Troels Dyhr Pedersen.indd - Solid Mechanics

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provided more ideal conditions for amplification of compression waves going from a
chamber with explosion to the other chambers with a less progressed reaction.
12.3 Detonations
12.3.1 Introduction
Detonation experiments are usually carried out with gas mixtures at atmospheric
conditions in long tubes. These conditions are clearly different from those within
combustion engines, in which initial conditions are a high pressure, temperature and a
partially reacted gas. Another important difference between detonations in laboratory and
combustion engines is that while the first requires a distance measured in meters to form
a detonation, the avaliable distance is less than ten centimeters in a normal sized engine.
In an SI engine, the compressed charge is burnt at a temperature considerably higher than
its auto ignition temperature. Reactions therefore progress at a very high rate once
enough radicals are produced. If the combustion timing of the engine is too early, the
temperature in the unburned region will become too high for the fuel to resist auto
ignition. This leads to engine knock, which is the common name for detonation. A typical
outcome of engine detonation is critical engine failure, such as melting of the piston.
The conditions in SI combustion engines therefore seem to be ideally suited for
development of detonations. It is however less certain if HCCI combustion can result in
the development of a detonation as well. It may be that detonations develop slower in
HCCI combustion and therefore are not as easily recognized as SI engine detonations.
Whether detonations are possible or not in HCCI combustion cannot be determined
theoretically. Apart from very well controlled experiments, the best way to get a better
understanding of detonations is to make simulations. Here, CFD has been chosen to
model constant volume combustion with variations to the intial conditions, with the
purpose of seeing if detonations will develop in the simulation.
Before the CFD approach is described, the basic theory for detonations is explained. The
equations and theory in the following sections are developed from thermodynamic
considerations only, by several researchers in the past century. Perhaps the most
fascinating fact about detonations is that the properties, such a propagation speed and
pressure increase, can be predicted with very high accuracy. In essence, the conservation
equations for a control volume and a chemical equilibrium is all that is required to
determine the exact speed of a detonation wave.
The main source used here is the book “Combustion” by Irvin Glassman [25]. Only the
essentials for understanding the phenomena has been included, since many derivations
are required to reach the usable equations. Sources focused on shock tube experiments
include those by John Bradley [26] as well as Edward Greene and J. Toennies [27] .