In fluid dynamics, a moving shock is a

shock wave In physics, a shock wave (also spelled 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 me ...

that is travelling through a fluid (often

gas Gas is one of the four fundamental states of matter (the others being solid, liquid, and plasma). A pure gas may be made up of individual atoms (e.g. a noble gas like neon), elemental molecules made from one type of atom (e.g. oxygen), or ...

eous) medium with a

velocity Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity i ...

relative to the velocity of the fluid already making up the medium.Shapiro, Ascher H., ''Dynamics and Thermodynamics of Compressible Fluid Flow,'' Krieger Pub. Co; Reprint ed., with corrections (June 1983), . As such, the normal shock relations require modification to calculate the properties before and after the moving shock. A knowledge of moving shocks is important for studying the phenomena surrounding

detonation Detonation () is a type of combustion involving a supersonic exothermic front accelerating through a medium that eventually drives a shock front propagating directly in front of it. Detonations propagate supersonically through shock waves with s ...

, among other applications.

Theory

To derive the theoretical equations for a moving shock, one may start by denoting the region in front of the shock as subscript 1, with the subscript 2 defining the region behind the shock. This is shown in the figure, with the shock wave propagating to the right. The velocity of the gas is denoted by ''u'',

pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and e ...

by ''p'', and the local speed of sound by ''a''. The speed of the shock wave relative to the gas is ''W'', making the total velocity equal to ''u₁'' + ''W''. Next, suppose a

reference frame In physics and astronomy, a frame of reference (or reference frame) is an abstract coordinate system whose origin, orientation, and scale are specified by a set of reference points― geometric points whose position is identified both mathe ...

is then fixed to the shock so it appears stationary as the gas in regions 1 and 2 move with a velocity relative to it. Redefining region 1 as ''x'' and region 2 as ''y'' leads to the following shock-relative velocities: :

\ u_y = W + u_1 - u_2,

\ u_x = W.

With these shock-relative velocities, the properties of the regions before and after the shock can be defined below introducing the

temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measurement, measured with a thermometer. Thermometers are calibrated in various Conversion of units of temperature, temp ...

as ''T'', the

density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...

as ''ρ'', and the Mach number as ''M'': :

\ p_1 = p_x \quad ; \quad p_2 = p_y \quad ; \quad T_1 = T_x \quad ; \quad T_2 = T_y,

\ \rho_1 = \rho_x \quad ; \quad \rho_2 = \rho_y \quad ; \quad a_1 = a_x \quad ; \quad a_2 = a_y,

\ M_x = \frac = \frac,

\ M_y = \frac = \frac.

Introducing the

heat capacity ratio In thermal physics and thermodynamics, the heat capacity ratio, also known as the adiabatic index, the ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure () to heat capacity at constant vol ...

as ''γ'', the speed of sound, density, and pressure ratios can be derived: :

\ \frac = \sqrt,

\ \frac = \frac,

\ \frac = 1 + \frac\left_x^2 - 1\right

One must keep in mind that the above equations are for a shock wave moving towards the right. For a shock moving towards the left, the ''x'' and ''y'' subscripts must be switched and: :

\ u_y = W - u_1 + u_2,

\ M_y = \frac.

References

{{Reflist

External links

NASA Beginner's Guide to Compressible Aerodynamics
Fluid dynamics Aerodynamics Shock waves

Theory

See also

References

External links