Shock wave
A shock wave is a type of propagating disturbance. Like a normal
wave, a shock wave carries energy and can propagate through a medium or, in special cases, through a field such as the electromagnetic field in the absence of a physical medium. Shock waves are characterized by a sudden change in the characteristics of the medium as a positive
step function. The corresponding negative step is an expansion wave. A shock wave travels through the medium at a higher speed than a normal wave.
Unlike solitons , the energy of a shock wave dissipates relatively quickly with distance.
Encyclopedia
A
shock wave is a type of propagating disturbance. Like a normal
wave, a shock wave carries energy and can propagate through a medium or, in special cases, through a field such as the electromagnetic field in the absence of a physical medium. Shock waves are characterized by a sudden change in the characteristics of the medium as a positive
step function. The corresponding negative step is an expansion wave. A shock wave travels through the medium at a higher speed than a normal wave.
Unlike solitons , 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.
Shock waves in supersonic flows
The
shock wave is one of several different ways in which a gas in a supersonic flow can be compressed. Two other methods are isentropic and
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 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 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 are not 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 in thickness. Shock waves in air are heard as a loud "crack" or "snap" noise. Over time 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.
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. 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.
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, sort of like a tailback on a road, and a shock wave forms, the pressure goes up and up and up there, and then spreads out sideways. Because of this amplification effect, a shock wave is very intense, more like an explosion when you hear it .
Analogous phenomena are known outside fluid mechanics. For example, particles accelerated beyond the
speed of light in a
refractive medium create visible shock effects, a phenomenon known as
Cherenkov radiation.
Types of shock wave
There are several types of shock wave:
- Shock propagating into a stationary flow
- 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 , and the gas behind the shock is supersonic in the laboratory frame. The shock propagates normal to the oncoming flow. The speed of the shock is a function of the original pressure ratio between the two bodies of gas.
- 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 , and the gas behind the shock system is either supersonic or 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.
- Recompression shock on a transonic body
- These shocks appear when the flow over a transsonic 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 recompression 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.
- 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 flowfield, 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 downstream Mach numbers, and the special case where the shock wave is at 90 degrees to the oncoming flow , is associated with a downstream Mach number of one. These follow the "weak-shock" solutions of the analytic equations.
- Detached shock on a supersonic body
- Such a shock occurs about a supersonic body that is too blunt for the shock to attach to the tip.
- Examples: Space return vehicles , 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.
- Detonation wave
A detonation wave is essentially a shock within which an exothermic reaction takes place. 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 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 , but in this case the shock proceeds at a velocity indicated by the noncombusted 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.
External links
-
-
-
-
- NASA Glenn Research Center information on:
- Selkirk college: Aviation intranet: High speed flight
See also
