Simulation of Flamboyant Gums (Power Fluid) with the Lattice Boltzmann Method

From results obtained in the rheological characterization of a 4% dispersion of flamboyant gum with the HaakeRT20 viscometer, for different conditions of pH = 3.0 and 9.0, temperature 5°C, 25°C and 45°C, the data of the rheological behavior of the gum dispersions were fitted to the power law model. To understand and predict the behavior of this gum, a model of Lattice Boltzmann D2Q9 was developed for the behavior, in addition to simulations for the conditions handled in the experiments performed with the HaakeRT20 viscometer.

A Review on Technologies for the Use of CO2 as a Working Fluid in Refrigeration and Power Cycles

The use of carbon dioxide as a working fluid has been the subject of extensive studies in recent years, particularly in the field of refrigeration where it is at the heart of research to replace CFC and HCFC. Its thermodynamic properties make it a fluid of choice in the efficient use of energy at low and medium temperatures in engine cycles. However, the performance of transcritical CO2 cycles weakens under high temperature and pressure conditions, especially in refrigeration systems;On the other hand, this disadvantage becomes rather interesting in engine cycles where CO2 can be used as an alternative to the organic working fluid in small and medium-sized electrical systems for low quality or waste heat sources. In order to improve the performance of systems operating with CO2 in the field of refrigeration and electricity production, research has made it possible to develop several concepts, of which this article deals with a review of the state of the art, followed by analyzes in-depth and critical of the various developments to the most recent modifications in these fields. Detailed discussions on the performance and technical characteristics of the different evolutions are also highlighted as well as the factors affecting the overall performance of the systems studied. Finally, perspectives on the future development of the use of CO2 in these different cycles are presented.

Drag characteristics of power law fluids on an upstream moving surface

The specific problem to be considered here concerns the boundary layer problem of a non-Newtonian fluid on a flat plate in length, whose surface has a constant velocity opposite in the direction to that of the mainstream with Uw 〉〉 U∞, or alternatively when the plate surface velocity is kept fixed but the stream speed is reduced to zero. A theoretical analysis for a boundary layer flow is made and the self-similar equation is determined. Solutions are presented numerically for special power index and the associated transfer behavior is discussed.

Computational analysis of the flow of pseudoplastic power-law fluids in a microchannel plate

The flow of pseudoplastic power-law fluids with different flow indexes at a microchannel plate was studied using computational fluid dynamic simulation.The velocity distribution along the microchannel plate and especially in the microchannel slits,flow pattern along the outlet arc and the pressure drop through the whole of microchannel plate were investigated at different power-law flow indexes.The results showed that the velocity profile in the microchannel slits for low flow index fluids was similar to the plug flow and had uniform pattern.Also the power-law fluids with lower flow indexes had lower stagnation zones near the outlet of the microchannel plate.The pressure drop through the microchannel plate showed huge differences between the fluids.The most interesting result was that the pressure drops for power-law fluids were very smaller than that of Newtonian fluids.In addition,the heat transfer of the fluids through the microchannel with different channel numbers in a wide range of Reynolds number was investigated.For power-law fluid with flow index(n=0.4),the Nusselt number increases continuously as the number of channels increases.The results highlight the potential use of using pseudoplastic fluids in the microheat exchangers which can lower the pressure drop and increase the heat transfer efficiency.

Characteristics of Convection Heat Transfer in Power⁃Law Fluid Saturated Porous Media Channel

Considering Brinkman⁃Forchheimer extended Darcy flow and local thermal non⁃equilibrium effect,a general model of forced convection with viscous dissipation in power⁃law fluid saturated porous media channel was established.The dimensionless temperature profiles and Nusselt number were numerically solved using the classical fourth⁃order Runge Kutta method under a constant heat flux boundary condition.The conclusion showed that the fluid⁃solid temperature distributions were significantly affected by dimensionless Bi,k,Da,Br,and F,and the effects of power⁃law indexes on convection heat transfer characteristics were also non⁃negligible.

Simplified Wave Models Applicability to Shallow Mud Flows Modeled as Power-Law Fluids

Simplified wave models- such as kinematic,diffusion and quasi-steady- are widely employed as a convenient replacement of the full dynamic one in the analysis of unsteady open-channel flows,and especially for flood routing.While their use may guarantee a significant reduction of the computational effort,it is mandatory to define the conditions in which they may be confidently applied.The present paper investigates the applicability conditions of the kinematic,diffusion and quasisteady dynamic shallow wave models for mud flows of power-law fluids.The power-law model describes in an adequate and convenient way fluids that at low shear rates fluids do not posses yield stress,such as clay or kaolin suspensions,which are frequently encountered in Chinese rivers.In the framework of a linear analysis,the propagation characteristics of a periodic perturbation of an initial steady uniform flow predicted by the simplified models are compared with those of the full dynamic one.Based on this comparison,applicability criteria for the different wave approximations for mud flood of power-law fluids are derived.The presented results provide guidelines for selecting the appropriate approximation for a given flow problem,and therefore they may represent a useful tool for engineering predictions.

Symmetries of boundary layer equations of power-law fluids of second grade

A modified power-law fluid of second grade is considered. The model is a combination of power-law and second grade fluid in which the fluid may exhibit normal stresses, shear thinning or shear thickening behaviors. The equations of motion are derived for two dimensional incompressible flows, and from which the boundary layer equations are derived. Symmetries of the boundary layer equations are found by using Lie group theory, and then group classification with respect to power-law index is performed. By using one of the symmetries, namely the scaling symmetry, the partial differential system is transformed into an ordinary differential system, which is numerically integrated under the classical boundary layer conditions. Effects of power-law index and second grade coefficient on the boundary layers are shown and solutions are contrasted with the usual second grade fluid solutions.

Effects of nonlinear velocity slip and temperature jump onpseudo-plastic power-law fluid over moving permeable surface in presence of magnetic field

Flow and heat transfer of a pseudo-plastic power-law fluid over a stretching permeable surface with the magnetic effect is investigated. In the boundary conditions,the nonlinear temperature jump and the velocity slip are considered. Semi-similarity equations are obtained and solved by bvp4c with MATLAB. The problem can be considered as an extension of the previous work done by Mahmoud(Mahmoud, M. A. A. Slip velocity effect on a non-Newtonian power-law fluid over a moving permeable surface with heat generation. Mathematical and Computer Modelling, 54, 1228–1237(2011)). Efforts are made to discuss the effects of the power-law number, slip velocity, and temperature jump on the dimensionless velocity and temperature distribution.

The axisymmetric long-wave interfacial stability of core-annular flow of power-law fluid with surfactant

The long wave stability of core-annular flow of power-law fluids with an axial pressure gradient is investigated at low Reynolds number. The interface between the two fluids is populated with an insoluble surfactant. The analytic solution for the growth rate of perturbation is obtained with long wave approximation. We are mainly concerned with the effects of shear-thinning/thickening property and interfacial surfactant on the flow stability. The results show that the influence of shear-thinning/thickening property accounts to the change of the capillary number. For a clean interface, the shear-thinning property enhances the capillary instability when the interface is close to the pipe wall. The converse is true when the interface is close to the pipe centerline. For shear-thickening fluids, the situation is reversed. When the interface is close to the pipe centerline, the capillary instability can be restrained due to the influence of surfactant. A parameter set can be found under which the flow is linearly stable.

SOLUTION OF THE RAYLEIGH PROBLEM FOR A POWER-LAW NON-NEWTONIAN CONDUCTING FLUID VIA GROUP METHOD

An investigation is made of the magnetic Rayleigh problem where a semi_infinite plate is given an impulsive motion and thereafter moves with constant velocity in a non_Newtonian power law fluid of infinite extent. The solution of this highly non_linear problem is obtained by means of the transformation group theoretic approach. The one_parameter group transformation reduces the number of independent variables by one and the governing partial differential equation with the boundary conditions reduce to an ordinary differential equation with the appropriate boundary conditions. Effect of the some parameters on the velocity u(y,t) has been studied and the results are plotted.

OBTAINING THE CRITICAL DRAW RATIO OF DRAW RESONANCE IN MELT SPINNING FOR POWER LAW POLYMER FLUIDS

A direct difference method has been developed for Non-Newtonian power law fluids to solve the simultaneous non-linear partial differential equations of melt spinning, and to determine the critical draw ratio for draw resonance. The results show that for shear thin fluids, the logarithm of the critical draw ratio has a well defined linear relationship with the power index for isothermal and uniform tension melt spinning. When the power index approaches zero, the critical draw ratio points at unity, indicating no melt spinning can be processed stably for such fluids. For shear thick fluids, the critical draw ratio increases in a more rapid way with increasing the power index.

Similarity solutions for non-Newtonian power-law fluid flow

The problem of the boundary layer flow of power law non-Newtonian fluids with a novel boundary condition is studied. The existence and uniqueness of the solutions are examined, which are found to depend on the curvature of the solutions for different values of the power law index n. It is established with the aid of the Picard-Lindelof theorem that the nonlinear boundary value problem has a unique solution in the global domain for all values of the power law index n but with certain conditions on the curva- ture of the solutions. This is done after a suitable transformation of the dependent and independent variables. For 0 〈 n ≤ 1, the solution has a positive curvature, while for n 〉 1, the solution has a negative or zero curvature on some part of the global domain. Some solutions are presented graphically to illustrate the results and the behaviors of the solutions.

Approximate analytical solutions and approximate value of skin friction coeffcient for boundary layer of power law fluids

This paper presents a theoretical analysis for laminar boundary layer flow in a power law non-Newtonian fluids. The Adomian analytical decomposition technique is presented and an approximate analytical solution is obtained. The approximate analytical solution can be expressed in terms of a rapid convergent power series with easily computable terms. Reliability and efficiency of the approximate solution are verified by comparing with numerical solutions in the literature. Moreover, the approximate solution can be successfully applied to provide values for the skin friction coefficient of the laminar boundary layer flow in power law non-Newtonian fluids.

Fully Developed Turbulence of Power⁃Law Fluids in Circular Pipe Based on Large Eddy Simulation

In this study,Large eddy simulation(LES)of the fully developed turbulence of power⁃law fluids in a circular pipe was performed using the dynamic subgrid⁃scale model.Under a specific Reynolds number,the flow information of three fluids with a range of power⁃law indexes was obtained.The trends of the mean axial velocity and the normalized apparent viscosity were analyzed.Simulation results show that shearing⁃thinning fluid displayed more noticeable non⁃Newtonian characteristics than shear⁃thickening fluid.The predicted friction factors were approximately equal to the Dodge and Metzner correlation and Gomes correlation.The peak values of root mean squares(RMS)and Reynolds stress increased as the power⁃law index increased.The turbulence statistics(skewness and flatness)from the wall to the pipe center were calculated.From the calculated results,the velocity fluctuation near the wall had strong intermittent and asymmetry.As demonstrated by the contours of the normalized instantaneous axial velocity and viscosity,the turbulence was more developed as the power⁃law index increased.It is concluded that the LES is feasible to predict the turbulence of pipe flow under higher Reynolds numbers.

Effect of thermal conductivity on heat transfer for a power-law non-Newtonian fluid over a continuous stretched surface with various injection parameters

The two-dimensional non-Newtonian steady flow on a power-law stretched surface with suction or injection is studied. Thermal conductivity is assumed to vary as a linear function of temperature. The transformed governing equations in the present study are solved numerically using the Runge-Kutta method. Through a comparison, results for a special case of the problem show excellent agreement with those in a previous work. Two cases are considered, one corresponding to a cooled surface temperature and the other to a uniform surface temperature. Numerical results show that the thermal conductivity variation parameter, the injection parameter, and the power-law index have significant influences on the temperature profiles and the Nusselt number.

MHD flow of power-law fluid on moving surface with power-law velocity and special injection/blowing

The problem of magnetohydrodynamic （MHD） flow on a moving surface with the power-law velocity and special injection/blowing is investigated. A scaling group transformation is used to reduce the governing equations to a system of ordinary differen- tial equations. The skin friction coefficients of the MHD boundary layer flow are derived, and the approximate solutions of the flow characteristics are obtained with the homotopy analysis method （HAM）. The approximate solutions are easily computed by use of a high order iterative procedure, and the effects of the power-law index, the magnetic parameter, and the special suction/blowing parameter on the dynamics are analyzed. The obtained results are compared with the numerical results published in the literature, verifying the reliability of the approximate solutions.

The Sixth International Conference on Fluid Power Transmission and Control(ICFP'2005)

Date: April 12-15, 2005 Venue: Zhejiang University, Hangzhou, P. R. China Organized by Institute of Mechatronic Control Engineering, Zhejiang University

Exact solution to peristaltic transport of power-law fluid in asymmetric channel with compliant walls

Effects of compliant wall properties on the peristaltic flow of a non-Newtonian fluid in an asymmetric channel are investigated.The rheological characteristics are characterized by the constitutive equations of a power-law fluid.Long wavelength and low Reynolds number approximations are adopted in the presentation of mathematical developments.Exact solutions are established for the stream function and velocity.The streamlines pattern and trapping are given due attention.Salient features of the key parameters entering into the present flow are displayed and important conclusions are pointed out.

On energy boundary layer equations in power law non-Newtonian fluids

The hear transfer mechanism and the constitutive models for energy boundary layer in power law fluids were investigated.Two energy transfer constitutive equations models were proposed based on the assumption of similarity of velocity field momentum diffusion and temperature field heat transfer.The governing systems of partial different equations were transformed into ordinary differential equations respectively by using the similarity transformation group.One model was assumed that Prandtl number is a constant,and the other model was assumed that viscosity diffusion is analogous to thermal diffusion.The solutions were presented analytically and numerically by using the Runge-Kutta formulas and shooting technique and the associated transfer characteristics were discussed.

Mixture flow of particles and power-law fluid in round peristaltic tube

The erythrocyte and blood flowing in the blood vessel can be treated as the two-phase flow of the mixture of particles and a power-law fluid in a peristaltic tube.In the present work, the peristaltic transport of a power-law fluid and the suspension of particles in a tube is investigated by a perturbation method using the long wavelength approximation. The influence of different parameters on the velocity profile and streamlines is explored. Results show that there is a deflection of the flow field when the power-law index n = 0.5 or 1.5 compared with the Newtonian fluid where the trapping zone is symmetric to a certain cross section. The flux rate and reflux of the material are identified,and the conditions under which the reflux appears are determined. Moreover, a reflux phenomenon occurs near the wall. The trapping zone is related to not only the tube geometry and the flow flux but also the fluid properties. Both the length and width of the trapping zone increase with an increase in θ or φ. The trapping zone is more difficult to produce in the shear-thinning fluid than the shear-thickening fluid.