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A bow shock, also called a detached shock or bowed normal shock, is a curved propagating disturbance wave characterized by an abrupt, nearly discontinuous, change in
A bow shock, also called a detached shock or bowed normal shock, is a curved propagating disturbance wave characterized by an abrupt, nearly discontinuous, change in 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 ...
, temperature
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.
Thermometers are calibrated in various temperature scales that historically have relied o ...
, and 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 ...
. It occurs when a supersonic flow encounters a body, around which the necessary deviation angle of the flow is higher than the maximum achievable deviation angle for an attached oblique shock
An oblique shock wave is a shock wave that, 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 compr ...
(see detachment criterion). Then, the oblique shock
An oblique shock wave is a shock wave that, 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 compr ...
transforms in a curved detached shock wave. As bow shocks occur for high flow deflection angles, they are often seen forming around blunt bodies, because of the high deflection angle that the body impose to the flow around it.
The thermodynamic transformation across a bow shock is non-isentropic and the shock decreases the flow velocity from supersonic
Supersonic speed is the speed of an object that exceeds the speed of sound ( Mach 1). For objects traveling in dry air of a temperature of 20 °C (68 °F) at sea level, this speed is approximately . Speeds greater than five times ...
velocity upstream to subsonic velocity downstream.
Applications
The bow shock significantly increases the drag in a vehicle traveling at a supersonic speed. This property was utilized in the design of the return capsules during space missions such as the Apollo program, which need a high amount of drag in order to slow down duringatmospheric reentry
Atmospheric entry is the movement of an object from outer space into and through the gases of an atmosphere of a planet, dwarf planet, or natural satellite. There are two main types of atmospheric entry: ''uncontrolled entry'', such as the entr ...
.
Shock relations
As innormal shock
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 ...
and oblique shock
An oblique shock wave is a shock wave that, 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 compr ...
,
* The upstream static pressure
In fluid mechanics the term static pressure has several uses:
* In the design and operation of aircraft, ''static pressure'' is the air pressure in the aircraft's static pressure system.
* In fluid dynamics, many authors use the term ''static pres ...
s is lower than the downstream static pressure
In fluid mechanics the term static pressure has several uses:
* In the design and operation of aircraft, ''static pressure'' is the air pressure in the aircraft's static pressure system.
* In fluid dynamics, many authors use the term ''static pres ...
.
* The upstream static density is lower than the downstream static density.
* The upstream static temperature
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.
Thermometers are calibrated in various temperature scales that historically have relied o ...
is lower than the downstream static temperature
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.
Thermometers are calibrated in various temperature scales that historically have relied o ...
.
* The upstream total pressure In physics, the term total pressure may indicate two different quantities, both having the dimensions of a pressure:
For compressible flow the Isentropic nozzle flow#Supersonic flow, isentropic relations can be used (also valid for incompressible ...
is greater than the downstream total pressure In physics, the term total pressure may indicate two different quantities, both having the dimensions of a pressure:
For compressible flow the Isentropic nozzle flow#Supersonic flow, isentropic relations can be used (also valid for incompressible ...
.
* The upstream total density is lower than the downstream total density.
* The upstream total temperature is equal to the downstream total temperature, as the shock wave is supposed isenthalpic
An isenthalpic process or isoenthalpic process is a process that proceeds without any change in enthalpy, ''H''; or specific enthalpy, ''h''.
Overview
If a steady-state, steady-flow process is analysed using a control volume, everything outside t ...
.
For a curved shock, the shock angle varies and thus has variable strength across the entire shock front. The post-shock flow velocity and vorticity can therefore be computed via the Crocco's theorem
Crocco's theorem is an aerodynamic theorem relating the flow velocity, vorticity, and stagnation pressure (or entropy) of a potential flow. Crocco's theorem gives the relation between the thermodynamics and fluid kinematics. The theorem was first e ...
, which is independent of any EOS (equation of state
In physics, chemistry, and thermodynamics, an equation of state is a thermodynamic equation relating state variables, which describe the state of matter under a given set of physical conditions, such as pressure, volume, temperature, or internal ...
) assuming inviscid flow.
See also
*Bow shock
In astrophysics, a bow shock occurs when the magnetosphere of an astrophysical object interacts with the nearby flowing ambient plasma such as the solar wind. For Earth and other magnetized planets, it is the boundary at which the speed of ...
* Gas dynamics
Compressible flow (or gas dynamics) is the branch of fluid mechanics that deals with flows having significant changes in fluid density. While all flows are compressible, flows are usually treated as being incompressible when the Mach number (the r ...
* Moving shock In fluid dynamics, a moving shock is a shock wave that is travelling through a fluid (often gaseous) medium with a velocity relative to the velocity of the fluid already making up the medium.Shapiro, Ascher H., ''Dynamics and Thermodynamics of Compr ...
* Prandtl–Meyer expansion fan
A supersonic expansion fan, technically known as Prandtl–Meyer expansion fan, a two-dimensional simple wave, is a centered expansion process that occurs when a supersonic flow turns around a convex corner. The fan consists of an infinite numb ...
References
* * {{cite book , last = Courant , first = R. , author2=Friedrichs, K.O. , title = Supersonic Flow and Shock Waves , origyear = 1948 , publisher = Interscience Publishers , location = New York , year = 1956 Aerodynamics Shock waves