Dewey Physical Properties of Blast Waves 2016

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  Measurement of the Physical Propertiesof Blast Waves John M. Dewey 1 Introduction to Blast Waves A blast wave is formed in an ambient atmosphere when there is a rapid release of energy from a concentrated source. Examples of such sources are the detonation of an exothermic material such as trinitrotoluene (TNT); nuclear   󿬁 ssion or fusion; therupture of a pressurized container; a spark, or the rapid heating caused by a focusedpulsed laser. The sudden release of energy causes the material of a symmetricalcentered source to expand rapidly as a spherical piston. This piston produces acompression wave in the ambient gas. If the speed of the piston is fast enough, or of long enough duration, the compression wave develops into a shock wave. A shockwave is characterized by the very rapid increase, within a distance of about tenmean-free-path lengths, of all the physical properties of the ambient gas, namely,the hydrostatic pressure, density, particle velocity, temperature and entropy.Immediately behind the shock front the properties decay in an exponential fashion,and in the cases of hydrostatic pressure and density will fall below the values of theambient atmosphere. The particle velocity also decreases until it comes to rest andbegins to move in the opposite direction. A typical time-history of a physicalproperty such as hydrostatic pressure, density, particle velocity and dynamicpressure at a  󿬁 xed point in a blast wave is shown in Fig. 1.The period when the physical properties are above the ambient value is known asthe positive phase, and the period when the properties are below the ambient valueis the negative phase. The duration of the positive phase is slightly different for eachof the physical properties. Close to the minimum of the negative phase a second J.M. Dewey ( & )Department of Physics and Astronomy, University of Victoria, Victoria,BC V8P 5C2, Canadae-mail: jdewey@uvic.caJ.M. DeweyDewey McMillin and Associates Ltd, Victoria, BC, Canada ©  Springer International Publishing Switzerland 2016O. Igra and F. Seiler (eds.),  Experimental Methods of Shock Wave Research ,Shock Wave Science and Technology Reference Library 9,DOI 10.1007/978-3-319-23745-9_253  shock arrives, produced by the over expansion and subsequent implosion of thedetonation products or source materials. 2 The Physical Properties of Blast Waves A uniform chemical detonation rapidly produces a high-pressure, high-temperaturesphere of gas, which expands in the ambient medium to produce a spherical shockwave. The contact surface between the detonation products and the ambient gassoon becomes irregular and there is considerable mixing of the twogases (Brouillette) [1], but only in extreme cases, such as when there has been anon-symmetrical detonation, does this affect the uniformity of the expandingspherical shock. The release of energy from a detonation is rapid, but not instan-taneous, and the rate of energy release has a small but measurable effect on thephysical properties of the resulting blast wave. Some of the energy from anexplosion may be released as radiation: about 5 % from a TNT detonation, andapproximately 50 % from a nuclear explosion. If the explosion is on or close to theground some of the energy will be disbursed as seismic waves and to excavate acrater. These are some of the reasons why blast waves from different sources and at different distances from the ground, are not identical even though the nominalenergy release may be the same.A characteristic of a shock is that it causes a change of entropy in the gas throughwhich it is passing. As the spherical shock produced by a centred explosion Time    P   h  y  s   i  c  a   l   P  r  o  p  e  r   t  y P S S 2 t + Fig. 1  The form of a time-history of hydrostatic pressure, density, particle velocity or dynamicpressure at a  󿬁 xed point in a free- 󿬁 eld blast wave. P S  is the peak value immediately behind theprimary shock, S 2  the second shock, and t  + the duration of the positive phase54 J.M. Dewey  expands in three dimensions, it monotonically decays in strength and leaves the air in a state of radially decreasing entropy and temperature. This means that there areno simple thermodynamic relationships between the physical properties of the gaspassing a  󿬁 xed point in a blast wave. In other words, if, for example, thetime-history of hydrostatic pressure is measured at a  󿬁 xed point, it is not possible tocalculate the time-histories of the density or temperature from that measurement. Tofully describe the physical properties of a gas element in a blast wave it is necessaryto independently measure at least three of the physical properties, such as,hydrostatic and total pressures, and density or particle velocity.More detailed information about the physical properties of blast waves is pro-vided by Needham [2] and Dewey [3].  2.1 De   󿬁  nitions of the Physical Properties In order to interpret and relate the measured physical properties of a blast wave it isimportant to have a precise understanding of the de 󿬁 nitions of those properties.A powerful tool in the study of blast waves is the fact that for most explosives thephysical properties accurately scale for charge mass, over several orders of mag-nitude, and for a large range of ambient atmospheric conditions. The appropriateHopkinson ’ s and Sachs ’  scaling laws are described in Sect. 4. In order for thephysical properties to be used in these scaling laws they are usually reported interms of the values of those properties in the ambient atmosphere, e.g.  P  /  P 0 ,  ρ  /   ρ 0 and  T   /  T  0 , where  P  is the hydrostatic pressure,  ρ  the density, and  T   the absolutetemperature, and the suf  󿬁 x 0 indicates the value in the ambient atmosphere. Thestrength of the shock front at the leading edge of the blast wave is usually stated interms of its Mach number relative to the speed of sound in the ambient atmosphere, i.e. M  S   =  V  S   /  a 0 , where  M  S   is the shock Mach number,  V  S   shock velocity, and  a 0  theambient sound speed. 2.1.1 Hydrostatic Pressure The hydrostatic pressure of a gas is de 󿬁 ned as the force per unit area on a surfacecaused by the random motion of the molecules in the gas. It does not include anycomponent due to the translational movement of the gas, and therefore can only bemeasured by a transducer that is  fl ush mounted in a surface that is parallel to the fl ow in a blast wave. It is a scalar quantity. In the case of a blast wave the most important feature of the hydrostatic pressure maybe that part that is greater than theambient pressure. This is called the overpressure, viz . OP  =  P  −  P 0 . After thepassage of a blast wave the hydrostatic pressure quickly returns to the ambient value because any pressure gradients equilibrate at the rate of the local sound speed.Hydrostatic pressure is the easiest of the physical properties of a blast wave tomeasure, and therefore is the property most usually quoted when de 󿬁 ning the Measurement of the Physical Properties of Blast Waves 55  magnitude or other features of the wave. Unfortunately, it is also the property that gives the least information about the blast wave because any changes of pressuredissipate at the local sound speed. An example of this is in the boundary layer which forms as the blast wave moves over the ground surface. The boundary layer in the blast wave from a large explosion is known to reach a height of about 30 cm[4]. Over that vertical distance there is no discernable change of the hydrostaticpressure, but the particle velocity, and therefore the dynamic pressure, changesfrom zero at the surface to what may be a very high value at the top of the boundarylayer. Also, a hydrostatic pressure measurement does not detect the passage of acontact surface, such as that between the detonation products and the air, althoughthere may be large changes in other physical properties such as density and tem-perature across that surface. If a hydrostatic pressure transducer does detect thepassage of a contact surface, this indicates that it is also sensitive to temperaturechanges so that the pressure measurements may not be valid. 2.1.2 Density The density of a gas is de 󿬁 ned as its mass per unit volume. The time-history of density in a blast wave is similar to that for hydrostatic pressure but the initial rateof decay after the primary shock and the positive duration are not the same. Thepassage of a blast wave leaves the ambient atmosphere at an elevated temperature,and therefore at a density lower than that of the srcinal ambient atmosphere. Thereis a residual density gradient with the lowest density at the explosion centre. Thebuoyancy effect of this density gradient creates the up-draught that produces thephenomenon referred to as the mushroom cloud. 2.1.3 Temperature The temperature of a gas is de 󿬁 ned as a measure of the kinetic energy of the randommolecular motion, and its gradient indicates the direction that heat will  fl ow. After the passage of a blast wave the gas is left in a state of radially decreasing tem-perature, higher than that in the original ambient atmosphere. As a result, thetime-history of temperature in a blast wave is dissimilar from that shown inFig. 1. The high temperature immediately behind the primary shock begins to decaybut then starts to increase again as the warm air shocked closer to the centre of theexplosion  fl ows past the measurement location. The temperature is normallyexpressed in Kelvin, and as a ratio of the ambient temperature, viz.  T   /  T  0 . 2.1.4 Particle Velocity A feature of a blast wave, unlike a sound wave, is that there is a net translation of the gas within the wave. For scaling purposes, the particle velocity within the blast  56 J.M. Dewey
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