California Institute of Technology

Explosion Dynamics Laboratory

Glossary on Explosion Dynamics

Some of the language used to describe explosions is very precise and scientific; other terms, including the very nature of an explosion itself, are quite ambiguous. The following list of terms is not intended to be exhaustive but simply to provide an explanation for some of the most commonly used concepts.

Autoignition temperature (AIT) The temperature that a fixed volume of fuel-oxidizer mixture must be heated to before an explosion will take place without an external ignition source, i.e., spark or flame. The values of the minimum AIT used in conventional hazard classifications (e.g., Appendix A of Kuchta) have been measured in a standardized test (ASTM E659) which involves injecting a fuel into a heated flask filled with hot air. Explosion does not take place immediately when fuel is injected but occurs after a delay of between 5 and 600 s. The minimum AIT is strong function of the fuel type (atomic composition and molecular structure), pressure, and fuel concentration. For common hydrocarbon fuels, the minimum AIT ranges between 600C (1350 F) for methane (CH4) to 200C (472F) for dodecane (C12H26). A minimum AIT of 190C (450F) is used for the purposes of hazard analysis for aviation kerosene. Note that the minimum AIT is much higher than the flash point and much lower than typical hot surface ignition temperatures, which can be as high as 900C (2000F) for common hydrocarbon fuels (Smyth, K. C.; Bryner, N. P. Combustion Science and Technology, Vol. 126, 225-253, 1997).

Blast or Blast Wave This is the rapid change in air pressure that propagates away from the region of an explosion. A sharp jump in pressure is known as a shock wave and a slow rise is known as a compression wave. Weak pressure waves propagate with the speed of sound and shock waves always travel supersonically, faster than the speed of sound. A blast wave is produced by an explosion because the explosive event displaces the surrounding air rapidly.

Burning speed This is the speed with which a smooth (laminar) flame advances into a stationary mixture of reactants. Burning speeds in hydrocarbon fuels mixed with air are typically less than 0.5 m/s. The burning speed is a function of the concentration of the fuel, temperature, and pressure of the mixture.

Cellular flame A flame with a wrinkled surface due to instabilities caused by gas expansion during combustion and the combined effects of thermal and species diffusion. Cellular flames appear for Lewis numbers (based on the deficient reactant) less than unity.

Critical tube diameter (detonation) The minimum diameter of a tube that will allow a detonation to diffract and continue into a larger volume as a self-sustained detonation wave. If the tube is smaller than this diameter, the detonation wave will "fail" when it emerges from the tube because the shock wave and reaction zone will decouple, resulting in a decaying shock wave followed by a flame. For many fuel-air mixtures, the critical diameter is about 13 detonation cell widths. For mixtures with regular cellular structure (high amounts of inert gas dilution), the critical tube diameter can be be as much 30 cell widths. For channels of different crossections (square, rectangular, etc) or openings of various shapes (triangular, elliptical), the critical channel or opening transverse dimension is roughly proportional to the cell width (or induction zone length) with the constant of proportionality depending on the specific geometry (e.g., 10 cell widths for square channels).

Critical Initiation Energy (detonation) This is the smallest amount of energy deposition that will cause direct initiation of a detonation wave. Direct initiation is associated with emergence of a detonation wave immediately out of a strong blast wave with transition through a deflagration phase. This is usually caused by blast waves created by rapid energy addition either from the detonation of solid or gaseous explosives in fuel-air mixtures, or exploding wires or spark discharges in fuel-oxygen mixtures. For solid explosives, the energy equivalent is usually based on the equivalent mass of explosive tetryl with an assigned energy value of 4.2 MJ/kg. Confinement by tubes or channels will decrease the critical energy since the blast waves decay more slowly than in the unconfined case. The critical initiation energy is observed to scale with the cube of the induction zone length or the detonation cell width for spherical geometry, the square for cylindrical geometry, and linearly for planar geometry.

Chapman-Jouguet Velocity This is the velocity that an ideal detonation travels at as determined by the Chapman-Jouguet (CJ) condition: the burned gas at the end of the reaction zone travel at sound speed relative to the detonation wave front. CJ velocities can be computed numerically by solving for thermodynamic equilibrium and satisfying mass, momentum, and energy conservation for a steadily-propagating wave terminating in a sonic point. CJ velocities in typical fuel-air mixtures are between 1400 and 1800 m/s.

Damkohler number Ratio of characteristic residence time or fluid motion time scale to characteristic reaction time. Large Damkohler number Da >> 1 corresponds to very rapid chemical reaction in comparison to all other processes. Small Damkohler number Da << 1 corresponds to very slow chemical reaction in comparison to all other processes.

Deflagration This is a propagating flame that moves subsonically (the flame speed is less than the speed of sound) in a mixture of fuel and oxidizer.

Deflagration to Detonation Transition (DDT) In certain circumstances, a flame may accelerate to high velocities (greater than 1000 m/s) and suddenly become a detonation instead of a deflagration. The circumstances involve a sufficiently sensitive mixture (very rapid chemical reaction) in a geometrical configuration that is favorable to flame acceleration - this usually requires confinement and obstructions or obstacles in the path of the flame. Such mixtures are characterized by a small detonation cell width, high flame speed, and high volume expansion ratio.

DDT distance or run-up length Distance between initiation of a flame and onset of detonation due to DDT. Strongly dependent on the geometry, type of mixture and presence of turbulence generating elements within the path of the flame propagation. The minimum distance needed for DDT appears to scale as a multiple of the detonation cell width.

Detonation This is a supersonic combustion wave. Detonations in gases propagate with velocities that range from 5 to 7 times the speed of sound in the reactants. For hydrocarbon fuels in air, the detonation velocity can be up to 1800 m/s. The ideal detonation speed, known as the Chapman-Jouguet velocity, is a function of the reactant composition, initial temperature and pressure.

Detonation cell width This is the characteristic width of the cellular pattern that is created by the instabilities that plague all propagating gaseous detonation waves. The cell width is measured by a sooted sheet or foil of metal inserted inside a tube used for detonation experiments. Detonation cell widths are used to characterize the sensitivity or susceptibility of a mixture to detonation. Sensitive mixtures (acetylene-oxygen) have cell sizes less than 1 mm; insensitive mixtures (methane-air or any lean hydrocarbon-air mixture) can have cell sizes of up to 1 m.

Explosion There is no fixed definition of an explosion. Events that are described as explosions include a rupturing water boiler, a flash of light created by an electrical short circuit, detonation of a high explosive, deflagration of a tank containing an explosive fuel-air mixture, or the shock wave, fireball, and debris cloud produced by a thermonuclear detonation. The AIChE suggests that an explosion is "A release of energy that causes a blast". Berthelot, the French chemist that pioneered the scientific study of explosions, is reputed (Bailey and Murray, Explosives, Propellants and Pyrotechnics, Brassey) to have defined an explosion in 1883 as "the sudden explosion of gases into a volume of much greater than their initial one, accompanied by noise and violent mechanical effects." A humourous definition was given by Joseph Needham, "An explosion may be defined as a loud noise accompanied by the sudden going away of things from the places where they were before." - see p. 110 of The Gunpowder Epic, Vol 5, Part 7, Science and Civilization in China.

Explosion limits Explosion limits usually refer to the range of pressure and temperature for which an explosive reaction at a fixed composition mixture is possible. The reaction is usually initiated by autocatalytic (sometimes called self-heating) reaction at those conditions, without any external ignition source. In practical terms, this means that the mixture needs to be sufficiently hot. Explosion and flammability limits are distinct. Flammability limits refer to the range of compositions, for fixed temperature and pressure, within which an explosive reaction is possible when an external ignition source is introduced. This can happen even when the mixture is cold.

Equivalence ratio Ratio of fuel to oxidizier divided by the same ratio at stoichiometric conditions.

Expansion ratio Ratio of burned gas volume to initial volume for a low-speed (constant pressure) flame. Expansion is responsible for flame-induced flow.

Fire This is a flame that is produced over a stationary fuel source such as a liquid hydrocarbon pool or solid such as wood.

Flame This is a thin zone of combustion in which diffusion plays a dominant role. Flames in hydrocarbon fuels and air are less than 0.1 mm thick for stoichiometric mixtures.

Flame acceleration Rapid increase in flame speed due to generation of large and small eddies - turbulence - as flow ahead of flame passes over objects or through orifices.

Flame speed This is the speed with which a flame, possibly turbulent, appears to move relative to a stationary observer. The flame speed can be much larger than the burning velocity due to expansion of the combustion products, instability, and turbulent deformation of the flame. Flame speeds of 10-100 m/s are commonly observed for hydrocarbon-air mixtures and it is possible under exceptional circumstances to have speeds up to 1000 m/s.

Flame Stretch Measure of the rate at which the area of a propagating flame surface is changing due to curvature of flame surface and strain (gradients in velocity) in flow ahead of the flame. Units of reciprocal time.

Flame Thickness Characteristic width of flame. One simple estimate is based on the ratio of the thermal diffusivity to the fame speed.

Flammability A fuel-air mixture is flammable when combustion can be started by an ignition source. The main fact is the proportions or composition of the fuel-air mixture. A mixture that has less than a critical amount of fuel, known as the Lean or Lower Flammability Limit (LFL), or greater than a critical amount of fuel, known as the rich or Upper Flammability Limit (UFL), will not be flammable. For example, the lean flammability limit for Jet A (aviation kerosene) in air at sea level is a concentration (by volume or partial pressure) of about 0.7%. The rich flammability limit is about 4.8% by volume or partial pressure. Flammability limits are not absolute, but depend on the type and strength of the ignition source. Studies on flammability limits of hydrocarbon fuels have shown that the stronger the source of the ignition stimulus, the leaner the mixture that can be ignited. Flammability limits also depend on the type of atmosphere (for example, limits are much wider in oxygen than in air), the pressure, and the temperature of atmosphere.

Flash point This is the minimum temperature at which the vapor above a liquid fuel will first support a combustion transient or "flash". The flash point is measured by a standardized test using a small quantity (50 cc) of liquid that is slowly heated (about 1 deg C/minute) until a flash is observed when an open flame is dipped down into a covered vapor space. The legal description of flammable is used for all liquids with a flash point less than 100 deg F (37.8 C), and the term combustible is used for liquids with a flash point in excess of 100 deg F (37.8 C).

Fuel-air mass ratio This is the ratio of the mass of fuel to the mass of air in the reactants. The fuel-air ratio is a method of measuring the composition of a potentially flammable mixture.

Heat of combustion Ideal amount of energy that can be released by burning a unit amount of fuel. This is between 45 and 50 MJ/kg for kerosenes.

Heat of reaction Energy that must be supplied in the form of heat to keep a system at constant temperature and pressure during a reaction.

Heat of formation Heat of reaction per unit of product needed to form a species by reaction from the elements at the most stable conditions.

High Explosives Liquids, solids or mixtures in which detonation waves can be initiated by electrical or chemical means. Common examples are TNT, nitroglycerin, PETN, lead azide, and mixtures of ammonium perchlorate and fuel oil. The detonation speeds are much higher in high explosives than in gases; they range from 5000 to 8000 m/s. Peak pressures are also much higher; ranging from 100 to 400 kbar (1 kbar = 100 MPa). See Bill Davis' article in Los Alamos science for an overview of HE behavior.

Ignition Delay Time Time elapsed from the sudden increase in temperature until ignition is observed. Ignition delay times are very strong functions of temperature and range between minutes at low temperatures (200 C) to microseconds for shock tube testing (1500-2500 C).

Karlovitz number Ratio of characteristic time for passage of of molecule through a flame to the time defined by flame stretch.

Lean mixture This is a mixture containing less than the stoichiometric amount of fuel, equivlance ratio less then unity. Combustion of a lean mixture will result in excess oxidizer remaining in the products.

Lewis number Ratio of thermal diffusivity to mass diffusivity of a specified species. For light molecules diffusing in heavier mixtures, the Lewis number is less than one; for heavy molecules diffusing in lighter mixtures, the Lewis number is greater than one.

Mach number Ratio of wave or flow speed to speed of sound. Supersonic waves or flows have M >1, this is true for detonations or shock waves. Subsonic waves or flows have M <1, this is true for most flames.

Mass loading Ratio of mass of fuel to volume of tank. Small values of the mass loading - corresponding to a thin layer of fuel on the bottom of the tank - results in differential vaporization of the light components.

Markstein length Length that measures the effect of curvature on a flame. The larger the Markstein length, the greater the effect of curvature on burning velocity. The Markstein length divided by the flame thickness is the Markstein number.

Maximum Safe Experimental Gap (MSEG) A flame can be initiated in the explosive atmosphere even when the height of a channel or gap connecting the ignition chamber with the explosive atmosphere is smaller than the laminar flame quenching height. Even after a flame stops actively propagating, there may still be sufficiently hot products and radical species to restart flame propagation when the products emerge from the channel and the loss mechanism, heat transfer to the channel walls, is removed. This was first observed experimentally when developing standards for gaps in enclosures of electrical equipment. The maximum gap height that prevents explosion transmission can be a factor of two or smaller than the laminar flame quenching diameter. Standardized tests have been developed to measure the MSEG and are used to certify "explosion-proof" electrical enclosures.

Minimum Ignition Energy This is the lowest possible energy that will result in the ignition of a flammable mixture by an electrical discharge. The minimum ignition energy depends on the composition of the mixture and can be as low as 200 microJoule for many common hydrocarbon fuels.

Minimum Tube Diameter The minimum diameter of a tube that will enable a self-sustaining detonation to propagate over extended distances. The exact value depends on the nature of the fuel and oxidizer but for common fuels in air, the rule of thumb is that the minimum diameter is on the order of 1/3 of the cell width (as measured in a much larger geometry). Near or just below the minimum tube diameter, various highly unsteady modes of propagation can be observed such as spinning, galloping, or stuttering detonation waves. For certain mixtures in long, small-diameter tubes, high speed combustion waves (velocities as low as 0.5-0.6 times the CJ velocity) can be observed to propagate.

Overpressure This is the pressure in excess of the ambient value that is created by the explosion process. The peak overpressure associated with deflagrations inside closed vessels can be as high as 10 times the initial pressure.

Partial pressure This is the pressure created by one component of gas mixture. The partial pressure of fuel vapor in a well-mixed ullage over a liquid fuel layer is equal to the vapor pressure of the liquid under those conditions. Strictly speaking, this is the case only for a single component fuel (such as hexane) but is also valid for multicomponent fuels like kerosene as long as sufficient liquid is present.

Peclet number Ratio of convection speed to characteristic diffusive velocity. When the velocity is the flame speed and the length is the size of the pores in the screen of the flame arrestor, a critical Peclet number determines if the flame will pass through the screen. When Pe < 40- 100, a flame will extinguish or quench.

Pool Fire This is a flame over a puddle or pool of liquid fuel. The heat released by the combustion of the vapor fuel supplies the energy to vaporize the liquid.

Products This is the mixture of molecules that result from the oxidation and decomposition of the fuel during the combustion process. Products can be divided into two classes: major species that are present in large amounts (greater than 1%) and minor species that are present in small amounts (usually much less than 1%). For hydrocarbon fuels burned in air, the major products are a mixture of water (H2O), carbon dioxide (CO2), molecular hydrogen (H2), carbon monoxide (CO) and nitrogen (N2). Minor species include hydroxyl radical (OH), atomic oxygen (O), atomic hydrogen (H), methylidyne (CH), nitric oxide (NO), formaldehyde (CH2O).

Quenching This is the cessation of combustion due to either heat transfer and mass transfer to the surface or aerodynamics effects like strain fields and rapid mixing.

Quenching Distance A characteristic length scale associated with laminar flame quenching during propagation in a narrow channel or tube. The minimum height of a channel in which a hydrocarbon-air flame can propagate at NTP is about 1.6 mm for mixtures with equivalence ratios between 1 and 2. The minimum diameter of a tube is about 2 mm. This distance varies inversely with initial pressure and is smaller for mixtures with higher laminar flame speeds. Turbulent explosions can be transmitted through openings smaller than the laminar flame quenching distance, see the entry about MSEG.

Reactants This is the mixture of Fuel and Oxidizer molecules that are burned in the combustion process.

Rich mixture This is a mixture containing more than the stoichiometric amount of fuel, equilvalence ratio greater than unity. Combustion of a rich mixture will result in partial oxidation of the fuel and the products will contain, in addition to CO2 and H2O, H2 and CO for hydrocarbon fuels.

Sonic point The point at which the flow velocity is equal to the speed of sound. When this is applied to detonations, the velocity is computed relative to leading shock front. The elementary Chapman- Jouguet condition is that the sonic point occurs at the end of the reaction zone when the products are in equilibrium.

Spinning detonation A mode of detonation propagation that occurs near the minimum tube diameter. One (single-head spin) or two (double-head spin) strong transverse waves rotate across the main shock front of the detonation, creating large fluctuations in the lead shock strength and characteristic high luminosity bands behind the detonation front that appear to rotate - leading to the term "spinning".

Stoichiometric ratio The proportions of fuel and oxidizer that will result in optimal combustion are known as a stoichiometric ratio. The optimal ratio is determined by finding the amount of air that will result in the products of the combustion reaction containing only water and carbon dioxide with no left over oxygen. A stoichiometric mixture of Jet A and air contains about 1.2% fuel by volume or partial pressure.

Taylor Wave Self-similar flow following a steadily propagating detonation. First analyzed by G.I. Taylor and Ya. Zeldovich. For detonation propagation starting from the closed end of a tube, the Taylor wave is an expansion wave that brings the flow to rest by isentropic expansion. For CJ detonation, the expansion wave extends from just behind the detonation wave to approximately half the distance to the closed end.

Turbulence intensity Characteristic magnitude of the velocity fluctuations in a turbulent flow.

Ullage This is the volume in a liquid fuel tank that is not occupied by liquid fuel. This is sometimes referred to as the vapor space since it is filled with a mixture of fuel vapor and a cover gas, air in the case of commercial airplanes.

von Neumann Spike Narrow region of high pressure that is observed just behind the shock in experimental measurements of propagating detonations. The magnitude of the pressure is given by the solution to the shock wave relations for the observed wave speed.

ZND model An idealized model of a detonation for a one-dimensional, steadily moving wave that was developed by separately by Zeldovich (1940), von Neumann (1942), and Doring (1943). The model consists of a non-reactive shock wave traveling at the Chapman-Jouguet velocity followed by a reaction zone. The high temperature behind the shock wave initiates chemical reactions that convert the reactants into products. The reaction zone usually consists of an induction zone that is almost thermally neutral (little or no temperature increase during reaction) followed by an exothermic recombination zone. The distance between the shock wave and the end of the reaction zone is known as the reaction zone thickness

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