressure drops and the Poiseuille number in the microchannels increase with an increase in Reynolds number. The values of the pressure drop and the friction factor increase by increasing the height and size of the roughness elements, but these values reduce with an increase in the distance of roughness elements.

The roughness elements types in this research are rectangular, trapezoidal, elliptical, triangular and complex (composed of multiple types of roughness elements). The effects of the Reynolds number, roughness height, roughness distance and roughness size on the pressure drop and friction in the rough microchannels are investigated and discussed. Furthermore, differences between the effects of five types of roughness elements are identified.