Numerical Study of Bubbling Fluidized Beds Operating at Sub-atmospheric Conditions

Fluidization at vacuum pressure has been a topic that is of growing research interest. Several industrial applications (such as drying, extractive metallurgy, and chemical vapor deposition (CVD)) can potentially take advantage of vacuum pressure fluidization. Particularly, the fine chemical industry requires processing under safe conditions for thermolabile substances, and reduced pressure fluidized beds offer an alternative. Fluidized beds under vacuum conditions provide optimal conditions for treatment of granular materials where the reduced gas pressure maintains an operational environment outside of flammability conditions. The fluidization at low-pressure is markedly different from the usual gas flow patterns of atmospheric fluidization. The different flow regimes can be characterized by the dimensionless Knudsen number. Nevertheless, hydrodynamics of bubbling vacuum fluidized beds has not been investigated to author’s best knowledge. In this work, the two-fluid numerical method was used to determine the impact of reduced pressure on the fundamental properties of a fluidized bed. The slip flow model implemented by Ansys Fluent User Defined Functions (UDF) was used to determine the interphase momentum exchange coefficient. A wide range of operating pressures was investigated (1.01, 0.5, 0.25, 0.1 and 0.03 Bar). The gas was supplied by a uniform inlet at 1.5Umf and 2Umf. The predicted minimum fluidization velocity (Umf) shows excellent agreement with the experimental data. The results show that the operating pressure has a notable impact on the bed properties and its hydrodynamics. Furthermore, it also shows that the existing Gorosko correlation that predicts bed expansion is not applicable under reduced pressure conditions.

Analysis of Slip Flow Heat Transfer between Asymmetrically Heated Parallel Plates

In the present study, analysis of heat transfer is carried out in the slip flow region for the fluid flowing between two parallel plates by employing the asymmetric heat fluxes at surface of the plates. The flow is assumed to be hydrodynamically and thermally fully developed for the analysis. The second order velocity slip and viscous dissipation effects are considered for the analysis. Closed form expressions are obtained for the Nusselt number as a function of Knudsen number and modified Brinkman number. The limiting condition of the present prediction for Kn = 0, Kn2 = 0, and Brq1 = 0 is considered and found to agree well with other analytical results.

Two Dimensional Simulation of Fluid Flow and Heat Transfer in the Transition Flow Regime using a Lattice Boltzmann Approach

The significant effects of the interactions between the system boundaries and the near wall molecules in miniaturized gaseous devices lead to the formation of the Knudsen layer in which the Navier-Stokes-Fourier (NSF) equations fail to predict the correct associated phenomena. In this paper, the well-known lattice Boltzmann method (LBM) is employed to simulate the fluid flow and heat transfer processes in rarefied gaseous micro media. Persuaded by the problematic deficiency of the LBM in capturing the Knudsen layer phenomena, present study tends to concentrate on the effective molecular mean free path concept the main essence of which is to compensate the incapability of this mesoscopic method in dealing with the momentum and energy transport within the above mentioned kinetic boundary layer. The results show qualitative and quantitative accuracy comparable to the solutions of the linearized Boltzmann equation or the DSMC data for the Knudsen numbers of O (1) .

Semi-Analytic Solution and Hydrodynamics Behavior of Fluid Flow in Micro-Converging plates

The hydrodynamics behavior of fluid flow in microconverging plates is investigated analytically. Effects of Knudsen number () on the microchannel hydrodynamics behavior and the coefficient of friction are investigated. It is found that as  increases the slip in the hydrodynamic boundary condition increases. Also, the coefficient of friction decreases as  increases.

Effects of Rarefaction and Compressibility on Fluid Flow at Slip Flow Regime by Direct Simulation of Roughness

A two dimensional numerical simulation has been performed for incompressible and compressible fluid flow through microchannels in slip flow regime. The Navier-Stokes equations have been solved in conjunction with Maxwell slip conditions for modeling flow field associated with slip flow regime. The wall roughness is simulated with triangular microelements distributed on wall surfaces to study the effects of roughness on fluid flow. Various Mach and Knudsen numbers are used to investigate the effects of rarefaction as well as compressibility. It is found that rarefaction has more significant effect on flow field in microchannels with higher relative roughness. It is also found that compressibility has more significant effects on Poiseuille number when relative roughness increases. In addition, similar to incompressible models the increase in average fRe is more significant at low Knudsen number flows but the increase of Poiseuille number duo to relative roughness is sharper for compressible models. The numerical results have also validated with some available theoretical and experimental relations and good agreements have been seen.

Direct Simulation Monte Carlo (DSMC) Algorithm – A Comparison of Mathematica Code with FLUENT 6.2 for Low Knudsen Number

A code has been developed in Mathematica using Direct Simulation Monte Carlo (DSMC) technique. The code was tested for 2-D air flow around a circular cylinder. Same geometry and flow properties were used in FLUENT 6.2 for comparison. The results obtained from Mathematica simulation indicated significant agreement with FLUENT calculations, hence providing insight into particle nature of fluid flows.

Particle Simulation of Rarefied Gas Flows witha Superimposed Wall Surface Temperature Gradient in Microgeometries

Rarefied gas flows are often occurred in micro electro mechanical systems and classical CFD could not precisely anticipate the flow and thermal behavior due to the high Knudsen number. Therefore, the heat transfer and the fluid dynamics characteristics of rarefied gas flows in both a two-dimensional simple microchannel and geometry similar to single Knudsen compressor have been investigated with a goal of increasing performance of a actual Knudsen compressor by using a particle simulation method. Thermal transpiration and thermal creep, which are rarefied gas dynamic phenomena, that cause movement of the flow from less to higher temperature is generated by using two different longitude temperature gradients (Linear, Step) along the walls of the flow microchannel. In this study the influence of amount of temperature gradient and governing pressure in various Knudsen numbers and length-to-height ratios have been examined.

A Novel Slip Correction Factor for Spherical Aerosol Particles

A 3D simulation study for an incompressible slip flow around a spherical aerosol particle was performed. The full Navier-Stokes equations were solved and the velocity jump at the gas-particle interface was treated numerically by imposition of the slip boundary condition. Analytical solution to the Stokesian slip flow past a spherical particle was used as a benchmark for code verification, and excellent agreement was achieved. The Simulation results showed that in addition to the Knudsen number, the Reynolds number affects the slip correction factor. Thus, the Cunningham-based slip corrections must be augmented by the inclusion of the effect of Reynolds number for application to Lagrangian tracking of fine particles. A new expression for the slip correction factor as a function of both Knudsen number and Reynolds number was developed.

Transient Hydrodynamic and Thermal Behaviors of Fluid Flow in a Vertical Porous Microchannel under the Effect of Hyperbolic Heat Conduction Model

The transient hydrodynamics and thermal behaviors of fluid flow in open-ended vertical parallel-plate porous microchannel are investigated semi-analytically under the effect of the hyperbolic heat conduction model. The model that combines both the continuum approach and the possibility of slip at the boundary is adopted in the study. The Effects of Knudsen number , Darcy number , and thermal relaxation time  on the microchannel hydrodynamics and thermal behaviors are investigated using the hyperbolic heat conduction models. It is found that as  increases the slip in the hydrodynamic and thermal boundary condition increases. This slip in the hydrodynamic boundary condition increases as  increases. Also, the slip in the thermal boundary condition increases as  decreases especially the early stage of time.

Simulation of Roughness Shape and Distribution Effects on Rarefied and Compressible Flows at Slip Flow Regime

A numerical simulation of micro Poiseuille flow has performed for rarefied and compressible flow at slip flow regimes. The wall roughness is simulated in two cases with triangular microelements and random micro peaks distributed on wall surfaces to study the effects of roughness shape and distribution on flow field. Two values of Mach and Knudsen numbers have used to investigate the effects of rarefaction as well as compressibility. The numerical results have also checked with available theoretical and experimental relations and good agreements has achieved. High influence of roughness shape can be seen for both compressible and incompressible rarefied flows. In addition it is found that rarefaction has more significant effect on flow field in microchannels with higher relative roughness. It is also found that compressibility has more significant effects on Poiseuille number when relative roughness increases.