Compressible Flow

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Compressible Flow the Hydraulic Analogy

• MER 501
• Brendon Keinath

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Outline

• Flow Classifications
• Compressible Flow Theory
• Supersonic Testing
• Hydraulic Analogy
• Conclusion

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Flow Classifications

• Incompressible
• Malt0.3
• Subsonic
• Ma gt 0.3 at some points but never greater than 1
  (no shockwaves)
• Transonic
• 0.8ltMalt1.2 (shockwaves may occur locally)
• Difficult to predict/increased drag/difficult to
  control
• Supersonic
• 1ltMalt3
• Hypersonic
• 3ltMalt10
• Hyper-velocity
• Magt10

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Compressible Flow Theory
Momentum Conservation
Mass Conservation
Energy Conservation
E.O.S.
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Supersonic Testing
hq.nasa.gov/
imperial.ac.uk
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The Hydraulic Analogy

• Analogy between pressure waves in a compressible
  flow and gravity waves on the free surface of a
  shallow liquid

vki.ac.be
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Theory
Assumptions

• Gas flow
• 2-D
• Isentropic

• Hydraulic flow
• 2-D
• inviscid

• Energy Equations

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What does the theory prove?
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Assumptions

• Gas flow
• 2-D
• Isentropic

• Hydraulic flow
• 2-D
• inviscid

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Test Apparatus
1
vki.ac.be
2
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Problems with the Theory
We all know that this is not the case with air
Water Flow is not inviscid
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Conclusions

• Good initial test apparatus
• Accuracies of plus or minus 10
• 2-D flows only
• Can use fudge factors to increase accuracy
• CFD

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References

• 1 Rani SL Wooldridge (2000) Quantitative flow
  visualization using the hydraulic analogy. Exp
  Fluids 27165-169.
• 2Chant LJ Caton JA (1998) Measurement of
  confined supersonic, 2-d jet lengths using the
  hydraulic analogy. Exp Fluids 24 58-65.
• Background picpaoc.mit.edu

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Questions?