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  • THERMODYNAMIC—COMPARISON BETWEEN A NOZZLE AND A DIFFUSER, VELOCITY OF STEAM AT ANY SECTION, NOZZLE EFFICIENCY, VELOCITY COEFFICIENT, DESIGN AND HIGHLIGHTS

THERMODYNAMIC—COMPARISON BETWEEN A NOZZLE AND A DIFFUSER, VELOCITY OF STEAM AT ANY SECTION, NOZZLE EFFICIENCY, VELOCITY COEFFICIENT, DESIGN AND HIGHLIGHTS

THERMODYNAMIC—COMPARISON BETWEEN A  NOZZLE AND A DIFFUSER, VELOCITY OF STEAM AT ANY SECTION, NOZZLE EFFICIENCY, VELOCITY COEFFICIENT, DESIGN AND HIGHLIGHTS

COMPARISON OF NOZZLES AND DIFFUSER

Nozzle                                                 DIFFUSER

Boundary layer is thin                      Boundary layer is thick.

Has negligible friction                      Has more friction.

Has favorable gradient                     Unfavorable gradient

More efficient                                       Less efficient

No shock formation                          Chances of shock formation

VELOCITY OF STEAM AT ANY SECTION OF THE NOZZLE

C = 44.72     Without friction

C = 44.72     With friction, k is the friction factor =0.7 to 0.9

 

VELOCITY COEFFICIENT

 It is the ratio of actual exit velocity to isentropic exit velocity for a certain same pressure drop

cv = Actual velocity/ isentropic velocity

      =√actual enthalpy drop/isentropic enthalpy drop

           =√η = square root of efficiency√

 

EFFICIENCY OF THE NOZZLE

It is a ratio of Actual enthalpy drop to  isentropic enthalpy drop between the same inlet and outlet pressures.

η = Actual enthalpy drop/  isentropic enthalpy drop

FACTORS ON WHICH THE EFFICIENCY OF A NOZZLE DEPENDS

  1. Material of the nozzle
  2. Inside surface condition of the nozzle
  3. Nature of the fluid flowing through the nozzle
  4. Size and shape of the nozzle
  5. Reynolds number of the flow
  6. Angle of divergence
  7. Orientation of the nozzle

DESIGN OF A STEAM NOZZLE

Data required

  • Inlet pressure and the condition of the steam
  • Back pressure
  • Mass flow rate

STEPS

  • Find the back pressure by the standard relation

pb = pi (2/(n+1))(n/(n-1)

  • If this calculated back pressure is more than the given back pressure, then the nozzle is a convergent nozzle.
  • If this calculated back pressure is less than the given back pressure, then the nozzle is a convergent-divergent  

Dimensions of the nozzle are calculated from the mass flow rate and the condition of the steam at inlet, throat and outlet of the nozzle. Mass flow rate is constant at the inlet, throat and outlet.

Area = m. sp. Volume/velocity

A = π d2/4

 

HIGHLIGHTS OF A NOZZLE

  1. Sonic velocity = C* =√γRT
  2. Critical pressure ratio
  • Isentropic

P*/p = [2/(γ+1)]γ/(γ—1)

  • Actual

          P*/p = [2/(n+1)]n/(n—1)

  1. Mach number 

         M = actual velocity/sonic velocity

        Sonic velocity = 332 m/s

  1. Relation between stagnation and static (local ) temperature

               T0 /T = 1 + (γ—1) M2/2

  1. Velocity increases in the convergent portion called nozzle.
  2. Velocity decreases in the divergent portion called diffuser.
  3. Velocity of the expanding steam

            Velocity of steam at any section of the nozzle

            C = 44.72     Without friction

            C = 44.72     With friction, k is the friction factor =0.7 to 0.9

 

  1. If the steam expands from pressure p1 and volume v1 to pressure p2

           c2 =     2{[(n/(n-1)] [p1v1 –p2v2]}0.5

  1. Maximum rate of flow or Discharge occurs when critical pressure ratio is achieved.
  2. Friction reduces the enthalpy drop and hence the velocity at the outlet.
  3. Normally it is assumed that there is no friction in the nozzle. There is frtriction in the diffuser only.