NOZZLE AND DIFFUSER CLASS NOTES FOR MECHANICAL ENGINEERING
NOZZLE AND DIFFUSER
CLASS NOTES FOR MECHANICAL
ENGINEERING
It is a passage of variable cross section
(area decreases from entrance onward).
Velocity increases and pressure decreases.
This is true as long as velocity at the inlet
of the nozzle is subsonic. Velocity is less
the velocity of sound or Mach number <1.
Diffuser is a duct (passage) of variable cross
section (area increases from entrance
onward). Velocity decreases and
pressure increases. This is true as long
as velocity at the inlet of the diffuser
is subsonic. Velocity is less the velocity
of sound or Mach number <1.
But a particular duct can be a nozzle
or a diffuser depending upon the
velocity at the inlet.
CONSERVATION OF MASS
m^{.} =ρAv=constant=C
Take the log of both sides, we get
ln ρ +ln A + ln v=ln C
Doing partial differentiation, we get
dρ/ρ +dA/A + dv/v=0
We know, for one dimensional isentropic flow
dA/A = (M^{2} –1)dv/v
dA/A positive means area is increasing, then for M>1, quantity in bracket is also positive. Therefore dv/v will be positive. Hence with increase in area, velocity increases if M>1.
Diffuser becomes a nozzle and vice versa.
Case 1
When M>1 at the ENTRANCE
As flow area decreases, velocity decreases and pressure increases, thus a convergent section becomes a diffuser with M>1 at entrance. Nozzle becomes a diffuser.
Case 2
When M>1 at the ENTRANCE
As flow area increases, velocity increases and pressure decreases, thus a divergent section becomes a nozzle with M>1 at entrance. A diffuser becomes a nozzle.
Case 3
When M< 1 at the ENTRANCE
As flow area decreases, velocity increases and pressure decreases, thus a convergent section is a nozzle with M< 1 at entrance.
Case 4
When M< 1 at the ENTRANCE
As area increases, velocity decreases and pressure increases, thus a divergent section becomes a diffuser with M < 1 at entrance.
Thus a nozzle remains a nozzle only if M < 1.
A diffuser remains a diffuser only if M < 1.
Thus flow is SUBSONIC at entrance.
VARIABLE AREA EFFECTS FLOW
NOZZLE
A nozzle is a passage of variable crosssection. In this, pressure of fluid converts into kinetic energy. The various practical applications of a nozzle are
 Steam turbines
 Water turbines
 Gas Turbines
 Flow measurements
 Used in all aircraft’s
 Jet engines
 As ejectors for removing air from the condensers
 As injectors for supplying feed water to boilers
 Artificial fountains
DIFFUSER
It is also a passage of varying cross section which converts the kinetic energy of the fluid into pressure energy. It is just reverse of a nozzle.
Applications of a diffuser
 Centrifugal compressors
 axial flow compressors
 Ramming of air in aircraft’s
In one dimensional flow, assume that the velocity and fluid properties change ONLY in the direction of flow. Therefore we can take mean value of velocity and other properties in one direction flow.
CONVERGENT DIVERGENT NOZZLE
This nozzle is a de Laval nozzle (or CD nozzle). In this, velocity increases in the convergent portion and becomes sonic velocity at the exit (throat). This exit of the of the nozzle has minimum area and maximum velocity. This exit is the THROAT. Now the fluid will enter the divergent portion with supersonic velocity. Here the velocity will further increase. It is necessary to run the turbine at very high speed to generate more power. Thus, convergent divergent nozzles are used in gas / steam turbines & rocket engines.
Used in steam turbines and all supersonic aircraft’s.
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
v_{2}=C [k(H_{1}– H_{2})]^{0.5}
Without friction C = 44.72 and k =1
With friction C = 44.72 and k is the friction factor =0.7 to 0.9
k is friction coefficient or nozzle efficiency
VELOCITY COEFFICIENT
It is the ratio of actual exit velocity to isotropic exit velocity for a certain same pressure drop
c_{v} = Actual velocity/ isotropic velocity
=√actual enthalpy drop/isotropic enthalpy drop
=√η = square root of efficiency√
EFFICIENCY OF THE NOZZLE
It is a ratio of Actual enthalpy drop to isotropic 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
 Material of the nozzle
 Inside surface condition of the nozzle
 Nature of the fluid flowing through the nozzle
 Size and shape of the nozzle
 Reynolds number of the flow
 Angle of divergence
 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
(i) Find the back pressure by the standard relation
p_{b = }p_{i} (2/(n+1))^{(n/(n1)}
(ii) If this calculated back pressure is more than the given back pressure, then the nozzle is a convergent nozzle.
(iii) If this calculated back pressure is less than the given back pressure, then the nozzle is a convergentdivergent
Calculate nozzle dimensions from the
(i) mass flow rate
(ii) 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 d^{2}/4
CONCLUSIONS

It converts pressure into kinetic energy.

No work done in a nozzle.

There is no energy transfer in a nozzle.

Nozzle is horizontal. Z1 = Z2

Spray nozzles are convergent nozzle

Air crafts use convergent nozzles.

Steam turbines use convergent –divergent nozzles.

Inlet velocity is negligible.

Pressure decreases with decrease of area.

Velocity increases with decrease of area.

Flow is 1dimensional.

Properties of the flowing fluid change only in the direction of flow.

Analysis uses steady flow energy.

Flow is isentropic unless otherwise specified.

The minimum area in a nozzle is throat.

Velocity is sub –sonic or sonic in the convergent portion and becomes supersonic in the divergent portion.

For liquids, specific volume is constant over a wide range of pressure and temperature. Liquids use convergent.

Critical pressure ratio is the ratio of pressure at inlet to pressure at throat. It gives sonic velocity at throat.

At the critical pressure ratio, mass flow rate is maximum. Choking occurs.

If the pressure at exit is higher than the designed pressure, it is an under expansion. It will cause a loss in thrust or power produced.

If the pressure at exit is lower than the designed pressure, it is an over expansion. It will cause a gain in thrust or power produced.

Angle of convergence is much greater than the angle of divergence.

The length of convergent portion is much smaller than that of the divergent portion.

Steam is a vapor. Properties can be read from enthalpy entropy chart. Properties are also available steam tables.

Sonic velocity = C* =√γRT

Critical pressure ratio fot
(a) Isentropic process
P^{*}/p = [2/(γ+1)]^{γ/(γ—1)}
^{ (b) Actual process}
P^{*}/p = [2/(n+1)]^{n/(n—1)}
27. Mach number
M = actual velocity/sonic velocity
Sonic velocity = 332 m/s
28. Relation between stagnation and static (local ) temperature
T_{0 }/T = 1 + (γ—1) M^{2}/2
.29. As steam is expanding, velocity 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
30. If the steam expands from pressure p_{1} and volume v_{1} to pressure p_{2}
c_{2} = 2{[(n/(n1)] [p_{1 }v_{1} –p_{2}v_{2}]}^{0.5}
31. Friction reduces the enthalpy drop and hence the velocity at the outlet.
32. Assume no friction in the nozzle. Friction is in the diffuser only.
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