non-Newtonian Bingham Fluid Research Articles

Numerical investigation on flow and heat transfer performance of non-Newtonian Bingham fluid in novel spiral wound tube heat exchangers

Based on the field of the coal chemical industry, exploring the applicability of high-performance heat exchangers for coal water slurry and their flow and heat transfer mechanism is of great significance for promoting the development of clean coal technology. In this paper, the flow pattern and forced convection heat transfer of a pair of tandem heated cylinders with different distances were discussed using the bi-viscous Bingham model by numerical simulation. And a novel spiral wound heat exchanger with variable diameter tubes was proposed. The results illustrate that the heat transfer coefficient under unit pressure drop h/△P of the heat exchanger decreases with the increase of the diameter of the variable tubes. When the diameter of variable tubes is 12 mm, h/△P is 19.83% larger than that of the original structure with uniform tube diameter. The empirical correlation between operating and structural parameters and heat exchanger performance is obtained. The research results provide guidance for the design of coal water slurry preheaters and the structural optimization of spiral wound tube heat exchangers.

MHD Mixed Convection of Non-Newtonian Bingham Nanofluid in a Wavy Enclosure with Temperature-Dependent Thermophysical Properties: A Sensitivity Analysis by Response Surface Methodology

The numerical investigation of magneto-hydrodynamic (MHD) mixed convection flow and entropy formation of non-Newtonian Bingham fluid in a lid-driven wavy square cavity filled with nanofluid was investigated by the finite volume method (FVM). The numerical data-based temperature and nanoparticle size-dependent correlations for the Al2O3-water nanofluids are used here. The physical model is a two-dimensional wavy square cavity with thermally adiabatic horizontal boundaries, while the right and left vertical walls maintain a temperature of TC and TH, respectively. The top wall has a steady speed of u=u0. Pertinent non-dimensional parameters such as Reynolds number (Re=10,100,200,400), Hartmann number (Ha=0,10,20), Bingham number (Bn=0,2,5,10,50,100,200), nanoparticle volume fraction (ϕ=0,0.02,0.04), and Prandtl number (Pr=6.2) have been simulated numerically. The Richardson number Ri is calculated by combining the values of Re with a fixed value of Gr, which is the governing factor for the mixed convective flow. Using the Response Surface Methodology (RSM) method, the correlation equations are obtained using the input parameters for the average Nusselt number (Nu¯), total entropy generation (Es)t, and Bejan number (Beavg). The interactive effects of the pertinent parameters on the heat transfer rate are presented by plotting the response surfaces and the contours obtained from the RSM. The sensitivity of the output response to the input parameters is also tested. According to the findings, the mean Nusselt numbers (Nu¯) drop when Ha and Bn are increased and grow when Re and ϕ are augmented. It is found that (Es)t is reduced by raising Ha, but (Es)t rises with the augmentation of ϕ and Re. It is also found that the ϕ and Re numbers have a positive sensitivity to the Nu¯, while the sensitivity of the Ha and Bn numbers is negative.

Investigation of Newtonian and non-Newtonian Bingham fluid models for lateral flow simulation of liquefied soil

This study applies a Newtonian model and non-Newtonian Bingham model to simulate the lateral flow of liquefied soil and investigates the models’ parameters. First, the study derives analytical solutions for the lateral flow velocity under free-field conditions in both the transient and steady states for both models. The study determines that the solution derived for the Newtonian model can be applied to derive that for the Bingham model through a simple transformation considering the contribution of undrained residual shear strength of liquefied soil. Second, three-dimensional numerical analyses are executed using COMSOL to investigate the boundary conditions of experimental models, which significantly affect the fluid behavior of liquefied soil. The results reveal that the model length and sidewall effects can be ignored at a length-to-thickness ratio of >30 and width-to-thickness ratio of >6, respectively. The Bingham model can describe the behavior of liquefied soil under different boundary conditions using a single set of parameters. Through normalization, the Bingham and Newtonian models can share the same normalized velocity–time curve. Additionally, the Bingham model with boundary conditions can have a similar curve to that under the free-field condition through the replacement of the original viscosity coefficient with an apparent viscosity coefficient.

Analytical and numerical studies on a moving boundary problem of non-Newtonian Bingham fluid flow in fractal porous media

Non-Darcy flow with a threshold in fractal porous media has been widely used in the development of unconventional petroleum resources such as heavy oil and tight oil. Mathematical modeling of such challenging “threshold flow” problems with strong nonlinearity has great significance in improving petroleum science and technology. Based on a fractal theory, a new non-Darcy kinematic equation with a fractal threshold pressure gradient (TPG) is mathematically deduced in order to describe the non-Darcy flow of a non-Newtonian Bingham fluid with a threshold in fractal porous media. Then mathematical modeling of planar radial non-Darcy flow in a fractal heavy oil reservoir is performed as a nonlinear moving boundary problem. In addition, a steady analytical solution method and a transient numerical solution method are developed. The analytical solution of an ordinary differential equation system for a simple steady model is derived directly, and the transient numerical solution of a partial differential equation system for an unsteady flow model is obtained based on the finite element method with good convergence. These two model solutions are validated by cross-comparisons. It is found from the calculation results that for the steady state, the extremely disturbed moving boundary and its corresponding pressure distribution are affected only by a TPG, production pressure, and a transport exponent; by contrast, for the unsteady state, the moving boundary and its corresponding pressure distribution are affected by many more factors including the fractal dimension. Furthermore, neglect of the fractal TPG and the induced moving boundary can lead to high overestimation of well productivity.

Numerical study on non-Newtonian Bingham fluid flow in development of heavy oil reservoirs using radiofrequency heating method

Nowadays, development of heavy oil usually demands massive hot water injection and meanwhile produces considerable carbon footprint. Radiofrequency (RF) heating, as a “Non-aqueous” method, has potentials to be a cleaner and efficient way for heavy oil development in near future. In this paper, we presented a novel numerical model for simulating non-Newtonian Bingham fluid flow in heavy oil reservoirs based on RF heating. Compared to previous studies, this paper focuses on issues including: (1) Application of RF heating in heavy oil reservoir; (2) Non-Darcy flow induced by threshold pressure gradient (TPG) of Bingham fluid; (3) Temperature dependent TPG and viscosity; (4) Two-way coupling between non-Darcy flow, transient heat transfer and electromagnetic (EM) field. To incorporate TPG in numerical analyses, an effective method was utilized by modifying the gravitational acceleration vector in Darcy's law. This method was verified with analytical solution. By doing this, the induced moving boundary by TPG can be simulated, and pressure-disturbed area can be determined. Results show that RF heating significantly mitigates the impediment induced by TPG and high viscosity near well. The moving boundary stops motion at around 1000th day of production and the extreme disturbed distance is 63 m. Besides, it is found that no matter whether TPG is considered or not, RF heating has a positive impact on the reservoir development. However, for the production time less than 1000 days, RF heating is more effective when TPG is considered. Finally, we also found it very necessary to incorporate TPG in the simulations to determine optimal well spacing. If TPG is neglected in kinematic equation, the optimal well spacing would be overestimated by over 50%. At the same time, the change of TPG value with temperature cannot be ignored. Otherwise, the optimal well spacing would be underestimated by 15%. This paper reveals the potentials of RF heating method for non-Newtonian Bingham fluid production and provides an alternative way for clean, environmental, and highly efficient development of heavy oil reservoir.

Municipal wastewater sludge rheology: Impact of temperature, solid content, and settling solids.

The analysis of the rheological properties of the sludge produced in biological purification plants is paramount for the design of equipment (pumping, mixing, conditioning, aeration, filtration, etc.) and the management of these plants. In particular, solid content in the sludge plays a significant role in the rheological quantities. In this study, an investigation of the sludge rheology produced in different sectors of an activated sludge plant (aerated sludge, recirculation sludge, and thickened sludge) has been performed. Specifically, for each sludge sample, various physical-chemical parameters have been analyzed, and rheological tests have been performed at different temperatures (10°C, 20°C, 30°C, and 40°C ± 0.1). The sludge was considered as a non-Newtonian Bingham fluid. Viscosity and critical stress were determined, and their dependence at different temperatures, on some physical parameters, such as solid content and settling solids, has been studied. Results evidenced that viscosity and critical stress increase with increasing solid concentration. Moreover, at the same concentration, as the temperature increases, the viscosity decreases, whereas the critical stress decreases until temperature values of about 30°C and then increases again. PRACTITIONER POINTS: An investigation of the sludge rheology produced in different sectors of an activated sludge plant has been performed. For each sludge sample, various physical-chemical parameters have been analyzed, and rheological tests have been performed at different temperatures. Viscosity and critical stress were determined, and their dependence at different temperatures, on some physical parameters, has been studied. Results evidenced that viscosity and critical stress increase with increasing solid concentration.

Bingham fluid sloshing phenomenon modelling and investigating in a rectangular tank using SPH method

ABSTRACT In the present work, the sloshing phenomenon in a rectangular tank with non-Newtonian Bingham fluid is modeled. The numerical method used is the Incompressible Smoothed particle Hydrodynamics (ISPH) method. In the present study, first, a proper algorithm has been developed for modeling the Bingham fluid with the free surface. The method is validated by the famous previous works and experimental results. Then, to investigate the behavior of Bingham fluid, first, a proper Bingham number for sloshing phenomena is defined and the results are extracted according to this number. Three different Bingham numbers are considered and sloshing phenomena are analyzed and discussed for each of them. Finally, the effect of the baffle on the control of the sloshing phenomenon for the Bingham fluid is examined. The results show that increasing the Bingham number decreases the amplitude of the sloshing phenomenon. Also, the vertical baffle significantly controls the sloshing phenomenon.

Analytical study on a moving boundary problem of semispherical centripetal seepage flow of Bingham fluid with threshold pressure gradient

It is well known that the Non-Newtonian Bingham fluid flow in porous media does not obey the conventional linear Darcy’s law due to the yield stress for the Bingham fluid: There exists a threshold pressure gradient, which means that the seepage flow only happens when the threshold pressure gradient is overcome. The principle of non-Darcy seepage flow with the threshold pressure gradient is also applicable into the situation of the fluid flow in the low-permeable porous media. Here, a nonlinear moving-boundary mathematical model is built for the semispherical centripetal non-Darcy seepage flow with the threshold pressure gradient in a three-dimensional infinite heavy oil reservoir with the type of Bingham fluid; wherein the moving boundary conditions are incorporated for describing the effect of the threshold pressure gradient. In consideration of the strong nonlinearity of the model, the similarity transformation method is applied into obtaining the exact analytical solution of the model. In order to keep full self-similarity for the model, the inner boundary condition is set as variable flow rate that increases linearly with the time. As a result, an exact analytical solution for the nonlinear moving-boundary mathematical model of semispherical centripetal non-Darcy seepage flow with the threshold pressure gradient is obtained. The existence and the uniqueness of the exact analytical solution are also strictly proved. It is also theoretically proved that as the threshold pressure gradient tends to zero, the exact analytical solution can be reduced to that of a mathematical model of semispherical centripetal Darcy’s seepage flow. The presented exact analytical solution can be used for strictly verifying the validity of the numerical methods for solving the three-dimensional moving boundary models of non-Darcy seepage flow with the threshold pressure gradient in the actual engineering problems. From the exact analytical solution, it is also revealed that when the threshold pressure gradient exists, the spatial pressure distribution exhibits an instructive feature of compact support; as the threshold pressure gradient tends to zero, the sensitivity of its effect on the transient distance of the moving boundary and the transient pressure will grow, which reveals the difficulty in accurately determining the position of the moving boundary by the numerical methods and the serious uncertainty problem in the interpretation of the threshold pressure gradient by the pressure transient analysis method in engineering as the threshold pressure gradient is rather small. Through the comparison of the two different exact analytical solutions that corresponds to the two different models with and without incorporating the moving boundary conditions for describing the effect of the threshold pressure gradient, it is demonstrated that when the moving boundary conditions are not incorporated in the modeling, the effect of the threshold pressure gradient on the spatial pressure distribution, the transient pressure and the productivity index can be overestimated largely. Therefore, it is very necessary to incorporate the moving boundary conditions in the modeling of non-Darcy seepage flow with the threshold pressure gradient. The study in the paper definitely provides solid theoretical basis of fluid mechanics for the relevant engineering applications in the development of heavy oil reservoirs and low-permeable reservoirs in petroleum engineering and in the development of water resources in low-permeable formations in hydraulic engineering.

Coupled Viscous Fluid Flow and Joint Deformation Analysis for Grout Injection in a Rock Joint

Fluid flow modeling is a major area of interest within the field of rock mechanics. The main objective of this study is to gain insight into the performance of grout injection inside jointed rock masses by numerical modeling of grout flow through a single rock joint. Grout flow has been widely simulated using non-Newtonian Bingham fluid characterized by two main parameters of dynamic viscosity and shear yield strength both of which are time dependent. The increasing value of these properties with injection time will apparently affect the parameters representing the grouting performance including grout penetration length and volumetric injection rate. In addition, through hydromechanical coupling a mutual influence between the injection pressure from the one side and the joint opening/closing behavior and the aperture profile variation on the other side is anticipated. This is capable of producing a considerable impact on grout spread within the rock joints. In this study based on the Bingham fluid model, a series of numerical analysis has been conducted using UDEC to simulate the flow of viscous grout in a single rock joint with smooth parallel surfaces. In these analyses, the time-dependent evolution of the grout fluid properties and the hydromechanical coupling have been considered to investigate their impact on grouting performance. In order to verify the validity of these simulations, the results of analyses including the grout penetration length and the injection flow rate were compared with a well-known analytical solution which is available for the simple case of constant grout properties and non-coupled hydraulic analysis. The comparison demonstrated that the grout penetration length can be overestimated when the time-dependent hardening of grout material is not considered. Moreover, due to the HM coupling, it was shown that the joint opening induced by injection pressure may have a considerable increasing impression on the values of penetration length and injected grout volume.

Effect of cone lift rate on the flow time of self-compacting concrete

A wide range of normal-strength self-compacting concrete (SCC) mixes ranging in compressive strength from 30 to 80 MPa with a maximum aggregate size of 20 mm were prepared in the laboratory, and the time taken by the flow to reach the spread diameter of 500 mm (t500) and to stop (tstop) of each mix in the slump cone flow test were recorded. The entire test was then numerically simulated from the moment the cone was lifted until the flow stopped, using a three-dimensional meshless smoothed particle hydrodynamics computational approach, treating the SCC mix as a non-Newtonian Bingham fluid. The aim was to investigate the effect of the cone lift rate on the flow pattern and t500. The results demonstrate that an increase in the cone lift rate from 0·1 to 0·5–0·7 m/s (i.e. cone raised to a height of 300 mm in 3 to 0·6–0·43 s depending on the cube compressive strength) leads to a significant reduction in t500, but the rate of reduction slows considerably when the cone lift rate is increased beyond 0·5–0·7 m/s (i.e. cone raised to 300 mm in under 0·6–0·43 s). This bilinear reduction in t500 with the increase in the cone lift rate was observed for all mixes having a cube compressive strength in the range 30–80 MPa.

Estimation of the yield stress and distribution of large aggregates from slump flow test of self-compacting concrete mixes using smooth particle hydrodynamics simulation

A wide range of normal strength self-compacting concrete (SCC) mixes with a maximum aggregate size (g) of 20 mm ranging in compressive strength from 30 to 80 MPa were prepared in the laboratory, and the times t500 and tstop of each mix were recorded in the slump flow test. The entire cone flow test was then simulated from the moment the cone was lifted until the mix stopped to flow using the three-dimensional mesh-less smoothed particle hydrodynamics computational approach, treating the SCC mix as a non-Newtonian Bingham fluid. This numerical simulation had two aims. First, to investigate whether the yield stress τy of the mix could be accurately estimated from the measured t500 and tstop times knowing the plastic viscosity of the mix. The latter was estimated by a micromechanical procedure. Second, to compare the distribution of coarse aggregate particles larger than or equal to 8 mm in the cone spread after it stopped to flow as revealed by the numerical simulation with the distribution of the aggregate particles of the corresponding sizes in the cut sections of the cured test cone spread. The large coarse aggregate particles in the size ranges (8 ≤ g < 12, 12 ≤ g < 16, 16 ≤ g < 20 and g ≥ 20 mm) of the test SCC mixes were color coded with non-toxic non-water soluble paints so that the outlines of the aggregate particles could be clearly distinguished in the cut sections of the hardened cone spread and compared with the numerical simulations. It is shown that both aims of the investigations were successfully attained.

Hall Effects on unsteady MHD flow of a Non-Newtonian fluid through a Porous medium with uniform suction and injection

In this Paper we discussed the unsteady magneto hydro dynamic flow of an electrically conducting viscous incompressible non-Newtonian Bingham fluid through a porous medium bounded by two parallel non- conducting porous plates with heat transfer considering the hall current effects into account. The fluid is driven by a uniform pressure gradient parallel to the channel plates and the entire flow field is subjected to a uniform magnetic field of strength Ho with the normal to the boundaries in the transverse xz-plane. An external uniform magnetic field is applied perpendicular to the plates and the fluid motion is subjected to a uniform suction and injection. The lower plate is stationary and the upper plate moves with a constant velocity and the two plates are kept at different but constant temperatures. Numerical solutions are obtained for the governing momentum and energy equations taking the Joule and viscous dissipations into consideration. The effects of the Hall term, the parameter describing the non-Newtonian behaviour, and the velocity of suction and injection on both the velocity and temperature distributions is studied.

Carbonyl iron suspension with halloysite additive and its magnetorheology

The magnetorheological (MR) characteristics of a micron-sized soft magnetic carbonyl iron-based MR fluid were examined using halloysite nanoclay mineral, as an additive. The flow curves measured from a rotational rheometer revealed non-Newtonian Bingham fluid behavior under an applied magnetic field. The sedimentation of the MR fluid with and without the halloysite additive was also measured using a Turbiscan. It was found that the added rod-like hollow nanotubular-structured halloysite improved the sedimentation problem despite the decrease in MR behavior, as determined from the significant decrease in sedimentation rate.

Viscosity evaluation of SCC based on flow simulation in the L-box test

Recent interest in self-compacting concrete (SCC) has increased as more structures around the world are now incorporating SCC where there is need to fill the framework and encapsulate the reinforcement without any mechanical consolidation. Fresh SCC flows under its own weight to fill the formwork completely and self-compacts without any segregation and blocking. To gain a better understanding of SCC properties and their effects on the passing ability of SCC, the present work aimed to simulate numerically the SCC flow in the L-box test. As concrete flow in the L-box test is a free surface flow with large deformations, a smooth particle hydrodynamics (SPH) method was used for the simulation. SCC was assumed as a non-Newtonian Bingham fluid where the shear-strain rate ratio was linear and characterised by viscosity and yield stress. The flow simulation for two kinds of concrete (SCC and high performance concrete) were numerically conducted using the SPH method and the results were compared with the experimental data. To propose the appropriate viscosity-yield stress range for SCC, a comprehensive parametric study was carried out considering different viscosities and yield stresses. The results showed that concrete with viscosity between 50 Pa s and 270 Pa s can be considered as SCC.

On the effectiveness of viscous dissipation and Joule heating on steady MHD flow and heat transfer of a Bingham fluid over a porous rotating disk in the presence of Hall and ion-slip currents

The combined effects of viscous dissipation and Joule heating on steady magnetohydrodynamics (MHD) flow of an electrically conducting viscous incompressible non-Newtonian Bingham fluid over a porous rotating disk in the presence of Hall and ion-slip currents is studied. An external uniform magnetic field is applied in the z-direction and the fluid is subjected to uniform suction. Numerical solutions are obtained for the governing momentum and energy equations. Results for the details of the velocity as well as temperature are shown graphically and the numerical values of the skin friction and the rate of heat transfer are entered in tables.

Unsteady MHD flow of a dusty non-Newtonian Bingham fluid through a circular pipe

In this paper, the transient magnetohydrodynamic (MHD) flow of a dusty incompressible electrically conducting non-Newtonian Bingham fluid through a circular pipe is studied taking the Hall effect into consideration. A constant pressure gradient in the axial direction and an uniform magnetic field directed perpendicular to the flow direction are applied. The particle-phase is assumed to behave as a viscous fluid. A numerical solution is obtained for the governing nonlinear equations using finite differences.

Hall effect on unsteady MHD Couette flow and heat transfer of a Bingham fluid with suction and injection

The unsteady magnetohydrodynamic flow of an electrically conducting viscous incompressible non-Newtonian Bingham fluid bounded by two parallel non-conducting porous plates is studied with heat transfer considering the Hall effect. An external uniform magnetic field is applied perpendicular to the plates and the fluid motion is subjected to a uniform suction and injection. The lower plate is stationary and the upper plate moves with a constant velocity and the two plates are kept at different but constant temperatures. Numerical solutions are obtained for the governing momentum and energy equations taking the Joule and viscous dissipations into consideration. The effect of the Hall term, the parameter describing the non-Newtonian behavior, and the velocity of suction and injection on both the velocity and temperature distributions are studied.

Hall effect on unsteady MHD Couette flow and heat transfer of a Bingham fluid with suction and injection

The unsteady magnetohydrodynamic flow of an electrically conducting viscous incompressible non-Newtonian Bingham fluid bounded by two parallel non-conducting porous plates is studied with heat transfer considering the Hall effect. An external uniform magnetic field is applied perpendicular to the plates and the fluid motion is subjected to a uniform suction and injection. The lower plate is stationary and the upper plate moves with a constant velocity and the two plates are kept at different but constant temperatures. Numerical solutions are obtained for the governing momentum and energy equations taking the Joule and viscous dissipations into consideration. The effect of the Hall term, the parameter describing the non-Newtonian behavior, and the velocity of suction and injection on both the velocity and temperature distributions are studied.

Creeping flow of a Bingham plastic through axisymmetric sudden contractions with viscous dissipation

The effects of the yield number on the steady, incompressible creeping flow of a non-Newtonian Bingham fluid through a four-to-one axisymmetric sudden contraction is studied numerically. The effects of both the yield and Peclet numbers on the thermal field, created due to the viscous dissipation associated with such flows, are investigated. The results demonstrate the dependency of the flow field on the yield number and the strong influence of both the yield and Peclet numbers on the macroscopic and local characteristics of the thermal field. The heat transfer results indicate the significance of heating via viscous dissipation, especially in the vicinity of the contraction plane at high yield numbers.