Salient Features of Gas Dynamics

P M V SubbaraoAssociate Professor

Mechanical Engineering DepartmentI I T Delhi

Understand Extent through the Qualities !!!

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

• { o = 1:16 kg/m3 to s = 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!!)

Modern Spacecrafts

Rentering Space Craft

De Laval Nozzle

• High Speed flows often seem “counter-intuitive” whenCompared 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.

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

Incompressible De Laval Nozzle

pI

VI

AI

pt

Vt

At

• When Continuity and Bernoulli are applied to a De Laval Nozzle and density is Assumed constant

At Throat

ContinuityBernoulli

• Pressure Drop• Velocity Increases

“classic” Venturi

High Pressure Inlet

Incompressible De Laval Nozzle

AeA I At

pI

VI

AI

pe

Ve

Ae

pt

Vt

At

At Exit

BernoulliContinuity

• Pressure Increases• Velocity Drops

High Pressure Inlet

De Laval Nozzle Conclusions : A Truth

AeA I At

pI

VI

AI

pe

Ve

Ae

pt

Vt

At

• 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! …

High Pressure Inlet

• Fundamental principle that makes rocket motors possible

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)

• 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)