Shock wave

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This article is about a type of disturbance. For other uses of the word, see shockwave (disambiguation).

Schlieren photograph of shock waves produced by a T-38 Talon during flight.

A shock wave (or simply "shock") is a type of propagating disturbance. Like an ordinary wave, a shock wave carries energy and can propagate through a medium (solid, liquid or gas), or, in special cases, through a field such as the electromagnetic field in the absence of a physical medium. Shock waves are characterized by an abrupt change (a discontinuity) in the characteristics of the medium. Across a shock there is always an abrupt rise in pressure, temperature and density of the flow. However, it is not possible to have a decrease in these properties across a shock wave. ^ref In supersonic flows, expansion is achieved through an expansion fan. A shock wave travels through most mediums at a higher speed than an ordinary wave.

Unlike solitons (another kind of nonlinear wave), the energy of a shock wave dissipates relatively quickly with distance. Additionally, the companion expansion wave from a shock approaches, and eventually merges with the shock, partially cancelling it out. Thus the sonic boom associated with the passage of an aircraft is the sound wave resulting from the degradation and merging of the shock-wave–expansion-wave pair produced by the passage of a supersonic aircraft.

Although the total energy is preserved when matter is processed by a shock wave, the available energy which can be extracted as work is decreased (Entropy is increased). This has the practical effect, for example, that an aircraft with shocks will experience an additional drag force to that which it would experience if the flow was shockless.

1 Terminology
2 Shock waves in supersonic flows
3 Shock waves due to nonlinear steepening
4 Analogies
5 Examples of shock waves
6 See also
7 References
8 External links

[edit] Terminology

In this article "Normal Shock" is meant in the mathematical sense of normal as in "at 90 degrees".

[edit] Shock waves in supersonic flows

Pressure-time diagram at an external observation point for the case of a supersonic object propagating past the observer. The leading edge of the object causes a shock (left, in red) and the trailing edge of the object causes an expansion (right, in blue).

The shock wave is one of several different ways in which a gas in a supersonic flow can be compressed. Some other methods are isentropic compressions, including Prandtl-Meyer compressions. The method of compression of a gas results in different temperatures and densities for a given pressure ratio, which can be analytically calculated for a non-reacting gas. A shock wave compression results in a loss of total pressure, meaning that it is a less efficient method of compressing gases for some purposes, for instance in the intake of a scramjet. The appearance of pressure-drag on supersonic aircraft is mostly due to the effect of shock compression on the flow.

When an object (or disturbance) moves faster than the information about it can be propagated into the surrounding fluid, fluid near the disturbance cannot react or "get out of the way" before the disturbance arrives. In a shock wave the properties of the fluid (density, pressure, temperature, velocity, Mach number) change almost instantaneously. Measurements of the thickness of shock waves have resulted in values approximately one order of magnitude greater than the mean free path of the gas investigated.

Shock waves form when the speed of a gas changes by more than the speed of sound. At the region where this occurs sound waves traveling against the flow reach a point where they cannot travel any further upstream and the pressure progressively builds in that region, and a high pressure shock wave rapidly forms.

However, shock waves are not conventional sound waves; a shock wave takes the form of a very sharp change in the gas properties on the order of a few mean free paths (roughly micro-meters at atmospheric conditions) in thickness. Shock waves in air are heard as a loud "crack" or "snap" noise. Over longer distances a shock wave can change from a nonlinear wave into a linear wave, degenerating into a conventional sound wave as it heats the air and loses energy. The sound wave is heard as the familiar "thud" or "thump" of a sonic boom, commonly created by the supersonic flight of aircraft.

[edit] Shock waves due to nonlinear steepening

Shock waves can form due to steepening of ordinary waves. The best-known example of this phenomenon is ocean waves that form breakers on the shore. In shallow water, the speed of surface waves is dependent on the depth of the water. An incoming ocean wave has a slightly higher wave speed near the crest of each wave than near the troughs between waves, because the wave height is not infinitesimal compared to the depth of the water. The crests overtake the troughs until the leading edge of the wave forms a vertical face and spills over to form a turbulent shock (a breaker) that dissipates the wave's energy as sound and heat.

Similar phenomena affect strong sound waves in gas or plasma, due to the dependence of the sound speed on temperature and pressure. Strong waves heat the medium near each pressure front, due to adiabatic compression of the air itself, so that high pressure fronts outrun the corresponding pressure troughs. While shock formation by this process does not normally happen to sound waves in Earth's atmosphere, it is thought to be one mechanism by which the solar chromosphere and corona are heated, via waves that propagate up from the solar interior.

[edit] Analogies

A shock wave may be described as the furthest point upstream of a moving object which "knows" about the approach of the object. In this description, the shock wave position is defined as the boundary between the zone having no information about the shock-driving event, and the zone aware of the shock-driving event, analogous with the light cone described in the theory of general relativity.

To get a shock wave something has to be travelling faster than the local speed of sound. In that case some parts of the air around the aircraft are travelling at exactly the speed of sound with the aircraft, so that the soundwaves leaving the aircraft pile up on each other, similar to a tailback on a road, and a shock wave forms, the pressure increases, and then spreads out sideways. Because of this amplification effect, a shock wave is very intense, more like an explosion when heard (not coincidentally, since explosions create shock waves).

Analogous phenomena are known outside fluid mechanics. For example, particles accelerated beyond the speed of light in a refractive medium (where the speed of light is less than that in a vacuum, such as water) create visible shock effects, a phenomenon known as Cherenkov radiation.

[edit] Examples of shock waves

Below are a number of examples of shock waves, broadly grouped with similar shock phenomena:

Here you can see the shock wave propogating into a stationary medium, ahead of the fireball of an explosion. Here the shock is made visible by the shadow effect (Trinity explosion.)

Shadowgraph of the detached shock on a bullet in supersonic flight, published by Ernst Mach in 1887.

Schlieren photograph of an attached shock on a sharp-nosed supersonic body.

Recompression shock on a transonic flow airfoil, at and above critical Mach number.

Shock propagating into a stationary medium (Moving shock)
- This shock is generally generated by the interaction of two bodies of gas at different pressure, with a shock wave propagating into the lower pressure gas, and an expansion wave propagating into the higher pressure gas.
- Examples: Balloon bursting, Shock tube, shock wave from explosion
- In this case, the gas ahead of the shock is stationary (in the laboratory frame), and the gas behind the shock is supersonic in the laboratory frame. The shock propagates with a wave front which is normal (at right angles) to the direction of flow. The speed of the shock is a function of the original pressure ratio between the two bodies of gas.
Detached shock on a supersonic body (see also bow shock or oblique shock)
- Such a shock occurs when the maximum deflection angle is exceeded. A detached shock is commonly seen on blunt bodies, but may also be seen on sharp bodies at low Mach numbers.
- Examples: Space return vehicles (Apollo, Space shuttle), bullets, the boundary of a magnetosphere
- These shocks are curved, and form a small distance in front of the body. Directly in front of the body, they stand at 90 degrees to the oncoming flow, and then curve around the body. Detached shocks allow the same type of analytic calculations as for the attached shock, for the flow near the shock. They are a topic of continuing interest, because the rules governing the shock's distance ahead of the blunt body are complicated, and are a function of the body's shape. Additionally, the shock standoff distance varies drastically with the temperature for a non-ideal gas, causing large differences in the heat transfer to the thermal protection system of the vehicle. See the extended discussion on this topic at Atmospheric reentry. These follow the "strong-shock" solutions of the analytic equations, meaning that for some oblique shocks very close to the deflection angle limit, the downstream Mach number is subsonic.
Attached shock on a supersonic body
- These shocks appear as "attached" to the tip of a sharp body moving at supersonic speeds.
- Examples: Supersonic wedges and cones with small apex angles
- The attached shock wave is a classic structure in aerodynamics because, for a perfect gas and inviscid flow field, an analytic solution is available, such that the pressure ratio, temperature ratio, angle of the wedge and the downstream Mach number can all be calculated knowing the upstream Mach number and the shock angle. Smaller shock angles are associated with higher upstream Mach numbers, and the special case where the shock wave is at 90 degrees to the oncoming flow (Normal shock), is associated with a Mach number of one. These follow the "weak-shock" solutions of the analytic equations.
Re-compression shock on a transonic body
- These shocks appear when the flow over a transonic body is decelerated to subsonic speeds.
- Examples: Transonic wings, turbines
- Where the flow over the suction side of a transonic wing is accelerated to a supersonic speed, the resulting re-compression can be by either Prandtl-Meyer compression or by the formation of a normal shock. This shock is of particular interest to makers of transonic devices because it can cause separation of the boundary layer at the point where it touches the transonic profile. This can then lead to full separation and stall on the profile, higher drag, or shock-buffet, a condition where the separation and the shock interact in a resonance condition, causing resonating loads on the underlying structure.
Shock in a pipe flow
- This shock appears when supersonic flow in a pipe is decelerated.
- Examples: Supersonic ramjet, scramjet, needle valve
- In this case the gas ahead of the shock is supersonic (in the laboratory frame), and the gas behind the shock system is either supersonic (oblique shocks) or subsonic (normal shock) (Although for some oblique shocks very close to the deflection angle limit, the downstream Mach number is subsonic.) The shock is the result of the deceleration of the gas by a converging duct, or by the growth of the boundary layer on the wall of a parallel duct.
Detonation wave
- A detonation wave is essentially a shock within which an exothermic reaction takes place. It involves a wave traveling through a highly combustible or chemically unstable medium, such as an oxygen-methane mixture or a high explosive. The chemical reaction of the medium occurs within the wave, and the chemical energy of the reaction drives the wave forward.
- It is also possible for a shock wave in a reactive mixture to initiate combustion (shock-induced combustion), but in this case the shock proceeds at a velocity indicated by the non-combusted mixture, since the actual combustion occurs in the region behind the shock wave, rather than within the wave. The velocity of a shock wave is independent of what is happening after it passes.
- A detonation wave follows slightly different rules from an ordinary shock since it is driven by the chemical reaction occurring inside the wave front itself. This change from a shock-induced combustion to detonation happens as the time for the exothermic reaction to occur approaches the time for the shock-wave to pass the reacting particles. Detonation waves proceed at the Chapman-Jouguet velocity, which is a function of the nature of the chemical reaction occurring. A detonation will also cause a shock of type 1, above to propagate into the surrounding air due to the overpressure induced by the explosion.