Flame acceleration and transition to detonation in ducts

We review recent progress in gaseous detonation experiment, modeling, and simulation. We focus on the propagating detonation wave as a fundamental combustion process. The picture that is emerging is that although all propagating detonations are unstable, there is a wide range of behavior with one extreme being nearly laminar but unsteady periodic flow and the other chaotic instability with highly turbulent flow. We discuss the implications of this for detonation propagation and dynamic behavior such as diffraction, initiation, and quenching or failure.

https://shepherd.caltech.edu/EDL/publications/reprints/proci_1374.pdf

Detonation in gases

Simulations of flame acceleration and deflagration-to-detonation transitions in methane–air systems

An analytical model for the impulse of a single-cycle pulse detonation tube has been developed and validated against experimental data. The model is based on the pressure history at the thrust surface of the detonation tube. The pressure history is modeled by a constant pressure portion, followed by a decay due to gas expansion out of the tube. The duration and amplitude of the constant pressure portion is determined by analyzing the gasdynamics of the self-similar flow behind a steadily moving detonation wave within the tube. The gas expansion process is modeled using dimensional analysis and empirical observations. The model predictions are validated against direct experimental measurements in terms of impulse per unit volume, specific impulse, and thrust. Comparisons are given with estimates of the specific impulse based on numerical simulations. Impulse per unit volume and specific impulse calculations are carried out for a wide range of fuel–oxygen–nitrogen mixtures (including aviation fuels) of varying initial pressure, equivalence ratio, and nitrogen dilution. The effect of the initial temperature is also investigated. The trends observed are explained using a simple scaling analysis showing the dependency of the impulse on initial conditions and energy release in the mixture.

/pdf/analytical-model-for-the-impulse-of-single-cycle-pulse-2ol2i7xxaq.pdf

Analytical Model for the Impulse of Single-Cycle Pulse Detonation Tube

Direct impulse measurements were carried out by using a ballistic pendulum arrangement for detonations
and deflagrations in a tube closed at one end. Three tubes of different lengths and inner diameters were tested
with stoichiometric propane– and ethylene–oxygen–nitrogen mixtures. Results were obtained as a function of
initial pressure and percent diluent. The experimental results were compared to predictions from an analytical
model and generally agreed to within 15% (Wintenberger, E., Austin, J., Cooper, M., Jackson, S., and Shepherd,
J. E., “Analytical Model for the Impulse of a Single-Cycle Pulse Detonation Engine, AIAA Paper 2001–3811,
July 2001). The effect of internal obstacles on the transition from deflagration to detonation was studied. Three
different extensions were tested to investigate the effect of exit conditions on the ballistic impulse for stoichiometric
ethylene–oxygen–nitrogen mixtures as a function of initial pressure and percent diluent.

/pdf/direct-experimental-impulse-measurements-for-detonations-and-x20q8v3h9o.pdf

Direct Experimental Impulse Measurements for Detonations and Deflagrations

Results of experimental study on DDT in a smooth tube filled with sensitive mixtures having detonation cell size from 1 to 3 orders of magnitude smaller than the tube diameter are presented. Stoichiometric hydrogen–oxygen mixtures were used in the tests with initial pressure ranging from 0.2 to 8 bar. A dependence of the run-up distance to DDT on the initial pressure is studied. This dependence is found to be close to the inverse proportionality. It is suggested that the flow ahead of the flame results in formation of the turbulent boundary layer. This boundary layer controls the scale of turbulent motions in the flow. A simple model to estimate the maximum scale of the turbulent pulsations (boundary layer thickness) at flame positions along the tube is presented. The largest scale of the turbulent motions at the location of the onset of detonation is shown to be 1 order of magnitude greater than the detonation cell widths, λ, in all the tests. It is suggested that the onset of detonation is triggered during flame acceleration as soon as the maximum scale of the turbulent pulsations increases up to about 10 λ. The model to estimate the maximum size of turbulent motions, δ, and the correlation δ≈ 10λ, give a basis for estimations of the run-up distances to DDT in tubes with internal diameter D > 20λ.

DDT in a smooth tube filled with a hydrogen–oxygen mixture

Critical conditions for onset of detonations are compared at (1) two significantly different scales, (2) for a range of 
$\rm H_2$
 -air mixtures diluted with C
 
$\rm O_2$
 , 
$\rm H_2$
 O, and (3) for two types of geometry – one a long obstructed channel and the other a room with a relatively small aspect ratios. For the range of scales, mixtures, and initial conditions tested, the detonation cell size 
$\lambda$
 was shown to be a reliable scaling parameter for characterization of detonation onset conditions. An experimental correlation is suggested for the critical detonation onset conditions. This correlation is based on a wide variety of available experimental data on DDT in mixtures of hydrogen and hydrocarbon fuels with air and on the use of detonation cell size 
$\lambda$
 as a scaling parameter characterizing the mixture.

Effect of scale on the onset of detonations

Formation of the preheated zone ahead of a propagating flame and the mechanism underlying the deflagration-to-detonation transition

The authors present experimental studies of the deflagration-to-detonation transition (DDT) in tubes with smooth and rough walls in stoichiometric hydrogen-oxygen and ethylene-oxygen mixtures. On the basis of experimental evidence, it is shown that formation of the preheat zone, where reaction is chemically frozen, promotes the transition to detonation if temperature and width of the preheat zone are above certain critical values. A sequence of high-speed Schlieren records permits an accurate determination of the minimal values of temperature and width of the preheat zone, leading to transition to detonation. The experimentally measured critical temperatures and widths of the preheat zone initiating restructuring of the flame and transition to detonation in hydrogen-oxygen and ethylene-oxygen mixtures are consistent with the developed theory.

Experimental Study of the Preheat Zone Formation and Deflagration to Detonation Transition

Experiments on the behavior of detonation waves in nonuniform mixtures are presented. The situation studied was the propagation of a detonation wave from a driver mixture of variable length through a concentration gradient of variable width into a less reactive acceptor mixture. The effect of the gradient on the transmission process were studied. A detonation tube of 174 mm id. was used. The tube was initially divided by a fast-opening, stretched rubber diaphragm. Stoichiometric hydrogen/air mixture was used in the driver section. Hydrogen/air mixtures (14.0–19.0% H 2 ) were used as acceptor mixtures. Natural diffusion was used to create a concentration gradient between two mixtures. It was shown that the behavior of detonations at concentration gradients depends significantly on the sharpness of the gradient. For relatively sharp gradients a detonation always decays in the nonuniform region. It can be reinitiated downstream in the acceptor mixture, if the driver length is large enough for a particular acceptor mixture. For relatively smooth gradients, detonation is able to propagate through without decay. The boundary between these cases is defined only by the value of sensitivity gradient for a particular pair of driver and acceptor mixtures. The critical value of the gradient depends strongly on the difference in energy content of driver and acceptor mixtures. The more overdriven is the detonation in the driver mixture compared to that in the acceptor, the sharper gradient is necessary for detonation decay. The order of magnitude of critical values of the gradient shows that evolution of the cellular structure may play a role effecting conditions for detonation decay at concentration gradients.

I. Matsukov

Papers

DDT in a smooth tube filled with a hydrogen–oxygen mixture

Effect of scale on the onset of detonations

Formation of the preheated zone ahead of a propagating flame and the mechanism underlying the deflagration-to-detonation transition

Experimental Study of the Preheat Zone Formation and Deflagration to Detonation Transition

Detonation propagation, decay, and reinitiation in nonuniform gaseous mixtures