Potential for ultrafast detonations revealed by new computer simulation

Explosive detonations at speeds faster than current theories predict have been shown to be possible in a powerful new computer simulation developed by a physical chemist and an aerospace engineer at Penn State. James B. Anderson, Evan Pugh Professor of Chemistry and Physics, and Lyle N. Long, Professor of Aerospace Engineering, say their simulation points the way toward the production of ultrafast detonations, which could lead to innovative propulsion systems for space travel and a better understanding of detonations in general, including those that occur at supersonic speeds in the tunnels of underground mines.

With the aid of an innovative chemical model supported by powerful computers, the researchers show that burning particles of highly reactive gas set on fire by an explosive shock wave can leap out in front of the wave and ride it like a surfer, sparking reactions in advance of the wave itself. “All the textbooks say that the velocity of a detonation in a reactive gas mixture can be no faster than the speed of sound in the hot burning gases, but our model shows this assumption may no longer be correct,” says Anderson, whose paper is published in the current issue of the Journal of Chemical Physics (volume 118, issue 7, page 3102).

According to the previous prevailing theory, a detonation occurs when a shock wave from an explosion first blasts its way through a reactive gas, heating it until it ignites, then causing a chemical reaction that continues to power the explosive wave forward. The chemical reaction, which proceeds at a slower speed behind the initial shock wave, was thought to be limited to the speed of sound in the hot gases. “Previous models did not predict ultrafast, supersonic detonations, in which the explosion can move even faster than a shock wave in the hot gases,” Anderson says.

Anderson and Long’s simulation shows that supersonic detonations can occur in highly reactive gas mixtures if the chemical reaction is fast enough to keep up with the wave, in which case some of the reactive atoms can blast ahead to initiate a reaction in front of the shock wave itself, speeding things up even faster. Now that they have shown it can be done, the researchers predict that experimenters will produce and observe ultrafast detonations in the laboratory. “The most likely gases where ultrafast detonations may occur are in two of the fastest-reacting systems, mixtures of hydrogen and chlorine (H2-Cl2) and mixtures of hydrogen and fluorine (H2-F2),” Anderson says.

The team’s model is the first to simultaneously include the full details of both the chemical reactions and the gas dynamics that occur during explosions, as well as temperature, velocity, density, pressure, and chemical composition of the detonation waves. Earlier approaches, which were based on the use of differential equations, required making approximations that oversimplified the physics and chemistry and were of limited usefulness because of their complexity, the researchers say.

Anderson and Long accomplished their innovation by incorporating finely detailed chemical modeling into a technique known as the Direct Simulation Monte Carlo method, which has been in use for over half a century in gas-dynamics calculations and is in wide use today for solving aerospace problems. Like a lottery in which those who have more tickets have a greater chance of winning, Monte Carlo calculations in Anderson and Long’s model assign to each pair of particles a higher or lower probability of interacting with each other, based on their particular characteristics at any given time. For example, particles that are moving rapidly toward each other are much more likely to be picked for a collision than those that are not moving, and those that are big are more likely to collide with each other than are those that are small.

To add some unpredictability to the game, Anderson and Long also incorporated into their model the technique of using random numbers to pick which reactions actually occur. As a result, the model imitates nature more realistically by allowing particles to interact with each other on a random basis in addition to taking into account their calculated probability of interacting. “The addition of chemical reactions to the Monte Carlo method makes it possible, for the first time, to realistically model simultaneously both the interactive chemistry and the gas dynamics that occur during an explosion,” Anderson says.

Anderson and Long’s computer model simulates the chemistry and tracks the movement, temperature, and speed of each particle in a group of about 100,000 as they react with each other. Like frames in a reel of movie film, the calculations in the model are finely detailed snapshots of chemical reactions as they take place step by step. “In these calculations, we break the whole system down into cells to model reactions in very, very small steps in order to model the overall explosion very accurately,” Anderson says.

We have treated our model atoms as simple hard spheres without internal structure in order to model the simplest kinds of reactions that one can imagine while still including some of the complicating effects that occur with real systems,” says Anderson. “The simplification makes it easier for us to understand and analyze the results, so when our calculations reveal an ultrafast detonation we can know it is not just the result an overly complex model producing extraneous errors.”

The researchers say the new model could be particularly useful in understanding situations involving combustion or propulsion in which the chemical reactions in a gas are dynamically coupled with the movement of the gas during an explosion. One such situation involves pulsed-detonation rocket engines, which create propulsion by sending detonation waves rearward through an explosive gas mixture in a combustion chamber, propelling the rocket forward. “The model might also help us to better understand, for example, the reentry of a space vehicle–which involves very complicated gas dynamics and very complicated chemical reactions in the upper atmosphere,” Long says. “We expect our model can be used to help make better predictions in such critical and complex situations.”

This research was supported by grants from the National Science Foundation.

Additional Contacts:
James B. Anderson: (+1)814-865-3933, jba@psu.edu
Lyle N. Long: (+1)814-865-1172, lnl@psu.edu