1 HEI Prop OBrien

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




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




Outline, cont.

• Application of equations for performance

predictions

• Application of results

– Design and optimization, testing

– Component performance sensitivities

– Useful range of performance

• Summary




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




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




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 /&=




The Control Volume

Forces

P s

u

)( nuumass

!=

I C N




Control Volume Equations

• Continuity• Momentum

• The First Law

• The Second Law

• Equation of State

! ! " #+=

cv cs

dAnuudV udt

d F )($ $




Control Volume Equations - 1-D Steady

Flow

• Continuity• Momentum

• First Law

• Second Law

• Equation of State

For

where

1 2

x




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 )(!=




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




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

!!!!=

!!!!=!




fuel/air ratio f

21

Continuity

1st Law

QR values Jet A 45,000

Hydrogen 120,900

combustor




fuel/air ratio f (cont.)

Solving for f,




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




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




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


TSFC,kg/kNsec; 2500K


QR=45,000 kJ/kg

Alt.=60,000 ft

r i=0.8

r c=0.8ηn=0.9

nozzle pe=pa




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 =




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 &/




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





QR=45,000

kJ/kg

Alt.=60,000 ft

r i=0.8

r c=0.8

ηn=0.9

nozzle pe=pa

1 HEI Prop OBrien

Documents

Transcript of 1 HEI Prop OBrien