John F. Clarke

On the direct initiation of a plane detonation wave

It is assumed that energy is transferred at a rapid rate through a plane wall into a spatially uniform and initially stagnant combustible gas mixture. This action generates a shock wave, just as it does in an inert mixture, and also switches on a significant rate of chemical reaction. The Navier-Stokes equations for plane unsteady flow are integrated numerically in order to reveal the subsequent history of events. Four principal time domains are identified, namely ‘early’, ‘transitional’, ‘formation’ and ‘ZND’. The first contains a conduction-dominated explosion and formation of a shock wave; in the second interval the shock wave is responsible for the acceleration of chemical activity, which becomes intense during the ‘formation’ period. Finally a wave whose structure is in essence that of a ZND detonation wave emerges.

Second Order Theory of Unsteady Burner-Anchored Flames With Arbitrary Lewis Number

Three theoretical models of plane flames burning on a cooled porous-plug type of flame-holder are reviewed and compared with experimentally observed relationships between stand-off distance, flame speed and temperature. It is shown that for most practical burners their conductance is large and that for near adiabatic conditions, the order of the non-dimensional stand-off distance ceases to be O (1), but is O (O) where O is the non-dimensional activation energy. Starting in 1946 as the College of Aeronautics, the Cranfield Institute of Technology was granted university status in 1969. In 1993 it changed its name to Cranfield University.

On the Evolution of Plane Detonations

Numerical solutions of the Navier–Stokes equations for the plane one-dimensional unsteady motion of a compressible, combustible gas mixture are used to follow the history of events that are initiated by addition of large heat power through a solid surface bounding an effectively semi-infinite domain occupied by the gas. Plane Zel’dovich–von Neumann–Doring detonations eventually appear either at the precursor shock (which exists in every set of circumstances) or in the regions, occupied by an unsteady induction-domain and an initially quasi-steady fast-flame, that lie behind the precursor shock.

The Structure of a Reaction-Broadened Diffusion Flame

Abstract Results of an experimental investigation of the structure of flat diffusion flames on a Parker-Wolf hard burner are compared with theoretical predictions of perturbation solutions which incorporate realistic schemes for the chemical kinetics. Measurements of hydroxyl radical concentrations show that the flames are reaction-broadened for temperatures below I950°K, while at higher temperatures reaction zone structure is of equilibrium-broadened type. Experiment also shows that, close to extinction, there is significant convective transfer of material from one stream to the other at the flame base. It is suggested that the consequent disruption of mixing in, or shielding of, the reaction zone makes extinction a progressive process. Complementary studies of spherical and counter flow diffusion flames suggest that the former geometry is preferable in future studies designed to test hypotheses about the role of kinetics in diffusion flame extinction.

On changes in the structure of steady plane flames as their speed increases

Abstract By identifying a number of simple distinguished limit relations between inlet flow Mach number and chemical reaction activation energy it is shown that the structural features of a plane steady flame fall into several distinct classes, as follows. When the Mach number is very small the flame is of the well-known thermal type, with a convection-diffusion-dominated preheat zone followed by a flame sheet within which diffusion and reaction balance one another. A small increase in Mach number requires the insertion of a zone [in which convection, diffusion, and a (slow) reaction are all balanced] between the plane flame holder and thermal type of flame, which now “rides” on this precursor at some substantial distance from the holder. Further increases in Mach number find a long convection-reaction balance precursor ahead of the convection-diffusion-reaction domain, with a weakening amplitude thermal flame riding far downstream on this combined form of precursor. Yet further increases in Mach number banish diffusive processes to lower-order significance; each fluid element now exists essentially independently of its neighbors and the flame is formed from a simple Semenov type of explosion process, convected downstream at the local flow velocity. All Mach numbers remain small.

A Numerical Study of Tunnel Fires

Abstract Abstract-Three theoretical models of plane flames burning on a cooled porous-plug type of flame-holder are reviewed and compared with experimentally observed relationships between stand-off distance, flame speed and temperature. It is shown that for most practical burners their conductance is large and that for near adiabatic conditions, the order of the non-dimensional stand-off distance ceases to be 0(1), but is O(ln θ) where θ is the non-dimensional activation energy.

Transient phenomena in the initiation of a mechanically driven plane detonation

Significant exothermic chemical activity in a combustible gas is switched on by a strong plane shock wave created by mechanical-power input from a piston. The Euler equations, written in terms of a lagrangian coordinate system, are used to model behaviour in the space between piston and shock. Since a primary aim is to follow the development of additional shocks, created by the release of chemical power, numerical solution of the problem is sought via the Random Choice Method combined with time-operator-splitting. Some effort is expended in bringing together in the text a number of facts, including some mathematically exact statements that are central to the analysis and comprehension of the numerical results. Thermal runaway takes place first in a small region, adjacent to the piston face, within which there is found high pressure, high temperature and comparatively low density. As a consequence of the way in which gas has been conditioned in the unsteady induction domain downstream of the precursor shock, a quasi-steady weak detonation appears at the head of the runaway region, and travels quickly into the induction domain. Continuing chemical power release behind this, decelerating, weak detonation creates a region of high pressure, high temperature and, now, high density too. A consequence of all of this activity is a gas velocity significantly in excess of the piston velocity. There must therefore be a region of strong expansion, between the location of peak-pressure and the piston face, whose task is to reduce flow velocities. Since intense chemical activity continues throughout the region within which all of these events take place, part of the pressure drop is accomplished through the action of a quasi-steady fast flame. As reactant material is consumed, further reductions of pressure take place through an inert expansion wave. The reaction shock, the unsteady reactive domain adjacent to it downstream, and the fast flame downstream of that, make up the elements of the ‘triplet’ that has been observed in earlier studies to precede formation of Zeldovich–von-Neumann–Döring (ZND) detonation. Precisely the same thing happens here, although this is the first time that creation of the ‘triplet’ from purely mechanical power input has been observed. The ZND-wave is of Chapman–Jouguet strength, and the inert expansion soon resolves itself into the classical Taylor wave. This system is still travelling in the slightly perturbed induction domain behind the precursor shock at the time that numerical calculations cease.

On the Structure of a Hydrogen-Oxygen Diffusion Flame

A simplified scheme of four chemical reactions is chosen to represent the kinetics of the hydrogen-oxygen system; in particular, this scheme includes the influence of the hydroxyl radical. The diffusion flame supported by this set of reactions is assumed to form behind a (planar, two-dimensional) body of parabolic meridian profile with downstream-pointing vertex. The body initially separates the oxygen and hydrogen streams, which are assumed to have equal speeds and pressures far upstream. (The pressure is subsequently assumed to be constant everywhere.) For pressures of about one atmosphere it is found that nett reaction rates can be treated as infinitely fast; the four reactions then yield four chemical equilibrium equations whose behaviour is dominated by the largeness of the equilibrium constant for the (thermal) dissociation-recombination reaction of hydrogen. The flame-sheet model emerges as the limiting solution when the reciprocal of this large quantity is allowed to vanish. The method of matched asymptotic expansions is used to investigate the structure of the flame which results from a relaxation of this limit. The results bear a satisfactory resemblance to some experimental measurements which, although made in other gas mixtures, exemplify the behaviour of the type of diffusion flames considered.

Some unsteady motions of a diffusion flame sheet

A study is made of the response of a diffusion flame sheet to perturbations of reactant concentration which are introduced, either as changes in the free streams, or as appropriate initial distributions throughout the field. Species’ and energy conservation requirements are approximated by linearized boundary-layer equations; general solutions are derived for species, enthalpy and temperature distributions, as well as for the flame sheet shape, and a number of specific problems are solved.

Accumulating sequence of ignitions from a propagating pulse

Abstract Some surprising effects are seen in studying numerically the evolution of a propagating pulse of pressure in a medium reacting via a one-step exothermic Arrhenius reaction. The length and amplitude of the pulse are taken to be large enough for steepening effects to be important and for enhanced reaction to lead to a substantial reduction in ignition time. The evolution proceeds through a repeated sequence of similar stages involving: shock-formation and growth; ignition behind the shock; and the generation of another propagating pressure pulse. Substantial unsteady behavior is seen to be engendered by the entropy released through shock formation. A number of unsteady reignitions are seen to culminate in a pressure-peak, substantially higher than the von Neumann spike of a Chapman-Jouget wave, during the formation of a transient overdriven detonation; this decays subsequently towards a Chapman-Jouget state. It is conjectured that this sort of evolution may well be generic to ignition via a range of pressure-pulses in state-sensitive systems. A saturation of, or relative reduction in, the reactions thermal sensitivity ultimately prevents the reignition process after shock-formation from happening quickly enough to continue its repetition. As such, the behavior should be strongly dependent on the nature of the chemical model and is likely to be modified significantly by changes in the chemical mechanism.