32 research outputs found
Towards Solving the Navier-Stokes Equation on Quantum Computers
In this paper, we explore the suitability of upcoming novel computing
technologies, in particular adiabatic annealing based quantum computers, to
solve fluid dynamics problems that form a critical component of several science
and engineering applications. We start with simple flows with well-studied flow
properties, and provide a framework to convert such systems to a form amenable
for deployment on such quantum annealers. We analyze the solutions obtained
both qualitatively and quantitatively as well as the sensitivities of the
various solution selection schemes on the obtained solution
Modeling electrospinning process and a numerical scheme using Lattice Boltzmann method to simulate viscoelastic fluid flows
In the recent years, researchers have discovered a multitude of applications
using nanofibers in fields like composites, biotechnology, environmental engineering,
defense, optics and electronics. This increase in nanofiber applications needs
a higher rate of nanofiber production. Electrospinning has proven to be the best
nanofiber manufacturing process because of simplicity and material compatibility.
Study of effects of various electrospinning parameters is important to improve the
rate of nanofiber processing. In addition, several applications demand well-oriented
nanofibers. Researchers have experimentally tried to control the nanofibers using
secondary external electric field. In the first study, the electrospinning process is
modeled and the bending instability of a viscoelastic jet is simulated. For this, the
existing discrete bead model is modified and the results are compared, qualitatively,
with previous works in literature. In this study, an attempt is also made to simulate
the effect of secondary electric field on electrospinning process and whipping instability.
It is observed that the external secondary field unwinds the jet spirals, reduces
the whipping instability and increases the tension in the fiber. Lattice Boltzmann method (LBM) has gained popularity in the past decade as
the method is easy implement and can also be parallelized. In the second part of this
thesis, a hybrid numerical scheme which couples lattice Boltzmann method with finite
difference method for a Oldroyd-B viscoelastic solution is proposed. In this scheme,
the polymer viscoelastic stress tensor is included in the equilibrium distribution function
and the distribution function is updated using SRT-LBE model. Then, the local
velocities from the distribution function are evaluated. These local velocities are used
to evaluate local velocity gradients using a central difference method in space. Next,
a forward difference scheme in time is used on the Maxwell Upper Convected model
and the viscoelastic stress tensor is updated. Finally, using the proposed numerical
method start-up Couette flow problem for Re = 0.5 and We = 1.1, is simulated. The
velocity and stress results from these simulations agree very well with the analytical
solutions
Thermomechanical Constitutive Modeling of Viscoelastic Materials undergoing Degradation
Materials like asphalt, asphalt concrete and polyimides that are used in the transportation and aerospace industry show viscoelastic behavior. These materials in the working environment are subject to degradation due to temperature, diffusion of moisture and chemical reactions (for instance, oxidation) and there is need for a good understanding of the various degradation mechanisms. This work focuses on: 1) some topics related to development of viscoelastic fluid models that can be used to predict the response of materials like asphalt, asphalt concrete, and other geomaterials, and 2) developing a framework to model degradation due to the various mechanisms (such as temperature, diffusion of moisture and oxidation) on polyimides that show nonlinear viscoelastic solid-like response. Such a framework can be extended to model similar degradation phenomena in the area of asphalt mechanics and biomechanics.
The thermodynamic framework that is used in this work is based on the notion that the 'natural configuration' of a body evolves as the body undergoes a process and the evolution is determined by maximizing the rate of entropy production.
The Burgers' fluid model is known to predict the non-linear viscoelastic fluid-like response of asphalt, asphalt concrete and other geomaterials. We first show that different choices for the manner in which the body stores energy and dissipates energy and satisfies the requirement of maximization of the rate of entropy production that leads to many three dimensional models. All of these models, in one dimension, reduce to the model proposed by Burgers.
A thermodynamic framework to develop rate-type models for viscoelastic fluids which do not possess instantaneous elasticity (certain types of asphalt show such a behavior) is developed next. To illustrate the capabilities of such models we make a specific choice for the specific Helmholtz potential and the rate of dissipation and consider the creep and stress relaxation response associated with the model.
We then study the effect of degradation and healing due to the diffusion of a fluid on the response of a solid which prior to the diffusion can be described by the generalized neo-Hookean model. We show that a generalized neo-Hookean solid - which behaves like an elastic body (i.e., it does not produce entropy) within a purely mechanical context - creeps and stress relaxes when infused with a fluid and behaves like a body whose material properties are time dependent.
A framework is then developed to predict the viscoelastic response of polyimide resins under different temperature conditions. The developed framework is further extended to model the phenomena of swelling due to diffusion of a fluid through a viscoelastic solid using the theory of mixtures. Finally, degradation due to oxidation is incorporated into such a framework by introducing a variable that represents the extent of oxidation. The data from the resulting models are shown to be in good agreement with the experiments for polyimide resins
Modeling the Non-linear Viscoelastic Response of High Temperature Polyimides
A constitutive model is developed to predict the viscoelastic response of
polyimide resins that are used in high temperature applications. This model is
based on a thermodynamic framework that uses the notion that the `natural
configuration' of a body evolves as the body undergoes a process and the
evolution is determined by maximizing the rate of entropy production in general
and the rate of dissipation within purely mechanical considerations. We
constitutively prescribe forms for the specific Helmholtz potential and the
rate of dissipation (which is the product of density, temperature and the rate
of entropy production), and the model is derived by maximizing the rate of
dissipation with the constraint of incompressibility, and the reduced energy
dissipation equation is also regarded as a constraint in that it is required to
be met in every process that the body undergoes. The efficacy of the model is
ascertained by comparing the predictions of the model with the experimental
data for PMR-15 and HFPE-II-52 polyimide resins.Comment: 16 pages, 4 figures, submitted to Mechanics of Material
On Modeling the Response of Synovial Fluid: Unsteady Flow of a Shear-Thinning, Chemically-Reacting Fluid Mixture
We study the flow of a shear-thinning, chemically-reacting fluid that could
be used to model the flow of the synovial fluid. The actual geometry where the
flow of the synovial fluid takes place is very complicated, and therefore the
governing equations are not amenable to simple mathematical analysis. In order
to understand the response of the model, we choose to study the flow in a
simple geometry. While the flow domain is not a geometry relevant to the flow
of the synovial fluid in the human body it yet provides a flow which can be
used to assess the efficacy of different models that have been proposed to
describe synovial fluids. We study the flow in the annular region between two
cylinders, one of which is undergoing unsteady oscillations about their common
axis, in order to understand the quintessential behavioral characteristics of
the synovial fluid. We use the three models suggested by Hron et al. [ J. Hron,
J. M\'{a}lek, P. Pust\v{e}jovsk\'{a}, K. R. Rajagopal, On concentration
dependent shear-thinning behavior in modeling of synovial fluid flow, Adv. in
Tribol. (In Press).] to study the problem, by appealing to a semi-inverse
method. The assumed structure for the velocity field automatically satisfies
the constraint of incompressibility, and the balance of linear momentum is
solved together with a convection-diffusion equation. The results are compared
to those associated with the Newtonian model. We also study the case in which
an external pressure gradient is applied along the axis of the cylindrical
annulus.Comment: 25 pages, 11 figures, accepted in Computers & Applications with
Mathematic
Diffusion of a fluid through a viscoelastic solid
This paper is concerned with the diffusion of a fluid through a viscoelastic
solid undergoing large deformations. Using ideas from the classical theory of
mixtures and a thermodynamic framework based on the notion of maximization of
the rate of entropy production, the constitutive relations for a mixture of a
viscoelastic solid and a fluid (specifically Newtonian fluid) are derived. By
prescribing forms for the specific Helmholtz potential and the rate of
dissipation, we derive the relations for the partial stress in the solid, the
partial stress in the fluid, the interaction force between the solid and the
fluid, and the evolution equation of the natural configuration of the solid. We
also use the assumption that the volume of the mixture is equal to the sum of
the volumes of the two constituents in their natural state as a constraint.
Results from the developed model are shown to be in good agreement with the
experimental data for the diffusion of various solvents through high
temperature polyimides that are used in the aircraft industry. The swelling of
a viscoelastic solid under the application of an external force is also
studied.Comment: 26 pages, 7 figures, submitted to International Journal of Solids and
Structure