Abstract: 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.
Abstract: 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.
Abstract: This paper presents a study on the effect of
second-order slip and jump on forced convection through a long
isothermally heated or cooled planar microchannel. The fully
developed solutions of thermal flow fields are analytically obtained on
the basis of the second-order Maxwell-Burnett slip and Smoluchowski
jump boundary conditions. Results reveal that the second-order term in
the Karniadakis slip boundary condition is found to contribute a
negative velocity slip and then to lead to a higher pressure drop as well
as a higher fluid temperature for the heated-wall case or to a lower
fluid temperature for the cooled-wall case. These findings are contrary
to predictions made by the Deissler model. In addition, the role of
second-order slip becomes more significant when the Knudsen
number increases.
Abstract: This paper presents a study on the effect of
second-order slip on forced convection through a long isoflux heated
or cooled planar microchannel. The fully developed solutions of flow
and thermal fields are analytically obtained on the basis of the
second-order Maxwell-Burnett slip and local heat flux boundary
conditions. Results reveal that when the average flow velocity
increases or the wall heat flux amount decreases, the role of thermal
creep becomes more insignificant, while the effect of second-order slip
becomes larger. The second-order term in the Deissler slip boundary
condition is found to contribute a positive velocity slip and then to lead
to a lower pressure drop as well as a lower temperature rise for the
heated-wall case or to a higher temperature rise for the cooled-wall
case. These findings are contrary to predictions made by the
Karniadakis slip model.
Abstract: 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.
Abstract: This work is focused on the steady boundary layer flow
near the forward stagnation point of plane and axisymmetric bodies
towards a stretching sheet. The no slip condition on the solid
boundary is replaced by the partial slip condition. The analytical
solutions for the velocity distributions are obtained for the various
values of the ratio of free stream velocity and stretching velocity, slip
parameter, the suction and injection velocity parameter, magnetic
parameter and dimensionality index parameter in the series forms with
the help of homotopy analysis method (HAM). Convergence of the
series is explicitly discussed. Results show that the flow and the skin
friction coefficient depend heavily on the velocity slip factor. In
addition, the effects of all the parameters mentioned above were more
pronounced for plane flows than for axisymmetric flows.
Abstract: 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.
Abstract: 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.