The early stages of hydrogen–air and methane–air flame dynamics and the development and evolution of tulip flames in closed tubes of various aspect ratios and in a semi-open tube are studied by solving the fully compressible reactive Navier–Stokes equations using a high-order numerical method coupled to detailed chemical models for stoichiometric hydrogen/air and methane/air mixtures. The use of adaptive mesh refinement (AMR) provides adequate resolution of the flame reaction zone, pressure waves, and flame–pressure wave interactions. The purpose of this study is to gain a deeper insight into the influence of chemical kinetics on the combustion regimes leading to the formation of a tulip flame and its subsequent evolution. The simulations highlight the effect of the flame thickness, flame velocity, and reaction order on the intensity of the rarefaction wave generated by the flame during the deceleration phase, which is the principal physical mechanism of tulip flame formation. The obtained results explain most of the experimentally observed features of tulip flame formation, e.g., faster tulip flame formation with a deeper tulip shape for faster flames compared to slower flames.

The effects of flame collision with pressure waves during hydrogen/air flame propagation in a two-dimensional channel with non-slip adiabatic walls are studied for channels with different aspect ratios and a semi-open channel. The problem is solved by direct numerical simulations of the fully compressible Navier-Stokes equations coupled to a detailed chemical model for a stoichiometric hydrogen-air mixture using a high-order numerical code in space and time that provides adequate resolution of a flame and the flame-pressure wave interactions. It is shown that the flame–pressure wave interactions play an important role in the tulip flame formation and its further evolution to a distorted tulip flame (DTF). In particular, flame collisions with pressure waves reflected from the opposite end of the tube significantly enhance the effect of the first rarefaction wave generated by the decelerating flame in the unburned gas when the skirt of the “finger” flame touches the tube sidewalls. This is why the tulip-shaped flame is more pronounced in channels with both ends closed than in a semi-open tube. It is shown that the flame instabilities are not involved in the tulip flame formation, while the Rayleigh-Taylor instability caused by the flame collisions with the reflected pressure waves is the main factor in the DTF formation, in agreement with previous studies. We show that the wavelength of the fastest growing mode of the RT instability corresponds to the size of the bulges formed on the tulip flame lips.

A hydrogen/air flame propagation and the development of tulip-shaped flame in 2D tubes of different aspect ratios with both closed ends and in a half-open rectangular channel were studied using high resolution direct numerical simulations of the fully compressible Navier–Stokes equations coupled with a detailed chemistry. Flame propagation in a 3D rectangular channel was studied using large eddy simulations and compared with the results of direct numerical simulations of flame propagation in a 2D rectangular channel with the same aspect ratio. It is shown that the interaction of the rarefaction wave generated by the flame at the deceleration stage with the “positive” flow of unburned gas generated by the flame at the previous accelerating stage leads to a significant decrease of the velocity of the unburned gas flow in the near field zone ahead of the flame front. As a result, the thickness of the boundary layer in the near-field zone ahead of the flame increases significantly, and the profile of the axial velocity of the unburned gas in the near-field zone ahead of the flame front takes the form of a tulip or an inverted tulip, which leads to corresponding changes in the velocities of different parts of the flame front, the flame front inversion, and the formation of a tulip-shaped flame.

The advancement of highly boosted internal combustion engines (ICEs) with high thermal efficiency is mainly constrained by knock and super-knock, respectively, due to the end gas autoignition and detonation development. The pressure wave propagation and reflection in a small confined space may strongly interact with local end gas autoignition, leading to combustion characteristics different from those in a large chamber or open space. The present study investigates the transient autoignition process in an iso-octane/air mixture inside a closed chamber under engine-relevant conditions. The emphasis is given to the assessment of effects of the pressure wave-wall reflection and the mechanism of extremely strong pressure oscillation typical for super-knock. It is found that the hot spot induced autoignition in a closed chamber can be greatly affected by shock/pressure wave reflection from the end wall. Different autoignition modes respectively from the hot spot and the end wall reflection are identified. A non-dimensional parameter quantifying the interplay between different length and time scales is introduced, which helps to identify different autoignition regimes including detonation development near the end wall. It is shown that detonation development from the hot spot may cause super-knock with devastating pressure oscillation. However, the detonation development from the end wall can hardly produce pressure oscillation strong enough for the super-knock. The obtained results provide a fundamental insight into the knocking mechanism in engines under highly boosted conditions.

This book provides the latest achievements and original research work in physics of combustion processes and application of the methods developed in combustion physics for astrophysical problems of stars burning, supernovae explosions and a confined thermonuclear fusion. All the materials in the book are presented in a concise and easily accessible way, but at the same time provides a deep physical inside in the phenomena considered. It is an effective theoretical course with the direct practical implications in engineering fields of engine’s development, energy production, safety issues inherent to terrestrial combustion, as well as in thermonuclear combustion in the inertial fusion. This book is aimed at university students, Ph.D. students and engineers, as well as professionals in combustion, energy-related research, astrophysics and researchers in neighboring fields. 

The Chern-Simons (CS) gauge field theory was widely used to explain and to deeper understand the fractional quantum Hall effects. In this work, we apply the Chern-Simons gauge field theory to a two-dimensional (2D) electron-hole (e-h) system in a strong perpendicular magnetic field under the influence of the quantum point vortices creating by the Chern-Simons (CS) gauge field. The composite electron-hole particles with equal integer positive numbers phi of the attached quantum point vortices are described by the dressed field operators that obey to either the Fermi or Bose statistics depending on the even or odd numbers phi. It is shown that the phase operators, as well as the vector and scalar potentials of the CS gauge field, depend on the difference between the electron and the hole density operators. They vanish in the mean field approximation, when the average values of the electron and of the hole densities coincide. Nevertheless, even in this case, quantum fluctuations of the CS gauge field lead to new properties of the 2D e-h system. It is found that the numbers of vortices attached to each electron and hole are the same. This result is not obvious, and a different distribution of vortices in the environment of electron-hole pairs could be expected. A simple analytical formula is obtained for the shift of the magnetoexciton energy level at the point k = 0 due to the influence of the CS gauge field.

We present a high-resolution convergence study of detonation initiated by a temperature gradient in a stoichiometric hydrogen-oxygen mixture using the PENCIL CODE and compare with a code that employs a fifth order weighted essentially non-oscillating (WENO) scheme. With Mach numbers reaching 10-30, a certain amount of shock viscosity is needed in the PENCIL CODE to remove or reduce numerical pressure oscillations on the grid scale at the position of the shock. Detonation is found to occur for intermediate values of the shock viscosity parameter. At fixed values of this parameter, the numerical error associated with those small wiggles in the pressure profile is found to decrease with decreasing mesh width like down to . With the WENO scheme, solutions are smooth at , but no detonation is obtained for . This is argued to be an artifact of a decoupling between pressure and reaction fronts.

Four different spin structures of two electrons and of two holes situated on the lowest Landau levels (LLLs) are taken into account to investigate possible bound states of the two-dimensional magnetic biexciton formed of two magnetoexcitons with opposite wave vectors and antiparallel dipole moments. The singlet and triplet states of the spins of two electrons and of two holes separately, as well as of two para- and two ortho-magnetoexcitons are considered. The general expressions describing the binding energy of the bound states and the normalization conditions characterized by the effective spin parameter η=±1,±1/2 for the corresponding wave functions are derived. The most favorable of the four considered spin configurations happened to be the triplet-triplet spin structure of two electrons and of two holes. In its frame a metastable bound state with activation barrier comparable with two ionization potentials of the magnetoexciton is revealed.

The bound states of two interacting two-dimensional magnetoexcitons with electrons and holes on the lowest Landau levels (LLLs) moving in-plane of the layer with equal but opposite oriented wave vectors and forming a molecular-type structures with the resultant wave vector (k) over right arrow = 0 were investigated. Four possible spin structures of two electrons and of two holes forming the bound states were considered. Two of them lead to the formation of the para and ortho magnetoexcitons in the presence of the electron-hole (e-h) Coulomb exchange interaction. In this case we have studied the interaction of two para magnetoexcitons and of two ortho magnetoexcitons with the resultant spin equal to zero. Another two variant, are actual when the Coulomb exchange e-h interaction is negligible small and the spin of two electrons separately and the effective spin of two holes are interconected and forms the singlet or the triplet states with zero spin projections on the magnetic field direction. The spin states of the four particles were constructed combining the singlet two electron state with the singlet two hole state as well as the triplet two electron state with the triplet two hole state. Only the bound states of two electrons and of two holes with singlet-singlet and with triplet-triplet spin structures were studied. It was shown that the spin structure of the type singlet-triplet and triplet-singlet do not exist due to the hidden symmetry of the magnetoexcitons. The orbital structure of the 2D magnetoexciton with wave vector (k) over right arrow not equal 0 is similar with an in-plane electric dipole with the dipole moment perpendicularly oriented to the wave vector. The bimagnetoexciton with resultant wave vector (k) over right arrow = 0 is composed from two antiparallel oriented electric dipoles moving with antiparallel wave vectors (k) over right arrow not equal 0 Their relative motion in the frame of the bound states is characterized by the variational wave functions phi(n) ((k) over right arrow) depending on the modulus vertical bar(k) over right arrow vertical bar. It was shown that the stable bound state in the lowest Landau levels approximation do not exist in four investigated spin combinations. Instead of them a deep metastable bound state with an activation barrier comparable with the ionization potential of the magnetoexciton with (k) over right arrow = 0 was revealed in the triplet-triplet spin configuration. Its orbital structure in the momentum space representation is characterized by the maximal exciton density on the in-plane ring and with zero density in the center.

The possible formation of two-dimensional (2D) magnetic biexcitons composed of two 2D magnetoexcitons with electrons and holes on the lowest Landau levels (LLLs) with opposite center-of-mass wave vectors (k)over-right-arrow and -(k)over-right-arrow and with antiparallel electric dipole moments perpendicular to the corresponding wave vectors was investigated. Two spinor structures of two electrons and of two holes were considered. In the singlet-singlet state the spins of two electrons as well as the effective spins of two holes create the combinations with the total spin S = 0 and its projection on the magnetic field S-z = 0. The triplet-triplet state corresponds to S = 1 and S-z = 0. Two orbital Gaussian variational wave functions depending on vertical bar(k)over-right-arrow vertical bar and describing the relative motion of two magnetoexcitons inside the molecule were used. Analytical calculations show that in the LLLs approximation the stable bound states of bimagnetoexcitons do not exist, but there is a metastable bound state with the orbital wave function, having the maximum on the in-plane ring for the triplet-triplet spin configuration. The metastable bound state has an energy activation barrier comparable with the magnetoexciton ionization potential and gives rise to the new luminescence band due to the metastable biexciton-para exciton conversion with the frequencies higher than those of the para magnetoexciton luminescence line.