Rankine-Hugoniot Relations in Relativistic Combustion Waves

As a foundational element describing relativistic reacting waves of relevance to astrophysical phenomena, the Rankine-Hugoniot relations classifying the various propagation modes of detonation and deflagration are analyzed in the relativistic regime, with the results properly degenerating to the non-relativistic and highlyrelativistic limits. The existence of negative-pressure downstream flows is noted for relativistic shocks, which could be of interest in the understanding of the nature of dark energy. Entropy analysis for relativistic shock waves are also performed for relativistic fluids with different equations of state (EoS), denoting the existence of rarefaction shocks in fluids with adiabatic index \Gamma < 1 in their EoS. The analysis further shows that weak detonations and strong deflagrations, which are rare phenomena in terrestrial environments, are expected to exist more commonly in astrophysical systems because of the various endothermic reactions present therein. Additional topics of relevance to astrophysical phenomena are also discussed.Comment: 34 pages, 9 figures, accepted for publication in Ap

Magnetic reconnection detonation in supernova remnants

As a key process that refreshes the interstellar medium, the dynamics and radiative properties of the supernova remnant (SNR) expansion front not only reflect the physical environment of the old interstellar medium (ISM) surrounding the supernova, but they also provide information about the refreshed ISM. However the expansion dynamics of SNRs cannot be simply explained by the conventional law of spherical shock wave propagation; on the other hand, the high energy radiation requires an additional electron acceleration mechanism in the shock front beyond thermal collision. We consider herein the detonation wave description of the SNR expansion, in which magnetic reconnection follows the shock front and transfers the SNR magnetic field energy to both fluid thermal energy and particle kinetic energy. The structure of the magnetic reconnection detonation (MRD) is identified based on scaling analysis in this paper. By applying the MRD description of the SNR expansion shock to the example of the Crab Nebula, this paper shows that the MRD description can explain both the accelerative expansion of the nebula as well as the origin of the luminous expanding shell.Comment: Accepted for publication in Ap

On the Structure and Stabilization Mechanisms of Planar and Cylindrical Premixed Flames

The configurational simplicity of the stationary one-dimensional flames renders them intrinsically attractive for fundamental flame structure studies. The possibility and fidelity of studies of such flames on earth, however, have been severely restricted by the unidirectional nature of the gravity vector. To demonstrate these complications, let us first consider the premixed flame. Here a stationary, one-dimensional flame can be established by using the flat-flame burner. We next consider nonpremixed flames. First it may be noted that in an unbounded gravity-free environment, the only stationary one-dimensional flame is the spherical flame. Indeed, this is a major motivation for the study of microgravity droplet combustion, in which the gas-phase processes can be approximated to be quasi-steady because of the significant disparity between the gas and liquid densities for subcritical combustion. In view of the above considerations, an experimental and theoretical program on cylindrical and spherical premixed and nonpremixed flames in microgravity has been initiated. For premixed flames, we are interested in: (1) assessing the heat loss versus flow divergence as the dominant stabilization mechanism; (2) determining the laminar flame speed by using this configuration; and (3) understanding the development of flamefront instability and the effects of the flame curvature on the burning intensity

Regulation of Wages and Hours Prior to 1938

Direct numerical simulations are performed to investigate the transient upstream propagation (flashback) of premixed hydrogen–air flames in the boundary layer of a fully developed turbulent channel flow. Results show that the well-known near-wall velocity fluctuations pattern found in turbulent boundary layers triggers wrinkling of the initially flat flame sheet as it starts propagating against the main flow direction, and that the structure of the characteristic streaks of the turbulent boundary layer ultimately has an important impact on the resulting flame shape and on its propagation mechanism. It is observed that the leading edges of the upstream-propagating premixed flame are always located in the near-wall region of the channel and assume the shape of several smooth, curved bulges propagating upstream side by side in the spanwise direction and convex towards the reactant side of the flame. These leading-edge flame bulges are separated by thin regions of spiky flame cusps pointing towards the product side at the trailing edges of the flame. Analysis of the instantaneous velocity fields clearly reveals the existence, on the reactant side of the flame sheet, of backflow pockets that extend well above the wall-quenching distance. There is a strong correspondence between each of the backflow pockets and a leading edge convex flame bulge. Likewise, high-speed streaks of fast flowing fluid are found to be always colocated with the spiky flame cusps pointing towards the product side of the flame. It is suggested that the origin of the formation of the backflow pockets, along with the subsequent mutual feedback mechanism, is due to the interaction of the approaching streaky turbulent flow pattern with the Darrieus–Landau hydrodynamic instability and pressure fluctuations triggered by the flame sheet. Moreover, the presence of the backflow pockets, coupled with the associated hydrodynamic instability and pressure–flow field interaction, greatly facilitate flame propagation in turbulent boundary layers and ultimately results in high flashback velocities that increase proportionately with pressure

Thermal-Diffusional Instability in White Dwarf Flames: Regimes of Flame Pulsation

Thermal-diffusional pulsation behaviors in planar as well as outwardly and inwardly propagating white dwarf carbon flames are systematically studied. In the 1D numerical simulation, the asymptotic degenerate equation of state and simplified one-step reaction rates for nuclear reactions are used to study the flame propagation and pulsation in white dwarfs. The numerical critical Zel'dovich numbers of planar flames at different densities ($\rho=2$, 3 and 4$\times 10^7$~g/cm$^3$) and of spherical flames (with curvature $c=$-0.01, 0, 0.01 and 0.05) at a particular density ($\rho=2\times 10^7$~g/cm$^3$) are presented. Flame front pulsation in different environmental densities and temperatures are obtained to form the regime diagram of pulsation, showing that carbon flames pulsate in the typical density of $2\times10^7~{\rm g/cm^3}$ and temperature of $0.6\times 10^9~{\rm K}$. While being stable at higher temperatures, at relatively lower temperatures the amplitude of the flame pulsation becomes larger. In outwardly propagating spherical flames the pulsation instability is enhanced and flames are also easier to quench due to pulsation at small radius, while the inwardly propagating flames are more stable.Comment: ApJ, 841, 21 (2017), 25 pages in arxiv versio

Influence of gas compression on flame acceleration in the early stage of burning in tubes

The mechanism of finger flame acceleration at the early stage of burning in tubes was studied experimentally by Clanet and Searby [Combust. Flame 105: 225 (1996)] for slow propane-air flames, and elucidated analytically and computationally by Bychkov et al. [Combust. Flame 150: 263 (2007)] in the limit of incompressible flow. We have now analytically, experimentally and computationally studied the finger flame acceleration for fast burning flames, when the gas compressibility assumes an important role. Specifically, we have first developed a theory through small Mach number expansion up to the first-order terms, demonstrating that gas compression reduces the acceleration rate and the maximum flame tip velocity, and thereby moderates the finger flame acceleration noticeably. This is an important quantitative correction to previous theoretical analysis. We have also conducted experiments for hydrogen-oxygen mixtures with considerable initial values of the Mach number, showing finger flame acceleration with the acceleration rate much smaller than those obtained previously for hydrocarbon flames. Furthermore, we have performed numerical simulations for a wide range of initial laminar flame velocities, with the results substantiating the experiments. It is shown that the theory is in good quantitative agreement with numerical simulations for small gas compression (small initial flame velocities). Similar to previous works, the numerical simulation shows that finger flame acceleration is followed by the formation of the "tulip" flame, which indicates termination of the early acceleration process.Comment: 19 pages, 20 figure

Turbulence decay and cloud core relaxation in molecular clouds

The turbulent motion within molecular clouds is a key factor controlling star formation. Turbulence supports molecular cloud cores from evolving to gravitational collapse and hence sets a lower bound on the size of molecular cloud cores in which star formation can occur. On the other hand, without a continuous external energy source maintaining the turbulence, such as in molecular clouds, the turbulence decays with an energy dissipation time comparable to the dynamic timescale of clouds, which could change the size limits obtained from Jean's criterion by assuming constant turbulence intensities. Here we adopt scaling relations of physical variables in decaying turbulence to analyze its specific effects on the formation of stars. We find that the decay of turbulence provides an additional approach for Jeans' criterion to be achieved, after which gravitational infall governs the motion of the cloud core. This epoch of turbulence decay is defined as cloud core relaxation. The existence of cloud core relaxation provides a more complete understanding in the competition between turbulence and gravity on the dynamics of molecular cloud cores and star formation.Comment: 18 pages, 1 figure, accepted for publication in Ap