258 research outputs found
Analytical solutions for the flow of Carreau and Cross fluids in circular pipes and thin slits
In this paper, analytical expressions correlating the volumetric flow rate to
the pressure drop are derived for the flow of Carreau and Cross fluids through
straight rigid circular uniform pipes and long thin slits. The derivation is
based on the application of Weissenberg-Rabinowitsch-Mooney-Schofield method to
obtain flow solutions for generalized Newtonian fluids through pipes and our
adaptation of this method to the flow through slits. The derived expressions
are validated by comparing their solutions to the solutions obtained from
direct numerical integration. They are also validated by comparison to the
solutions obtained from the variational method which we proposed previously. In
all the investigated cases, the three methods agree very well. The agreement
with the variational method also lends more support to this method and to the
variational principle which the method is based upon.Comment: 27 pages, 6 figure
One-Dimensional Navier-Stokes Finite Element Flow Model
This technical report documents the theoretical, computational, and practical
aspects of the one-dimensional Navier-Stokes finite element flow model. The
document is particularly useful to those who are interested in implementing,
validating and utilizing this relatively-simple and widely-used model.Comment: 46 pages, 1 tabl
Modeling the Flow of Yield-Stress Fluids in Porous Media
Yield-stress is a problematic and controversial non-Newtonian flow
phenomenon. In this article, we investigate the flow of yield-stress substances
through porous media within the framework of pore-scale network modeling. We
also investigate the validity of the Minimum Threshold Path (MTP) algorithms to
predict the pressure yield point of a network depicting random or regular
porous media. Percolation theory as a basis for predicting the yield point of a
network is briefly presented and assessed. In the course of this study, a
yield-stress flow simulation model alongside several numerical algorithms
related to yield-stress in porous media were developed, implemented and
assessed. The general conclusion is that modeling the flow of yield-stress
fluids in porous media is too difficult and problematic. More fundamental
modeling strategies are required to tackle this problem in the future.Comment: 27 pages and 5 figure
Emissivity: A Program for Atomic Emissivity Calculations
In this article we report the release of a new program for calculating the
emissivity of atomic transitions. The program, which can be obtained with its
documentation from our website www.scienceware.net, passed various rigorous
tests and was used by the author to generate theoretical data and analyze
observational data. It is particularly useful for investigating atomic
transition lines in astronomical context as the program is capable of
generating a huge amount of theoretical data and comparing it to observational
list of lines. A number of atomic transition algorithms and analytical
techniques are implemented within the program and can be very useful in various
situations. The program can be described as fast and efficient. Moreover, it
requires modest computational resources.Comment: 20 pages, 0 figures, 0 table
Variational approach for the flow of Ree-Eyring and Casson fluids in pipes
The flow of Ree-Eyring and Casson non-Newtonian fluids is investigated using
a variational principle to optimize the total stress. The
variationally-obtained solutions are compared to the analytical solutions
derived from the Weissenberg-Rabinowitsch-Mooney equation and the results are
found to be identical within acceptable numerical errors and modeling
approximations.Comment: 18 pages, 2 figure
Flow of Navier-Stokes Fluids in Converging-Diverging Distensible Tubes
We use a method based on the lubrication approximation in conjunction with a
residual-based mass-continuity iterative solution scheme to compute the flow
rate and pressure field in distensible converging-diverging tubes for
Navier-Stokes fluids. We employ an analytical formula derived from a
one-dimensional version of the Navier-Stokes equations to describe the
underlying flow model that provides the residual function. This formula
correlates the flow rate to the boundary pressures in straight cylindrical
elastic tubes with constant-radius. We validate our findings by the convergence
toward a final solution with fine discretization as well as by comparison to
the Poiseuille-type flow in its convergence toward analytic solutions found
earlier in rigid converging-diverging tubes. We also tested the method on
limiting special cases of cylindrical elastic tubes with constant-radius where
the numerical solutions converged to the expected analytical solutions. The
distensible model has also been endorsed by its convergence toward the rigid
Poiseuille-type model with increasing the tube wall stiffness.
Lubrication-based one-dimensional finite element method was also used for
verification. In this investigation five converging-diverging geometries are
used for demonstration, validation and as prototypes for modeling
converging-diverging geometries in general.Comment: 31 pages, 9 figures, 2 table
Special Relativity: Scientific or Philosophical Theory?
In this article, we argue that the theory of special relativity, as
formulated by Einstein, is a philosophical rather than a scientific theory.
What is scientific and experimentally supported is the formalism of the
relativistic mechanics embedded in the Lorentz transformations and their direct
mathematical, experimental and observational consequences. This is in parallel
with the quantum mechanics where the scientific content and experimental
support of this branch of physics is embedded in the formalism of quantum
mechanics and not in its philosophical interpretations such as the Copenhagen
school or the parallel worlds explanations. Einstein theory of special
relativity gets unduly credit from the success of the relativistic mechanics of
Lorentz transformations. Hence, all the postulates and consequences of Einstein
interpretation which have no direct experimental or observational support
should be reexamined and the relativistic mechanics of Lorentz transformations
should be treated in education, academia and research in a similar fashion to
that of quantum mechanics.Comment: 12 page
Further validation to the variational method to obtain flow relations for generalized Newtonian fluids
We continue our investigation to the use of the variational method to derive
flow relations for generalized Newtonian fluids in confined geometries. While
in the previous investigations we used the straight circular tube geometry with
eight fluid rheological models to demonstrate and establish the variational
method, the focus here is on the plane long thin slit geometry using those
eight rheological models, namely: Newtonian, power law, Ree-Eyring, Carreau,
Cross, Casson, Bingham and Herschel-Bulkley. We demonstrate how the variational
principle based on minimizing the total stress in the flow conduit can be used
to derive analytical expressions, which are previously derived by other
methods, or used in conjunction with numerical procedures to obtain numerical
solutions which are virtually identical to the solutions obtained previously
from well established methods of fluid dynamics. In this regard, we use the
method of Weissenberg-Rabinowitsch-Mooney-Schofield (WRMS), with our adaptation
from the circular pipe geometry to the long thin slit geometry, to derive
analytical formulae for the eight types of fluid where these derived formulae
are used for comparison and validation of the variational formulae and
numerical solutions. Although some examples may be of little value, the
optimization principle which the variational method is based upon has a
significant theoretical value as it reveals the tendency of the flow system to
assume a configuration that minimizes the total stress. Our proposal also
offers a new methodology to tackle common problems in fluid dynamics and
rheology.Comment: 31 pages, 7 figure
Using the stress function in the flow of generalized Newtonian fluids through pipes and slits
We use a generic and general numerical method to obtain solutions for the
flow of generalized Newtonian fluids through circular pipes and plane slits.
The method, which is simple and robust can produce highly accurate solutions
which virtually match any analytical solutions. The method is based on
employing the stress, as a function of the pipe radius or slit thickness
dimension, combined with the rate of strain function as represented by the
fluid rheological constitutive relation that correlates the rate of strain to
stress. Nine types of generalized Newtonian fluids are tested in this
investigation and the solutions obtained from the generic method are compared
to the analytical solutions which are obtained from the
Weissenberg-Rabinowitsch-Mooney-Schofield method. Very good agreement was
obtained in all the investigated cases. All the required quantities of the flow
which include local viscosity, rate of strain, flow velocity profile and
volumetric flow rate, as well as shear stress, can be obtained from the generic
method. This is an advantage as compared to some traditional methods which only
produce some of these quantities. The method is also superior to the numerical
meshing techniques which may be used for resolving the flow in these systems.
The method is particularly useful when analytical solutions are not available
or when the available analytical solutions do not yield all the flow
parameters.Comment: 15 pages, 2 figures, 2 tables. arXiv admin note: text overlap with
arXiv:1503.0126
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