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1010:. A type of these inlets is wedge-shaped to compress air flow into the combustion chamber while minimizing thermodynamic losses. Early supersonic aircraft jet engine intakes were designed using compression from a single normal shock, but this approach caps the maximum achievable Mach number to roughly 1.6.
200:
can be supersonic (weak shock wave) or subsonic (strong shock wave). Weak solutions are often observed in flow geometries open to atmosphere (such as on the outside of a flight vehicle). Strong solutions may be observed in confined geometries (such as inside a nozzle intake). Strong solutions are
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Oblique shocks are often preferable in engineering applications when compared to normal shocks. This can be attributed to the fact that using one or a combination of oblique shock waves results in more favourable post-shock conditions (smaller increase in entropy, less stagnation pressure loss,
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1021:
Many supersonic aircraft wings are designed around a thin diamond shape. Placing a diamond-shaped object at an angle of attack relative to the supersonic flow streamlines will result in two oblique shocks propagating from the front tip over the top and bottom of the wing, with
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required when the flow needs to match the downstream high pressure condition. Discontinuous changes also occur in the pressure, density and temperature, which all rise downstream of the oblique shock wave.
124:
changes in the thermodynamic properties of a gas occur. While the upstream and downstream flow directions are unchanged across a normal shock, they are different for flow across an oblique shock wave.
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108:, is inclined with respect to the direction of incoming air. It occurs when a supersonic flow encounters a corner that effectively turns the flow into itself and compresses. The upstream
231:
971:{\displaystyle M_{2}={\frac {1}{\sin(\beta -\theta )}}{\sqrt {\frac {1+{\frac {\gamma -1}{2}}M_{1}^{2}\sin ^{2}\!\beta }{\gamma M_{1}^{2}\sin ^{2}\!\beta -{\frac {\gamma -1}{2}}}}}.}
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As the Mach number of the upstream flow becomes increasingly hypersonic, the equations for the pressure, density, and temperature after the oblique shock wave reach a mathematical
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lines. The red line separates the strong and weak solutions. The blue line represents the point when the downstream Mach number becomes sonic. The chart assumes
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For a perfect atmospheric gas approximation using γ = 1.4, the hypersonic limit for the density ratio is 6. However, hypersonic post-shock dissociation of O
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etc.) when compared to utilizing a single normal shock. An example of this technique can be seen in the design of supersonic aircraft engine intakes or
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1014:(which first flew in 1969) used variable geometry wedge-shaped intakes to achieve a maximum speed of Mach 2.2. A similar design was used on the
81:
664:{\displaystyle {\frac {\rho _{2}}{\rho _{1}}}={\frac {(\gamma +1)\ M_{1}^{2}\sin ^{2}\!\beta }{(\gamma -1)M_{1}^{2}\sin ^{2}\!\beta +2}}}
399:, with the larger angle called a strong shock and the smaller called a weak shock. The weak shock is almost always seen experimentally.
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does not change across the shock, trigonometric relations eventually lead to the θ-β-M equation which shows θ as a function of M
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are uniformly deflected after the shock wave. The most common way to produce an oblique shock wave is to place a wedge into
1356:{\displaystyle {\frac {T_{2}}{T_{1}}}\approx {\frac {2\gamma \ (\gamma -1)}{(\gamma +1)^{2}}}\ M_{1}^{2}\sin ^{2}\!\beta .}
367:
and θ, but this approach is more complicated, the results of which are often contained in tables or calculated through a
1007:
68:
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353:{\displaystyle \tan \theta =2\cot \beta \ {\frac {M_{1}^{2}\sin ^{2}\!\beta -1}{M_{1}^{2}(\gamma +\cos 2\beta )+2}}}
39:
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created at the two corners of the diamond closest to the front tip. When correctly designed, this generates lift.
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Supersonic wind tunnel test demonstration (Mach 2.5) with flat plate and wedge creating an oblique shock(Video)
391:. A θ-β-M diagram, common in most compressible flow textbooks, shows a series of curves that will indicate θ
120:. Similar to a normal shock wave, the oblique shock wave consists of a very thin region across which nearly
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into O and N lowers γ, allowing for higher density ratios in nature. The hypersonic temperature ratio is:
1023:
1452:
1133:{\displaystyle {\frac {p_{2}}{p_{1}}}\approx {\frac {2\gamma }{\gamma +1}}\ M_{1}^{2}\sin ^{2}\!\beta }
152:
This chart shows the oblique shock angle, β, as a function of the corner angle, θ, for a few constant M
512:{\displaystyle {\frac {p_{2}}{p_{1}}}=1+{\frac {2\gamma }{\gamma +1}}(M_{1}^{2}\sin ^{2}\!\beta -1)}
402:
The rise in pressure, density, and temperature after an oblique shock can be calculated as follows:
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762:{\displaystyle {\frac {T_{2}}{T_{1}}}={\frac {p_{2}}{p_{1}}}{\frac {\rho _{1}}{\rho _{2}}}.}
387:, the oblique shock wave is no longer attached to the corner and is replaced by a detached
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for each Mach number. The θ-β-M relationship will produce two β angles for a given θ and M
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Supersonic flow encounters a wedge and is uniformly deflected forming an oblique shock.
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1209:{\displaystyle {\frac {\rho _{2}}{\rho _{1}}}\approx {\frac {\gamma +1}{\gamma -1}}.}
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188:, and corner angle, θ, the oblique shock angle, β, and the downstream Mach number, M
1018:(the F-14D was first delivered in 1994) and achieved a maximum speed of Mach 2.34.
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Shock wave that is inclined with respect to the incident upstream flow direction
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It is always possible to convert an oblique shock into a normal shock by a
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The
Dynamics and Thermodynamics of Compressible Fluid Flow, Volume 1
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It is more intuitive to want to solve for β as a function of M
1038:. The pressure and density ratios can then be expressed as:
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192:, can be calculated. Unlike after a normal shock where M
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Within the θ-β-M equation, a maximum corner angle, θ
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176:=1.4, which is valid for an ideal diatomic gas.
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196:must always be less than 1, in oblique shock M
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1001:F-14D Tomcat showing wedge-shaped intakes
796:is the post-shock flow deflection angle:
69:Learn how and when to remove this message
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32:This article includes a list of general
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1512:Liepmann, Hans W.; Roshko, A. (2001) .
1489:Anderson, John D. Jr. (January 2001) .
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1475:: CS1 maint: archived copy as title (
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1495:McGraw-Hill Science/Engineering/Math
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1561:NASA oblique shock wave calculator
85:An oblique shock at the nose of a
38:it lacks sufficient corresponding
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89:aircraft is made visible through
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215:tangential velocity component
1491:Fundamentals of Aerodynamics
1024:Prandtl-Meyer expansion fans
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1535:Shapiro, Ascher H. (1953).
1417:Hall, Nancy (13 May 2021).
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221:, β and ɣ, where ɣ is the
1373:Bow shock (aerodynamics)
375:Maximum deflection angle
1514:Elements of Gasdynamics
789:{\displaystyle \theta }
169:{\displaystyle \gamma }
130:Galilean transformation
53:more precise citations.
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213:and the fact that the
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1419:"Oblique Shock Waves"
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59:November 2019
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1593:Aerodynamics
1536:
1513:
1490:
1460:. Retrieved
1453:the original
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1428:. Retrieved
1422:
1412:
1388:Moving shock
1378:Gas dynamics
1218:
1033:
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1004:
771:
401:
378:
362:
208:
180:For a given
179:
127:
106:normal shock
97:
95:
65:
56:
37:
1603:Shock waves
1572:Java applet
1393:Shock polar
1016:F-14 Tomcat
182:Mach number
136:Wave theory
110:streamlines
51:introducing
1587:Categories
1462:2013-01-01
1404:References
1398:Shock wave
209:Using the
114:supersonic
102:shock wave
100:wave is a
34:references
1348:β
1297:γ
1283:−
1280:γ
1271:γ
1262:≈
1195:−
1192:γ
1181:γ
1175:≈
1164:ρ
1154:ρ
1128:β
1087:γ
1082:γ
1073:≈
950:−
947:γ
941:−
938:β
909:γ
904:β
866:−
863:γ
841:θ
838:−
835:β
829:
784:θ
746:ρ
736:ρ
650:β
615:−
612:γ
604:β
563:γ
543:ρ
533:ρ
501:−
498:β
457:γ
452:γ
389:bow shock
336:β
330:
321:γ
295:−
292:β
257:β
254:
242:θ
239:
164:γ
1564:Archived
1471:cite web
1367:See also
1012:Concorde
991:Concorde
47:improve
1543:
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