Blast wave parameters at diminished ambient pressure

Blast wave parameters at diminished ambient pressure

Acta Astronautica 109 (2015) 235–240 Contents lists available at ScienceDirect Acta Astronautica journal homepage:

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Acta Astronautica 109 (2015) 235–240

Contents lists available at ScienceDirect

Acta Astronautica journal homepage:

Blast wave parameters at diminished ambient pressure M.V. Silnikov a,b, M.V. Chernyshov a,b,n, A.I. Mikhaylin a,b a b

Special Materials Corp., 28A Bolshoy Sampsonievsky Ave., 194044 St. Petersburg, Russia Saint Petersburg State Polytechnical University, 29 Politechnicheskaya Str., 195251 St. Petersburg, Russia

a r t i c l e i n f o


Article history: Received 2 October 2014 Received in revised form 5 December 2014 Accepted 11 December 2014 Available online 19 December 2014

Relation between blast wave parameters resulted from a condensed high explosive (HE) charge detonation and a surrounding gas (air) pressure has been studied. Blast wave pressure and impulse differences at compression and rarefaction phases, which traditionally determine damage explosive effect, has been analyzed. An initial pressure effect on a post-explosion quasi-static component of the blast load has been investigated. The analysis is based on empirical relations between blast parameters and non-dimensional similarity criteria. The results can be directly applied to flying vehicle (aircraft or spacecraft) blast safety analysis. & 2014 IAA. Published by Elsevier Ltd. All rights reserved.

Keywords: Flying vehicle Blast safety Diminished pressure Blast wave

1. Goals of study Currently reported acts of terrorism on board of aircrafts draw great attention to a problem of suppression of damage effects caused by blast shock waves and following co-current flows (explosive effect). The presence of improvised HEs onboard spacecraft (the elastic HE charges based on PETN can be used for undocking and so they should be kept inside a spaceship, for example) requires us to consider the application of this problem to space flight safety as well. A physical nature of a condensed HE charge explosion inside a civil flying vehicle is an impulse energy release inside a closed pressurized space heavily encumbered by objects including survival systems and constructive elements and bounded by a thin-wall shell. Interaction of blast wave and co-current flows with those systems and elements [1] becomes more complicated due to the waves multiple amplification caused by reflections or refraction on

n Corresponding author at: Special Materials Corp., 28A Bolshoy Sampsonievsky Ave., 194044 St. Petersburg Russia. Tel./fax: þ 78122941274. E-mail address: [email protected] (M.V. Chernyshov). 0094-5765/& 2014 IAA. Published by Elsevier Ltd. All rights reserved.

porous and multi-layer surfaces [2,3]and the waves propagation through pre-perturbed non-uniform flows. Normally, a civil flying vehicle construction is not designed to resist inner impulse mechanical loads. For instance, the experience of terrorist explosions and results of full-scale testing [4] have revealed that an explosion of a charge about 100 g in TNT equivalent (100 g TNT) results in the aircraft cabin depressurizing, control units failure, hull cracks growth and its fast destruction, loss of the aircraft flight capability, death of passengers and crew, sometimes people on the ground. For example, the notorious explosion over Lockerbie (Scotland) on board the Boeing 747 aircraft was caused by detonation of a 440 g HE charge. The International Civil Aviation Organization (ICAO) and the Russian Federation government require to equip all newly designed aircrafts of seating capacity for more than 60 people with special means of bomb protection (blast inhibitors) that are capable to mitigate a potential damage explosive effects of a suspicious object found on board. The analogous blast protection devices can be applied onboard the spaceships to store the necessary HE charges [5]. G.V. Novohzilov, academician of RAS, initiated a project involving some institutions (“Ilyushin” aerospace company, “Special Materials, Corp.”, 294 Center of the Russian Federation Emergency Ministry and CIS International Aviation


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Committee). The project included a cycle of theoretical and experimental studies completed by designing, development and production of special bomb inhibitors “Fountain” family for flying vehicles. A mitigating effect of the destructible blast inhibitors “Fountain” is based on pressure amplitude and impulse reduction and blast wave head front transformation from a gas-dynamic discontinuity into Riemanntype compression wave resulted from its interaction with a multi-phase system [6–8]. Theoretical analysis, numerical simulation data, data obtained in laboratory, field tests and full-scale testing have revealed that application of developed “Fountain” blast inhibitors “Fountain 3MK-2000” allows to preserve an wide-body aircraft (or a space vehicle of analogous size) flight capability after onboard explosion of a HE charge up to 2 kg in TNT equivalent; “Fountain 4M500” and “Fountain 4MK-500” do this job in case of up to 500 g TNT charge explosion on board of a narrow-body aircraft or analogous space vehicle [5]. The conclusive stage of the aforementioned investigation project was multiple full-scale testing of the developed blast inhibitors on board of wide- and narrow-body passenger aircrafts (“IL-96”, “IL-114”). Based on those test results the blast inhibitors were formally accepted as a part of those aircrafts onboard equipment. The testing was performed on an airfield at normal atmospheric pressure inside the aircrafts cabins. However, ICAO recommends an aircraft to descend to about 3000 m altitude and to equalize onboard and overboard pressure if a potentially dangerous object is found on its board [9]. Pressure difference acting on the aircraft hull is absent then, and it is not necessary to increase the cabin pressure above the atmospheric level (approximately 1.4–1.5 atm [4,10] for its physical simulation during the airfield testing. It is also evident that the ambient pressure inside a space vehicle can also differ from the normal atmospheric meaning. Overpressures and pressure impulses of blast waves propagating along the cabin and affecting the structural elements at lower pressure (p0  0:64 atmospheres according [9]) differ from similar values under normal atmospheric conditions. For full-scale testing data verification pressures and impulses of blast waves generated as recommended by ICAO conditions, and quasi-static gas pressure in the closed space should not exceed the similar values of those parameters resulted from the same power charge explosion at normal initial conditions. Pressure reduction in the surroundings could result in decrease of generating blast wave amplitude Δp1 (thus, in 1=3 some cases, Δp1 value is in proportion to p0 [11], that is proven by the theory of similarity). However, solution of the pressure discontinuity disintegration problem has revealed that increase in relation ratio between the detonation pressure and the surrounding pressure leads to the blast  wave strength (i.e. pressure ratio J 1 ¼ p=p0 ¼ p0 þΔp1 =p0 at its head front [12]) sufficient growth. 2. Empirical relations for blast wave parameters Overpressures and blast wave impulses at voluntary surrounding pressure have been evaluated using dimensionless Sachs variables [11,13]. In practically important

dimensionless distance range 0:27r R r10 where 1=3 — R ¼ R U p0 =E , R is dimensional distance to the blast epicenter, E is blast energy, blast wave amplitude Δp1 at the compression phase is defined from [14]: p¼

0:46 4=3



0:099 R



0:065 3




where p ¼ Δp1 =p0 is dimensionless overpressure. Rarefac tion wave amplitude Δp  ¼ p  p0 following the N-blast wave compression phase is evaluated at the distance 0:45 r R r10 from the blast epicenter, 1:1

p  ¼ Δp  =p0 ¼ 0:113=R


Here p  is minimal pressure at the blast wave negative phase, Δp  is negative phase dimensionless amplitude. Dimensionless compression phase impulse I ¼ c0 I= 1=3 1=3 Ep20 or rarefaction phase impulse I  ¼ c0 I  = Ep20 of the blast wave are calculated as it follows: 0:97

I ¼ 0:055=R


; I  ¼ 0:052=R


at 0:27 r Rr 10 and 0:45 rR r 10, respectively. Here, as it is admitted in physics of explosion, I and I  are dimensional pressure impulses (pressure integrals on the time spans of the positive blast wave phase and negative one, correspondingly), c0 is sound speed in undisturbed ambient media. Since a damage blast shock wave effect is determined by dimensional amplitude (Δp1 ) and impulse (I) of its compression phase, then the following relations (1)–(3) are written in dimensional form: 5=9

Δp1 ¼

0:46E4=9 p0

Δp  ¼





0:099E2=3 p0 R

0:055E0:657 p0:343 0 c0 R0:97 0:113E0:367 p0:633 0 1:1




0:065E R3



; I ¼


0:052E0:617 p0:383 0 c0 R0:85



reveal attenuation of a blast shock wave explosive effect both at compression and rarefaction phases. Effect of p0 value  on the  quasi-static pressure growth amplitude Δp qs ¼ pqs  p0 =p0 resulted from a HE charge explosion of energy E ¼ GE1 inside a volume V can be estimated from [15,16],  Δp qs ¼ 1:047

E p0 V

0:64 ;


Here pqs is dimensional quasi-static overpressure remaining in closed space after all dynamic shock-wave processes, Δpqs is dimensionless quasi-static overpressure, G is TNT charge equivalent, kg; E1 is blast specific energy, J/kg; pressures are given in Pa, volume are given in m3. Relation (6) shows that pressure fall in a certain volume confinement (for example, V¼706 m3 is over-deck space in “IL-96” aircraft cabin) leads to unambiguous reduction of quasi-static component Δpqs .

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3. Theoretical comparison of the main characteristics of explosion effect Comparison between main characteristics of explosion effects calculated by (1)–(6) at reduced and normal pressure of unperturbed surroundings is performed using dimensionless factors [17]: K p1 ¼

Δpa1 =Δp1 ;

Kp ¼

Δpa =Δp  ;


K I ¼ I =I;

K I  ¼ I a =I  ;

K qs ¼ Δpaqs =Δpqs ;


where the upper index (a) corresponds to blast parameters at reduced pressure, lack of that index corresponds to those parameters at normal pressure of non-perturbed surroundings. Curves 1–5 in Fig. 1 show K factors variation depending on the reduced distance to the blast epicenter in Sadovsky–Hopkinson variables Rn ¼ R=G1=3 , kg/m1/3, at the same order as in (7). So, curve 1 corresponds to blast wave amplitude variation due to ambient pressure diminishing, curve 2 corresponds to negative phase pressure variation, curve 3 – to positive phase impulse variation, curve 4 – to negative phase impulses, curve 5 – to quasistatic pressure components. A noticeable reduction of amplitudes/impulses of positive and negative phases of a traveling shock wave as well as residual overpressure in lower pressure surroundings (p0 ¼0.64 atm) in comparison with the normal pressure surroundings has been recorded. Blast wave amplitude reduction (curve 1) is in between 4% and 21% within the distance range of practical value. Decreasing of other damage blast effect parameters does not depend on the distance to the charge and on energy of compared explosions and inner volume of the fuselage; it is approximately 25.2% for the rarefaction phase amplitude, 1.1% and 4.5% for the pressure impulses of compression/rarefaction phases, and for residual pressure loads it is 25.5%. Relations (1), (3) and (4) allow us to calculate dimensional blast wave positive phase pressures and impulses for practically important range of distances both at normal and diminished ambient pressure. Shown at “blast wave impulse – overpressure” plot, they forms so-called damage diagram. Damage diagrams of the initial shock wave constructed in “blast wave impulse – overpressure” coordinates (Fig. 2) K 3

4 0.95

0.90 0.85






5 1










R*, m/kg

Fig. 1. Factors of blast damage effects variation at reduces surroundings pressure.


I,Pa. sec 7a

400 350




300 250




4a 3a

4b 3b 2b

150 100 50

2a 1a

1b 100








Fig. 2. Diagram of shock wave damage effect in “overpressure – impulse” coordinates at detonation of 0.1 kg charge in TNT equivalent (curves 1a, 1b); 0.25 kg (curve 2a, 2b); 0.5 kg (3a, 3b); 1 kg (4a, 4b); 2 kg (5a, 5b); 5 kg (6a, 6b); 10 kg (7a, 7b). Curves 1a–7a corresponds to explosion at normal atmospheric pressure, curves 1b–7b—to the pressure reduced to 0.64 atm.

allow to compare the explosion damage capability at normal atmospheric (curves 1a 7a) pressure and at the lower one (curves 1b7b). In compliance with those diagrams, both impulse and pressure resulted from a certain power explosion decrease at some given distance from the blast epicenter when the surroundings pressure is reduced (in particular, on board an aircraft). Thus, a blast at lower pressure conditions produces lower explosion effect. That conclusion on reduction of the main parameters characterizing an explosive effect in surroundings with lower initial pressure is also true for normally or obliquely reflected shock waves. In particular, overpressure Δpr of a shock wave normally reflected from a rigid surface (for example, aircraft fuselage or door) is defined using the Izmaylov–Crussard relation (see, for example, [18]): Δpr Δp1 ¼ 2þ Δp1 εΔp1 þ ð1 þ εÞp0


where ε ¼ ðγ  1Þ=ðγ þ1Þ is inverse maximum densities ratio on a shock wave in an ideal gas, γ is the ratio of gas specific heats (γ ¼1.4 here). Calculation of K pr ¼ Δpar =Δpr factor (see curve 6 in Fig. 1; here Δpar and Δpr are reflected wave amplitude at diminished and normal ambient pressures) shows that reduction of the surroundings pressure down to p0 ¼0.64 atm leads to up to 20% decrease of the reflected wave amplitude depending on a distance from the blast epicenter and, therefore, attenuates the explosive effect. Since the relation between the pressure impulses of reflected and incident waves are approximately equal to the relation between their amplitudes [19], it can be assumed that the similar conclusion is true for normally reflected wave compression phase impulse I ar . Analysis of regular and different types of the Mach blast wave reflection from various constructive elements resulted in formation of extreme triple configurations [20–23] has proved the correctness of the drawn conclusions about reduction of the main factors of a blast mechanical effect at surroundings pressure decreasing in case of incident reflection. Similar conclusions were drawn based on other empirical relations characterizing an explosion at voluntary


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atmospheric pressure (in particular, on G.I. Pokrovsky formulae). Theoretical results based on the empirical blast wave formulas lead to the following results at whole. The pressure p0 decrease on board of a flying vehicle resulted from emergency measures in case an explosive device (or potentially dangerous object) is found onboard reduces shock-wave effects. Loads on an aircraft fuselage, doors and load-bearing elements are less than in case when a similar explosion occurs at normal pressures (1 atm) onboard and outboard the aircraft. It means that it is not necessary to increase the onboard pressure during the land testing. “Pressurization” up to increased levels will lead to overload of the aircraft or spacecraft walls, load-bearing elements and distort a real picture of an onboard explosion. In particular, the conclusions [5] on the flight capability drawn based on full-scale testing at atmospheric pressure onboard can be spread to an emergency scenario considered by ICAO regulations. Though these theoretical results are based on the results of the theory of similarity and numerous (hundreds and even thousands times repeated) results provided by Sadovsky, Adushkin, Korotkov, Tsikulin and other Soviet and Russian researchers, they seem to need some experimental proof.

Fig. 4. Blast wave overpressure for the detonation of HE charge equivalent to 0.5 kg TNT at the diminished ambient pressure. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article).

4. Experimental results The experimental results achieved onboard wide-body airplane IL-96 and narrow-body airplane IL-114 at the conditions described in [5] are presented here. HE charges approximately equivalent to 0.2, 0.5, 1.0 and 2.0 kg TNT at the normal (1 atm) pressure onboard were used at the diminished (0.64 atm) ambient pressure. The upper (red) lines in Figs. 3–7 correspond to the positive phase overpressures and impulses calculated according to formulas (1) and (3). The red points in the same figures are experimental results given by piezoelectric pressure sensors. We should recognize that the measured values of the overpressure and impulse differ from the theoretically calculated not more than on 5–10%, as a rule. Fig. 5. Blast wave overpressure for the detonation of HE charge equivalent to 1.0 kg TNT at the diminished ambient pressure. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article).

Fig. 3. Blast wave overpressure for the detonation of HE charge equivalent to 0.2 kg TNT at the diminished ambient pressure. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article).

Because there are positive phase overpressure (blast wave amplitude) and pressure impulse that define the blast shock wave destructive action, Figs. 3–7 confirm the applicability and reliability of blast wave action analysis of Chapter 3 based on the empirical relations. Blast wave negative phase analysis is not so valuable. The dimensionless relations between incident and (normally or obliquely) reflected shock wave strengths do not depend on the ambient pressure. As the simplest example, relation (8) between incident shock wave strength and the normally reflected one was chosen and analyzed at the text. The results are analogous for the oblique (regular or Mach) reflection as well. The lower (blue and green) experimental points correspond to the blasts of the same HE charges at the same ambient pressures, but inside the stationary destructible blast inhibitor “Fountain 3MK-2000” (blue points at Figs. 6

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Fig. 6. Blast wave overpressure for the detonation of HE charge equivalent to 1.0 kg TNT at the diminished ambient pressure. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article).


their effect on its constructive elements. In particular, it has been shown that the shock-wave effect at reduced surroundings pressure is less than in case of the similar explosion occurs at normal atmospheric pressure inside the aircraft cabin and outboard. The well-known empirical relations derived in [18] occurred to be quite reliable and applicable for HE explosion at lowered ambient pressure. Experimental results for blast overpressure and impulse provided at the tests both at wide-body (IL-96) and narrow-body (IL-114) airplanes correspond to this conclusion with the enough accuracy. Though the experiments inside the space vehicles were not provided, the results achieved inside the aircraft points to the correctness of the analogous conclusions for space vehicles theoretically based on the empirical relations. As the main practically important conclusion, we should mention that the experimental results on airworthiness saving achieved at the normal ambient pressure inside and outside the flying vehicle can be widespread under the lowered ambient pressure conditions (according to ICAO regulations, for example).

Acknowledgments Authors are grateful to the colleagues who contribute a lot to the experimental results: Academician of RAS G.V. Novozhilov, V.I. Terentyev, N.A. Soin (“Ilyushin” Aircraft Corporation), Mayor General N.V. Vdovin (EMERCOM of Russia, the 294th Center “Leader”), N.N. Vasilyev, V.Ya. Dmitriev, V.N. Shishkin, V.A. Ermolaev (Special Materials, Corp.) References

Fig. 7. Blast wave impulse for the detonation of HE charge equivalent to 2.0 kg TNT at the diminished ambient pressure. (For interpretation of the references to color in this figure,the reader is referred to the web version of this article).

and 7) and the portative destructible blast inhibitors “Fountain 4M-500” and “Fountain 4MK-500” (blue and green points in Figs. 3–5) of small own weight (21 kg and 26 kg, correspondingly). Blue and green curves are experimentally based trend lines. It is evident that the application of “Fountain” blast inhibiting technology (see, for example, [5–8]) suppresses the blast wave overpressure and impulse sufficiently and made these factors practically safe and almost harmless for humans and constructions at the distances shown in Figs. 3–7. 5. Conclusions The present paper is devoted to calculations, comparison and analysis of parameters (overpressure and impulse) of blast waves resulted from similar power explosions on board a flying vehicle at normal and reduced onboard pressure and

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