1 hei prop obrien
TRANSCRIPT
8/2/2019 1 HEI Prop OBrien
http://slidepdf.com/reader/full/1-hei-prop-obrien 1/20
Hypersonic Educational Initiative
Ramjet and ScramjetRamjet and Scramjet
Cycle AnalysisCycle Analysis
Walter F. O’Brien
Virginia Tech
8/2/2019 1 HEI Prop OBrien
http://slidepdf.com/reader/full/1-hei-prop-obrien 2/20
Hypersonic Educational Initiative
Outline
• Cycle Analysis, or Performance Prediction
– What is it?
– What is the application?
• To all propulsion engines, but here, toRamjets and Scramjets
– What are the fundamentals?
• Control volumes and integral equations
• Thermodynamics
• Reductions to equations for modeling applications
8/2/2019 1 HEI Prop OBrien
http://slidepdf.com/reader/full/1-hei-prop-obrien 3/20
Hypersonic Educational Initiative
Outline, cont.
• Application of equations for performance
predictions
• Application of results
– Design and optimization, testing
– Component performance sensitivities
– Useful range of performance
• Summary
8/2/2019 1 HEI Prop OBrien
http://slidepdf.com/reader/full/1-hei-prop-obrien 4/20
Hypersonic Educational Initiative
Background and Definitions
• “Cycle” analysis name comes for
thermodynamics of engines, where a
working fluid circulated continuously totransfer heat, produce work.
• Air breathing combustion propulsion
engines execute processes, not cycles
T
s
p
v
8/2/2019 1 HEI Prop OBrien
http://slidepdf.com/reader/full/1-hei-prop-obrien 5/20
Hypersonic Educational Initiative
Ramjet, Scramjet Processes
• Compression, energy addition, expansion
Inlet
Air Combustion
Products
I n le t C o m b u s t o r N o z z
l e
8/2/2019 1 HEI Prop OBrien
http://slidepdf.com/reader/full/1-hei-prop-obrien 6/20
Hypersonic Educational Initiative
Goal of process analysis, modeling• Basically, to predict thrust and fuel consumption.
However,performance analysis has many applications indesign, optimization, testing and evaluation
• Thrust is the reaction to the force on the working fluid in theflow path, as predicted by the momentum equation.
• Engine thrust per unit mass flow of air is commonly used,
• Fuel consumption per unit thrust is the TSFC
T F
f m&
a
mT &/
T mTSFC f /&=
8/2/2019 1 HEI Prop OBrien
http://slidepdf.com/reader/full/1-hei-prop-obrien 7/20
Hypersonic Educational Initiative
The Control Volume
Forces
P s
u
)( nuumass
!=
I C N
8/2/2019 1 HEI Prop OBrien
http://slidepdf.com/reader/full/1-hei-prop-obrien 8/20
Hypersonic Educational Initiative
Control Volume Equations
• Continuity• Momentum
• The First Law
• The Second Law
• Equation of State
! ! " #+=
cv cs
dAnuudV udt
d F )($ $
8/2/2019 1 HEI Prop OBrien
http://slidepdf.com/reader/full/1-hei-prop-obrien 9/20
Hypersonic Educational Initiative
Control Volume Equations - 1-D Steady
Flow
• Continuity• Momentum
• First Law
• Second Law
• Equation of State
For
where
1 2
x
8/2/2019 1 HEI Prop OBrien
http://slidepdf.com/reader/full/1-hei-prop-obrien 10/20
Hypersonic Educational Initiative
The Thrust Equation
)()()( aa sa saeaaeeeeeaaaa x umumumumum A p A A p A p F !!
"++"="""+ &&&&&
)( aeeaaee x p p Aumum F !+!= &&
e
ua
paa
sm&
I C N
a
Aa
Aeue
pe
x F T )(!=
8/2/2019 1 HEI Prop OBrien
http://slidepdf.com/reader/full/1-hei-prop-obrien 11/20
Hypersonic Educational Initiative
T/maand TSFC
)1(1
))1((/
))(/())1((
e
a
e
e
e
aea
aeaeaea
p
p RT
M
f uu f mT
p pm Auu f mT
!
+
+!+=
!+!+=
" &
&&
stoic
a
fstoic
fstoic
f
a
f f
m
m
m
m
m
m f !=""
#
$%%&
'""
#
$%%
&
'== (
&
&
&
&
&
&where
a
f
mT
f
T
mTSFC
&
&
/==
and
8/2/2019 1 HEI Prop OBrien
http://slidepdf.com/reader/full/1-hei-prop-obrien 12/20
Hypersonic Educational Initiative
Calculating T/ma and TSFC for a
Ramjet and Scramjet• Finding the terms in the equations:
– Ma, Ta, and pa are given, yielding ua
– ue can be found from the 1st Law
• For a nozzle,
• The pressure ratio (poe/pe) is determined by the flight Mach
number, the total pressure ratios (losses) of the
components, and the nozzle area ratio
!!
"
#
$$
%
&'
'=
'
e
e
oe
e
e
oeeee
p
pT Ru
(
(
(
( 1
)(11
2
( )e
anozzlecombustor inlet a
e
oe
e
a
ocombustor
onozzle
oinlet
ocombustor
oa
oinlet
a
oa
e
oe
p
pr r r M f
p
p
p
p
p
p
p
p
p
p
p
p
p
p
!!!!=
!!!!=!
8/2/2019 1 HEI Prop OBrien
http://slidepdf.com/reader/full/1-hei-prop-obrien 13/20
Hypersonic Educational Initiative
fuel/air ratio f
21
Continuity
1st Law
QR values Jet A 45,000
Hydrogen 120,900
combustor
8/2/2019 1 HEI Prop OBrien
http://slidepdf.com/reader/full/1-hei-prop-obrien 14/20
Hypersonic Educational Initiative
fuel/air ratio f (cont.)
Solving for f,
8/2/2019 1 HEI Prop OBrien
http://slidepdf.com/reader/full/1-hei-prop-obrien 15/20
Hypersonic Educational Initiative
Application of the Ramjet-Scramjet
Models• A typical application involves a computer
program allowing study of the effects of design and flight variables on engine
performance• The results of this analysis are design-
point performance predictions. Off-designpredictions require additional models thatcan be developed from the sameequations
8/2/2019 1 HEI Prop OBrien
http://slidepdf.com/reader/full/1-hei-prop-obrien 16/20
Hypersonic Educational Initiative
Example EXCEL Computer program
Hypersonic Education Initiative Revision 3A
W. F. O'Bri
RAMJET-SCRAMJET PERFORMANCE ANALYSI S
Based on total losses including the nozzle efficiency, inlet, flameholder, and combustor
Flight Parameters
pa,kPa Ma poa/pa poa, kPa
60000 ft 7.2 5 529 3809 FLOW RATE ma, kg/sec
Ta,K ua,m/s Toa/Ta Toa,K 1
217 1476 6.000 1302 INLET P0a,kPa 3809
with rd= 0.8 P03,kPa 3048
NOZZLE NOZZLE DATA (at Station 4)
uen=(2 * ( !R/( !-1) *To4 * "n*(1 - (pe/po4)^( !-1/ !))^.5 ! T04,K rd
po4/pe=po4/po3*po3/po2*po2/po1*p0a/pa*pa/pe 1.3 2500 0.8
(Assuming pe=pa) M4 2.5 P04,kPa
T4,K 1290
po4/pe=rd*rb*poa/papo4/pe 338.6 COMBUSTOR DATA (at Station 3)
QR T03 f
Thrust=[(mdot nozzle) * ((1+f)*(ue-ua)] + [Ae * ( pe-pa)] 45,000 1302 0.027
let (pe-pa)=0; (ideal expansion) M3 2.5 t fuel, kg/se
T3,K 672 0.027
8/2/2019 1 HEI Prop OBrien
http://slidepdf.com/reader/full/1-hei-prop-obrien 17/20
Hypersonic Educational Initiative
Typical Results
PERFORMANCE of RAMJETS and SCRAMJETS
-0.20
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0 2 4 6 8
Mach Number Ma
T/ma,kN/kg/sec; 2500K
T/ma,kN/kg/sec; 3000K
TSFC,kg/kNsec; 2500K
TSFC,kg/kNsec; 3000K
QR=45,000 kJ/kg
Alt.=60,000 ft
r i=0.8
r c=0.8ηn=0.9
nozzle pe=pa
8/2/2019 1 HEI Prop OBrien
http://slidepdf.com/reader/full/1-hei-prop-obrien 18/20
Hypersonic Educational Initiative
Discussion• Valid input data to the models will produce accurate
results. However, much technology underlies the
value of the key parameters
• For example, the total pressure losses of a
combustor are entered as
• In a scramjet, r c involves losses associated with
isolators, fuel injection, flameholders, heat addition
and boundary layers
oin
out
c p
pr =
8/2/2019 1 HEI Prop OBrien
http://slidepdf.com/reader/full/1-hei-prop-obrien 19/20
Hypersonic Educational Initiative
Summary• We have developed the thrust and fuel
consumption (“performance”) equations for a
ramjet or scramjet from 1st principles
• The key performance variables and TSFC
have been derived• Exit velocity ue is a key parameter, strongly driven
by nozzle variables Toe and poe
– Combustion temperature determines Toe
– Component losses determine poe, given poa
• Look for discussion of these points in the followingHEI presentations
amT &/
8/2/2019 1 HEI Prop OBrien
http://slidepdf.com/reader/full/1-hei-prop-obrien 20/20
Hypersonic Educational Initiative
Thanks for your attention..
• Questions welcomed
PERFORMANCE of RAMJETS and SCRAMJETS
-0.20
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0 2 4 6 8
Mach Number Ma
T/ma,kN/kg/sec; 2500K
T/ma,kN/kg/sec; 3000K
TSFC,kg/kNsec; 2500K
TSFC,kg/kNsec; 3000K
QR=45,000
kJ/kg
Alt.=60,000 ft
r i=0.8
r c=0.8
ηn=0.9
nozzle pe=pa