The morphology of flame fronts propagating in reactive systems composed of randomly positioned, pointlike sources is studied. The solution of the temperature field and the initiation of new sources is implemented using the superposition of the Green's function for the diffusion equation, eliminating the need to use finite-difference approximations. The heat released from triggered sources diffuses outward from each source, activating new sources and enabling a mechanism of flame propagation. Systems of 40000 sources in a 200×200 two-dimensional domain were tracked using computer simulations, and statistical ensembles of 120 realizations of each system were averaged to determine the statistical properties of the flame fronts. The reactive system of sources is parameterized by two nondimensional values: the heat release time (normalized by interparticle diffusion time) and the ignition temperature (normalized by adiabatic flame temperature). These two parameters were systematically varied for different simulations to investigate their influence on front propagation. For sufficiently fast heat release and low ignition temperature, the front roughness [defined as the root mean square deviation of the ignition temperature contour from the average flame position] grew following a power-law dependence that was in excellent agreement with the Kardar-Parisi-Zhang (KPZ) universality class (β=1/3). As the reaction time was increased, lower values of the roughening exponent were observed, and at a sufficiently great value of reaction time, reversion to a steady, constant-width thermal flame was observed that matched the solution from classical combustion theory. Deviation away from KPZ scaling was also observed as the ignition temperature was increased. The features of this system that permit it to exhibit both KPZ and non-KPZ scaling are discussed.

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The critical dimension necessary for a flame to propagate in suspensions of fuel particles in oxidizer is studied analytically and numerically. Two types of models are considered: First, a continuum model, wherein the individual particulate sources are not resolved and the heat release is assumed spatially uniform, is solved via conventional finite difference techniques. Second, a discrete source model, wherein the heat diffusion from individual sources is modeled via superposition of the Green's function of each source, is employed to examine the influence of the random, discrete nature of the media. Heat transfer to cold, isothermal walls and to a layer of inert gas surrounding the reactive medium are considered as the loss mechanisms. Both cylindrical and rectangular (slab) geometries of the reactive medium are considered, and the flame speed is measured as a function of the diameter and thickness of the domains, respectively. In the continuum model with inert gas confinement, a universal scaling of critical diameter to critical thickness near 2:1 is found. In the discrete source model, as the time scale of heat release of the sources is made small compared to the interparticle diffusion time, the geometric scaling between cylinders and slabs exhibits values greater than 2:1. The ability of the flame in the discrete regime to propagate in thinner slabs than predicted by continuum scaling is attributed to the flame being able to exploit local fluctuations in concentration across the slab to sustain propagation. As the heat release time of the sources is increased, the discrete source model reverts back to results consistent with the continuum model. Implications of these results for experiments are discussed.

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Numerical modeling is a powerful tool for predicting the acoustic signature of pneumatic marine seismic sources in order to maximize low frequency content and minimize high frequency content. Idealized source models often overpredict the peak acoustic pressure, a key quantity in assessing source performance. The dynamics of the shuttle, the mechanical component that controls the early-time gas flow rate from the source, contribute to this signal overprediction but are often neglected. We perform numerical solution of a quasi-one-dimensional model of a pneumatic source suitable for large volume sources fired underwater. In our model, we couple shuttle dynamics to the gas dynamics in multiple, adjacent chambers in the source. We compare model results against data from field tests, where acoustic pressure signals, local pressure within and just outside the source, and temperature inside the source were measured. The source is coupled to a spherical bubble through mass and energy conservation conditions. The air exiting the source experiences a change in flow area as it expands or contracts during flow from a constant cross-sectional area firing chamber to a port area dependent on shuttle position. To capture the compressible effect of flow area change, we invoke a set of steady-state nozzle flow approximations.The maximum value and slope of the initial acoustic pressure peak are overpredicted by the model but internal pressure and temperature data agree with model predictions. We attribute early-time discrepancy between model and data to unmodeled pressure losses in the gas flow to the bubble and discrepancy over the bubble oscillation timescale to bubble modeling error. We quantify the effects of design parameters on the mass flow rate to the bubble, and find that shuttle oscillations can lead to briefly reduced mass flow rates as the shuttle partially obstructs the port.