Bingham Fluid Flow Research Articles

The isolated effect of yield stress in viscoplastic turbulent flow

Turbulent flows of viscoplastic fluids are present in several industrial and natural applications. The effects of yield stress on this problem have always been studied as a part of a larger physical context, because real viscoplastic materials have many properties that cannot be easily isolated. Direct numerical simulations have recently emerged as a viable tool for investigating non-Newtonian fluid flow in turbulent regimes. In the present work, we solve the turbulent flow of an ideal Bingham fluid, focusing on the isolated effect of yield stress. A numerical scheme for viscoplastic flows was implemented based on the lattice Boltzmann method. An outstanding characteristic of this scheme is the possibility of representing infinite viscosity by setting the relaxation frequency to zero, enabling the representation of the Bingham constitutive equation without artifacts, and producing a more accurate representation of the yield surfaces. In the turbulent channel flow simulations, the friction Reynolds number was fixed at 180, while the Bingham number varied from 0 (Newtonian) to 0.15. It is shown that unyielded portions of material travel along with the flow near the centerline. These unyielded spots do not disappear quickly, but rather have a significant lifetime. Another interesting outcome is that the yield stress increases the turbulence anisotropy, by lowering the spanwise and normal velocity fluctuations, while the streamwise component becomes higher. Reynolds stresses and budgets of turbulent kinetic energy have been analyzed regarding the increased bulk velocities that were found by increasing the yield stress.

Numerical computations of MHD mixed convection flow of Bingham fluid in a porous square chamber with a wavy cylinder

This work examines the behavior of Bingham fluids in porous media under magnetohydrodynamic (MHD) conditions, addressing a significant issue in fluid dynamics and heat transport. The authors study mixed convection in a porous square chamber with twisted cylinders using COMSOL Multiphysics and finite element techniques. Compared to other research, this one offers a more complicated and realistic model since it integrates Bingham fluid flow and MHD effects in a porous chamber with wavy cylinders. Plotting of streamlines, isotherms, and Nusselt numbers is done for several parameters: Numbers Reynolds (1, 5, 10, 50), Hartmann (0, 25, 50, 100), Bingham (0, 1, 5, 10), Darcy (10−4, 10−3, 10−2, 10−1), and Grashof (102,103,104,105) are among those assigned numbers. According to findings, larger Bn values promote thermal stratification and decrease flow mobility, which results in dominating conductive heat transmission. The nusselt number falls with Ha and Bn but rises with Re, Da, and Gr. The study aims to provide useful insights into several industrial disciplines, such as nuclear power plant architecture and petroleum engineering, by enhancing heat transfer in non-Newtonian fluids under magnetic fields. It also boosts the efficiency of chemical reactors and filters. Based on our findings, for lower Re = 1, the lowest value of Numean is 2.602, while at Re = 50, its values rise to 6.425.

Lattice Boltzmann simulations of unsteady Bingham fluid flows

Transient flows of viscoplastic fluids have very peculiar characteristics. The startup and cessation flows of viscoplastic materials have been subject to many theoretical and numerical investigations. The most challenging aspect of numerical solutions of viscoplastic fluids is the viscosity singularity during the transition from yielded to unyielded material. Hence, the proper representation of yield surfaces is the most critical aspect of numerical methods in viscoplastic fluid flow. In the present work, we use a lattice Boltzmann scheme to solve an ideal Bingham fluid’s startup and cessation flows. This numerical scheme advantage is that can represent infinite viscosity without noticeable numerical instabilities, producing yield surfaces with more accuracy and quality. Theoretical solutions for the startup flow are available in the literature. However, it is unclear which is more accurate and what their validity ranges are. Nonetheless, these solutions served as a reference for the present simulations. The overall aspect of the numerical solutions agreed with the theoretical models. The cessation flow of the Bingham fluid was also simulated. Unlike a Newtonian fluid, this type of flow is known to have a finite period until cessation. The simulations correctly reproduced this behavior. The transient yield surfaces matched very well with augmented Lagrangian solutions.

Effect of MHD and radiation on biviscous Bingham fluid flow on Marangoni boundary for heat source/sink with chemical reaction

A significance of Marangoni-driven convective magnetohydrodynamics (MHD) was investigated in a planned study. The present study examines the impact of radiation and chemical reactions on the two dimensional boundary layer flow of bi-viscous Bingham fluid on a thermosolutal Marangoni boundary with magnetic field and heat source/sink. The physical flow problem is mathematically modelled into Navier–Stokes equations. These nonlinear partial differential equations are then mapped into a set of nonlinear ordinary differential equations using similarity transformation. The elegant analytical method is used to obtain analytic approximations for the resulting system of nonlinear differential equations. The analytical solution for the temperature and concentration profiles is expressed in terms of Kummer's confluent hypergeometric function. The features of flow characteristics such as velocity, temperature, and concentration profiles in response to the variations of the emerging parameters are simulated and examined with a physical explanation through graphs. Surface tension is considered to be corresponding to heat and mass. The results reveal that the velocity profile decreases with increasing the magnetic field, while the Marangoni number value increases with increasing the velocity profile. Moreover, the temperature profile rises with rising the radiation parameter and whereas the value chemical reaction parameter upsurges with decline concentration profile. The present problem has great interest due to its applications in industrial applications such as drying of silicon wafers, thin layers of paint, glues, in heat exchangers, crystal growth in space, biological fluids, blood, synovial liquids, plasma, lubricants, many pharmaceutical products, proteins, sewage sludge, china clay, and many more.

Migration of particles suspended in yield stress fluids: Insights from numerical simulation of pipe flow of 3D printable concrete

In this work, we present a numerical model to analyse particle migration and its impact on local rheological properties when a high-yield stress suspension like 3D printable concrete is transported through a narrow circular pipe. The particle migration is studied through the lens of suspension rheology, where the effect of local particle concentration on rheological properties is accounted for using Krieger–Dougherty-type models. 3D printable mixtures with different aggregate-to-binder (a/b) ratios and flows at various discharge rates are evaluated. It is observed that, depending on the discharge rate and a/b ratio, the flow behaviour could deviate from that expected in a Poiseuille flow of Bingham fluid owing to shear-induced particle migration. Interestingly, as a consequence of particle migration, the formation of a local unsheared region close to the pipe wall is observed, apart from the plug zone at the pipe centre in the partially unsheared pipe flow of Bingham fluids. Often, for concrete pipe flow simulation, the particle size is not small enough to warrant local treatment since the finite size of the particle is not fully reflected in the flow domain. In this work, the developed numerical model is also extended to account for the finite particle size to study the transition between the sheared and unsheared regions and assess the effect of considering finite size in our simulation. Finally, the model’s capability to predict global pressure loss in pipe flow is assessed through comparisons with experimental results.

Optimization of entropy and heat transfer in a magnetohydrodynamic marangoni convection flow of biviscosity bingham hybrid nanofluid through convergent channel

This study examines the entropy generation and heat transfer performance in a Jeffrey-Hamel flow of biviscosity Bingham fluid with the addition of Al2O3 and Cu nanomaterials in the presence of a thermal Marangoni convective process. An emerging Jeffrey-Hamel problem is extended with the implementation of the Bingham fluid stress tensor in a Naiver Stokes equation. The governing equations with Marangoni boundary conditions due to surface tension are solved computationally utilizing the Keller-Box methodology. The findings demonstrate the complex interplay of entropy production processes, fluid-solid interfaces, and thermal Marangoni convection. Findings demonstrated that increasing Marangoni, Bingham parameters, and thermal radiation enhances the rate of heat transmission. The influence of the Marangoni and Bingham parameters on skin friction is conflicting in a narrow channel. System entropy and flow field uplift with a higher Marangoni convection parameter. Increasing the Reynolds number significantly increases the drag force, whereas the effect of the magnetic variable is the reverse. Velocity is an increasing function of the Reynolds and Bingham parameters and deteriorates with the load of nanomaterials. Temperature is a rising function of nanomaterial load, Eckert, and Bingham parameter. The results of this investigation have important ramifications for improving heat transfer, coolant systems, and nozzles design.

Heat Transfer Analysis of Bingham Fluid Flow in the Entrance Region of Concentric Annuli with Outer Cylinder Rotating

Heat Transfer Analysis of Bingham Fluid Flow in the Entrance Region of Concentric Annuli with Outer Cylinder Rotating

Influence of the imposed flow rate boundary condition on the flow of Bingham fluid in porous media

Influence of the imposed flow rate boundary condition on the flow of Bingham fluid in porous media

Precision calculation of the entrance length for laminar flow of Bingham fluid between parallel plates with yield number from 0 to 1000

An estimate of the entrance length for a Bingham fluid flowing between parallel plates is needed in engineering applications. The dimensionless entrance length is a function of yield number. The primary objective of this study was to construct plots of dimensionless entrance length vs. yield number that could be used by practitioners for a quick estimation of the entrance length in a Bingham fluid entering between parallel plates, in a range of yield numbers from 0 to 1000. Three well-known calculation methods were used. The methods were found to yield mutually consistent results. A secondary objective of this study was to examine the sensitivity of the calculated entrance length to the value of a dimensionless parameter somewhat arbitrary chosen during the calculations. This parameter specifies the dimensionless value of the unyielded core velocity that is accepted as the core velocity at the end of the entrance region. In all three calculation methods, the entrance length was found to have a noticeable sensitivity to the variation of this parameter. The least sensitive method was the one based on the momentum integral solution. The findings necessitate further, more fundamental research on the entrance length in non-Newtonian fluids.

Modeling slip flow of Bingham fluid induced by a porous revolving disk with viscous dissipation and Joule heating effects

Modeling slip flow of Bingham fluid induced by a porous revolving disk with viscous dissipation and Joule heating effects

Analysis of the Effect of Peristaltic Transport Flux on Channel Wall: Bingham Fluid as A Model

This study is concerned with analyzing the peristaltic flow of Bingham fluid through an irregular tube with a short wavelength “relative to channel width” and using the governing equations of Bingham fluid in the Navier-Stokes equations in the Cartesian coordinate system. Significant results of the problem were obtained and analyzed using the Wolfram-Mathematica Computational Notebook.

Flow of Bingham fluid through a three dimensional thin layer

The paper is devoted to the study of asymptotic behavior of the solution of three dimensional steady flow of Bingham fluid through a three dimensional thin layer with Dirichlet boundary conditions. We are interested in the asymptotic behavior, to this aim we prove some convergence results concerning the velocity and pressure when the thickness tends to zero. The limit problem obtained after transforming the original problem into one posed over a fixed reference domain and the parameter representing the thickness of the layer tend to zero is studied. The lower-dimensional constitutive law and the differential equation satisfied by the limit variables in the non rigid zone are obtained. In addition, the uniqueness of limit solution has been also established. Existence and uniqueness results and a lower-dimensional constitutive law are obtained. An identical study of a two-dimensional problem yields a one dimensional model prevalent in engineering literature.

Exact Solution of Tank Drainage for Bingham Fluid flow circular tube

Unsteady tank drainage of Bingham Plastic fluid whose flow of the fluid is due to gravity, is considered in this study. The separation of variables method is used to obtain the exact solution of the fluid. Due to very high yield stress of the fluid no slip condition is used to find out the velocity profile of the fluid. The primary objective of this work is to find the velocity profile, flow rate, shear stress, average velocity, time efflux, the relationship between the time (varying with the depth of a tank) and the time required for complete drainage from emerging partial differential equation. It has been observed that when the Bingham model parameters, flow region and pipe length increase, the time required to drain the fluid from the tank also increases. Furthermore, findings indicate that higher density and a larger pipe radius result in quicker drainage of Bingham plastic fluid from the circular tank.

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.

Similarity relations for laminar pipe flows of Bingham fluids in friction coordinates

Similarity relations for laminar pipe flows of Bingham fluids in friction coordinates

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.

Physics-Informed Neural Networks for Bingham Fluid Flow Simulation Coupled with an Augmented Lagrange Method

As a class of non-Newtonian fluids with yield stresses, Bingham fluids possess both solid and liquid phases separated by implicitly defined non-physical yield surfaces, which makes the standard numerical discretization challenging. The variational reformulation established by Duvaut and Lions, coupled with an augmented Lagrange method (ALM), brings about a finite element approach, whereas the inevitable local mesh refinement and preconditioning of the resulting large-scaled ill-conditioned linear system can be involved. Inspired by the mesh-free feature and architecture flexibility of physics-informed neural networks (PINNs), an ALM-PINN approach to steady-state Bingham fluid flow simulation, with dynamically adaptable weights, is developed and analyzed in this work. The PINN setting enables not only a pointwise ALM formulation but also the learning of families of (physical) parameter-dependent numerical solutions through one training process, and the incorporation of ALM into a PINN induces a more feasible loss function for deep learning. Numerical results obtained via the ALM-PINN training on one- and two-dimensional benchmark models are presented to validate the proposed scheme. The efficacy and limitations of the relevant loss formulation and optimization algorithms are also discussed to motivate some directions for future research.

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.

Theoretical Approach to Predicting the Diffusion Radius of Fracture Grouting in Soil–Rock Mixtures

Previously conducted studies have established that the soil–rock mixture in the Chongqing area has the characteristics of loose structure, poor stability, strong permeability, and so on. When building a tunnel in a soil–rock mixture stratum, it is necessary to reinforce the surface rock mass and surrounding rock by grouting to improve the safety of tunnel excavation. To study the diffusion mechanism of cement slurry (Bingham fluid) in soil–rock mixtures, based on the Bingham fluid flow equation and slurry diffusion model, the Bingham fluid fracture diffusion formula was derived, and field grouting tests and indoor model tests were carried out with soil–rock mixtures in the Chongqing area as the research object. The fracture grouting diffusion formula was verified and analyzed using the test data. The research results show that the theoretical calculation results of various working conditions are close to the actual test results (the error of indoor model test results is less than 3%, and the error of field test results is less than 5%). A Bingham fluid fracture diffusion formula has been developed that applies to various working conditions of fracture grouting of soil–rock mixtures and has a good prediction effect on the value of the fracture diffusion radius.

Study of multilayer flow of a bi-viscous Bingham fluid sandwiched between hybrid nanofluid in a vertical slab with nonlinear Boussinesq approximation

Bi-viscosity Bingham plastic fluids are used to understand the rheological characteristics of pigment–oil suspensions, polymeric gels, emulsions, heavy oil, etc. In many industrial and engineering problems involving high-temperature situation, a linear density-temperature variation is inadequate to describe the convective heat transport. Therefore, the characteristics of the nonlinear convective flow of a bi-viscous Bingham fluid (BVBF) through three layers in a vertical slab are studied. The two outer layers of the oil-based hybrid nanofluid and the intermediate layer of BVBF are considered. The thermal buoyancy force is governed by the nonlinear Boussinesq approximation. Continuity of heat flux, velocity, shear stress, and temperature are imposed on the interfaces. The governing equations are derived from the Navier–Stokes equation, conservation of energy, and conservation of mass for three layers. The nonlinear multi-point (four-point) boundary value problem is solved using the differential transform method (DTM). Converging DTM solutions are obtained, and they are validated. The entropy equation and Bejan number were also derived and analyzed. It is established that the nonlinear density–temperature variation leads to a significant improvement in the magnitude of the velocity and temperature profiles due to the increased buoyancy force, and as a result, the drag force on the walls gets reduced. The drag force on the slab gets reduced by decreasing the volume fraction of nanoparticles. Furthermore, nonlinear convection and mixed convection give rise to an advanced rate of heat transport on the walls and thereby to an enhanced heat transport situation.