Jouguet Condition Research Articles

Asymptotic Analysis of Plane Steady Detonations

Steady-state solutions for a first order, one-step, irreversible unimolecular reaction of the Arrhenius kind are analyzed on the basis of activation-energy asymptotics. In this limit, it is found that steady solutions exist only when the flame temperature $T_ * $ lies in an interval $[ T_{ * \min } ,T_{ * \max } )$. Here $T_{ * \min } $ corresponds to the weak detonation and $T_{ * \max } $ corresponds to the ZND limit of strong detonation. In particular, when $T_ * $ is sufficiently large (and hence for the ZND limit), not all the reactant is consumed at the flame, a small remainder being burnt over large distances behind the flame. The analysis covers both the weak detonation and all strong detonations for general and Chapman–Jouguet conditions. Typical velocity and temperature profiles are computed and plotted for $T_ * $ ranging from the ZND detonation limit to the shock-after-weak detonation limit.

Ponderomotive pressure effects in laser driven high-temperature plasma flows

Gasdynamical equations taking radiation energy density and ponderomotive pressure into account are investigated. Conditions for these quantities to be important are stated: low absorption, reflexion at cut-off. The density ratio in a discontinuity is studied as a function of ponderomotive pressure, absorbed intensity and Mach number in the initial state. Chapman–Jouguet conditions are defined. Compressive (R type) flows and rarefaction (D type) appear. The structure of the latter is discussed including plasma effects.

Self-similar motion of laser half-space plasmas. I. Deflagration regime

The one-dimensional self-similar motion of an initially cold, half-space plasma of electron density n0, produced by the (anomalous) absorption of a laser pulse of irradiation φ =φ0t/τ (0<t⩽τ) at the critical density nc(nc/n0≡ε≪1), is considered. The analysis allows for electron heat conduction and ion-electron energy exchange and retains three dimensionless numbers: ε, Zi (ion charge number), and α= (9k/4mi) (τk2n20/φ0K̄e)2/3, where k, mi are Boltzmann’s constant and the ion mass, and K̄e × (electron temperature)5/2 = heat conductivity. If α ≫ε−4/3, a deflagration wave separates an isentropic compression with a shock bounding the undisturbed plasma, and an isentropic expansion flow to the vacuum. The structures of these three regions are completely determined; in particular, the Chapman–Jouguet condition is proved and the density behind the deflagration is found. The deflagration-compression thickness ratio is large (small) for α≪ε−5/3(α≫ε−5/3). The compression to expansion ratio for both energy and thickness is O (ε1/2). For Zi large, a deflagration exists even if α∼ε−4/3. Condition α≫ε−4/3 may be applied to pulses that are not linear.

Flow of a gas behind a Chapman-Jouguet detonation wave in the vicinity of a line of discontinuity of a surface wave curvature

This paper discusses questions of constructing a solution of the gasdynamic equations near a line of curvature discontinuity at the surface of a detonation wave, propagating under Chapman—Jouguet conditions. It describes the construction of the solution in two cases: in a flow arising with the initiation of a detonation along a half-plane in a quiescent homogeneous combustible gas and in a flow arising with the initiation of a detonation along a half-line under these same conditions.

On scattering of a gas behind deflagration waves propelled by powerful radiation fluxes

Two self-similar problems about plane nonstationary gas scattering in a vacuum behind a deflagration wave for which the conservation laws are satisfied are considered. The energy flux density is considered to vary according to a power law. In the first problem the gas is transparent and scattered adiabatically. The solution is found analytically. It is shown that the Jouguet condition is conserved for a flux growing with time, while such a condition is not satisfied for a decreasing flux, and the parameters on the wave depend on the flow behind it. In the second problem, the gas absorbs radiation, where the absorption coefficient varies from infinitely large to infinitely small at some transparency temperature. The motion is isothermal. A definite fraction of the incident energy, corresponding to the effective optical thickness ∼0.25, is extracted in the gas.

Transverse ionizing MHD detonation waves. Part 2. Numerical simulation

A numerical method for simulating the temporal evolution of an ionizing MHD detonation, is presented, together with flow profiles for various combinations of imposed magnetic field and ionization temperature in the limit of large downstream conductivity. The propagation speeds asymptotically approach the values predicted by the jump relations and the MHD Chapman–Jouguet condition. The downstream flow approaches a self-similar solution. The wave evolution is discussed for situations where the Chapman–Jouguet and jump relations admit either no solution or multiple solutions.

Magnetogasdynamic deflagration under the Chapman-Jouguet condition

An investigation is made into the propagation of a one-dimensional combustion wave, which consists of a flame front and a precursor shock wave which pass down a tube closed at one end, in the presence of a transverse magnetic field in the undisturbed gas at rest. The shock wave is assumed to be of sufficient strength to ionize completely the initially non-electrically-conducting gas and the conditions at the flame front are taken to satisfy the Chapman–Jouguet condition. Details of the solution are compared with the corresponding results for ordinary gasdynamic deflagration.