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 116 kg/m3 to rs 664 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 19th 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
  Bernoullis 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 lt 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 Bernoullis 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 (gt 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 gt 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)