Shock Wave GDJP Anna University Review: It has been observed for many years that a compressible fluid under certain conditions can experience an abrupt change of state. Familiar examples are the phenomena associated with detonation waves, explosions, and the wave system formed at the nose of a projectile moving with a supersonic speed. In all of those cases the wave front is very steep and there is a large pressure rise in traversing the wave, which is termed a shock wave. Here we will study the conditions under which shock waves develop and how they affect the flow. PDF created with pdfFactory trial version www.pdffactory.com
Gas Dynamics and Propulsion BY Dr.G.KUMARESAN, PROFESSOR, ANNA UNIVERSITY
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Shock Wave
GDJP Anna University
Review:Ø It has been observed for many years that a compressible
fluid under certain conditions can experience an abruptchange of state.
ØFamiliar examples are the phenomena associated withdetonation waves, explosions, and the wave system formedat the nose of a projectile moving with a supersonic speed.
ØIn all of those cases the wave front is very steep and thereis a large pressure rise in traversing the wave, which istermed a shock wave.
Here we will study the conditions under which shockwaves develop and how they affect the flow.
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Ø By definition, a normal shock wave is a shock wave that isperpendicular to the flow.
Ø Because of the large pressure gradient in the shock wave,the gas experiences a large increase in its density anddecrease in its velocity.
Ø The flow is supersonic ahead of the normal shock waveand subsonic after the shock wave.
Ø Since the shock wave is a more or less instantaneouscompression of the gas, it cannot be a reversible process.
Ø Because of the irreversibility of the shock process, thekinetic energy of the gas leaving the shock wave is smallerthan that for an isentropic flow compression between thesame pressure limits.
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Ø The reduction in the kinetic energy because of the shockwave appears as a heating of the gas to a statictemperature above that corresponding to the isentropiccompression value.
Ø Consequently, in flowing through the shock wave, the gasexperiences a decrease in its available energy and,accordingly, an increase in its entropy.
Ø A shock wave is a very thin region, its thickness is in theorder of m.
Ø The flow is adiabatic across the shock waves.
810−
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q Pressure pulsestransmitted through thegas to the rightwardmovement of the piston.q The waves traveltowards the right withthe acoustic speed.qThe portion of the gaswhich has beentraversed by thepressure waves is set inmotion.qThe pressure wavesin the upstream regiontravel at highervelocities.qThus the upstreamwaves are continuouslyovertaking those in thedownstream region.
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q In subsonic flow, sound wavescan work their way upstream andforewarn the flow about the presenceof the body.
Therefore, the flow streamlinesbegin to change and the flowproperties begin to compensate for thebody far upstream.
q In contrast, if the flow issupersonic, sound waves can nolonger propagate upstream. Instead,they tend to coalesce a short distanceahead of the body (shock wave)
Ahead of the shock, the flow hasno idea of the presence of the body.Immediately behind the shock, thestreamlines quickly compensate for theobstruction.
Shock wave
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The equation of continuity for constant flow rate through the shock gives
22
1
22
11
xM
xM
yx
xcyc
+
−+
==γ
γ
ρρ
Another expression for the density ratio across the shock can be derived interms of the pressure ratio alone. This is useful for comparing the densityratios in isentropic process and a shock for given values of the pressure ratio.
We know that the pressure ratio across the shock
( )( )
2
1
2121
121
222
1-1
xTyT
; xTyT
in 2M
21
212
xM 112
12
xM
xMxM
xngSubstituti
xpyp
xMxpyp
−+
−
−
+
=
−+
+=⇒
+−
−+
=
γγ
γγγ
γγ
γγ
γγ
γγ
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