Transient analysis of an M/G/1 retrial queue subject to disasters and server failures

An M/G/1 retrial queueing system with disasters and unreliable server is investigated in this paper. Primary customers arrive in the system according to a Poisson process, and they receive service immediately if the server is available upon their arrivals. Otherwise, they will enter a retrial orbit and try their luck after a random time interval. We assume the catastrophes occur following a Poisson stream, and if a catastrophe occurs, all customers in the system are deleted immediately and it also causes the server’s breakdown. Besides, the server has an exponential lifetime in addition to the catastrophe process. Whenever the server breaks down, it is sent for repair immediately. It is assumed that the service time and two kinds of repair time of the server are all arbitrarily distributed. By applying the supplementary variables method, we obtain the Laplace transforms of the transient solutions and also the steady-state solutions for both queueing measures and reliability quantities of interest. Finally, numerical inversion of Laplace transforms is carried out for the blocking probability of the system, and the effects of several system parameters on the blocking probability are illustrated by numerical inversion results.     

Towards understanding the critical heat flux for industrial applications

Understanding CHF is of an upmost importance in many industries, especially in the design and operation of boilers, nuclear power plants, cryogenic systems, etc. Due to safety issues related to the nuclear power plants, and the adaptation of CHF as the limiting criterion of power generation, it is important to understand the mechanisms of CHF relevant to nuclear systems operation. Moreover, CHF is expected to occur during transients than steady-state conditions. Therefore, knowledge of transient CHF is of great importance for the safety evaluation of nuclear reactors under transient condition. In this paper, the existing CHF experimental and modeling studies are discussed in order to understand the phenomena leading to CHF. Also, the effect of transient conditions on CHF for nuclear fuels has been evaluated.     

Mechanism of interaction of pressure waves at a discrete partial blockage

This paper analyses the mechanism of interaction between an incident pressure wave and blockages of different geometrical characteristics (i.e., a butterfly and a ball valves, two short stretches of pipe with a reduced diameter, and a device simulating a longitudinal body blockage) by means of laboratory and numerical tests. Experiments have shown that the mechanism of interaction with pressure waves is influenced by their path through the device: sinuous because of the device body for partially closed in-line valves (type I mechanism), and straight for the small bore pipe devices (type II mechanism). Type I mechanism is characterized by a rise followed by an almost constant value whereas in type II one a drop occurs after the rise. To complete the investigation the effect of the pre-transient condition is discussed.     

An efficient transient Navier–Stokes solver on compact nonuniform space grids

In this paper, we propose an implicit higher-order compact (HOC) finite difference scheme for solving the two-dimensional (2D) unsteady Navier–Stokes (N–S) equations on nonuniform space grids. This temporally second-order accurate scheme which requires no transformation from the physical to the computational plane is at least third-order accurate in space, which has been demonstrated with numerical experiments. It efficiently captures both transient and steady-state solutions of the N–S equations with Dirichlet as well as Neumann boundary conditions. The proposed scheme is likely to be very useful for the computation of transient viscous flows involving free and wall bounded shear layers which invariably contain spatial scale variation. Numerical results are presented and compared with analytical as well as established numerical data. Excellent comparison is obtained in all the cases.     

Numerical simulation of the horizontal Bridgman growth. Part II: Three-dimensional flow

We study the steady-state three-dimensional flow which occurs in a horizontal crucible of molten metal under the action of a horizontal temperature gradient. The geometry and the boundary conditions are similar to those encountered in the Bridgman growth process of semiconductor crystals. We find that three-dimensional effects can have a dramatic influence upon the flow, which, before the onset of periodic disturbances, differs appreciably from its two-dimensional counterpart. We also investigate the sensitivity of the flow to non-symmetric disturbances.     

Coupled boundary element method and finite difference method for the heat conduction in laser processing

This paper is presented as a way to model transient heat conduction in a 3-D axisymmetric case where large rates of heat fluxes are applied on the surfaces as done in the case of laser processing. This would result in large temperature gradients in a small area irradiated by the laser on the incident surface that could also reach melting and subsequent vaporization. BEM can handle large fluxes very easily and it also can be formulated if needed to incorporate the moving boundary problem in a unique manner while on the other hand FDM is a fast and efficient method. For these reasons a coupled BEM–FDM method is formulated to simulate the heat conduction process. In the BEM method linear elements for the boundary and quadratic elements for the domain were used. The integrals in BEM were integrated in time using the asymptotic expansion for the modified Bessel functions in the Green’s function. To further improve the accuracy, special techniques were employed in the spatial integration. As for the FDM formulation, a flux conservation scheme with a 4th order formula for the fluxes was used. The FDM and BEM were coupled at the interface by the temperature from the FDM formulation being imposed on the BEM and the flux from the BEM being utilized by the FDM elements near to the interface. To advance in time, the Crank–Nicholson scheme was used on the FDM directly and due to coupling indirectly on the BEM. The relative errors for the simulation of constant and variable flux cases demonstrate the successful nature of the numerical model.     

Orientational relaxation of pheophorbide-a molecules in the ground and in the first excited state measured by transient dichroism spectroscopy

We report on transient dichroism spectroscopy carried out on pheophorbide-a in ethanol to measure the response time of the pump-beam induced anisotropy after selective excitation at high excitation levels. From the observed time behaviors of induced absorption, transient amplification, and of the bleaching signal, the orientational relaxation times of pheophorbide-a in the first excited singlet state and in the ground state were obtained separately to be 370 and 250 ps, respectively. It is found that pheophorbide-a behaves like a spherical rotor in the first excited state, while in the ground state randomization of molecules is dominated by the rotation around its quasi-symmetry axis. Because of rotation free measurement of ordinary transient absorption spectra fail in the case of ground state depletion, the observed orientational relaxation time of the ground state have to be taken into account to fit the bleaching kinetics obtained from transient absorption spectra very well to determine the intersystem crossing yield of pheophorbide-a to be 0.46.     

Characterization of transient cavitation activity during sonochemical modification of magnesium particles

Investigation of the cavitation activity during ultrasonic treatment of magnesium particles during nanostructuring has been performed. Cavitation activity is recorded in the continuous mode after switching the ultrasound on with the use of ICA-5DM cavitometer. It has been demonstrated that this characteristic of the cavitation zone may be varied in a wide range of constant output parameters of the generator. The speed and nature of the cavitation activity alteration depended on the concentration of Mg particles in the suspension and the properties of the medium in which the sonochemical treatment has been performed. Three stages of the cavitation area evolution can be distinguished: 1 – the initial increase in cavitation activity, 2 – reaching a maximum with a subsequent decrease, and 3 – reaching the plateau (or the repeated cycles with feedback loops of enlargement/reduction of the cavitation activity).The ultrasonically treated magnesium particles have been characterized by scanning electron microscopy, X-ray diffraction analysis and thermal analysis. Depending on the nature of the dispersed medium the particles can be characterized by the presence of magnesium hydroxide (brucite) and magnesium hydride. It is possible to reach the incorporation of magnesium hydride in the magnesium hydroxide/magnesium matrix by varying the conditions of ultrasonic treatment (duration of treatment, amplitude, dispersed medium etc.). The influence of the magnesium reactivity is also confirmed by the measurements of cavitation activity in organic dispersed media (ethanol, ethylene glycol) and their aqueous mixtures.     

Transient deformation and heat generation of solid polyurethane under impact compression

This investigation examines the transient deformation and heat generation of a solid polyurethane subjected to dynamic compression. A special method is presented to prepare the solid polyurethane from raw materials which are commonly used to make polyurethane foams. Testing methods including infrared spectrum, differential scanning calorimetry, quasi-static and dynamic compression were applied to study the basic physical properties of the solid polyurethane. High-speed optical and infrared imaging systems are used to obtain visual and thermo-graphic images during impact tests. Under quasi-static compression, the solid polyurethane presents a good performance in toughness. This is confirmed by its Poisson's ratio. Under impact compression, the adiabatic heat generation are identified statistically. Temperature distribution confirms the fact of transient heat generation in specimens. Adiabatic self-heating mechanism provides a consideration to understand the negative strain-rate effect and post-yield softening effect found in the solid polyurethane. Mechanical properties including quasi-static and dynamic responses are related with the composition of molecular and structure of polymer.     

Comparison of multicomponent fuel droplet vaporization experiments in forced convection with the Sirignano model

The vaporization of multicomponent fuel droplets was studied experimentally in a heated flow and the results were compared to the model proposed by Abramzon and Sirignano. The droplet was suspended on a permanent holder which was set up in a thermal wind-tunnel. This wind-tunnel was fitted with a video recording system and an infra-red camera. The period during which the droplet was suspended on the holder before the opening of the hot air flow damper was recorded. This first sequence corresponds to the droplet vaporization in natural convection, whose initial experiment conditions, especially diameter, temperature, composition of the droplet, are well known. Then the damper was turn on, and the sequence of forced convection begun. The initial diameter of the droplet was recorded by the video system. The other initial conditions of this second sequence cannot be determined experimentally. The distribution of temperature in the droplet and the surface temperature, the mass fraction distribution in the droplet and the surface mass fraction were unknown. These unknown parameters were determined by coupling our experiment with a model using “the film concept” in natural convection. Experimental results were compared with the calculations and found satisfactory, in natural convection as well as in forced convection initiated by this method. The method was tested in the case of a fuel mixture droplets (heptane–decane) for different initial concentrations and variable durations of the sequence in natural convection.