Shock wave
In mechanics, specifically acoustics, a shock wave, shockwave, or shock, is a type of propagating disturbance that moves faster than the local speed of sound in the medium. Like an ordinary wave, a shock wave carries energy and can propagate through a medium, but is characterized by an abrupt, nearly discontinuous, change in pressure, temperature, and density of the medium.
For the purpose of comparison, in supersonic flows, additional increased expansion may be achieved through an expansion fan, also known as a Prandtl–Meyer expansion fan. The accompanying expansion wave may approach and eventually collide and recombine with the shock wave, creating a process of destructive interference. The sonic boom associated with the passage of a supersonic aircraft is a type of sound wave produced by constructive interference.
Unlike solitons, the energy and speed of a shock wave alone dissipates relatively quickly with distance. When a shock wave passes through matter, energy is preserved but entropy increases. This change in the matter's properties manifests itself as a decrease in the energy which can be extracted as work, and as a drag force on supersonic objects; shock waves are strongly irreversible processes.
Terminology
Shock waves can be:; Normal: At 90° to the shock medium's flow direction.
; Oblique: At an angle to the direction of flow.
; Bow: Occurs upstream of the front of a blunt object when the upstream flow velocity exceeds Mach 1.
Some other terms:
- Shock front: The boundary over which the physical conditions undergo an abrupt change because of a shock wave.
- Contact front: In a shock wave caused by a driver gas, the boundary between the driver and the driven gases. The contact front trails the shock front.
In supersonic flows
When an object moves faster than information can propagate into the surrounding fluid, the 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 change almost instantaneously. Measurements of the thickness of shock waves in air have resulted in values around 200 nm, which is on the same order of magnitude as the mean free path of gas molecules. In reference to the continuum, this implies the shock wave can be treated as either a line or a plane if the flow field is two-dimensional or three-dimensional, respectively.
Shock waves are formed when a pressure front moves at supersonic speeds and pushes on the surrounding air. At the region where this occurs, sound waves travelling against the flow reach a point where they cannot travel any further upstream and the pressure progressively builds in that region; a high-pressure shock wave rapidly forms.
Shock waves are not conventional sound waves; a shock wave takes the form of a very sharp change in the gas properties. 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.
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.
Normal shocks
In elementary fluid mechanics utilizing ideal gases, a shock wave is treated as a discontinuity where entropy increases abruptly as the shock passes. Since no fluid flow is discontinuous, a control volume is established around the shock wave, with the control surfaces that bound this volume parallel to the shock wave. The two surfaces are separated by a very small depth such that the shock itself is entirely contained between them. At such control surfaces, momentum, mass flux and energy are constant; within combustion, detonations can be modelled as heat introduction across a shock wave. It is assumed the system is adiabatic and no work is being done. The Rankine–Hugoniot conditions arise from these considerations.Taking into account the established assumptions, in a system where the downstream properties are becoming subsonic: the upstream and downstream flow properties of the fluid are considered isentropic. Since the total amount of energy within the system is constant, the stagnation enthalpy remains constant over both regions. However, entropy is increasing; this must be accounted for by a drop in stagnation pressure of the downstream fluid.
Other shocks
Oblique shocks
When analyzing shock waves in a flow field, which are still attached to the body, the shock wave which is deviating at some arbitrary angle from the flow direction is termed oblique shock. These shocks require a component vector analysis of the flow; doing so allows for the treatment of the flow in an orthogonal direction to the oblique shock as a normal shock.Bow shocks
When an oblique shock is likely to form at an angle which cannot remain on the surface, a nonlinear phenomenon arises where the shock wave will form a continuous pattern around the body. These are termed bow shocks. In these cases, the 1d flow model is not valid and further analysis is needed to predict the pressure forces which are exerted on the surface.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 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. There is a theory that the sound pressure levels in brass instruments such as the trombone become high enough for steepening to occur, forming an essential part of the bright timbre of the instruments. While shock formation by this process does not normally happen to unenclosed 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.
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 special relativity.To produce a shock wave, an object in a given medium must travel faster than the local speed of sound. In the case of an aircraft travelling at high subsonic speed, regions of air around the aircraft may be travelling at exactly the speed of sound, so that the sound waves leaving the aircraft pile up on one another, similar to a traffic jam on a motorway. When a shock wave forms, the local air pressure increases and then spreads out sideways. Because of this amplification effect, a shock wave can be very intense, more like an explosion when heard at a distance.
Analogous phenomena are known outside fluid mechanics. For example, charged particles accelerated beyond the speed of light in a refractive medium create visible shock effects, a phenomenon known as Cherenkov radiation.
Phenomenon types
Below are a number of examples of shock waves, broadly grouped with similar shock phenomena:Image:Trinity explosion film strip.jpg|thumb|right| Shock wave propagating into a stationary medium, ahead of the fireball of an explosion. The shock is made visible by the shadow effect.
Moving shock
- Usually consists of a shock wave propagating into a stationary medium
- In this case, the gas ahead of the shock is stationary and the gas behind the shock can be supersonic in the laboratory frame. The shock propagates with a wavefront which is normal to the direction of flow. The speed of the shock is a function of the original pressure ratio between the two bodies of gas.
- Moving shocks are usually 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.
Detonation wave
- A detonation wave is essentially a shock supported by a trailing exothermic reaction. It involves a wave travelling 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 following the shock wave, and the chemical energy of the reaction drives the wave forward.
- A detonation wave follows slightly different rules from an ordinary shock since it is driven by the chemical reaction occurring behind the shock wavefront. In the simplest theory for detonations, an unsupported, self-propagating detonation wave proceeds at the Chapman–Jouguet flow velocity. A detonation will also cause a shock to propagate into the surrounding air due to the overpressure induced by the explosion.
- When a shock wave is created by high explosives such as TNT, it will always travel at high, supersonic velocity from its point of origin.