In order to solve a Boltzmann transport equation (BTE) of phonons for investigating heat conduction in non-metallic solids, we propose to employ a DSMC (direct simulation Monte Carlo) scheme to simulate dynamics of phonons in analogy with rarefied gas. In this paper, we describe the DSMC scheme for phonon dynamics and present some results with our prototype codes for a face-centered cubic model. The dynamics of phonons with two branches of acoustic modes is discussed, in the case where the distribution of phonons in strong nonequilibrium situation is driven into equilibrium.

We have developed a hybrid numerical simulation code to investigate the dynamics of nanobubbles. The idea is based on a combination of a molecular dynamics (MD) technique for the region containing a bubble and surrounding area, and the lattice Boltzmann method (LBM) for the region well away from the bubble. The boundary between the two regions is movable and driven by their pressure difference. As a test of the developed code, we have performed a simulation of a collapsing nanobubble. After equilibrating the system, we introduce a uniaxial pressure wave in the continuum region far from the bubble. The pressure wave propagates through the LBM region, and the pressure difference deforms the MD-LBM boundary. As the MD region deforms, the bubble inside the region starts to collapse non-spherically. We have analyzed the bubble collapse dynamics with several different pressure waves. Vapor bubbles and bubbles containing noncondensable particles are compared.

We investigated the initial stage of nucleate boiling on ideally smooth surface with a molecular dynamics simulation technique. Lennard-Jones model liquid was confined in a rectangular simulation cell, contacting with a flat smooth heating wall. Extra kinetic energy was given to particles in vicinity of the wall. As the temperature of liquid on the wall increases, the liquid thermally expands, which causes the pressure decrease, leading to formation of bubble nuclei, or cavitation, of atomic scale. We found that the nucleation is affected by surface wettability (hydrophobic or hydrophilic) as well as the magnitude of heat flux. When the surface is hydrophobic and the heating area is small, a size oscillation of generated bubbles was observed, which is determined by the balance among the heating flux from the wall, thermal diffusion into the surrounding liquid, and latent heat consumption during the phase change.

We carried out MD simulations of glancing angle deposition on a high temperature substrate (HT-GLAD) to elucidate the mechanism of whisker growth, assuming Lennard-Jones model potential. The deposit shape depends on the vapor velocity, the vapor density, and the deposition angle. Through analyses of the crystalline structure and the temperature distribution inside the deposit during the whisker growth, it is found that heat transfer from the deposit to the substrate strongly affects the growth dynamics.

As the scale of electronic devices decreases, heat transfer analysis and thermal design becomes more important. In particular, heat transfer through various solid thin films is strongly affected by thickness dependence of thermal conductivity and interfacial thermal resistance. Analysis of phonon dynamics based on a linearized Boltzmann transport equation, or the so-called relaxation time approximation, has been widely used, but detailed analysis using molecular dynamics simulation reveals that couplings among various phonon modes can affect the energy transfer. In this study, we propose a DSMC scheme to simulate phonon dynamics starting from the original Boltzmann transport equation. In contrast to the linearized model, this scheme requires no relaxation time as an input parameter, and we can investigate the couplings among phonons with different modes, although we have to assume some appropriate model of phonon-phonon collisions. As a test calculation, energy flux was evaluated for model thin films of various thicknesses, and a phenomenon similar to the Casimir limit was retrieved. This scheme will enable us to include other factors, such as phonon-electron couplings.

We have developed hybrid numerical simulation codes to investigate the dynamics of nanobubbles. The idea is based on a combination of a molecular dynamics (MD) technique and a continuum dynamics with the CIP method. The MD technique enables us to examine rapid change of the bubble surface and the inside region of nanobubbles at molecular scale. The CIP method enables us to trace the mass and energy transfer processes far from the bubble surface at continuum scale. In the hybrid simulation, the simulation cell is divided into two parts. The inner region containing a bubble (or bubbles) consists of sufficiently large number of particles and is treated with the MD method. The outer region is treated with a computational fluid dynamics (CFD) scheme. The boundary between the inner and outer regions is movable and driven with the pressure difference between the two regions. To deal with the moving boundary, we adopt the CIP scheme. Two different codes have been developed, i.e., one-dimensional CFD with assuming a spherical symmetry, and full three-dimensional CFD. Examples will be given in the paper to demonstrate each code. The first example is the oscillating dynamics of a spherical bubble with one-dimensional CFD. The bubble is initially located at the center of the MD region with no translational motion. The outer (continuum) region is treated one dimensionally, with the assumption of spherical symmetry. Under the equilibrium condition, where there is no pressure difference between the two regions, we give a sudden pressure increase in the continuum region far from the bubble. The spherical pressure wave propagates through the continuum region, and the pressure difference drives the boundary to shrink the MD region. As the MD region shrinks, the bubble inside the region starts to collapse. The collapsed bubble bounces back. We have analyzed the oscillation dynamics under several different conditions, such as different initial pressures and the state of gas inside the bubble. The second one is the deformation of a non-spherical bubble. For that purpose, the continuum region is treated with full three-dimensional CIP scheme. Furthermore, we use the level set method in order to capture the interfaces (boundary) between the MD region and the continuum region.

Modern semiconductor industry and nanotechnology have profoundly impacted the study on thermal transport in dielectric solids such as single-crystal silicon. For these heat conduction phenomena whose characteristic length and time shrink into nano scale, it is efficient to utilize phonon dynamics as a promising approach to investigate the fundamental features of heat transfer at nano scale as well as the distinguished thermal properties of nano-materials. A new computational method is proposed to explore phonon dynamics in single-crystals on the basis of classical Molecular Dynamics technique. This method utilizes the Fourier-Laplace transformation of molecular trajectory, with anharmonicity of molecular vibrations accounted in the investigation on phonon dynamics. Instantaneous mode-dependent energy of phonons and density of vibration state is obtained at each simulated time step. Mode-dependent phonon relaxation is simulated and verified with perturbation method, which gives a way to measure relaxation time of single-mode phonon. The feasibility of the proposed scheme is confirmed by a series of simulations which are carried out in this paper on 1) monatomic crystal of argon with FCC structure and 2) diatomic crystal of silicon with diamond structure, under Lennard-Jones 6-12 potential and Tersoff-1989 model, respectively.

We propose a novel technique of molecular dynamics simulation to evaluate the relaxation time of phonons in solids for investigation of solid heat conductivity. The basic idea is to observe relaxation behavior of the power spectrum of atomic velocities after energetically stimulating modes in a specific frequency region. The transient entropy S(t) is defined with the power spectrum based on non-equilibrium statistical mechanics to quantitatively evaluate the relaxation speed. In this paper, two example systems are shown: a Lennard-Jones model crystal and a silicon crystal. For both systems, we found that the observed S(t) is well fitted to a single exponential function, from which we can obtain a frequency-dependent relaxation time.

This paper deals with the characteristics of a pipe flange connection with a compressed asbestos sheet gasket (JIS) subjected to an internal pressure and a bending moment. The contact gasket stress distributions at the interfaces between pipe flanges and a gasket are calculated by the elasto-plastic finite element method taking account a hysteresis and a non-linearity in the stress-strain curve of the compressed asbestos sheet gasket. In addition, measurements of a change in axial bolt force and leakage test were conducted using an actual pipe flange connection with the gasket subjected to the internal pressure and the bending moment. The new gasket constants are calculated by using the results of the leakage test and the calculated average contact gasket stress. The values of the new gasket constants obtained by the present study are in a fairly good agreement with those from ROTT (PVRC). It is found that the value of the tightness parameter is increased as the bending moment is increased. This is because the average contact gasket stress under the bending moment is increased, while it is decreased under the internal pressure.

Bolt load changes due to internal pressure are very important in order to evaluate the integrity of gasketed flange connections in the sealing performance point of view, because its gasket stress which dominates leak rate changes according to the bolt load changes. For establishing a connection possesses high reliability and sufficient integrity, it is necessary to clarify the mechanics ofgasketed flange connections. For this purpose, authors carried out experimental pressurizing tests for 3B and 20B gasketed flange connections clamped by various bolt preloads and measured the bolt load changes with increasing internal pressure up to 5MPa. Also a load factor, which is defined as the ratio of axial bolt force increment to pressure thrust force, was calculated using the test results. The test results indicate that 3B and 20B flange connections with the spiral wound gaskets have a constant load factors under sufficient initial clamping forces in assemble.

It has been well known that a scatter in axial bolt forces of pipe flange connections tightened by the torque control method is substantial. It is necessary for evaluating the sealing performance of the pipe flange connections with the gaskets subjected to intemal pressure to know the contact gasket stress distributions due to the scatter of the axial bolt forces in the connections tightened by the torque control method. This paper deals with the leakage of the pipe flange connections with a spiral wound gasket and that with a compressed sheet gasket tightened by the torque control method. The scatter in the axial bolt forces was measured in the experiments. The contact gasket stress distributions at the interfaces of the pipe flange connections with the gaskets were calculated under the measured axial bolt forces by using elasto-plastic finite element method (FEM) taking into account hysteresis and non-linearity in the stress-strain curves of the gaskets. The effects of the scatter in the axial bolt forces tightened by the torque control method on the gas leakage were also examined by using the actual pipe flange connections. As the result, a difference in an amount of gas leakage measured was found to be substantial between our study and PVRC procedure. By using the calculated contact gasket stress distributions under the internal pressure and the results of the leakage tests, the sealing performance was evaluated. It is found that the sealing performance is worse in the actual pipe flange connection than that evaluated by PVRC procedure.

The leakage evaluation when gas is used is more severe than that when liquid is used in pipe flange connections. In a practical design, it is also necessary to examine the leakage in the connection under liquid internal pressure. This paper deals with the contact gasket stress distributions in the pipe flange connections with a spiral wound gasket and a compressed sheet gasket by using elasto-plastic finite element method (FEM) taking account hysteresis and non-linearity in the stress-strain curves of the gaskets, when bending moments as well as internal pressure are applied to the connections. In the FEM calculations, the effects of the gaskets and the initial clamping bolt force (bolt preload) on the contact gasket stress distributions are examined. The leakage tests for the connections under bending moments were also conducted by using liquid (water). By using the results of the leakage tests and the calculated contact gasket stress distributions, the sealing performance of the connections is evaluated. It is found that the sealing performance of the connection under the bending moment can be estimated when internal fluid is liquid (water).

Gasketed flange connections should be designed taking actual behavior of the connections under their operating conditions into consideration. However, such actual behavior as bolt load change, gasket load change and flange rotation were not clear because adequate calculation method was not developed due to difficulty and complicacy to solve statically indetermine problem among three bodies, bolt, flange and gasket. In this paper, authors develop a method to calculate load factor for gasketed flange connection. Load factor describes bolt load change when an external force is applied to the connection. Load factor represents flange rigidity including gasket stiffness that dominates not only the behavior of joint after pressurising but also its sealing performance. By using the load factor, bolt load change as well as gasket load change due to internal pressure can be obtained by simple equations. When the required gasket stress is given to achieve a prescribed sealing thightness, the required initial bolt preload can also be calculated. Authors also proposed a load equilibrium diagram for gasketed flange connection with internal pressure. The diagram helps us to understand schematically how bolt load and gasket load change under pressurized condition. In addition, experimental tests are performed using 3 inch and 20 inch flange connections with spiral wound gasket in order to demonstrate validity of the proposed calculation method based on load factor and load equilibrium diagram. In conclusion, it is found that the proposed calculation method can estimate bolt load change and gasket load change under pressurized condition.