Flow Of Power-law Fluid Research Articles

A comprehensive study on the power-law fluid flow around and through a porous cylinder with different aspect ratios

This paper presents a numerical investigation of power-law fluid flow past and through elliptical porous cylinder, considering heat transfer effects. The study covers a wide range of parameters, including Reynolds number, power-law index, cylinder aspect ratio and Darcy number. The wake pattern, streamline distribution, drag coefficient, pressure distribution, and Nusselt number are analyzed comprehensively for various cases. Within the investigated parameter range, four distinct vortices are observed: an external vortex separated from the cylinder, an external vortex attached to the cylinder, a boundary vortex partially inside and outside the cylinder, and an internal vortex entirely inside the cylinder. The occurrence of the external and separated vortex is limited to AR = 0.2 and =10−3 , while the internal and boundary vortices are exclusively observed at AR = 2.0. Additionally, increasing the aspect ratio of the elliptical cylinder results in shorter vortices at a given Reynolds and Darcy number. For example, at Re = 40 and Da=10−4, vortex lengths decrease from 5 to 0.6 with increasing aspect ratio from 0.2 to 2. Furthermore, by decreasing aspect ratio, the drag coefficient generally increases and the Nusselt number decreases from 0.2 to 1, but this trend reverses as the aspect ratio rises from 1 to 2.

On the Analysis of Power Law Fluid over a Diamond Shaped Cylindrical Surface with Screen Boundary Conditions at High Reynolds Number

This study analyses physical aspects of power-law fluid flow over a diamond shaped cylinder under the impact of a movable screen fixed in the middle of a channel keeping an aspect ratio as 0.5 with height of the channel. The perforated plate is a screen at the middle especially settled at orientation of π/6, π/4 or π/3 degrees. The Reynolds number (Re) has been kept in the range of 1000-10,000 with power-law index in the range 0.8-1.2. For the corresponding two-dimensional problem, the governing momentum equations coupled with energy equation have been solved numerically using non-isothermal laminar fluid flow interface in the software COMSOL Multiphysics 5.4. The dimensionless velocity magnitude and the non-dimensional temperature on the diamond shaped cylinder along the vertical non-dimensional length are expressed via fixing any two parameters from (Re), angle of screen θ and power-law index. The heat transfer coefficient, effective thermal conductivity and the Nusselt number are also expressed besides the dimonsionless length of the surface of the chosen cylinder. In conclusion, we will be going to suggest points to increase the dynamics and thermal variables with the use of selected parameters Re, θ, and power law index n.

Power-law fluid annular flows between concentric rotating spheres subject to hydrodynamic slip

ABSTRACT We report analytical solutions to the problem of non-Newtonian power-law fluid flows in the annular space between a pair of concentric spherical surfaces rotating at distinct angular velocities with the inner and outer wall boundaries subject to general asymmetric hydrodynamic slip conditions. Analytical solutions are possible because of assuming constant valued apparent hydrodynamic slip lengths in the linearized kinematic slip conditions, and our solutions can be validated against the limiting results of Newtonian fluids, no-slip conditions or a single rotating sphere reported in previous literature. Comprehensive systematic parametric studies show that (additional to the power-law fluid flow behavior index) the degree of hydrodynamic slip at the inner surface is the dominant factor that determines the limiting values of the viscous torque exerted on the inner sphere as the outer-to-inner radius ratio assumes significantly large values. Nonetheless, the flow behavior index and outer slip length prove to be the crucial key parameters responsible for a variety of torque responses, which can be categorized by a compact analytical expression, as the outer-to-inner radius ratio is increased in the small to moderate regime. We propose a criteria which identifies the proper slip length and outer-to-inner radius ratio combinations for a given power-law flow behavior index such that the hydrodynamic slip wall effects of the outer surface can be minimized or eliminated. A simple method is also presented to characterize and quantify the apparent hydrodynamic slip effects by use of the concentric rotating spheres viscometer.

PERCOLATION CHARACTERISTICS OF POWER-LAW FLUID IN THE FRACTAL TREE-LIKE BIFURCATION NETWORKS WITH ROUGH SURFACES

In order to study the seepage characteristics of power-law fluids in the fractal tree-like bifurcation networks with rough surfaces based on fractal theory, the shape factor of rough surfaces is treated as the randomly distributed cones. According to the generalized Darcy's law and the constitutive equation of power-law fluids, the fully-developed laminar and incompressible flow of power-law fluids in rough pipelines is explored, and the velocity graduation and flow rate expressions of fluids in rough pipelines are obtained. Then, the fractal model for the permeability of power-law fluid in the tree-like bifurcation network with rough surfaces is proposed, and the total flow rate, total pressure drop, and permeability of power-law fluid in the tree bifurcation network with rough surfaces are derived. The relative increase in pressure and the relative decrease in permeability are also obtained. Finally, the analytical expression for the permeability of power-law fluids is analyzed. It can be seen that the permeability of a rough tree-like bifurcation network is inversely proportional to relative roughness, length ratio, bifurcation angle, etc., and directly proportional to the power-law index and diameter ratio. At the same time, the predicted values of the model are compared with existing models, proving the correctness and rationality of the model.

Convective heat transfer of electrically conducting MHD power law fluid through annular sector duct

This study deals with the effect of Lorentz force on forced convection flow of electrically conducting magneto-hydrodynamic, (MHD) power law fluid through the annular sector duct by using finite volume method. In existence literature, hydro-thermal flow of MHD power law fluid within an annular sector duct has not been reported. The effect of Lorentz force on hydro-thermal power law fluid flow makes it very much novel in its own right. Here the main objective is to explore the effect of Lorentz force on hydro-thermal flow characteristics. The influence of uniform magnetic field is taken parallel to the radial direction. The effects of Hartman parameter, [Formula: see text] and power law index, [Formula: see text], corresponding to Lorentz force and power law fluid respectively, on the quantities of interest such as velocity and temperature profiles, friction factor and average Nusselt number [Formula: see text] are discussed for different geometric configuration parameters’ values of the annular sector duct. Computer code is developed and validated by comparing the results of limiting cases with the available literature. It has been observed that [Formula: see text] increases with the increase in [Formula: see text]. This trend is prevalent in both pseudo-plastic and dilatant fluids. The impact of [Formula: see text] is pronounced in the later case.

Hydrodynamical characteristics of a pair of elliptical squirmers in a channel flow of power-law fluids

Hydrodynamical characteristics of a pair of elliptical squirmers in a channel flow of power-law fluids

Wall-modeled large-eddy simulation of turbulent non-Newtonian power-law fluid flows

For high-fidelity predictions of turbulent flows in complex practical engineering problems, the Wall-Modeled (WM) Large-Eddy Simulation (LES) has aroused great interest. In the present study, we prove that the conventional Wall-Stress Models (WSMs) developed for WMLES of Newtonian fluids fail to predict the shear-thinning-induced drag reduction in power-law fluids. Therefore, we propose novel algebraic, integrated, and Ordinary-Differential-Equation (ODE) WSMs, for the first time, for WMLES of power-law Non-Newtonian (NN) fluids and assess their performance against reference Wall-Resolved (WR) LES solutions. In addition, the effects of the key model parameters, including the WSM type, sampling height, sampling cell, and axial grid resolution are explored, and it is revealed that turbulent NN flow predictions have a much higher sensitivity to the choice of WSM, compared to their Newtonian counterparts. It is manifested that, in contrast to WRLES, accurate modeling of the mean apparent and subgrid-scale NN viscosities in the Non-Newtonian ODE (NNODE) model can improve the predictions considerably. Therefore, closures with lower uncertainties on coarse WMLES grids are sought for these terms. Finally, the best performance for the present test cases is obtained via the integrated NN WSM, sampling at the lower edge of the log layer within the third off-the-wall grid cell. Nevertheless, the new NNODE WSM can have an advantage in the presence of non-equilibrium effects in more complex problems.

Natural convective Power law fluid flow in a crown cavity with heated cylinder: Application to energy transfer

The present study investigates heat transfer characteristics of power law fluid flow and energy transfer in a crown cavity with adjustment of the heated cylinder. The flow distribution is generated by the response of the heated cylinder. Additionally, the enclosure is partially adiabatic and the influence of cold interfaces is also taken. This whole setup generates a partial differential system in its mathematical translation. The numerical simulation is performed for the mathematical formulation by adopting the Galerkin Finite element method. The obtained results are analyzed against pertinent parameters of interest and presented via line graphs and contour maps for better explanation. The findings indicate that the K.E (energy motion) and Nu (Nusselt number) are higher for shear thinning While K.E energy motion) and Nu (Nusselt number) are higher is minimum for shear thickening.

Multiple inlet sudden expansion flow of power-law fluids

Multiple inlet sudden expansion flow of power-law fluids

Comparison of ellipsoidal particle migration in square channel flow of power-law fluids with equivalent spheres

Comparison of ellipsoidal particle migration in square channel flow of power-law fluids with equivalent spheres

Analysis of periodic pulsating blood flow of fractional Maxwell power-law fluid in carotid artery with elastic vessel wall

Hemodynamic analysis reveals a highly significant effect on the prevention, diagnosis, and treatment of human vascular diseases. This article goes deeply into the periodic pulsatile blood flow in the carotid artery with an elastic vessel wall. In view of blood rheological experimental data, the constitutive equation of fractional Maxwell power-law fluid with yield stress, which can describe the four characteristics of yield stress, viscoelasticity, shear thinning, and thixotropy is established. Meanwhile, drawing support from the data of pulsatile flow, the finite Fourier series of pressure gradient with a period of 1 s has been proposed. Leading into Hooke’s law can build the fluid-structure coupling boundary condition of blood flow and elastic vessel wall. The numerical solutions are got hold of finite difference method integrated with the newly developed L1-algorithm, and their convergence and stability of which are verified. The axial velocities of blood under different constitutive relationships are compared. The results throw light that other constitutive relationships underestimate the velocity of blood. Furthermore, the flow rate and wall shear stress on different fluid are calculated. It can be concluded that compared with Bingham fluid, the maximum and minimum flow rate/wall shear stress of fractional Maxwell power-law fluid with yield stress increases by 19% and 32%, respectively. The flow rate lags behind the pressure gradient and has time delay effect, on the contrary, the velocity of blood vessel wall is keeping pace with the pressure gradient. The effects of relevant physical parameters on velocity are discussed. In addition, the spatiotemporal distribution of blood flow in cerebral artery and femoral artery are analyzed.

Comparative study of the accuracy of friction factor correlations developed for flow of inelastic yield power-law fluids in pipes

An extensive review of the friction factor correlations used for pressure loss prediction of yield power-law (YPL) fluid flow in pipes has been conducted, and the results are summarized in this paper.A comparative study was also conducted to determine the predictive performances of various laminar and turbulent friction factor models developed for YPL fluid flow in pipes. Model predictions of frictional pressure losses were validated by comparing them with the experimentally measured pressure drop data obtained from the flow of several YPL fluids in pipes.Investigations were further extended to determine the impact of the variation of YPL fluid rheological characteristics (resulting from using different rheological characterization methods) on the pressure drop predictions.A wide range of generalized Reynolds numbers (i.e., 20 to 9000, as defined by the API-RP:13D) in a pipe flow configuration was considered in the analyses. The yield stress of the test fluids (determined by using the nonlinear curve fitting technique recommended by the API RP:13D) varied from 0.10 to 0.95 Pa.The results indicated that Hanks and Ricks' model predicted the pressure drop of YPL fluid flow in pipes better than any other models, both in laminar and turbulent flow regimes, matching the experimental data within a ±10% error range.Variations of the YPL model parameters (resulting from using different rheological characterization methods) significantly impacted the pressure drop predictions. Using YPL model parameters obtained from the non-iterative dual power law (DPL) approximation method (as recommended by API-RP:13D) and Hanks and Ricks' model yielded the most accurate pressure drop predictions for the pipe flow of YPL fluids.

Equilibrium Position of a Particle in a Microchannel Flow of Newtonian and Power-Law Fluids with an Obstacle

The equilibrium position yep/H of a particle in a microchannel flow of Newtonian and power-law fluids with an obstacle is numerically studied using the lattice Boltzmann method in the range of the ratio of an obstacle to particle diameter 0.5 ≤ β ≤ 2, fluid power-law index 0.4 ≤ n ≤ 1, Reynolds number 20 ≤ Re ≤ 60, and blockage ratio 0.15 ≤ k ≤ 0.3. Some results are validated by comparing them with the available results. The results showed that, when a particle migrates around an obstacle in the flow behind and near the obstacle, the particle with a different initial, y/H, migrates downstream in a different lateral position, yep/H, and the larger the value of β, the closer the value of yep/H is to the centerline. Therefore, the value of yep/H can be controlled by changing β in the wake zone of the obstacle. However, in the flow far downstream from the obstacle, the particle with a different initial y/H tends to have the same yep/H when n, Re and k are fixed, but the values of yep/H are different for different n, Re and k; i.e., the larger the values of n, Re and k, the closer the value of yep/H is to the centerline. The value of β has no effect on the value of yep/H. In the flow far downstream from the obstacle, the flow distance required for the particle to reach yep/H increases with increasing β and n but decreases with decreasing Re and k.

Theoretical exploration of heat transport in a stagnant power-law fluid flow over a stretching spinning porous disk filled with homogeneous-heterogeneous chemical reactions

The distinction between homogeneous and heterogeneous chemical reactions is crucial because many chemically reactive systems, such as hydrometallurgical processes, cooling towers, biological systems, fog dispersion, catalysis, etc., involve both types of reactions. Thus, this study analyzes the heat transmission (HT) characteristics in an MHD stagnant flow of power-law fluid caused by a spinning disk that is stretched and saturated in a porous medium. The study considers homogeneous-heterogeneous (HH) reactions and nonlinear thermal radiation subject to no-slip and convection boundary conditions. The leading equations are switched into ordinary differential equations (ODEs) employing similarity variables. The study focuses on the dimensionless concentration, velocity, temperature, Nusselt number, and skin friction coefficient, which are discussed in detail in the results and discussion section. The study observes that for power-law fluids with an index value less than 1, the skin friction coefficient decays as the power-law index grows. It also notes that the dimensionless skin friction of power-law fluids decreases as the velocity ratio increases. The dimensionless concentration increases with Schmidt and modified Prandtl numbers for both power-law fluids over a stretching spinning porous disk. The HH reaction parameters decline the concentration of power-law fluids.

On flow of power-law fluids between adjacent surfaces: Why is it possible to derive a Reynolds-type equation for pressure-driven flow, but not for shear-driven flow?

Flows of incompressible Navier–Stokes (Newtonian) fluids between adjacent surfaces are encountered in numerous practical applications, such as seal leakage and bearing lubrication. In seals, the flow is primarily pressure-driven, whereas, in bearings, the dominating driving force is due to shear. The governing Navier–Stokes system of equations can be significantly simplified due to the small distance between the surfaces compared to their size. From the simplified system, it is possible to derive a single lower-dimensional equation, known as the Reynolds equation, which describes the pressure field. Once the pressure field is computed, it can be used to determine the velocity field. This computational algorithm is much simpler to implement than a direct numerical solution of the Navier–Stokes equations and is therefore widely employed by engineers. The primary objective of this article is to investigate the possibility of deriving a type of Reynolds equation also for non-Newtonian fluids, using the balance of linear momentum. By considering power-law fluids we demonstrate that it is not possible for shear-driven flows, whereas it is feasible for pressure-driven flows. Additionally, we demonstrate that in the full 3D model, a normal stress boundary condition at the inlet/outlet implies a Dirichlet condition for the pressure in the Reynolds equation associated with pressure-driven flow. Furthermore, we establish that a Dirichlet condition for the velocity at the inlet/outlet in the 3D model results in a Neumann condition for the pressure in the Reynolds equation.

Application extension of the meshless local Petrov-Galerkin method: Non-Newtonian fluid flow implementations

A computer code is developed to enhance the meshless local Petrov-Galerkin method capability to solve non-Newtonian fluid flow problems. In particular, the mesh-free method here, is to be empowered to simulate and solve the two-dimensional laminar incompressible power-law cases for the first time. The newly developed computer code expresses the appropriate governing equations in terms of the vorticity-stream function formulation and sustains a weighting function of unity. The local quadrature domain integrated by parts over the appropriate control volumes provides the local weak form of the considered governing equations. The extended scheme implements the moving least square interpolation technique to approximate the obtained field variables. The ability of the developed code to handle the Ostwald-de Waele (also known as the power-law) fluid flow occurrences were assessed through comparing the obtained results of the extended method to those of the conventional mesh-based methods for some benchmarking cases available in the paper. Based on this comparison, the extended code demonstrates a good capability to address the power-law fluid flow problems for different indices for one of the most popular non-Newtonian fluid flow models.

Drag and uncertainty of power-law fluid flows in fractal multiparticle systems

In this study, new approaches are developed to predict the drag and assess its potential uncertainty of a non-Newtonian fluid in a multiparticle system. First, a new and simpler approximate solution of power-law fluid flow is developed using the free surface cell model. Second, the uncertainty of drag in a fractal multiparticle system is investigated by treating the heterogeneous voidage in the system as a truncated power-law fractal distribution. The results demonstrate that the developed simpler approximate solution works well compared to the analytical solutions and experimental data. Incorporating truncated power-law fractal voidage can better capture the experimental data. The voidage heterogeneity increases the drag of the power-law fluid moving through the multiparticle system. Strong shear-thinning effects of power-law fluids and high mean voidage diminish the effect of voidage heterogeneity. The flow drag of power-law fluid in the heterogeneous multiparticle system decreases with increasing fractal dimension.

Forced convective power-law fluid flow through porous annular sector duct

In this paper, we discuss the forced convective heat transfer of power-law fluid flow through porous annular sector duct by applying the Brinkman-extended Darcy flow model. A strongly implicit procedure (SIP) is utilized to solve the algebraic momentum and energy equations which was discretized by using the finite volume method (FVM). The effects of permeability factor and power-law index corresponding to the Brinkman-extended Darcy flow model and power-law fluid, respectively, on flow and heat transfer rate are carried out numerically and graphically against different values of parameters corresponding to geometrical configuration. In the pseudo-plastic fluids, a maximum decrease of more than [Formula: see text] has been observed in [Formula: see text], whereas maximum decrease in dilatant fluid is around [Formula: see text], when we increase the values of k. A decrease of 16.02% in Nu has been carried out in pseudo-plastic fluid, whereas unforeseen decrease in Nu has been observed in both Newtonian and dilatant fluids comparably pseudo-plastic fluid for particular values of k.

Numerical investigation of effect of surface pattern and rotation on power-law fluid flow and heat transfer around a cylinder in laminar flow regime

We have studied the effect of surface topography, fluid behavior, and rotation on fluid flow and heat transfer phenomena over a cylinder. In this study, we have incorporated a sinusoidal surface topography to account for the impact of surface patterns and a power-law model to include fluid behavior. The governing equations are solved numerically for a range of pattern frequency (ω=5 and 11), pattern amplitude (δ=0.01 and 0.1), power-law index (0.4≤n≤1.6), Prandtl number (1≤Pr≤100), rotational speed (0.5≤α≤2), and Reynolds number (5≤Re≤40). In particular, the study aims to determine the degree to which various macroscopic parameters, such as the drag and lift coefficients, the average Nusselt number in relation to the Reynolds number, the Prandtl number, the rotating speed, and the power-law index, vary. In this range of Reynolds number, the flow around a circular cylinder is steady, with two symmetric vortices in the rear side. The sliding mesh method is used to deal with dynamic interface between solid and fluid. The streamlines are drawn to visualize the flow field around the patterned cylinder. For a non-rotating patterned cylinder, small recirculation zones are observed over the trough, which are absent in circular cylinders. The size of these recirculation regions increases on increase in Reynolds number and power-law index. On adding rotation to the cylinder, these recirculation zones move away from the cylinder and appear over the crest. On increasing the rotating speed of the cylinder, the frontal vortices disappear. The enveloping vortex gets larger with increase in rotating speed and power-law index. The size of the rear detached vortex increases with power-law index and Reynolds number and decreases with rotating speed. It is observed that the results are contrasted with the previous studies on smooth circular cylinder. The drag force acting on the patterned cylinder is seen to be reduced. Compared to a circular cylinder, a significant reduction in drag can be achieved by choosing suitable value of pattern frequency (ω) and amplitude (δ). Overall, there is a decrease in the amount of drag reduction as the Reynolds number increases. The behavior of the fluid has a considerable influence on the reduction of drag. It has been observed that shear-thickening fluid significantly contributes to the enhancement of drag reduction. For a higher value of pattern frequency and amplitude (ω=11,δ=0.1), the drag force reduces significantly for Newtonian and shear-thickening fluids at higher rotating speed (α=2). Also, the pattern frequency and amplitude substantially impact the average Nusselt number. On increase in pattern frequency and amplitude, a progressive decrease in the average Nusselt number is observed. Compared to shear-thinning and Newtonian fluid, shear-thickening fluid exhibits a greater reduction in average Nusselt number. One correlation is provided at the end to show the relationship between the average Nusselt number, the Prandtl number, the Reynolds number, the rotating speed, and the power-law index.

Entrance length estimates for flows of power-law fluids in pipes and channels

Entrance length estimates for flows of power-law fluids in pipes and channels