Michael Shusser

Energy and velocity of a forming vortex ring

It is known that vortex rings formed by large stroke ratios (in a piston/cylinder arrangement) pinch off from their generating jets at a fairly constant universal time scale. In this paper we show that the hypothesis that at the pinch off the translational velocity of the ring equals the jet flow velocity near the ring is equivalent to the recently proposed idea based on a variational principle by Kelvin and Benjamin that the pinch off occurs when the apparatus is no longer able to deliver energy at a rate required for steady vortex ring existence. A formula for the propagation velocity of a thick vortex ring is also proposed and compared with available experimental data and empirical relations.

Combustion Response of Ammonium Perchlorate Composite Propellants

The Cohen and Strand model for ammonium perchlorate (AP) composite propellants is applied as boundary conditions, one for AP and one for binder, in solving the heat conduction equation in each to compute linear and nonlinear combustion response properties for each and for the aggregate propellant. Iterations couple AP and binder through the quasi-steady flame processes. Illustrative results for linear response functions (pressure coupled and velocity coupled) are presented for a monomodal AP propellant showing effects of varying AP size, pressure, and crossflow speed. Examples of nonlinear responses to arbitrary waveforms are also shown. The model predicts a very large response at high pressures with coarse AP due to AP monopropellant combustion, underpredicts peak response amplitude for low pressures due to a possible change in mechanism, and shows a stabilizing effect of the diffusion flame. A quantitative comparison with response function data is limited to one well-characterized research formulation. Mechanistic implications are discussed, including recommendations for future modeling work.

Explosive boiling of a liquid droplet

Abstract A mathematical model describing growth of an internal vapor bubble produced by homogeneous nucleation within a liquid droplet during explosive boiling is presented. Existing experimental results for explosive boiling of superheated droplets confirm the predictions of the model. The difference between the present model and the classical theories of bubble growth is discussed.

A Physical Model Describing the Mechanism for Formation of Gas Microbubbles in Patients with Mitral Mechanical Heart Valves

AbstractThis study was aimed at developing a physical model, supported by experimental observations, to describe the formation and growth of microbubbles seen in patients with mitral mechanical heart valves (MHV). This phenomenon, often referred to as high intensity transient signals (HITS), appears as bright, intense, high-velocity and persistent echoes detected by Doppler ultrasonography at the instant of closure. The long-term clinical implications of HITS has yet to be determined. However, there are reports of a certain degree of neurological disorder in patients with mitral MHV. The numerical analysis has shown the existence of a twofold process (1) nucleation and (2) microbubble growth as a result of cavitation. While mild growth of nuclei is governed by diffusion, explosive growth of microbubbles is controlled by pressure drop on the atrial side of mitral MHV. It was demonstrated that there exist limits on both microbubble size and regurgitant velocity, above which microbubbles grow explosively, and below which growth is almost nonexistent. Therefore, prevention of excessive pressure drops induced by high closing velocities related to the dynamics of closure of mitral MHV may offer design changes in the future generations of mechanical valves.

A model for vortex ring formation in a starting buoyant plume

Vortex ring formation in a starting axisymmetric buoyant plume is considered. A model describing the process is proposed and a physical explanation based on the Kelvin–Benjamin variational principle for steady vortex rings is provided. It is shown that Lundgren et al.s (1992) time scale, the ratio of the velocity of a buoyant plume after it has travelled one diameter to its diameter, is equivalent to the time scale (formation time) proposed by Gharib et al. (1998) for uniform-density vortex rings generated with a piston/cylinder arrangement. It is also shown that, similarly to piston-generated vortex rings (Gharib et al. 1998), the buoyant vortex ring pinches off from the plume when the latter can no longer provide the energy required for steady vortex ring existence. The dimensionless time of the pinch-off (the formation number) can be reasonably well predicted by assuming that at pinch-of the vortex ring propagation velocity exceeds the plume velocity. The predictions of the model are compared with available experimental results.

Effect of time-dependent piston velocity program on vortex ring formation in a piston/cylinder arrangement

An analytical model describing laminar vortex ring formation in a nozzle flow generator (piston/cylinder arrangement) proposed previously by the authors is extended to time-dependent velocity programs. The predictions of the model are in good agreement with the available numerical data for impulsive, linear, and trapezoidal velocity programs. We also show that properly scaled vortex circulation is another universal quantity, in addition to the dimensionless energy, related to vortex rings and verify this by comparing with available numerical simulations and experimental results.

Combustion Response of Ammonium Perchlorate

A modified Price–Boggs–Derr model is applied to compute the linear and nonlinear combustion response properties of monopropellant ammonium perchlorate (AP). The kinetics constants were changed to achieve good agreement with response function data as well as with steady-state data.The numerical method was first validated with the classical theory. Computations using the Levine and Culick boundary condition in the limit of small perturbations were compared with the exact mathematical solution for linear response, and the effect of perturbation amplitude was explored. Then, using the AP model for the boundary condition, various linear and nonlinear computations were performed. Supplemental mathematical analyses relate the AP model to the basic two parameters of the classical theory and show the key factors determining the nature of the combustion response.

Stability of rapidly evaporating droplets and liquid shells

Abstract The paper presents a study of stability of rapidly evaporating droplets and liquid shells occurring in the process of explosive boiling, where, in addition to surface evaporation, a vapor bubble grows within a highly superheated liquid droplet immersed in a liquid or gas medium. To get better insight into the problem, two simpler but related problems are studied before the full stability problem is treated. First, the stability of an evaporating, highly superheated liquid droplet is analyzed, in order to estimate the influence of the outer evaporation from the droplet surface. The linear stability of the process at the final stages of explosive boiling, when the droplet forms an expanding liquid shell, is studied next. Finally, the general case of explosive boiling stability is considered. It is shown that the process is unstable, as indeed has been found in existing experiments.

Kinetic theory analysis of laser ablation of carbon: Applicability of one-dimensional models

The paper discusses the applicability of a one-dimensional approximation in a recently proposed model of ablation of carbon by a nanosecond laser pulse that considers the kinetics of the process. The model approximates the process as sublimation and combines conduction heat transfer in the target with the gas dynamics of the ablated plume which are coupled through the boundary conditions at the interface. The ablated mass flux and the temperature of the ablating material are obtained from the conservation relations at the interface derived from the moment solution of the Boltzmann equation for arbitrarily strong evaporation. It is shown that in the one-dimensional approximation the surface pressure and the ablation rate are too low and that the ablation rate is restricted most of the time by the kinetic theory limitation on the maximum mass flux that can be attained in a phase-change process. As a consequence, the model overpredicts the surface temperature and the duration of the process. However, it pred...

Kinetic theory analysis of laser ablation of carbon: Importance of second-order calculation

Following some recent works that used first-order numerical schemes in modeling laser ablation, this paper compares the predictions of first- and second-order calculations for a one-dimensional kinetic theory model of laser ablation of carbon based on the moment solution of the Boltzmann equation for arbitrary strong evaporation. The model considers both conduction heat transfer in the target and gas dynamics of the ablated plume coupled through the interface boundary conditions. It was found that the difference between the first-order and the second-order calculations is limited to the parts of the flow with high gradients, such as the shock wave and the contact surface. Since the ablation rate is determined by the conditions at the solid surface, which is most of the time situated far from that area, the first-order calculation predicts ablation rate correctly.