Laminar Flow Of non-Newtonian Fluids Research Articles

Heat transfer of laminar non-Newtonian fluid flow through pipes boosted by inlet swirl

Heat transfer of laminar non-Newtonian fluid flow through pipes boosted by inlet swirl

Viscous Dissipation and Fluid Axial Heat Conduction Effect on the Heat Transfer to a Laminar Non-Newtonian Fluid Flow in Cylindrical Annular Duct with an Axially Moving Core

Viscous Dissipation and Fluid Axial Heat Conduction Effect on the Heat Transfer to a Laminar Non-Newtonian Fluid Flow in Cylindrical Annular Duct with an Axially Moving Core

Numerical investigation on the interaction of an oscillating bubble with the interface of a non-Newtonian fluid

The dynamics of an oscillating bubble near a liquid–liquid interface is a complex multiphase flow problem due to the highly nonlinear interaction, such as interface fragmentation and bubble tearing. When one of the liquid mediums is non-Newtonian, its constitution would significantly influence both the bubble motion and the interface evolution. In this study, a numerical model is established based on the Eulerian finite element method with the non-Newtonian fluid described by the Herschel–Bulkley model. The numerical model is validated by comparing with experimental results for a non-spherical pulsating bubble at a water–oil interface and the analytical solution for the laminar flow of non-Newtonian fluids in a circular tube. According to the simulation and analysis with different case parameters, our findings suggest that the non-Newtonian fluid forms a crater when squeezed by the bubble, and the downward jet can penetrate the bubble and further deepen the crater. As the distance parameter increases, the crater gradually disappears or even bulges. Furthermore, the yield shear stress can give non-Newtonian fluid plastic properties similar to a solid, effectively reducing the bubble's pulsation and jet load. Additionally, the flow behavior index n comes from the power-law model for non-Newtonian fluids and significantly impacts the jet's impact process. When n≤1, the crater is likelier to become funnel-shaped, whereas when n > 1, it is likelier to become bullet-head-shaped. In addition to enhancing the bubble's nonsphericity, the reduction in Reynolds number also weakens the crimp deformation of the interface. When the distance parameter is zero, the larger the buoyancy parameter and the less deformable the non-Newtonian fluid, the easier the bubble to split by the annular jet.

Numerical simulation of non-Newtonian fluid flow in partially blocked eccentric annuli

A cuttings bed formed on the lower side of the wellbore is the most common drilling problem confronted when horizontal or highly deviated wells are drilled. The phenomenon is undesirable and has a detrimental effect on wellbore hydraulics and drilling performance. To achieve an efficient drilling operation, hydraulics optimization should be implemented by precisely predicting annular pressure loss and other hydraulic parameters.The accumulation of cuttings at the lower side of horizontal or highly inclined wellbores, combined with wellbore eccentricity and fluid rheological properties, create a complex behavior of pressure loss. In this study, a numerical approach is used to investigate the influence of the aforementioned factors. A numerical solution is performed for laminar flow of non-Newtonian fluids. A non-orthogonal, boundary-fitted curvilinear coordinate is developed, which is based on elliptic partial differential equations (PDE) to accommodate annular flow geometry with arbitrary cross-sections. Finite difference numerical schemes adapted to the coordinates is then used to analyze the problem. The numerical model determines the effect of hydraulic parameters of fluid flow thorough an irregularly shaped annulus and considers the following factors: flow rate, fluid rheological parameters, annular geometry and bed appearance. Numerical predictions from the model are verified against existing models and experimental data in literature; and good agreements are obtained. The developed numerical model can be combined with a 1-D solids transport model for designing oil and gas well drilling operations.

Non-Newtonian fluid flow dynamics in rotating annular media: Physics-based and data-driven modeling

A thorough understanding and accurate prediction of non-Newtonian fluid flow dynamics in rotating annular media are of paramount importance to numerous engineering applications. This is in particular relevant to oil and gas industry where this type of flow could occur during, e.g., drilling, well completion, and enhanced oil recovery scenarios. Here, mathematically we report on physical-based (numerical) and data-driven (intelligent) modeling of three-dimensional laminar flow of non-Newtonian fluids driven by axial pressure gradient in annular media that consist of a coaxially rotating inner cylinder. We focus on the dynamics of pressure loss ratio (PLR)—the ratio of total pressure loss in presence of rotation to that in stationary condition. We develop a novel and computationally efficient machine-learning based predictive model based on a Least Square Support Vector Machine (LSSVM) optimized with a Coupled Simulated Annealing (CSA) algorithm, which is trained and tested by 730 experimental data collected for this study. We then perform numerous CFD simulations governed by Navier-Stokes set of equations, which correspond to each of the experimental cases. Comparing the results with those obtained from a widely used empirical correlation for PLR, we find that the both of our numerical and machine-learning based models are more accurate and present a larger applicability domain. The predictive LSSVM model enjoys a supervised learning paradigm and leads to the highest accuracy, while the physically originated CFD approach captures more consistently the nonlinear behavior of PLR versus key system features. Following the validation of our models, we study the less understood effects of fluid viscosity, axial velocity and rotational velocity on PLR dynamics. We employ a dimensionless parameter analogous to Strouhal number and identify specific regimes where PLR shows a distinct behavior. Our study elucidates the role of shear-thinning effect and its interplay with inertial forces on the dynamical behavior of pressure loss (ratio) in rotating yield-power-law fluids.

On the Weissenberg effect of turbulence

Within the framework of the Navier–Stokes equations, the Weissenberg effect of turbulence is investigated. We begin with our investigation on the elastic effect of homogeneous turbulent shear flow. First, in the sense of Truesdell (Physics of Fluids, 1964) on the natural time of materials, we derive the natural time of turbulence, and use it together with the natural viscosity of turbulence derived in the article of Huang et al. (Journal of Turbulence, 2003) to define the natural Weissenberg number of turbulence as a measure of the elastic effect of homogeneous turbulence. Second, we define a primary Weissenberg number of turbulence, which in laminar flow reduces to the Weissenberg number widely applied in rheology to characterize the elasticity of visco-elastic fluids. Our analysis based on the experimental results of Tavoularis and Karnik (Journal of Fluid Mechanics, 1989) indicates that the larger is the Weissenberg number of turbulence, the more elastic becomes the turbulent flow concerned. Furthermore, we put forth a general Weissenberg number of turbulence, which includes the primary Weissenberg number of turbulence as a special case, to measure the overall elastic effects of turbulence. Besides, it is shown that the general Weissenberg number can also be used to characterize the elastic effects of non-Newtonian fluids in laminar flow.

Accurate Approximate Methods for the Fully Developed Flow of Shear-Thinning Fluids in Ducts of Noncircular Cross Section

The fully developed laminar flow of Non-Newtonian fluids in ducts has broad application in engineering. The power-law viscosity model is utilized most often in the engineering literature, but it is deficient for many fluids as it does not admit limiting Newtonian viscosities at low and high shear rates. The goal of this work is to demonstrate two approximate but accurate and efficient methods for computing the pressure gradient in ducts of noncircular cross section for shear-thinning fluids following a general viscosity curve. Both methods predict the pressure gradient to better than 1% as established by full numerical solutions for ten cross-sectional shapes, a result representing an order-of-magnitude improvement over previous approximate methods. In the first method, an approach recently proposed and demonstrated to be accurate for a circular duct is shown to be equally applicable to noncircular ducts. In the second method, a widely used approach for noncircular ducts based on a generalization of the Rabinowitsch–Mooney equation is improved through an alternate evaluation of its parameters. Both methods require one-time numerical solutions of the power-law viscosity model for a duct shape of interest, and the necessary results are tabulated for the ten cross-sectional shapes analyzed. It is additionally demonstrated that the pressure-gradient error of the second method is approximately halved by simply replacing the hydraulic diameter with a viscous diameter obtained from the Hagen–Poiseuille equation.

Simultaneous design of non-Newtonian lubricant and surface texture using surrogate-based multiobjective optimization

Surface textures decrease friction in lubricated sliding with Newtonian fluids. Viscoelastic non-Newtonian lubricants can enhance frictional performance, but the optimal rheological material properties and their coupling to the texture design are non-obvious. In this study, we present a simultaneous design of both surface texture shape and non-Newtonian properties, which can be achieved by fluid additives that introduce viscoelasticity, shear thinning, and normal stress differences. Two models with different fidelity and computational cost are used to model laminar non-Newtonian fluid flow between a rotating flat plate and a textured disk. At lower fidelity, we use the Criminale-Ericksen-Filbey (CEF) constitutive model and a thin-film approximation for conservation of momentum (Reynolds equation). At higher fidelity, we use a fully nonlinear constitutive model typically applicable to polymer solutions (multimode Giesekus model) and the full 3-D momentum equations. Fluid additive design is parameterized by two relaxation modes each having a timescale, added viscosity, and a nonlinear anisotropic drag parameter. To manage the computational complexity and constraints between design variables, we use our previously developed multiobjective adaptive surrogate modeling-based optimization (MO-ASMO) method. A new data-driven extension of MO-ASMO is introduced that constructs general boundaries to prevent attempts to evaluate designs that would lead to simulation failure. We demonstrate the efficiency of our MO-ASMO method and provide insights into co-designing the lubricant and textured surface. The Pareto-optimal solutions include fluid designs with both high and low viscoelastic additive loading. We rationalize this trade-off and discuss how the optimal design targets can be physically realized.

Numerical investigation of laminar forced convection for a non-Newtonian nanofluids flowing inside an elliptical duct under convective boundary condition

PurposeThe purpose of this study is to investigate the thermal response of the laminar non-Newtonian fluid flow in elliptical duct subjected to a third-kind boundary condition with a particular interest to a non-Newtonian nanofluid case. The effects of Biot number, aspect ratio and fluid flow behavior index on the heat transfer have been examined carefully.Design/methodology/approachFirst, the mathematical problem has been formulated in dimensionless form, and then the curvilinear elliptical coordinates transform is applied to transform the original elliptical shape of the duct to an equivalent rectangular numerical domain. This transformation has been adopted to overcome the inherent mathematical deficiency due to the dependence of the ellipsis contour on the variables x and y. The yielded problem has been successfully solved using the dynamic alternating direction implicit method. With the available temperature field, several parameters have been computed for the analysis purpose such as bulk temperature, Nusselt number and heat transfer coefficient.FindingsThe results showed that the use of elliptical duct enhances significantly the heat transfer coefficient and reduces the duct’s length needed to achieve the thermal equilibrium. For some cases, the reduction in the duct’s length can reach almost 50 per cent compared to the circular pipe. In addition, the analysis of the non-Newtonian nanofluid case showed that the addition of nanoparticles to the base fluid improves the heat transfer coefficient up to 25 per cent. The combination of using an elliptical duct and the addition of nanoparticles has a spectacular effect on the overall heat transfer coefficient with an enhancement of 50-70 per cent. From the engineering applications view, the results demonstrate the potential of elliptical duct in building light-weighted compact shell-and-tube heat exchangers.Originality/valueA complete investigation of the heat transfer of a fully developed laminar flow of power law fluids in elliptical ducts subject to the convective boundary condition with application to non-Newtonian nanofluids is addressed.

On Laminar Flow of Non-Newtonian Fluids in Porous Media

Flow of generalized Newtonian fluids in porous media can be modeled as a bundle of capillary tubes or a pore-scale network. In general, both approaches rely on the solution of Hagen–Poiseuille equation using power law to estimate the variations in the fluid viscosity due to the applied shear rate. Despite the effectiveness and simplicity, power law tends to provide unrealistic values for the effective viscosity especially in the limits of zero and infinite shear rates. Here, instead of using power law, Carreau model (bubbles, drops, and particles in non-Newtonian fluids. Taylor & Francis Group, New York, 2007) is used to determine the effective viscosity as a function of the shear strain rate. Carreau model can predict accurately the variation in the viscosity at all shear rates and provide more accurate solution for the flow physics in a single pore. Using the results for a single pore, normalized Fanning friction coefficient has been calculated and plotted as a function of the newly defined Reynolds number based on pressure gradient. For laminar flow, the variation in the friction coefficient with Reynolds number has been plotted and scaled. It is observed that generalized Newtonian fluid flows show Newtonian nature up to a certain Reynolds number. At high Reynolds number, deviation from the Newtonian behavior is observed. The main contribution of this paper is to present a closed-form solution for the flow in a single pore using Carreau model, which allows for fast evaluation of the relationship between flux and pressure gradient in an arbitrary pore diameter. In this way, we believe that our development will open the perspectives for using Carreau models in pore-network simulations at low computational costs to obtain more accurate prediction for generalized Newtonian fluid flows in porous media.

Simplified method for estimating heat transfer coefficients: constant wall temperature case

This work completes a previous study (Cruz et al., in J Heat Transf 134:091703, 2012) by evaluating the performance of the simplified method proposed therein for calculating the Nusselt number for laminar flow of non-Newtonian fluids in pipes with constant wall temperature. The methodology was tested using the Herschel-Bulkley, Bingham, Casson and Carreau-Yasuda generalized Newtonian models, and also the simplified form of the Phan-Thien–Tanner viscoelastic model. The error of the approximate methodology is below 3 %, except for yield stress fluids, for which the maximum error increases to 7.4 % for the cases analyzed, which cover a wide range of shear viscosity curves. An explicit expression of Nusselt number for Casson fluids is also presented.

Laminar heat transfer performance of power law fluids in coiled square tube with various configurations

This study addresses heat transfer performance of laminar non-Newtonian fluid flow in various configurations of coiled square tubes e.g., in-plane spiral ducts, helical spiral ducts and conical spiral ducts. The non-Newtonian fluid considered in this study is the aqueous solution of carboxymethyl cellulose (CMC) which is modeled as power-law fluid. Effects of tube geometries, power-law index (concentration of CMC) and other parameters are quantified and discussed to analyze flow behavior and heat transfer performance. Results are compared with those for a straight square tube of the same length as that used to form the coils. A Figure of Merit is defined to compare the heat transfer performance of different geometries with respect to the pumping power. The results suggest that CMC solution yields better heat transfer performance of about twice than that of water at Re~1000. Among all considered designs, helical coil gives the best heat transfer performance; however, when the pumping power is considered, in-plane coil design performs the best in term of Figure of Merit.

Evaluation of friction factor correlations and equivalent diameter definitions for pipe and annular flow of non-Newtonian fluids

Abstract Friction pressure estimation is an important part of pipe and annular hydraulics useful for determining hydraulic horsepower requirements and the maximum wellhead pressure. For non-Newtonian fluids in laminar flow, the friction factor can be calculated with the Hagen–Poiseuille type equation. In turbulent flow, however, several correlations have been developed for smooth pipes. Many of these correlations are in the form of the Dodge–Metzner equation for flow in smooth pipes. The Dodge–Metzner correlation was developed using carbopol aqueous solution which is not used for oilfield operations. Previous studies on friction factor correlation comparison have been limited to the use of non-Newtonian fluid friction factor equations for smooth pipes neglecting the significant effect of pipe roughness on wellbore hydraulics. Generally, tubulars in oilfield applications have some degree of roughness which results in higher friction pressure than that for smooth pipes of the same size especially for less viscous fluids. A few studies have addressed the effect of roughness on friction pressure loss. In this study, friction factor correlations with relative roughness are compared with experimental measured friction factor data using a statistical approach as the basis for comparison. Further, equivalent diameter definitions for annular flow are evaluated to determine the friction factor–equivalent diameter combination that best describes the experimental data. The objective of this work is to recommend the non-Newtonian friction factor correlation that allows for accurate prediction of frictional pressure losses in rough pipes and annular sections.

An Explicit and Continuously Differentiable Flow Equation for Non-Newtonian Fluids in Pipes

Summary A simple model approximates Herschel-Bulkley (HB) non-Newtonian fluids in laminar flow in pipes. It is continuously differentiable and explicit in the frictional pressure gradient. Such properties are needed for control, real-time optimization, and prediction in drilling operations. The accuracy of the new model is evaluated by comparing it with a numerical implementation of the implicit HB model and some representative approximations used in the literature. Very little loss in accuracy is experienced compared with the implicit solution.

Residence Time Distribution Models Derived from Non‐Ideal Laminar Velocity Profiles in Tubes

AbstractThe theoretical E‐curve for the laminar flow of non‐Newtonian fluids in circular tubes may not be accurate for real tubular systems with diffusion, mechanical vibration, wall roughness, pipe fittings, curves, coils, or corrugated walls. Deviations from the idealized laminar flow reactor (LFR) cannot be well represented using the axial dispersion or the tanks‐in‐series models of residence time distribution (RTD). In this work, four RTD models derived from non‐ideal velocity profiles in segregated tube flow are proposed. They were used to represent the RTD of three tubular systems working with Newtonian and pseudoplastic fluids. Other RTD models were considered for comparison. The proposed models provided good adjustments, and it was possible to determine the active volumes. It is expected that these models can be useful for the analysis of LFR or for the evaluation of continuous thermal processing of viscous foods.

Numerical study of laminar mixed convection heat transfer of power-law non-Newtonian fluids in square enclosures by finite volume method

In this study, we have numerically considered mixed convection heat transfer in a square enclosure with cold left and right walls, insulated moving upper wall and hot fixed lower wall. The governing flows of two reliable articles were initially modeled and after validating calculations, the given flow of the study was solved by finite volume method. To examine the effects of different factors, such as Prandtl, Reynolds and Rayleigh numbers on heat transfer in a square enclosure, the laminar flow of Newtonian fluids was approximated and then laminar flow of non-Newtonian fluids, such as carboxy methyl cellulose (CMC) andcarboxy poly methylene (Carbopol) water solutions were studied for different Richardson numbers. It was found from the results obtained in the present study that when Ri is less than 1, governing heat transfer inside the enclosure is forced convection for non-Newtonian fluids similar to Newtonian ones. When Ri increases, the effect of forced convection is reduced and natural convection heat transfer increases. It was also found that in constant Grashof numbers, if n decreases, the dimensionless temperature increases. Also, if n is constant, any increase in Grashof number causes a higher dimensionless temperature. It may be related to the fact that in similar conditions, any increase in forced convection, makes shear stresses more. Key words: Richardson number, power-law non-Newtonian fluids, mixed convection heat transfer, square enclosure, finite volume method.

Numerical simulations of flow through channels with T-junction

The paper deals with numerical solution of laminar and turbulent flows of Newtonian and non-Newtonian fluids in branched channels with two outlets. Mathematical model of the flow is based on the Reynolds averaged Navier–Stokes equations for the incompressible fluid. In the turbulent case, the closure of the system of equations is achieved by the explicit algebraic Reynolds stress (EARSM) turbulence model. Generalized non-Newtonian fluids are described by the power-law model. The governing equations are solved by cell-centered finite volume schemes with the artificial compressibility method; dual time scheme is applied for unsteady simulations. Channels considered in presented calculations are of constant square or circular cross-sections. Numerical results for laminar flow of non-Newtonian fluid are presented. Further, turbulent flow through channels with perpendicular branch is simulated. Possible methods for setting the flow rate are discussed and numerical results presented for two flow rates in the branch.

Friction factor-Reynolds number relationship for laminar flow of non-Newtonian fluids in open channels of different cross-sectional shapes

The effect of channel shape on the friction factor-Reynolds number relationship for laminar, open channel flow of three non-Newtonian fluids was investigated. For each channel shape, the data can be described by a general relationship, f= K/Re where f is the Fanning friction factor and Re is the appropriate Haldenwang et al. (2002) Reynolds number corresponding to the flow curve model used to describe the non-Newtonian behaviour exhibited by the test fluid. The K values were found to be 14.6 for triangular channels with a vertex angle of 90°, 16.2 for semi-circular channels, 16.4 for rectangular channels and 17.6 for trapezoidal channels with 60° sides. These K values were found to be in line with those reported by Straub et al. (1958) and Chow (1959) for open channel flow of Newtonian fluids as opposed to the assumption made by Haldenwang et al. (2002, 2004) of using a constant value of 16 based on the pipe flow paradigm for all channel shapes.

Laminar Non-Newtonian Fluid Flow in Noncircular Ducts and Microchannels

Abstract Non-Newtonian fluid flow in noncircular ducts and microchannels is examined. A simple model is proposed for power law fluids based on the Rabinowitsch–Mooney formulation. By means of a new characteristic length scale, the square root of the cross-sectional area, it is shown that dimensionless wall shear stress can be made a weak function of duct shape. The proposed model is based on the solution for the rectangular duct and has an accuracy of ±10% or better. The current model eliminates the need for tabulated data or equations for several common shapes found in handbooks, namely, circular tube, elliptic tube, parallel channel, rectangular duct, isosceles triangular duct, circular annulus, and polygonal ducts.

Mathematical simulation of outer-die extrusion of large-size, improved-reliability, insulating porcelain casings

A computation-experimental study of the technological process of outer-die extrusion of large-size porcelain casings is performed. The extrusion of cylindrical tubular blanks from alumina paste is simulated mathematically. The paste is treated as non-Newtonian fluid in laminar flow along the shaping channel of a vacuum-press. Recommendations are made for an efficient configuration of the shaping system of the vacuum-press for manufacturing cylindrical tubular intermediate product.