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Normal Shock Waves Lecture 24 ME EN 412 Andrew Ning - - PDF document
Normal Shock Waves Lecture 24 ME EN 412 Andrew Ning - - PDF document
Normal Shock Waves Lecture 24 ME EN 412 Andrew Ning aning@byu.edu Outline Normal Shock Waves Example Normal Shock Waves Normal Shock Waves 1 2 Prandtl relation u 1 u 2 = a 2 = 2 + ( 1) M 2 u 2 = 1 1 ( + 1) M 2 u 1 2
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Prandtl relation u1u2 = a∗2 u2 u1 = ρ1 ρ2 = 2 + (γ − 1)M 2
1
(γ + 1)M 2
1
P2 P1 = 1 + 2γ γ + 1(M 2
1 − 1)
T2 T1 = h2 h1 = P2 P1 ρ1 ρ2
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1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 M1 2 4 6 8 10 ρ2 /ρ1 P2/P1 T2/T1
M2 =
- 2 + (γ − 1)M 2
1
2γM 2
1 − (γ − 1) 1 2 3 4 5 M1 0.0 0.2 0.4 0.6 0.8 1.0 M2
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Total temperature is constant across a shock wave T01 = T02 Total pressure decreases. P02 P01 =
- γ + 1
2γM 2
1 − (γ − 1)
- 1
γ−1
(γ + 1)M 2
1
2 + (γ − 1)M 2
1
- γ
γ−1
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 M1 0.0 0.2 0.4 0.6 0.8 1.0 P0 2/P0 1
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For each of these quantities, do they increase, decrease, or stay the same after passing through a normal shock wave?
- Mach number
- velocity
- pressure
- stagnation pressure
- temperature
- stagnation temperature
- density
- entropy
1 2 3 4
An Album of Fluid Motion, Van Dyke
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Example
The SR-71 aircraft was design to fly at M∞ = 3.2 at 85,000 feet. Assume there was a bow shock in front of the aircraft1, what would the stagnation temperature and pressure be at the nose.
1the aircraft is designed with a pointed nose to create oblique shocks,
but we haven’t covered oblique shocks yet, instead think of a blunt nosed missile