Analytical solutions for the flow of Carreau and Cross fluids in circular pipes and thin slits

In this paper, analytical expressions correlating the volumetric flow rate to the pressure drop are derived for the flow of Carreau and Cross fluids through straight rigid circular uniform pipes and long thin slits. The derivation is based on the application of Weissenberg-Rabinowitsch-Mooney-Schofield method to obtain flow solutions for generalized Newtonian fluids through pipes and our adaptation of this method to the flow through slits. The derived expressions are validated by comparing their solutions to the solutions obtained from direct numerical integration. They are also validated by comparison to the solutions obtained from the variational method which we proposed previously. In all the investigated cases, the three methods agree very well. The agreement with the variational method also lends more support to this method and to the variational principle which the method is based upon.Comment: 27 pages, 6 figure

CFD Analysis of Non-Newtonian Pseudo Plastic Liquid Flow through Bends

Non-Newtonian pseudo plastic liquid flow through different types of 0.0127 m diameter pipe bends as well as straight pipe have been investigated experimentally to evaluate frictional pressure drop across the bends in laminar and water flow in turbulent condition. We have studied here the effect of flow rate, bend angle, fluid behavior on static pressure and pressure drop. A Computational Fluid Dynamics (CFD) based software is used to predict the static pressure, pressure drop, shear stress, shear strain, flow structure, friction factor, loss co- efficient inside the bends for Sodium Carboxy Methyl Cellulose (SCMC) solution as a non-Newtonian pseudo plastic fluids and water as a Newtonian fluid. Laminar Non-Newtonian pseudo plastic Power law model is used for SCMC solution to numerically solve the continuity and the momentum equations. The experimental data are compared with the CFD generated data and is well matched. The software predicted data may be used to solve any industrial problem and also to design various equipment

Theoretical study of Oldroyd-b visco-elastic fluid flow through curved pipes with slip effects in polymer flow processing

The characteristics of the flow field of both viscous and viscoelastic fluids passing through a curved pipe with a Navier slip boundary condition have been investigated analytically in the present study. The Oldroyd-B constitutive equation is employed to simulate realistic transport of dilute polymeric solutions in curved channels. In order to linearize the momentum and constitutive equations, a perturbation method is used in which the ratio of radius of cross section to the radius of channel curvature is employed as the perturbation parameter. The intensity of secondary and main flows is mainly affected by the hoop stress and it is demonstrated in the present study that both the Weissenberg number (the ratio of elastic force to viscous force) and slip coefficient play major roles in determining the strengths of both flows. It is also shown that as a result of an increment in slip coefficient, the position of maximum velocity markedly migrates away from the pipe center towards the outer side of curvature. Furthermore, results corresponding to Navier slip scenarios exhibit non-uniform distributions in both the main and lateral components of velocity near the wall which can notably vary from the inner side of curvature to the outer side. The present solution is also important in polymeric flow processing systems because of experimental evidence indicating that the no-slip condition can fail for these flows, which is of relevance to chemical engineers

Uniformly Valid Asymptotic Flow Analysis in Curved Channels

The laminar incompressible flow in a two-dimensional curved channel having at its upstream and downstream extremities two tangent straight channels is considered. A global interactive boundary layer (GIBL) model is developed using the approach of the successive complementary expansions method (SCEM) which is based on generalized asymptotic expansions leading to a uniformly valid approximation. The GIBL model is valid when the non dimensional number μ = δmath is O(1) and gives predictions in agreement with numerical Navier-Stokes solutions for Reynolds numbers Re ranging from 1 to 10 puissance 4 and for constant curvatures δ = math ranging from 0.1 to 1, where H is the channel width and Rc the curvature radius. The asymptotic analysis shows that μ, which is the ratio between the curvature and the thickness of the boundary layer of any perturbation to the Poiseuille flow, is a key parameter upon which depends the accuracy of the GIBL model. The upstream influence length is found asymptotically and numerically to be O(math)

Fluid Flow through 90 Degree Bends

Pressure drop measurement and prediction in curved pipes and elbow bends is reviewed for both laminar and turbulent single-phase fluid flow. For curved pipe under laminar flow, the pressure loss can be predicted both theoretically and using empirical relations. The transitional Reynolds number can be predicted from an empirical relation. Turbulent flow in curved pipes can only be theoretically predicted for large bends but there are a large number of empirical relations that have proved to be accurate. Elbow bends have proven to be difficult to both measure and represent the pressure loss. Methods of overcoming such problems are outlined. There was no reliable method of theoretically predicting pressure drop in elbow bends. Experimental measurements showed considerable scatter unless care was taken to eliminate extraneous effects. Reliable data are highlighted and an empirical method is proposed for calculation of pressure drop in elbow bends

Non-Newtonian Rheology in Blood Circulation

Blood is a complex suspension that demonstrates several non-Newtonian rheological characteristics such as deformation-rate dependency, viscoelasticity and yield stress. In this paper we outline some issues related to the non-Newtonian effects in blood circulation system and present modeling approaches based mostly on the past work in this field.Comment: 26 pages, 5 figures, 2 table