Faculty of Engineering
http://hdl.handle.net/1828/74
Tue, 27 Jun 2017 15:36:24 GMT2017-06-27T15:36:24ZA moment model for phonon transport at room temperature
http://hdl.handle.net/1828/8281
A moment model for phonon transport at room temperature
Mohammadzadeh, Alireza; Struchtrup, Henning
Heat transfer in solids is modeled by deriving the macroscopic equations for phonon transport from the phonon-Boltzmann equation. In these equations, the Callaway model with frequency-dependent relaxation time is considered to describe the Resistive and Normal processes in the phonon interactions. Also, the Brillouin zone is considered to be a sphere, and its diameter depends on the temperature of the system. A simple model to describe phonon interaction with crystal boundary is employed to obtain macroscopic boundary conditions, where the reflection kernel is the superposition of diffusive reflection, specular reflection and isotropic scattering. Macroscopic moments are defined using a polynomial of the frequency and wave vector of phonons. As an example, a system of moment equations, consisting of three directional and seven frequency moments, i.e., 63 moments in total, is used to study one-dimensional heat transfer, as well as Poiseuille flow of phonons. Our results show the importance of frequency dependency in relaxation times and macroscopic moments to predict rarefaction effects. Good agreement with data reported in the literature is obtained.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/1828/82812017-01-01T00:00:00ZBoolean and multiple-valued functions in combinational logic synthesis
http://hdl.handle.net/1828/8276
Boolean and multiple-valued functions in combinational logic synthesis
Dubrova, Elena Vladimirovna
The subject of this dissertation is the theory of Boolean and multiple-valued functions.
The main areas considered are: functional completeness, canonical forms,
minimization of functions, discrete differences and functional decomposability. The
results obtained are used as a foundation for the development of several new algorithms
for logic synthesis of combinational logic circuits. These include an efficient
algorithm for three-level AND-OR-XOR minimization for Boolean functions, an algorithm
for generating the composition trees for Boolean and multiple-valued functions
in a certain class, and an algorithm for computing a new canonical form of multiple-valued
functions. Several other problems, related to logic synthesis, such as test
generation for combinational logic circuits and synthesis of easily testable circuits are also addressed. Possible directions for future research are discussed.
Wed, 14 Jun 2017 00:00:00 GMThttp://hdl.handle.net/1828/82762017-06-14T00:00:00ZDSMC and R13 Modeling of the Adiabatic Surface
http://hdl.handle.net/1828/8274
DSMC and R13 Modeling of the Adiabatic Surface
Mohammadzadeh, Alireza; Rana, Anirudh; Struchtrup, Henning
Adiabatic wall boundary conditions for rarefied gas flows are described with the isotropic scattering model. An appropriate sampling technique for the direct simulation Monte Carlo (DSMC) method is presented, and the corresponding macroscopic boundary equations for the regularized 13-moment system (R13) are obtained. DSMC simulation of a lid driven cavity shows slip at the wall, which, as a viscous effect, creates heat that enters the gas while there is no heat flux in the wall. Analysis with the macroscopic equations and their boundary conditions reveals that this heat flux is due to viscous slip heating, and is the product of slip velocity and shear stress at the adiabatic surface. DSMC simulations of
the driven cavity with adiabatic walls are compared to R13 simulations, which both show this non-linear effect in good agreement for Kn < 0.3.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/1828/82742016-01-01T00:00:00ZMacroscopic and kinetic modelling of rarefied polyatomic gases
http://hdl.handle.net/1828/8270
Macroscopic and kinetic modelling of rarefied polyatomic gases
Rahimi, Behnam; Struchtrup, Henning
A kinetic model and corresponding high-order macroscopic model for the accurate
description of rarefied polyatomic gas flows are introduced. The different energy
exchange processes are accounted for with a two term collision model. The proposed
kinetic model, which is an extension of the S-model, predicts correct relaxation of
higher moments and delivers the accurate Prandtl (Pr) number. Also, the model has
a proven linear H-theorem. The order of magnitude method is applied to the primary
moment equations to acquire the optimized moment definitions and the final scaled set
of Grad’s 36 moment equations for polyatomic gases. At the first order, a modification
of the Navier–Stokes–Fourier (NSF) equations is obtained. At third order of accuracy,
a set of 19 regularized partial differential equations (R19) is obtained. Furthermore,
the terms associated with the internal degrees of freedom yield various intermediate
orders of accuracy, a total of 13 different orders. Thereafter, boundary conditions for
the proposed macroscopic model are introduced. The unsteady heat conduction of a
gas at rest is studied numerically and analytically as an example of a boundary value
problem. The results for different gases are given and effects of Knudsen numbers,
degrees of freedom, accommodation coefficients and temperature-dependent properties
are investigated. For some cases, the higher-order effects are very dominant and the
widely used first-order set of the NSF equations fails to accurately capture the gas
behaviour and should be replaced by the proposed higher-order set of equations.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/1828/82702016-01-01T00:00:00Z