Generalized Stefan models accounting for a discontinuous temperature field

We construct a class of generalized Stefan models able to account for a discontinuous temperature field across a nonmaterial interface. The resulting theory introduces a constitutive scalar interfacial field, denoted by and called the equivalent temperature of the interface. A classical procedure, based on the interfacial dissipation inequality, relates the interfacial energy release to the interfacial mass flux and restricts the equivalent temperature of the interface. We show that previously proposed theories are obtained as particular cases when or or, more generally, when for We study in a particular constitutive framework the solidification of an under-cooled liquid and we are able to give a sufficient condition for the existence of travelling wave solutions.Received: 29 January 2003, Accepted: 18 October 2003, Published online: 3 February 2004PACS: 64.70.Dv, 68.35.Md, 68.35.Rh     

Energetic formulation of multiplicative elasto-plasticity using dissipation distances

We introduce a new energetic formulation for the inelastic rate-independent behavior of standard generalized materials. This formulation is solely based on the classical elastic energy-storage potential and a dissipation potential , and it replaces the classical variational inequalities which describe the flow rules for the inelastic variables like the plastic deformation and the hardening parameters. The energetic formulation has the major advantage that it is defined for a larger class of processes since it does not involve any derivatives of the strains or the internal variables, thus allowing for an analysis of processes involving sharp interfaces, localization or microstructure. Two new quantities are derived from and . First, this is the global dissipation distance on the manifold of internal states. Second, the reduced stored-energy density contains the comprised information of the elastic and plastic material properties via minimization of over the new internal variable. Several stability concept are derived and used to analyze failure mechanism. Finally, a natural incremental method is proposed which reduces to a minimization problem and can be solved efficiently using .Received: 5 December 2002, Accepted: 10 February 2003, Published online: 27 June 2003PACS: 66.20.F2, 62.40.+i, 80.40.cmA. Mielke: Research partially supported by DFG within the SFB 404 Multifield Problems     

Kinetics and oxidation mechanism of cyclopentadiene behind the shock waves

Oxidation of cyclo-C₅H₅ was investigated by monitoring O atoms and also CO molecules behind the reflected shock of cyclo-C₅H₆ / O₂ /Ar and C₆H₅OCH₃ /O₂ /Ar mixtures. In both mixtures we could observe the formation of O atoms produced by the reaction of cyclo-C₅H₅ + O cyclo-C₅H₅O + O and from the kinetic analysis of these time profiles the rate constant for this reaction was determined to be kJ/RT) cm³ mol^-1 s^-1. The possibility of CO formation by the reaction of cyclo-C₅H₅O C₄H₅ + CO was also investigated but because of the subsequent reactions forming CO molecules no direct information for the reaction of cyclo-C₅H₅O C₄H₅ + CO was derived.Received: 3 February 2003, Accepted: 17 June 2003, Published online: 5 August 2003     

The structure and evolution of a two-dimensional H2/O2/Ar cellular detonation

This paper reports on two-dimensional numerical simulation of cellular detonation wave in a / / mixture with low initial pressure using a detailed chemical reaction model and high order WENO scheme. Before the final equilibrium structure is produced, a fairly regular but still non-equilibrium mode is observed during the early stage of structure formation process. The numerically tracked detonation cells show that the cell size always adapts to the channel height such that the cell ratio is fairly independent of the grid sizes and initial and boundary conditions. During the structural evolution in a detonation cell, even as the simulated detonation wave characteristics suggest the presence of an ordinary detonation, the evolving instantaneous detonation state indicates a mainly underdriven state. As a considerable region of the gas mixture in a cell is observed to be ignited by the incident wave and transverse wave, it is further suggested that these two said waves play an essential role in the detonation propagation.Received: 16 September 2003, Accepted: 14 June 2004, Published online: 20 August 2004[/PUBLISHED]PACS: 47.40.-x, 82.40.Fp, 82.33.Vx, 83.85.PtX.Y. Hu: Correspondence to Current address: Institut für Strömungsmechanik, Technische Universität Dresden, 01062 Dresden, Deutschland     

Burnett equations for the ellipsoidal statistical BGK model

In order to discuss the agreement of the ellipsoidal statistical BGK (ES-BGK) model with the Boltzmann equation, Burnett equations are computed by means of the second-order Chapman-Enskog expansion of the ES-BGK model. It is found that the Burnett equations for the ES-BGK model with the correct Prandtl number are identical to the Burnett equations for the Boltzmann equation for Maxwell molecules (fifth-order power potentials). However, for other types of particle interaction, the Boltzmann Burnett equations cannot be reproduced from the ES-BGK model.Furthermore, the linear stability of the ES-BGK Burnett equations is discussed. It is shown that the ES-BGK Burnett equations are linearly stable for Prandtl numbers of and for , while they are linearly unstable for and .Received: 29 April 2003, Accepted: 20 June 2003PACS: 510.10.-y, 47.45.-n Correspondence to: Y. Zheng     

A study of shock wave interaction with a rotating cylinder

Shock wave reflection over a rotating circular cylinder is numerically and experimentally investigated. It is shown that the transition from the regular reflection to the Mach reflection is promoted on the cylinder surface which rotates in the same direction of the incident shock motion, whereas it is retarded on the surface that rotates to the reverse direction. Numerical calculations solving the Navier-Stokes equations using extremely fine grids also reveal that the reflected shock transition from RR MR is either advanced or retarded depending on whether or not the surface motion favors the incident shock wave. The interpretation of viscous effects on the reflected shock transition is given by the dimensional analysis and from the viewpoint of signal propagation.Received: 24 April 2002, Accepted: 16 August 2002, Published online: 25 March 2003     

Effect of energy addition on MR $\rightarrow$ RR transition

A combined computational and experimental study was performed to investigate the effect of a single laser energy pulse on the transition from a Mach Reflection (MR) to a Regular Reflection (RR) in the Dual Solution Domain (DSD). The freestream Mach number is 3.45 and two oblique shock waves are formed by two symmetric wedges. These conditions correspond to a point midway within the DSD wherein either an MR or an RR is possible. A steady MR was first obtained experimentally and numerically, then a single laser pulse was deposited above the horizontal center plane. In the experiment, the laser beam was focused resulting in a deposition volume of approximately 3 mm³, while in the simulation, the laser pulse was modeled as an initial variation of the temperature and pressure using Gaussian profile. A grid refinement study was conducted to assess the accuracy of the numerical simulations. For the steady MR, the simulation showed the variation of Mach stem height along the span due to side effects. The predicted spanwise averaged Mach stem height was 1.96 mm within 2% of the experimental value of 2 mm. The experiment showed that the Mach stem height decreased to 30% of its original height due to the interaction with the thermal spot generated by the laser pulse and then returned to its original height by s. That the Mach stem returned to its original height was most likely due to freestream turbulence in the wind tunnel. The numerical simulation successfully predicted the reverse transition from a stable MR to a stable RR and the stable RR persisted across the span. This study showed the capability of a laser energy pulse to control the reverse transition of MR RR within the Dual Solution Domain.     

Time-of-flight diode-laser velocimeter using a locally seeded atomic absorber: Application in a pulse detonation engine

A diode-laser velocimeter based on atomic absorption spectroscopy has been developed and applied to a pulse detonation engine (PDE). The velocimeter uses a salt-coated sting to seed an atomic absorber at any desired location and a single, fixed-wavelength diode laser to monitor the absorber's presence downstream of the sting. Salt particles stripped from the sting tend to form distinct "clouds" of the atomic absorber rather than a uniform absorber stream. Gas velocity is inferred by measuring the time of flight of these clouds over a known distance. The properties of the salt coating can, in principle, be adjusted to tailor the velocimeter to a variety of flows and optimize its time response. In a PDE operating on C₂H₄ / O₂, CsCl salt was seeded from a 150 m diameter sting, and the D₂ transition of atomic Cs near 852 nm was probed. Gas velocity histories, spanning 0-1000 m/s over a duration of 6 ms, were recorded in the PDE and used to validate detonation models. Images obtained using an array of stings in a PDE are presented to demonstrate the potential for multidimensional velocimetry and to provide insight into the physics of the salt seeding.Received: 24 June 2002, Accepted: 23 January 2003, Published online: 25 March 2003PACS: 07.60.-j, 47.40.-x, 82.33.VxS.T. Sanders: Present address: 109 Engineering Research Bldg., 1500 Engineering Dr., Madison, WI 53706, USAAn abridged version of this paper was presented at the 23rd Int. Symposium on Shock Waves at Fort Worth, Texas, from July 22 to 27, 2001     

On the Local Smoothness of Solutions of the Navier–Stokes Equations

We consider the Cauchy problem for incompressible Navier–Stokes equations with initial data in , and study in some detail the smoothing effect of the equation. We prove that for T < ∞ and for any positive integers n and m we have , as long as stays finite.     

Unsteady drag on a sphere by shock wave loading

The dynamic drag coefficient of a sphere by shock wave loading is investigated numerically and experimentally. The diameter of the sphere is varied from 8 m to 80 mm in numerical simulation. The axisymmetric Navier-Stokes equations are solved on a fine grid, and the grid convergence of the drag coefficient is achieved. The numerical result is validated by comparing the experimental data of a 80 mm sphere, measured by the accelerometer in a vertical shock tube. It is found that the sphere experiences in the early interaction one order higher drag than in the steady state. A transient negative drag, mainly resulting from the focusing of shock wave on the rear side of the sphere, is observed only for high Reynolds number flows, and the drag becomes positive because of increased skin friction for low Reynolds number flows.Received: 10 March 2004, Accepted: 24 May 2004, Published online: 20 August 2004[/PUBLISHED]M. Sun: Send offprints requests to     

Nonextensive statistical mechanics: A brief introduction

Boltzmann-Gibbs statistical mechanics is based on the entropy . It enables a successful thermal approach to ubiquitous systems, such as those involving short-range interactions, markovian processes, and, generally speaking, those systems whose dynamical occupancy of phase space tends to be ergodic. For systems whose microscopic dynamics is more complex, it is natural to expect that the dynamical occupancy of phase space will have a less trivial structure, for example a (multi)fractal or hierarchical geometry. The question naturally arises whether it is possible to study such systems with concepts and methods similar to those of standard statistical mechanics. The answer appears to be yes for ubiquitous systems, but the concept of entropy needs to be adequately generalized. Some classes of such systems can be satisfactorily approached with the entropy (with , and ). This theory is sometimes referred in the literature as nonextensive statistical mechanics. We provide here a brief introduction to the formalism, its dynamical foundations, and some illustrative applications. In addition to these, we illustrate with a few examples the concept of stability (or experimental robustness) introduced by B. Lesche in 1982 and recently revisited by S. Abe.Received: 27 May 2003, Accepted: 27 August 2003, Published online: 11 February 2004PACS: 05.10.-a, 05.20.Gc, 05.20.-y, 05.45.-a, 05.70.Ln, 05.90. + m, 05.60.CdCorrespondence to: C. Tsallis     

Structure and stability of one-dimensional detonationsin ethylene-air mixtures

The propagation of one-dimensional detonations in ethylene-air mixtures is investigated numerically by solving the one-dimensional Euler equations with detailed finite-rate chemistry. The numerical method is based on a second-order spatially accurate total-variation-diminishing scheme and a point implicit, first-order-accurate, time marching algorithm. The ethylene-air combustion is modeled with a 20-species, 36-step reaction mechanism. A multi-level, dynamically adaptive grid is utilized, in order to resolve the structure of the detonation. Parametric studies over an equivalence ratio range of for different initial pressures and degrees of detonation overdrive demonstrate that the detonation is unstable for low degrees of overdrive, but the dynamics of wave propagation varies with fuel-air equivalence ratio. For equivalence ratios less than approximately 1.2 the detonation exhibits a short-period oscillatory mode, characterized by high-frequency, low-amplitude waves. Richer mixtures ( 1.2$" align="middle" border="0"> ) exhibit a low-frequency mode that includes large fluctuations in the detonation wave speed. At high degrees of overdrive, stable detonation wave propagation is obtained. A modified McVey-Toong short-period wave-interaction theory is in excellent agreement with the numerical simulations.Received: 13 September 2004, Revised: 1 November 2004, Published online: 3 March 2005[/PUBLISHED]Correspondence to: S. Yungster     

Superstable Manifolds of Semilinear Parabolic Problems

We investigate the dynamics of the semiflow φ induced on H₀¹(Ω) by the Cauchy problem of the semilinear parabolic equation

On the Deformation of the Circumflex Coronary Artery During Inflation Tests at Constant Length

Here we investigate whether the deformation observed in an experiment in which the porcine circumflex coronary artery is subjected to inflation at constant length included in the class, , , . We find that this is not the case and discuss its implications in the study of the mechanics of this artery. Moreover, we identify and quantify the uncertainty in the value of the invariants of the left Cauchy–Green tensor inferred from the 2D motion of markers affixed to the surface of the test specimen, and suggest that 3D tracking of markers is needed due to inherent bending and twisting induced by pressurization in vitro.     

Two-dimensional numerical study of planar shock-wave/moving-body interactions

The interaction of a planar shock wave with a body moving at supersonic speed has been considered with particular focus on shock-on-shock interactions. Three interaction types were previously identified by Smyrl (1964). This work adds a fourth type to these interactions and restates the interaction type classification and the transitions between the various interaction types. A pseudo-steady analysis of key interaction points and flow features is used to predict the various transitions. The criteria presented here are compared to results from a numerical Euler model of the interactions. A comparison of results from the numerical model with experimental results shows good agreement and thus the existence of the various interaction types and transition criteria have been confirmed using the numerical model.Received: 28 November 2002, Accepted: 23 August 2003, Published online: 12 November 2003Correspondence to: C. LawL.T. Felthun: Present address: Fluent Inc., 10 Cavendish Court, Centerra Resource Park, Lebanon, NH 03766, USAAspects of this work were presented at the 23 ISSW by Law et al. (2001)     

Convection induced by the selective absorption of radiation for the Brinkman model

Convection induced by the selective absorption of radiation in a porous medium is studied analytically and numerically using the Brinkman model. Both linear instability analysis and nonlinear stability analysis are employed. The thresholds show excellent agreement so that the region of potential subcritical instabilities is very small, demonstrating that linear theory is accurate enough to predict the onset of convective motion. A surprising result shows that the critical Rayleigh number increases linearly as (Darcy number x Brinkman coefficient / dynamic viscosity of the fluid) increases.Received: 6 May 2003, Accepted: 26 May 2003     

Global Attractors: Topology and Finite-Dimensional Dynamics

Many dissipative evolution equations possess a global attractor with finite Hausdorff dimension d. In this paper it is shown that there is an embedding X of into , with N=[2d+2], such that X is the global attractor of some finite-dimensional system on with trivial dynamics on X. This allows the construction of a discrete dynamical system on which reproduces the dynamics of the time T map on and has an attractor within an arbitrarily small neighborhood of X. If the Hausdorff dimension is replaced by the fractal dimension, a similar construction can be shown to hold good even if one restricts to orthogonal projections rather than arbitrary embeddings.     

Thermodynamic stability conditions for nonadditive composable entropies

The thermodynamic stability conditions (TSC) of nonadditive and composable entropies are discussed. Generally the concavity of a nonadditive entropy with respect to internal energy is not equivalent to the corresponding TSC. It is shown that both the TSC of Tsallis entropy and that of the -generalized Boltzmann entropy are equivalent to the positivity of the standard heat capacity.Received: 29 May 2003, Accepted: 28 August 2003, Published online: 9 December 2003PACS: 05.20.-y, 05.70.-a, 05.90. + m     

On the Helmholtz-Boltzmann thermodynamics of mechanical systems

In an 1884 paper, Boltzmann showed that for a one-dimensional mechanical system with a convex potential energy that depends on a parameter V, it is possible to define a temperature T, pressure p, and entropy S that satisfy the Gibbs relation TdS = de + p dV, where . In the paper we review the extension of the Boltzmann construction to general natural mechanical systems endowed with a fibration over the (possibly multidimensional) space of macroscopic parameters. Moreover, for certain discrete mechanical systems with non-convex potential energies, which are used as models for phase transitions in solids, we compare the thermodynamic pressure p = p(e,V) introduced above with the quasi-static, macroscopic, stress-strain relation.Received: 20 February 2002, Accepted: 19 May 2003PACS: 5.20.y, 5.45.a, 5.70.ce Correspondence to: F. Cardin