Gas Dynamics ESA 341 Chapter 3

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Presentation transcript:

Gas Dynamics ESA 341 Chapter 3 Dr Kamarul Arifin B. Ahmad PPK Aeroangkasa

Normal shock waves Definition of shock wave Formation of normal shock wave Governing equations Shock in the nozzle

Definition of shock wave Shock wave is a very thin region in a flow where a supersonic flow is decelerated to subsonic flow. The process is adiabatic but non-isentropic. Shock wave V P T

Formation of Shock Wave A piston in a tube is given a small constant velocity increment to the right magnitude dV, a sound wave travel ahead of the piston. A second increment of velocity dV causing a second wave to move into the compressed gas behind the first wave. As the second wave move into a gas that is already moving (into a compressed gas having a slightly elevated temperature), the second waves travels with a greater velocity. The wave next to the piston tend to overtake those father down the tube. As time passes, the compression wave steepens.

b Types of Shock Waves: Normal shock wave - easiest to analyze Oblique shock wave - will be analyzed based on normal shock relations Curved shock wave - difficult & will not be analyzed in this class The flow across a shock wave is adiabatic but not isentropic (because it is irreversible). So:

Governing Equations Conservation of mass: Conservation of momentum: Rearranging: Combining: Conservation of energy: Change of variable: combine

Governing Equations cont. Continued: Multiplied by r2/p1: Rearranging: or

Governing Equations cont. From conservation of mass: From equation of state:

Governing Equations cont. Conservation of mass C O M B I N E Conservation of momentum Conservation of energy Expanding the equations

Governing Equations cont. Solution: Mach number cannot be negative. So, only the positive value is realistic.

Governing Equations cont. Temp. ratio Dens. ratio 1 Pres. ratio Simplifying: 3 2

Governing Equations cont. Stagnation pressures: Other relations:

Governing Equations cont. Entropy change: But, S02=S2 and S01=S1 because the flow is all isentropic before and after shockwave. So, when applied to stagnation points: But, flow across the shock wave is adiabatic & non-isentropic: And the stagnation entropy is equal to the static entropy: So: Shock wave 1 2  Total pressure decreases across shock wave !

Group Exercises 3 Consider a normal shock wave in air where the upstream flow properties are u1=680m/s, T1=288K, and p1=1 atm. Calculate the velocity, temperature, and pressure downstream of the shock. A stream of air travelling at 500 m/s with a static pressure of 75 kPa and a static temperature of 150C undergoes a normal shock wave. Determine the static temperature, pressure and the stagnation pressure, temperature and the air velocity after the shock wave. Air has a temperature and pressure of 3000K and 2 bars absolute respectively. It is flowing with a velocity of 868m/s and enters a normal shock. Determine the density before and after the shock. 2)[76.6kPa, 374.4K, 247.5kPa, 412.5K, 276m/s]

Stationary Normal Shock Wave Table – Appendix C: