1,721,041 research outputs found
Surface tension in a reactive binary mixture of incompressible fluids
No full textStruchtrup, Henning; Dold, John. (2000). Surface tension in a reactive binary mixture of incompressible fluids. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/3465
Positivity of entropy production and phase density in approximate solutions of the Boltzmann equation
No full textStruchtrup, Henning; Dold, John. (2000). Positivity of entropy production and phase density in approximate solutions of the Boltzmann equation. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/3467
Twenty-six moment equations for the Enskog–Vlasov equation
Full text linkThe Enskog–Vlasov equation is a phenomenological kinetic equation that extends the Enskog equation for the dense (non-ideal) hard-sphere fluid by adding an attractive soft potential tail to the purely repulsive hard-sphere contribution. Simplifying assumptions about pair correlations lead to a Vlasov-like self-consistent force field that adds to the Enskog non-local hard-sphere collision integral. Within the limitations imposed by the underlying assumptions, the extension gives the Enskog–Vlasov equation the ability to give a unified description of ideal and non-ideal fluid flows as well as of those fluid states in which liquid and vapour regions coexist, being separated by a resolved interface. Furthermore, the Enskog–Vlasov fluid can be arbitrarily far from equilibrium. Thus the Enskog–Vlasov model equation provides an excellent, although approximate, tool for modelling processes with liquid–vapour interfaces and adjacent Knudsen layers, and allows us to look at slip, jump and evaporation coefficients from a different perspective. Here, a set of 26 moment equations is derived from the Enskog–Vlasov equation by means of the Grad moment method. The equations provide a meaningful approximation to the underlying kinetic equation, and include the description of Knudsen layers. This work focuses on the – rather involved – derivation of the moment equations, with only a few applications shown
Evaporation/condensation boundary conditions for the regularized 13 moment equations
Full text linkThe regularized 13 moment equations (R13) are a macroscopic model for the description of rarefied gas flows in the transition regime. The equations have been shown to give meaningful results for Knudsen numbers up to about 0.5. Here, their range of applicability is extended by boundary conditions for evaporating and condensing interfaces, derived from the microscopic interface conditions of kinetic theory. Simple 1-D problems are used to test the R13 equations with evaporation and condensation
Evaporation boundary conditions for the R13 equations of rarefied gas dynamics
Full text linkThe regularized 13 moment (R13) equations are a macroscopic model for the description of rarefied gas flows in the transition regime. The equations have been shown to give meaningful results for Knudsen numbers up to about 0.5. Here, their range of applicability is extended by deriving and testing boundary conditions for evaporating and condensing interfaces. The macroscopic interface conditions are derived from the microscopic interface conditions of kinetic theory. Tests include evaporation into a half-space and evaporation/condensation of a vapor between two liquid surfaces of different temperatures. Comparison indicates that overall the R13 equations agree better with microscopic solutions than classical hydrodynamics
Modeling and simulation of the dual stage pressure retarded osmosis systems
Full text linkUtilization of renewable energy sources, as an approach to reduce greenhouse
gas (GHG) emissions, have been globally popular in the last few decades. Among
renewable energy sources, pressure retarded osmosis (PRO) has been scrutinized by
scientists since the mid 70's. However, even today, the existing river-sea PRO systems
can only marginally meet the generally approved criterion of 5 W/m2 power density,
a threshold for an economically feasible PRO system. As an approach to increase the
performance of PRO systems, multi-staging of PRO modules are investigated.
A mathematical model of the scaled up PRO process is proposed with consideration
for internal and external concentration polarization, reverse salt flux, and spatial
variations along the membrane. A thermodynamic model is also developed with consideration
for entropy generation and losses in the process. It predicts the percentile
of each work loss source compared to the net work in the system. Several confi gurations
of dual stage PRO system are presented and compared to single stage PRO.
The comparison is based on three proposed target functions of power density (PD),
specifi c energy (SE), and work per drawn freshwater (Wdrawn). Applied hydraulic
pressures and flow rates of draw and feed solutions are optimized for maximizing the
target functions. The results indicate that overall performance of the system could
be improved by up to 8 % with a dual stage PRO in the case of SE. The system performance is not improved by depressurizing the draw solution before the second
module in cases of SE and Wdrawn. The thermodynamic analysis demonstrate the
contribution of each work loss and justify the reason of diminishing the net work over
the losses. The effect of membrane area and membrane characteristics on the SE target
function is also investigated. The distribution of membrane area in each module
depends on the selected con figuration and inlet draw solution. In the dual stage systems,
the SE value increases up to 14% by improving the membrane characteristics.
Reducing the salt rejection coefficient (B) is the most e ective membrane characteristic
in our con figurations. Replacing seawater with RO brine in draw solution results
in a signifi cant improvement in SE values.Graduat
Non-equilibrium evaporation and condensation : modeled with irreversible thermodynamics, kinetic theory, and statistical rate theory
No full textThe purpose of this work is to demonstrate the usability of irreversible thermodynamics and kinetic theory in describing slow steady state evaporation and condensation, analyze the statistical rate theory (SRT) approach, and investigate the physical phenomena involved. Recently large interface temperature jumps have been observed during steady state evaporation and condensation experiments; the vapor interface temperature was greater than the liquid interface temperature for condensation and evaporation. To predict the temperature jump, the SRT mass flux was introduced as an alternative to the established approaches of irreversible thermodynamics and kinetic theory of gases. Simple one dimensional planar and spherical models were developed for slow evaporation and condensation based on the experiments. We considered pure liquid water evaporation and condensation to, and from its own vapor. Expressions for the mass and energy fluxes across the interface were found using irreversible thermodynamics, kinetic theory, and SRT. The SRT theory does not have an energy flux expression, as a substitute we use the irreversible thermodynamics energy flux in the SRT model. The equations were then solved to yield the mass and energy fluxes, and the liquid and vapor temperature profiles. We find the interface temperature jump is dependant on the energy flux expression. The irreversible thermodynamics energy flux closely predicts the measured temperature jump and direction. Kinetic theory models do not predict the jump, however with incorporation of a velocity dependant condensation coefficient, kinetic theory can predict the correct temperature jump direction, and vapor interface temperature. All the models predict mass fluxes that agree with the measured data. We suggest the temperature jump direction is established based on the direction of the vapor conductive energy flux, and not the direction of the mass flux (condensation or evaporation). We conclude that irreversible thermodynamics, kinetic theoiy, and SRT can all be used to model steady state evaporation and condensation
Analysis of kinetic models and macroscopic continuum equations for rarefied gas dynamics
Full text linkThe Boltzmann equation is the basic equation to describe rarefied gas flows. Some
kinetic models with simple expressions for the collision term have been proposed to
reduce the mathematical complexity of the Boltzmann equation. All macroscopic
continuum equations can be derived from the Boltzmann equation or kinetic models
through the Chapman-Enskog method, Grad's moment method, etc.
This thesis is divided into three parts. In the first part, existing kinetic models (BGK
model, ES-BGK model, v(C) -BGK model, S model, and Liu model), and two newly
proposed v(C)-ES-BGK type kinetic models are described and compared, based on
properties that need to be satisfied for a kinetic model. In the new models a meaningful
expression for the collision frequency is used, while the important properties for a kinetic
model are retained at the same time.
In the second part of this work, the kinetic models (BGK, ES-BGK, v(C) -BGK, and
two new kinetic models) are tested numerically for one-dimensional shock waves and
one-dimensional Couette flow. The numerical scheme used here is based on Mieussens's
discrete velocity model (DVM). Computational results from the kinetic models are
compared to results obtained from the Direct Simulation Monte Carlo method (DSMC).
It is found that for hard sphere molecules the results obtained from the two new kinetic
models are very similar, and located in between the results from the ES-BGK and the
v(C)-BGK models, while for Maxwell molecules the two new kinetic models are
identical to the ES-BGK model. For one-dimensional shock waves, results from the new
kinetic model II fit best with results from DSMC; while for one-dimensional Couette
flow, the ES-BGK model is suggested.
Also in the second part of the work, a modified numerical scheme is developed from
Mieussens's original DVM. The basic idea is to use a linearized expression of the reference distribution function, instead of its exact expression, in the numerical scheme.
Results from the modified scheme are very similar to the results from the original scheme
for almost all done tests, while 20-40 percent of the computational time can be saved.
In the third part, several sets of macroscopic continuum equations are examined for
one-dimensional steady state Couette flow. For not too large Knudsen numbers
(Knc=O.l) in the transition regime, it is found that the original and slightly linearized
regularized 13 moment equations give better results than Grad's original 13 moment
equations, which, however, give better results than the Burnett equations, while the
Navier-Stokes-Fourier equations give the worst results, which is in agreement with the
expectation. For large Knudsen number situations (Kn>O.l), it turns out that all
macroscopic continuum equations tested fail in the accurate description of flows, while
the Grad's 13 moment equations can still give better results than the Burnett equations
Thermodynamics of sorption and distribution of water in nafion
Full text linkIn this work a model for the wetting and swelling of pores with water within a Nafion membrane is developed. This model is based on minimizing all contributions to the total free energy of the proposed system. We find that equilibrium state depends on entropic mixing forces and energetic surface forces. The wetting of the pore relies on the entropic forces exceeding the energetic forces. Specifically this indicates a critical pore size in which liquid is the favorable state. If the pore fills with liquid it will swell until balanced by the energy of the deforming membrane. Several factors including pressure relative to saturation and the phase which hounds the membrane are shown to dramatically affect the final equilibrium state of the system
Macroscopic description of rarefied gas flows in the transition regime
Full text linkThe fast-paced growth in microelectromechanical systems (MEMS), microfluidic fabrication, porous media applications, biomedical assemblies, space propulsion, and vacuum technology demands accurate and practical transport equations for rarefied gas flows. It is well-known that in rarefied situations, due to strong deviations from the continuum regime, traditional fluid models such as Navier-Stokes-Fourier (NSF) fail. The shortcoming of continuum models is rooted in nonequilibrium behavior of gas particles in miniaturized and/or low-pressure devices, where the Knudsen number (Kn) is sufficiently large.
Since kinetic solutions are computationally very expensive, there has been a great desire to develop macroscopic transport equations for dilute gas flows, and as a result, several sets of extended equations are proposed for gas flow in nonequilibrium states. However, applications of many of these extended equations are limited due to their instabilities and/or the absence of suitable boundary conditions.
In this work, we concentrate on regularized 13-moment (R13) equations, which are a set of macroscopic transport equations for flows in the transition regime, i.e., Kn≤1. The R13 system provides a stable set of equations in Super-Burnett order, with a great potential to be a powerful CFD tool for rarefied flow simulations at moderate Knudsen numbers.
The goal of this research is to implement the R13 equations for problems of practical interest in arbitrary geometries. This is done by transformation of the R13 equations and boundary conditions into general curvilinear coordinate systems. Next steps include adaptation of the transformed equations in order to solve some of the popular test cases, i.e., shear-driven, force-driven, and temperature-driven flows in both planar and curved flow passages. It is shown that inexpensive analytical solutions of the R13 equations for the considered problems are comparable to expensive numerical solutions of the Boltzmann equation. The new results present a wide range of linear and nonlinear rarefaction effects which alter the classical flow patterns both in the bulk and near boundary regions. Among these, multiple Knudsen boundary layers (mechanocaloric heat flows) and their influence on mass and energy transfer must be highlighted. Furthermore, the phenomenon of temperature dip and Knudsen paradox in Poiseuille flow; Onsager's reciprocity relation, two-way flow pattern, and thermomolecular pressure difference in simultaneous Poiseuille and transpiration flows are described theoretically. Through comparisons it is shown that for Knudsen numbers up to 0.5 the compact R13 solutions exhibit a good agreement with expensive solutions of the Boltzmann equation
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