An electrical network for the numerical solution of transient mhd couette flow of a dusty fluid: Effects of variable properties and hall current

The Network Simulation Method (NSM) has been used to study the variations with velocity of suction, hall effect, Reynolds and Hartmann number, particle concentration and Eckert number on the unsteady MHD Couette Flow and heat transfer of a dusty and electrically conducting fluid between parallel plates in the presence of an external uniform magnetic field and uniform suction and injection. The solutions are obtained with the network model proposed and the electric circuit simulation program PSpice. The fluid is acted upon by a constant pressure gradient and an external uniform magnetic field is applied perpendicular to the plates. Due to the presence of uniform suction and injection, the Hall Effect is not dismissed. The NSM is applied to solve the steady-state and transient problems of flow and heat transfer for both the fluid and dust particles. This method requires only discretization of the spatial co-ordinates, while time remains a real continuous variable. Velocity and temperature are studied for different values of the viscosity and magnetic field parameters and for different particle concentrations and upper wall velocities.     

Stability of ferrofluid flow between concentric rotating cylinders with an axial magnetic field

A linear stability analysis for the ferrofluid flow between two concentric rotating cylinders in the presence of an axial magnetic field is implemented in this study. Both of the wide-gap and small-gap cases are considered and the governing equations with respect to three-dimensional disturbances including axisymmetric and non-axisymmetric modes are derived and solved by a direct numerical procedure. A parametric study covering wide ranges of ?, the volume fraction of colloidal particles; ξ, the strength of axial magnetic field; μ, the ratio of angular velocity of the outer cylinder to that of the inner cylinder; and ε, the ratio of radius of the inner cylinder to that of the outer cylinder, is conducted. Results show that the stability characteristics depend heavily on these factors. It is found that the increases of ? and ξ, and decrease of ε tend to stabilize the basic flow for an assigned value of μ. The variations of the onset mode with these parameters are discussed in detail. An example for the practical application of present results is given to help the understanding of stability behaviour of this flow.     

Nonequilibrium molecular dynamics of liquid crystals

During the last 15 years, noneyuilibrium molecular dynamics (NEMD) has been successfully applied to study transport phenomena in fluids that are isotropic at equilibrium. A natural extension is therefore to study liquid crystals, which are anisotropic al equilibrium. The lower symmetry of these systems means that the linear transport coefficients are considerably more complicated than in an isotropic system. Part of the reason for this is that there are crosscouplings between tensors of different rank and parity. Such couplings arc symmetry-forbidden in isotropic phases. In this paper. we review some of fundamental theoretical results we have derived concerning the rheology of liquid crystals. report NEMD simulations of thermal conductivity and shear viscosity of liquid crystals, and present NEMD simulations of shear cessation phenomena. All of the NEMD results are presented for a model liquid crystal fluid which is a modification of the Gay-Borne fluid. The results obtained are in qualitative agreement with experimental measurements on liquid crystal systems.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

拟压缩性方法在非定常球形Couette—Taylor流模拟中的应用

本文以拟压缩性法和物理时间／伪时间双重时间推进，数值求解非定常不可压缩流Ｎ－Ｓ方程。拟压缩性英是对伪时间的导数项，在每一物理时间层，进行对伪时间的推进使拟压缩性项趋于零，从而使连续方程得到满足。用Ｌｏｗｅｒ－Ｕｐｐｅｒ ＳｙｍｍｅｔｒｉｃＧａｕｓｓ－Ｓｅｉｄｅｌ格式求解用所得的方程。针对前人ＬＵ－ＳＧＳ格式未计及陷式物理粘性，在计算中低Ｒｅ数流动时容易发散或造成收敛率低的问题，利用简化的隐式粘性     

Hydromagnetic stability of dissipative couette flow: Wide-gap problem

A numerical solution to the eigenvalue problem of MHD stability of Couette flow between concentric rotating cylinders with nonconducting walls, is presented here. The numerical values of the critical Taylor number, Ta_c, and the critical wave number, a_c are listed in a table for different values of η (ratio of the two radii), μ (ratio of the angular velocities of the two cylinders) and Q, the magnetic field parameter. It is observed that, owing to an increase in the gap-width, Ta_c decreases or the flow becomes destabilized. a_c increases with increasing Q and μ < 0, but decreases when μ > 0 and by increasing the width between two cylinders.     

Numerical Simulation of Sterilization Processes for Shear‐Thinning Food in Taylor‐Couette Flow Systems

The performance of the Taylor‐Couette flow apparatus as a heat sterilizer is numerically investigated. The destruction of Clostridium botulinum and thiamine (vitamin B1) was selected as model reaction. When Taylor vortices were formed in the annular space, the heat transfer significantly enhanced as compared to the case without vortex flow. As a result, the equivalent lethality calculated from the temperature field increased, which is regarded as a quantum leap. Conversely, the improvement of heat transfer induced destruction of thiamine. These results suggest that there is a trade‐off relationship between the enhancement of heat transfer and the avoidance of thermal destruction of nutritional components. In conclusion, the Taylor‐Couette flow sterilizer has the potential for process intensification in heat sterilization processes.     

Modeling rheological behavior of bentonite suspensions as Casson and Robertson-Stiff fluids using Newtonian and true shear rates in Couette viscometry

The Casson model and the Robertson-Stiff model have been used to determine whether they can describe the rheology of aqueous bentonite suspensions. The assessment utilized a total of twelve sets of experimental viscometric data from literature and from this work. Equations have been presented which allowed the determination of the true shear rates experienced by the fluids within the gap of the rotational viscometer for both rheological models. Non-linear regression has been applied to determine the two rheological parameters for the Casson model and the three rheological parameters for the Robertson-Stiff model using true shear rates and Newtonian shear rates, which are used most often in the analysis of rheometric data. The results showed that both models describe well the experimental data of these bentonite suspensions with good statistical indicators. Furthermore, analysis showed that true shear rates are always higher than Newtonian shear rates for both models. The differences depend on the particular suspension and are larger at low shear rates while they become smaller at higher shear rates indicating that the fluid behavior approaches Newtonian behavior at higher shear rates. The shapes of the rheograms remained essentially unchanged indicating that the rheological parameters determined with the use of true shear rates are very similar to the rheological parameters determined with the use of Newtonian shear rates. This was further confirmed with the computation of the rheological parameters for both models and both approaches. For the Casson model differences in the yield value computed with true shear rates were at most at 7% while for the plastic viscosity at 3%. For the Robertson-Stiff model, differences of the order of 2 to 5% were observed for the K-values, of 7% for γ˙₀-values while no differences were observed for the n-values. These small differences, however, do not justify use of Newtonian shear rates when analytical solutions exist which allow use of true shear rates without any compromise.     

Basic viscoelastic fluid flow problems using the Jeffreys model

Using Laplace transformation technique, semi-analytical solutions are obtained for three basic viscoelastic fluid flow problems under the effect of the Jeffreys model. These semi-analytical solutions are not available in the literature. The present work investigates the effect of two types of driving forces on the flow behavior. These two types are the velocity-type and shear-type driving forces. The effect of the relaxation and retardation times on the flow behavior for these two types of driving forces may be viewed well using the obtained semi-analytical solutions. The three fundamental problems are transient Couette flow, transient wind-driven flow over finite domains and the transient Poiseuille flow in parallel-plates channels. It is shown that as the dimensionless relaxation time (λ₁) increases, the flow response to the imposed driving force becomes slower. This implies that the flow needs more time to feel the presence of the driving force and hence needs more time to attain steady-state behavior. On the other hand, the effect of the dimensionless retardation time (λ₂) depends on the type of the driving force imposed on the system. For a velocity-type driving force, the flow response becomes faster as the dimensionless retardation time (λ₂) increases and for a shear-type driving force the flow response becomes slower as the dimensionless retardation time (λ₂) increases.     

Continuous separation of molybdenum and zirconium from simulated high-level liquid waste with a Taylor–Couette contactor

Reprocessing of spent nuclear fuels generates high-level liquid waste (HLLW) which undergoes vitrification into borosilicate glass before final geological disposal. To ensure the quality of the glass, control of the concentration of chemical species such as molybdenum (Mo), which has an adverse impact on the vitrification process, is critical. Also, zirconium (Zr) can cause crud in washing process and Zr-93 is a long-lived fission product needed to be separated. In this study, a liquid–liquid countercurrent centrifugal contactor with Taylor–Couette flow (TC contactor) was applied to practical multi-species cases. Continuous separation of Mo and Zr from a simulated HLLW with bis(2-ethylhexyl) phosphoric acid (HDEHP) as extractant has been performed. Among a variety of metals in simulated HLLW, Mo, Zr, Y, and Fe are extractable, Mo and Zr were separated from HLLW by equilibrium, and Fe/Y separation was achieved by the effect of non-equilibrium state in TC contactor. Addition of tributyl phosphate could improve extraction of Mo. This study has expanded the scope of the TC contactor to multi-species separation processes.     

The effect of particle shape on simple shear flows

Simple shear flows, (without gravity force and implemented using periodic boundary conditions or in Couette flow configurations with gravity) have been the subject of study using DEM simulation for more than two decades. Earlier studies explored the effect of attributes such as shear rate, particle size and domain scale on the distribution of the particles in the flow, velocity profiles and the stress distributions. These studies were conducted using simple shapes for the particles such as spheres. In recent years, the importance of particle shape on flow has been recognized in a range of industrial application including mixing, comminution, hopper discharge and chute flows. In this paper, we return to the simple shear flows and quantitatively explore the effect of particle shape on velocity, volume fraction, granular temperature and stress distributions across the channel. Particle shape is found to sharply increase the strength of the material making it stronger and harder to shear. The generation of particle spin throughout the flow of non-circular particles leads to high granular temperatures, dilative pressures and lower solid fractions in the core of the flow. For aspect ratios between 0.6 and 0.5, a transition in the effective behaviour of the wall boundary conditions is identified. The connections of shape to spin, to granular temperature, to bulk flow changes are elaborated.