the thrust generator p m v subbarao professor mechanical engineering department another passive...
TRANSCRIPT
The Thrust Generator
P M V Subbarao
Professor
Mechanical Engineering Department
Another Passive Device…… An Obvious Concept for Generation of Motive Power ….
Frictional Flow with Variable Area
Effect of Shape of duct on Flow
2
0p
'''
h
22
2
2
2
M1TC
q
A
dA2
D
fdxM
M1
M2
11
M
dMγ
δγ
γ
Pure shape effects:
A
dA
1M2
M12
M
dM2
2γ
p
dp1
u
duM2
γ
p
dp1
A
dA
M1
M2
2
γ
ρ
dρ
p
dpγ
ρ
dρ
A
dA
M1
M2
2
Subsonic Nozzle
dA < 0 & M <1So, du > 0 & dp <0
A
dA
1M
1
u
du2
T
dT
A
dA
M1
M12
2
γ
Supersonic Nozzle
dA > 0 & M >1So, du >0 & dp<0
p
dp1
A
dA
1M
M2
2
γ
ρ
dρ
p
dpγ
ρ
dρ
A
dA
1M
M2
2
T
dT
A
dA
1M
M12
2
γ
p
dp1
u
duM2
γ A
dA
1M
1
u
du2
Generation of Supersonic Velocity from Rest
p
dpM
u
du 2
γ
p
dp1
M
M1
A
dA2
2
γ
p
dp1
ρ
dρ
γ
p
dp1
T
dT
γ
γ
The Rocket
RAMJET Engine
Nozzle at Design Exit Pressure
p1 p2d
pthroat
pp1
p*
p2d
0p
dp1
M
M1
A
dA2
2
γ
At M=1
Minimum Area = A* : Also called throat
*** AcuA
u
RT
ρ
ρ
u
c
ρ
ρ
A
A **
γ
Throat of an Isentropic Nozzle
The Isentropic Design of A Nozzle
pin
pb
Design Variables :
ininin T,p,m or V Outlet Condition: pb
pb = Back Pressure
pin
Isentropic Nozzle under Designed Conditions
11
11
,0,0,0,0 &
γγ
γ
γγ
γ
exitinexitin
γ
γ
TTpp
2exit
exit
in0,
exit
in0,
2in
in
in0,
in
in0,
M2
11
T
T
p
p
M2
11
T
T
p
p
exitexitexitininin uAuA m
inininin
in MRTART
p minin
in
in MART
pm
exitexit
exit
exit MART
pm
The Design Conditions of an Isentropic Nozzle
12
1
γ
γ
γ
γ
2exit
exitexit
in0,
in0,
M2
11
MA
T
p
Rm
12
1
γ
γ
γ
γ
2in
inin
in0,
in0,
M2
11
MA
T
p
Rm
Under design conditions the gas pressure at the exit plane of the nozzle is applied back pressure.
11
γ
γγ
γ
γ 2exit
exit
in0,
b
in0, M2
11
T
T
p
pbexit pp
12
1
γ
γ
γ
γ
2exit
2in
inexit
in
M2
11
M2
11
M
M
A
A tixe
Profile of an Isentropic Nozzle
12
1
γ
γ
γ
γ
2exit
2
exit
exit M2
11
M(x)2
11
M(x)
M
A
A(x)
1
γ
γ
γ
γ2
2exit
b M(x)12
M12
p
p(x)
1
γ
γ
γ
γ2
2exit
exit M(x)12
M12
p
p(x)
At design Conditions :
Full Capacity Convergent Nozzle
1
γ
γ
γ
γ2
criticalb, M(x)12
1
p
p(x)
12
1
γ
γ
γ
γ
21
M(x)2
11
M(x)
1
A
A(x)2
criticalexit,
1
γ
γ
γ
γ2
2exit
exit M(x)12
M12
p
p(x)
Remarks on Isentropic Converging Nozzle Design
• Length of the nozzle is immaterial for an isentropic nozzle.
• Strength requirements of nozzle material may decide the nozzle length.
• Either Mach number variation or Area variation or Pressure variation is specified as a function or arbitrary length unit.
• A converging Nozzle Design attains maximum capacity when the exit Mach number is unity.
Full Capacity Converging Nozzle
1
γ
γ
γ
2
1
p
p
criticalb,
in0,
1
γ
γ
γ 1
2pp in0,criticalb,
pin
pb, critical
11
,0,0,0,0 &
γγ
γ
exitinexitin
γ
TTpp
2exit
exit
in0,
exit
in0, M2
11
T
T
p
p
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