Shock wave structure

The width of high-intensity shock waves is of the order of the mean free path of gas molecules (more precisely, ~ 10 mean free paths, and cannot be less than 2 mean free paths; this result was obtained by Chapman in the early 1950s). Since in macroscopic gas dynamics the mean free path should be considered equal to zero, purely gas-dynamic methods are unsuitable for studying the internal structure of high-intensity shock waves.

The kinetic theory is used for the theoretical study of the microscopic structure of shock waves. Analytically, the problem of the structure of the shock wave is not solved, but a number of simplified models are used. One such model is the Tamm-Mota-Smith model.

Shock Wave Velocity

The speed of propagation of a shock wave in a medium exceeds the speed of sound in a given medium. The excess is the greater, the higher the intensity of the shock wave (the ratio of pressures in front of and behind the wave front): (p sp.wave - p c.medium) / p c.medium.

For example, not far from the center of a nuclear explosion, the speed of propagation of a shock wave is many times higher than the speed of sound. When moving away with a weakening of the shock wave, its speed rapidly decreases and at a large distance the shock wave degenerates into a sound (acoustic) wave, and the speed of its propagation approaches the speed of sound in the environment. A shock wave in the air during a nuclear explosion with a capacity of 20 kilotons travels the distances: 1000 m in 1.4 s, 2000 m - 4 s, 3000 m - 7 s, 5000 m - 12 s. Therefore, a person who sees a flash of an explosion has some time for shelter (folds of the terrain, ditches, etc.) and thereby reduce the damaging effect of the shock wave (unless, of course, the person is blinded by the flash).

Shock waves in solids (for example, caused by a nuclear or conventional explosion in a rock, a meteorite impact, or a cumulative jet) at the same speeds have significantly higher pressures and temperatures. The solid behind the front of the shock wave behaves like an ideal compressible liquid, that is, there are no intermolecular and interatomic bonds in it, and the strength of the substance has no effect on the wave. In the case of a ground and underground nuclear explosion, the shock wave in the ground cannot be considered as a damaging factor, since it quickly dies out; the radius of its propagation is small and will be entirely within the size of the explosive funnel, inside which the complete defeat of durable underground targets is already achieved.

Detonation

Detonation- this is a combustion mode in which a shock wave propagates through the substance, initiating chemical combustion reactions, in turn supporting the movement of the shock wave due to the heat released in exothermic reactions. A complex consisting of a shock wave and a zone of exothermic chemical reactions behind it propagates through the substance at a supersonic speed and is called a detonation wave. The detonation wave front is the surface of the hydrodynamic normal discontinuity.

The speed of propagation of the detonation wave front relative to the initial stationary substance is called detonation speed... The detonation speed depends only on the composition and state of the detonating substance and can reach several kilometers per second both in gases and in condensed systems (liquid or solid explosives). The detonation speed is much higher than the slow combustion speed, which is always much less than the speed of sound in the substance and does not exceed tens of centimeters per second or several meters per second (when burning hydrogen-oxygen mixtures).

Many substances are capable of both slow combustion and detonation. In such substances, for the propagation of detonation, it must be initiated by an external effect (mechanical or thermal). Under certain conditions, slow combustion can spontaneously turn into detonation.

Detonation, as a physicochemical phenomenon, should not be equated with an explosion.

An explosion is a process in which a large amount of energy is released in a short time in a limited volume and gaseous explosion products are formed that can perform significant mechanical work or cause destruction at the explosion site. An explosion can also take place during the ignition and rapid combustion of gas mixtures or explosives in a confined space, although this does not generate a detonation wave. So, the rapid (explosive) combustion of gunpowder in the barrel of an artillery gun in the process of firing is not detonation. The knock that occurs in internal combustion engines during explosive combustion of fuel is also called detonation.

Organic solvents - chemical compounds for dissolving solids (resins, plastics, paints, etc.). This group includes alcohols, ethers, chlorinated hydrocarbons, ketones, hydrocarbons, etc.

The concept of a shock wave, its characteristics

The rapid and uncontrolled release of energy creates explosion.

The released energy manifests itself in the form of heat, light, sound and mechanical shock wave. The source of the explosion more often a chemical reaction is used. But an explosion can be the release of mechanical and nuclear energy (steam boiler, nuclear explosion). Combustible, dust, gas and steam mixed with air (a substance that supports combustion) can explode when ignited. In technological processes, it is impossible to completely exclude the possibility of an explosive situation. One of the main damaging factors of the explosion is the shock wave.

Shock wave- this is an area of ​​sharp compression of the medium, which in the form of a spherical layer spreads in all directions from the explosion site at supersonic speed.

The shock wave is generated by the energy released in the reaction zone. The vapors and gases generated during the explosion, expanding, produce a sharp blow to the surrounding air layers, compress them to high pressures and densities, and heat them to high temperatures. These layers of air drive the subsequent layers. And so, the compression and movement of air occurs from one layer to another, forming a shock wave. The magnitude of pressure changes in time at a point in space when a shock wave passes through it. With the arrival of the shock wave at a given point, the pressure reaches a maximum Pf = Po + ΔPf, where Po is atmospheric pressure. The resulting layers of compressed air are called compression phase. After the passage of the wave, the pressure decreases and becomes below atmospheric. This zone of reduced pressure is called rarefaction phase.

Air masses move directly behind the shock front. Due to the deceleration of these air masses, when meeting an obstacle, pressure arises velocity head air shock wave.

The main characteristics of the damaging effect of a shock wave are:

- Excessive pressure in the front shock wave (Рф) is the difference between the maximum pressure in the front of the shock wave and normal atmospheric pressure (Ро), measured in Pascals (Pa). The excess pressure in the shock front is calculated by the formula:

where: ΔРф - excess pressure, kPa;

qe is the TNT equivalent of the explosion (qe = 0.5q, q is the power of the explosion, kg);

R is the distance from the center of the explosion, m.

- Velocity head pressure - it is the dynamic load created by the air flow; the velocity head of the Rivers depends on the velocity and density of the air.

where V is the velocity of air particles behind the shock front, m / s;

ρ - air density, kg / m3.

- The duration of the compression phase, that is, the time of action of the increased pressure.

τ = 0.001 q1 / 6 R1 / 2,

where R is in meters, q is in kilograms and τ is in seconds.

A shock wave in water differs from an air one in that at the same distances the pressure in the shock front in water is much greater than in air, and the action time is shorter. Compression waves in soil, in contrast to a shock wave in air, are characterized by a less sharp increase in pressure in the wave front and a slower attenuation behind the front.

The shock wave can injure a person and cause death. Defeat can be direct or indirect. Direct damage arises from the action of excess pressure and high-speed air pressure. The shockwave compresses the person violently for several seconds. The high-speed pressure can lead to the movement of the body in space. Indirect human injury can be the result of impacts from debris flying at high speed.

The nature and degree of damage to a person depends on the power and type of explosion, distance, as well as on the location and position of the person. Extremely heavy contusions and injuries occur at an overpressure of more than 100 kPa (1 kgf / cm 2): ruptures of internal organs, fractures of guests, internal bleeding, etc. At overpressures from 60 to 100 kPa (from 0.6 to 1 kgf / sq. Cm), there are severe contusion and injuries: loss of consciousness, bone fractures, bleeding from the nose and ears, possible damage to internal organs. Medium severity lesions occur at an overpressure of 40-60 kPa (0.4-0.6 kgf / cm2): dislocations, damage to the hearing organs, etc. AND light lesions at a pressure of 20-40 kPa (0.2-0.4 kgf / sq.cm). The shock wave has a mechanical effect on buildings, structures, and can cause their destruction. Buildings with a metal frame receive average destruction at 20-40 kPa and complete at 60-80 kPa, brick buildings at 10-20 kPa and 30-40, wooden buildings at 10 and 20 kPa.

In a nuclear explosion in the atmosphere, approximately 50% of the explosion energy is spent on the formation of a shock wave. In the reaction zone, the pressure reaches billions of atmospheres (up to 10 billion Pa). An air blast wave of a nuclear explosion of average power travels 1000 m in 1.4 s, and 5000 in 12 C. 3 km 30 kPa (0.3 kgf / cm 2).

Protective earth

There are the following protection methods used separately or in combination with each other: protective grounding, neutralization, protective shutdown, electrical separation of networks of different voltages, the use of low voltage, isolation of live parts, potential equalization.

In electrical installations (EU) with a voltage of up to 1000 V with an insulated neutral and in an EU of direct current with an isolated midpoint, protective grounding is used in combination with insulation monitoring or protective shutdown.

In these electrical installations, a network with a voltage of up to 1000 V, connected to a network with a voltage of more than 1000 V through a transformer, is protected against the appearance of high voltage in this network in the event of insulation damage between the low and high voltage windings by a breakdown fuse, which can be installed in each phase on the low voltage side transformer.

In electrical installations with voltages up to 1000 V with a solidly grounded neutral or a grounded midpoint in DC power plants, neutralization or protective shutdown is used. In these EUs, grounding of the cases of electrical receivers without grounding them is prohibited.

Protective shutdown is used as the main or additional method of protection in the event that safety cannot be ensured by using protective grounding or neutralization, or their application causes difficulties.

If it is impossible to use protective grounding, grounding or protective shutdown, it is allowed to service the power plant from insulating sites.

A shock wave is an area of ​​sharp and strong compression of the medium, propagating in all directions from the center of the explosion.

at supersonic speed.

Shock waves occur during explosions in almost any medium and transmit the effect of the explosion over a considerable distance.

Depending on the environment in which the shock wave propagates, the following waves are distinguished: air waves (propagating in air); percussion (distributed in the aquatic environment); seismic explosive

(spread in the ground).

2.3. 1. Basic properties and mechanism of formation

shock waves

Let us consider the process of formation of a shock wave using the example of an explosion of an explosive charge (HE).

When an explosive charge explodes, the gaseous products of the explosion, which are under pressure of the order of tens and even hundreds of thousands of atmospheres, expand, compressing the environment (air, water, soil, etc.). The development of the explosion process in the medium is schematically shown in Fig. 2.2. After the detonation wave M1 passes through the explosive charge (the dashed line indicates the detonated part of the charge), the detonation products begin to expand.

The zone of expanding products at a given time is bounded by the СМ1 С 1 curve, the front of the shock wave excited by the explosion is BA and A1 В 1 The detonation velocity is related to the impact velocities

A compression wave, causing a noticeable heating of the medium, can sustainably

only in the form of a shock wave with a jump

a uniform change in pressure in the front; front with a smooth increase in pressure

unstable and quickly turns into an abrupt change in pressure.

The shock wave is followed by a rarefied wave.

Rice npouecca. 2.2. Explosion development scheme in the environment

188 Section 2. Explosions in

which, moving through the compressed and heated air, will overtake the front of the shock wave.

A diagram of the pressure variation with time during the passage of a shock wave is shown in Fig. 2.3.

1 0 l 1 1 e 1 2

Rice. 2.3. Scheme of pressure variation in time during the passage of a shock wave:

1 - compression phase; 2 - rarefaction phase (for explosions in dense media - the phase of races

pulling or unloading)

At the moment the wave arrives at a certain point in space, the pressure in the adjacent region increases abruptly from p0 (in an unperturbed medium) to p1 (at the shock front). Behind the front, the pressure drops rapidly and after a time / ech (the time of the compression phase), after the wave arrives at the point, it turns out to be less than p0 — the compression phase is replaced by the rarefaction phase.

The time during which the pressure in the shock wave remains above atmospheric is called the compression phase, and the time during which the pressure remains below atmospheric is called the rarefaction phase.

At the moment of arrival of a shock wave at a certain point, the medium lying at this point begins to move with the speed and in the direction of propagation of this wave. The nature of the change in u (t) is similar to the nature of the change in p (t). In the compression phase, the medium moves in the direction of movement of the shock wave; in the rarefaction phase, in the opposite direction, but at a slightly lower velocity.

The front of the shock wave is spreading from a supersonic soon

stu (V> c0), and its tail, where p< -р0, движется со скоростью, близкой к скорости звука с0 в невозмушенной среде, поэтому по мере движения ударная волна растягивается во времени. Давление во фронте ударной волны р 1 , скорость перемешения фронта V и скорость потока среды и не являются постоянными. При удалении удар­ ной волны от очага взрыва она уменьшается, и на больших расстоя-

as V approaches c0, and u approaches zero, i.e., the shock wave of degeneracy

goes into an acoustic (elastic) wave. Therefore, the shock wave

has both compression and rarefaction regions. In practice, the action

the shock wave is determined by the compression phase. Rare phase action

nia is usually insignificant, therefore it is not taken into account, with the exception of

Some private effects.

2.3.2. Shock wave parameters

The main parameters of the shock wave are:

excessive pressure in the front of the shock wave;

the high-speed pressure of the shock wave acting on the surface of the object;

the duration of the shock wave;

wave impulse, etc.

Excessive pressure in the front of the shock wave is characterized by the difference between the pressure in the front of the wave and atmospheric pressure.

dr = P1 - Po,

where p1 is the pressure in the shock front;

p 0 - pressure in an undisturbed medium (atmospheric pressure).

The shock wave is characterized by the rate of pressure rise to its maximum value.

Under maximum explosion pressure the greatest

the pressure that arises during the deflagration combustion of the most explosive gas, steam, dust-air mixture in a closed vessel at an initial pressure of 1 0 1.3 kPa. The maximum pressure during the explosion of the air mixture can be calculated by the formula:

where p0 is the initial pressure at which the air suspension is located, kPa;

T 0 - initial temperature of the initial mixture, K;

Tr is the adiabatic combustion temperature of the stoichiometric

mixtures with air at constant volume, K; pc is the number of moles of gaseous combustion products; f / 11 is the number of moles of the initial gas mixture.

The shock wave is characterized by a peak. The peak is the section of the shock

waves from the moment of shock compression to the completion of a chemical reaction,

where the highest pressure forms.

The parameter of the shock wave is the impulse of the wave. The magnitude of the wave impulse will be different depending on the environment in which the explosion is taking place. In general, the wave impulse is described by the law

where G R is the mass of the explosive (combustible) substance; - distance of the shock wave action;

<р - угол отражения волны.

The propagation of a shock wave depends on many factors that determine its effect and strength.

To assess the action of a shock wave, it is necessary to know the nature of the load and the parameters of the system on which this load acts. The nature of the load is usually described by the function of the change in the pressure of the shock wave in time p (t) in the range from zero to the time of the compression phase tсzh

The nature of the impact of a shock wave on a given system depends on the ratio between the time of the action of the compression phase tсzh and the time

Let us change the relaxation of the system "t, and for other systems, by the oscillation period T.

If fсж >> "t, then the action of the shock wave is determined by the magnitude of the excess pressure at its front, since in this case the system will be deformed in such an interval of time (of the order

(1 / 4- 1 / З) t), during which the pressure in the front will not subside.

it is urgent to take away. If, on the contrary, tszh<< "t, то давление за фронтом волны

decreases in such a short period of time that the system practically

she does not get tired of deforming, and further deformations of it are determined by the amount of motion acquired by it, and, consequently, by the specific impulse of the shock wave.

The time of the compression phase depends on many factors: the size and shape of the explosive charge, the environment in which the explosion takes place, the nature of the explosion.

substance, explosion energy, etc. The duration of the compression phase tсzh n, using the appropriate forms of the laws of similarity, will express

formulas (2.4).

		fсж = г0
		r fсж = WF ()
		fc w = VE F3
where r0	Charge radius;
G is the mass of the charge;
	Shock wave distance;
E is the energy of the explosion;

F1, F2, F3 - functional dependence.

Of great importance for evaluating the parameters of shock waves and their action is the similarity law in explosions, which makes it possible to compare the characteristics of shock waves excited by explosions of charges of different masses, consisting of different explosives, as well as explosions caused by the combustion of explosive mixtures.

Detonation combustion occurs in an explosive environment when a sufficiently strong shock wave (or shock compression wave) passes through it. For example, if a point charge of an explosive is blown up in a closed volume with a combustible gas mixture, or a fire has occurred from an ignition source, then a shock wave will propagate throughout the gas mixture from the point where the charge is located, in which a sudden jump-like increase in the state parameters of the gas mixture - pressure , temperature, density. The increase in the gas temperature upon compression in a shock wave is much greater than upon a similar adiabatic compression. Therefore, the absolute temperature of the gas compressed by the shock wave is

pr. is torsional to the pressure of the shock wave.

Therefore, if the shock wave is strong enough, then the tempo

the gas temperature under the action of the shock wave can rise to the autoignition temperature. The shock wave is characterized by a high-velocity head. High-speed

the head is formed as a result of braking on any obstacle

moving air masses in a shock wave. The speed of movement is

expanding gases, forming a velocity head, depends on the degree of compression of gases and their heating by a shock wave. The pressure causes the overturning and throwing of various objects over considerable distances.

The shock wave propagates in space at supersonic speed. For example, a shock wave in a nuclear explosion travels the first 1000 m in 2 s, 2000 m in 5 s, 3000 m in 8 s.

The force of the shock wave is very high and leads to significant destruction. If the rate of pressure rise is relatively low, then the least durable parts, such as windows and doors, will be destroyed first. In the case of a building structure of uniform strength, the rise of the roof and the destruction of all walls will occur simultaneously. Excessive shock wave pressure leads to severe damage during an explosion. Table 2.3 contains data indicating the degree of damage.

Table 2.3. Explosion Damage from Shock Wave

Damener b5, shock STEP OF INSURANCE

wave to Pa

	Destruction of glass in windows with large areas of
	tekpeniya
	Loud sound (1 43 dB); damaged glass; 5%
	glass breakage
	Damage to the cladding of houses; destruction up to 1 0%
	window panes
	Minor structural damage
	90% destruction of glazing, damage
	window frames
	Minor damage to house structures
	Partial destruction of houses to a state in which
	rum living in them is impossible
	Destruction of corrugated asbestos. Corrugated
	steel sludge and aluminum solids are weakened in the
	laziness and and are subject to bending. Wooden paiels are
2 .3. Shock wave characteristics
	The end of the table. 2.3

Damage degree

Unreinforced concrete and slag block walls collapse

Lower Limit of Serious Structural Damage

50% destruction

Heavy machines (1.35 tonnes) in industrial buildings are subject to minor damage. Steel structures are bent

		Destruction of frameless structures glued from
		steel panels. Destruction of oil storage
		Tear off coverings of light industrial buildings
		Cracking of wooden poles (telegraph and
		NS.). High hydraulic presses are damaged
		(weighing 1, 8 t)
		Almost complete destruction of houses
		Rolling over of heavy-duty railway wagons
		Kirnichny walls 200-300 mm thick, not reinforced
		nye, they lose their accuracy as a result of shear or bending
		Heavy freight railroad cars in full
		collapse
		Destruction of more than 75% of internal brickwork
		General destruction of buildings is possible. Heavy (> 3 t)
		machines and machine tools move and severely damage
		Xia. Very heavy (> 5 t) machines and machine tools are retained
		Destruction with crater formation

A shock wave with P s = 1 9 kPa causes significant destruction

urban buildings, and at Ps = 98 kPa, complete destruction occurs

buildings and the death of living organisms.

The degree of destruction is influenced by the structural features of the structures, as well as by the terrain.

SHOCK WAVE

An example of the emergence and spread of U. century. can serve as a gas in a pipe as a piston. If the piston moves in slowly, then acoustic runs along the gas at the speed of sound a. (elastic) compression wave. If the piston is not small in comparison with the speed of sound, a U.V. arises, the speed of propagation of the cut through the unperturbed gas is greater than the speed of movement of the ch-c gas (the so-called mass velocity), which coincides with the speed of the piston. Distances between ch-ts in U. century. less than in undisturbed gas due to gas compression. If the piston is first pushed into the gas at a low speed and gradually accelerated, then U. in: is not formed immediately. First, a compression wave arises with continuous distributions of density r and pressure p. Over time, the steepness of the front of the compression increases, since the perturbations from the accelerated moving piston catch up and intensify, as a result of which there is a sharp jump in all hydrodynamics. quantities, i.e.

Shock compression laws. When gas passes through the U. in. its parameters change very sharply and in a very narrow range. The thickness of the front of the U. century. has the order of the mean free path of molecules, however, for many theoretical. researches it is possible to neglect such a small thickness and with great accuracy replace the front of the U. in. the discontinuity surface, assuming that when passing through it, the gas parameters change abruptly (hence the name ""). The values ​​of the gas parameters on both sides of the shock are related. relations arising from the laws of conservation of mass, momentum and energy:

r1v1 = r0v0, p1 + p1v21 = p0 + r0v20, e1 + p1 / r1 + v21 / 2 = e0 + p0 / r0 + v20 / 2, (1)

Shock wave

In everyday practice, the word “wave” is associated with the idea of ​​a periodic process, a clear example of which is the excitement at sea. Swaying on the "waves" is a favorite pastime of bathers.

In physics, they use the word "wave" in a broader sense and speak of wave propagation even when a local increase or decrease in pressure is caused by a single blow, explosion or air suction.

The air wave created by the explosion looks very peculiar. (We said earlier that an air wave can be photographed, so the word “looks” is quite appropriate for a pressure wave.)

In fig. 128 shows the instantaneous profile of such a blast wave — the curve depicts the distribution of pressure along some direction of wave propagation. The wave profile is formed by a gradual ascent, culminating in a steep descent. The direction of wave movement is shown in the diagram from left to right. The air sections located to the right of the front are at rest at the considered instant - the wave will still reach them.

The main feature of the described explosive or, as it is called, shock wave is a sharp pressure jump at the "front"; the points at rest are captured by the maximum pressure almost instantly: the air particle has just been at atmospheric pressure, and the next instant the pressure in this place is maximum. Then, as the shock wave further advances, the pressure at the point at which we focused our attention will gradually decrease in accordance with the profile of the left gentle slope of the hill.

In fig. 128 depicts the distribution of pressure along any line of wave propagation. The wave propagates in space, and the surface is the front.

The shock front carries with it a jump not only in pressure, but also in density and temperature.

In addition to changes in pressure and temperature, the shock wave carries with it movement. And in a sound wave, air starts to move along the line of wave propagation, but there this phenomenon is hardly noticeable. In the shock wave, the air is carried away so strongly that “fascination” becomes too soft a word. A shock wave creates a strong wind, a hurricane ... For movement in powerful shock waves, perhaps, you will not find a suitable word at all.

The jump in properties that we are talking about is extremely sharp - the transition from complete rest to the maximum speed of movement occurs on a segment of the path equal to several free path lengths of a gas molecule. For air, this is a submicroscopic value of the order of hundred-thousandths of a centimeter. The jump time is measured in ten-billionth (10 × 10) fractions of a second. Such a truly instantaneous change in the state of pressure, density, temperature, speed of movement is a sign of a shock wave.

Depending on the strength of the explosion, the pressure jump carried by the shock wave, or, in other words, the height of the front, can be very different: at the moment of arrival of the shock wave, the pressure can increase from several percent to tens of times.

The values ​​of the jumps of all quantities at the shock front are related to one another. Knowing the magnitude of the jump in pressure, one can also calculate the magnitude of the jump in density, temperature, and speed. The height of the front also determines the speed of propagation of the shock wave. The speed of weak shock waves does not differ from the speed of propagation of an ordinary sound wave. As the height of the front increases, the velocity of propagation of the shock wave also increases.

Let us give numerical data for a "modest" shock wave that increases the pressure by one and a half times. It turns out that such an increase in pressure entails an increase in air density by 30% and an increase in temperature by 35 °. The front velocity of such a shock wave is about 400 m / s. Even with a relatively small pressure jump of 1.5 times, the shock wave will entrain air with it at a speed of about 100 m / s, i.e. 360 km / h No hurricane will give such wind speed.

However, explosions are possible that can create incomparably stronger shock waves. If the wave carries with it a tenfold increase in pressure, then at the wave front there is an abrupt increase in density by four times and an increase in temperature by 500 °. The wind speed reaches 725 m / s. The propagation speed of such a shock wave is already equal to 1 km / s.

Shock waves generated by strong explosions travel tens of kilometers. The jump in properties that the shock wave brings with it acts as a sharp blow against obstacles encountered in the path of the wave. Weak shock waves knock out window panes, destroy walls of houses, and uproot trees. The destructive effect of mortars is largely based on the action of shock waves.

The destructive effect of shock waves sharply depends on many circumstances, and in particular on the duration of the wave action. In order to still give some idea of ​​the relationship between the destructive action of the wave and its main parameter - an increase in pressure, we point out that a shock wave with a front height of only 2% is capable of knocking out glass, and a wave carrying a doubling of pressure breaks thick walls.

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