Moving shock
Encyclopedia
In fluid dynamics
, a moving shock is a shock wave
that is traveling through a fluid
(often gas
eous) medium with a velocity
relative to the velocity of the fluid already making up the medium. 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
, among other applications.
is denoted by p and the local speed of sound
by a.
Next, suppose a reference frame
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:
With these shock-relative velocities, the properties of the regions before and after the shock can be defined below introducing the temperature
as T, the density
as ρ, and the Mach number
as M:
Introducing the heat capacity ratio
as γ, the speed of sound
, density, and pressure ratios can be derived:
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:
Fluid dynamics
In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids in motion. It has several subdisciplines itself, including aerodynamics and hydrodynamics...
, a moving shock is a shock wave
Shock wave
A shock wave is a type of propagating disturbance. Like an ordinary wave, it carries energy and can propagate through a medium or in some cases in the absence of a material medium, through a field such as the electromagnetic field...
that is traveling through a fluid
Fluid
In physics, a fluid is a substance that continually deforms under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids....
(often gas
Gas
Gas is one of the three classical states of matter . Near absolute zero, a substance exists as a solid. As heat is added to this substance it melts into a liquid at its melting point , boils into a gas at its boiling point, and if heated high enough would enter a plasma state in which the electrons...
eous) medium with a velocity
Velocity
In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...
relative to the velocity of the fluid already making up the medium. 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
Detonation involves a supersonic exothermic front accelerating through a medium that eventually drives a shock front propagating directly in front of it. Detonations are observed in both conventional solid and liquid explosives, as well as in reactive gases...
, 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 speed of the shock wave relative to the gas is W, making the total velocity equal to u1 + W. Additionally, the pressurePressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...
is denoted by p and the local speed of sound
Speed of sound
The speed of sound is the distance travelled during a unit of time by a sound wave propagating through an elastic medium. In dry air at , the speed of sound is . This is , or about one kilometer in three seconds or approximately one mile in five seconds....
by a.
Next, suppose a reference frame
Frame of reference
A frame of reference in physics, may refer to a coordinate system or set of axes within which to measure the position, orientation, and other properties of objects in it, or it may refer to an observational reference frame tied to the state of motion of an observer.It may also refer to both an...
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:
With these shock-relative velocities, the properties of the regions before and after the shock can be defined below introducing the temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...
as T, the density
Density
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...
as ρ, and the Mach number
Mach number
Mach number is the speed of an object moving through air, or any other fluid substance, divided by the speed of sound as it is in that substance for its particular physical conditions, including those of temperature and pressure...
as M:
Introducing the heat capacity ratio
Heat capacity ratio
The heat capacity ratio or adiabatic index or ratio of specific heats, is the ratio of the heat capacity at constant pressure to heat capacity at constant volume . It is sometimes also known as the isentropic expansion factor and is denoted by \gamma or \kappa . The latter symbol kappa is...
as γ, the speed of sound
Speed of sound
The speed of sound is the distance travelled during a unit of time by a sound wave propagating through an elastic medium. In dry air at , the speed of sound is . This is , or about one kilometer in three seconds or approximately one mile in five seconds....
, density, and pressure ratios can be derived:
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:
See also
- Shock waveShock waveA shock wave is a type of propagating disturbance. Like an ordinary wave, it carries energy and can propagate through a medium or in some cases in the absence of a material medium, through a field such as the electromagnetic field...
- Oblique shockOblique shockAn oblique shock wave, unlike a normal shock, is inclined with respect to the incident upstream flow direction. It will occur when a supersonic flow encounters a corner that effectively turns the flow into itself and compresses. The upstream streamlines are uniformly deflected after the shock wave...
- Normal shock
- Gas dynamicsGas dynamicsGas dynamics is a branch of fluid dynamics concerned with studying the motion of gases and its consequent effects. Gas dynamics combines the principles of fluid mechanics and thermodynamics...
- Compressible flowCompressible flowCompressible flow is the area of fluid mechanics that deals with fluids in which the fluid density varies significantly in response to a change in pressure. Compressibility effects are typically considered significant if the Mach number of the flow exceeds 0.3, or if the fluid undergoes very large...
- Bow shock (aerodynamics)Bow shock (aerodynamics)A bow shock, also called a detached shock, is a curved, stationary shock wave that is found in supersonic flow past a finite body. Unlike an oblique shock, the bow shock is not necessarily attached to the tip of the body...
- Prandtl-Meyer expansion fanPrandtl-Meyer expansion fanA Prandtl–Meyer expansion fan is a centered expansion process, which turns a supersonic flow around a convex corner. The fan consists of an infinite number of Mach waves, diverging from a sharp corner. In case of a smooth corner, these waves can be extended backwards to meet at a point. Each wave...