Salient Features of Gas Dynamics

1. Salient Features of Gas Dynamics P M V Subbarao Associate Professor Mechanical Engineering Department I I T Delhi Understand Extent through the Qualities !!!

2. Gas Dynamics of Re-entry • A range of phenomena are present in the re-entry of a vehicle into the atmosphere. • This is an example of an external flow. • Bow shock wave : Suddenly raises density, temperature and pressure of shocked air; consider normal shock in ideal air • { ro= 1:16 kg/m3 to rs= 6:64 kg/m3(over five times as dense!!) • { To = 300 K ! Ts = 6100 K (hot as the sun's surface !!) • { Po = 1.0 atm ! Ps = 116.5 atm (tremendous force change!!)

3. Modern Spacecrafts

4. Rentering Space Craft

5. De Laval Nozzle • • High Speed flows often seem “counter-intuitive” when • Compared with low speed flows • • Example: Convergent-Divergent Nozzle (De Laval) • In 1897 Swedish Engineer Gustav De Laval designed A turbine wheel powered by 4- steam nozzles. • De Laval Discovered that if the steam nozzle first narrowed, and then expanded, the efficiency of the turbine was increased dramatically. • Furthermore, the ratio of the minimum area to the inlet and outlet areas was critical for achieving maximum efficiency … Counter to the “wisdom” of the day.

6. De Laval Nozzle Initial Trials • Mechanical Engineers of the 19’th century were Primarily “hydrodynamicists” . • That is they were Familiar with fluids that were incompressible … liquids and Low speed gas flows where fluid density was Essentially constant • Primary Principles are Continuity and Bernoulli’s Law

7. Incompressible De Laval Nozzle • When Continuity and Bernoulli are applied to a De Laval Nozzle and density is Assumed constant High Pressure Inlet pI VI AI r pt Vt At r At Throat • Pressure Drop • Velocity Increases Continuity Bernoulli “classic” Venturi

8. Incompressible De Laval Nozzle High Pressure Inlet pI VI AI r pe Ve Ae r pt Vt At r At Exit • Pressure Increases • Velocity Drops Continuity Bernoulli

9. De Laval Nozzle Conclusions : A Truth High Pressure Inlet pI VI AI r pe Ve Ae r pt Vt At r • But De Laval Discovered that when • the Nozzle throat Area was adjusted downward until the pressure ratio became pt / pI < 0.5484 • then the exit Pressure dropped (instead of Rising … compared to the throat pressure). • And the exit velocity rose (instead of dropping)… • Which is counter to What Bernoulli’s law predicts • … he had inadvertently ,,, Generated supersonic flow! … • Fundamental principle that makes rocket motors possible

10. Salient Features of Gas Dynamics • A Complete Fluid Mechanics. • Sudden transfer of energy from one form to another form. • Shock : kinetic (ordered) to thermal (random). • Expansion Wave : Thermal to Kinetic. • Introduces inviscid entropy/vorticity layers. • Momentum boundary layer • occurs in thin layer near surface where velocity relaxes from freestream to zero to satisfy the no-slip condition. • Necessary to predict viscous drag forces on body. • Thermal boundary layer • As fluid decelerates in momentum boundary layer kinetic energy is converted to thermal energy • Temperature rises can be significant (> 1000 K)

11. Caloric gas behavior to Non-Caloric gas behavior. • vibrational relaxation effects • energy partitioned into vibrational modes in addition to translational • lowers temperature that would otherwise be realized • important for air above 800 K • unimportant for monatomic gases • Perfect gas behavior to Imperfect gas behavior. • dissociation effects • effect which happens when multi-atomic molecules split into constituent atoms O2 totally dissociated into O near 4000 K. • N2 totally dissociated into N near 9000 K. • For T > 9000 K, ionized plasmas begin to form • Vibrational relaxation, dissociation, and ionization can be accounted for to some extent by introducing a temperature-dependent specific heat cv(T)