Download - MAE 278 intro to flight(5&6 - Rev A)
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7/17/2019 MAE 278 intro to flight(5&6 - Rev A)
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MAE 278
Thermodynamic Processes
So far, we have only considered two thermodynamicprocesses:
Constant volume processes
Constant pressure processes
Other important processes defined: Adiabatic: a process in which no heat is added or taken
away
Reversible: one in which no friction or other dissipativelosses occur
Isentropic: a process which is both adia-batic andreversible
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7/17/2019 MAE 278 intro to flight(5&6 - Rev A)
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MAE 278
!sentropic "low #elations $%
&diabatic flow implies
'ividin( deby dh
'efinin( $) constant *+ for air%
Substitutin( and inte(ratin(:
dTcdePdvPdvdeq v===+= 0dTcdhvdPvdPdhq P==== 0
v
dv
c
c
P
dP
c
c
vdP
Pdv
v
P
P
v
==
c
cP
v
==
==
==
1
2
1
2
1
2
1
2
1
2
1
2
,1
sinceand
lnln
2
1
2
1
P
Pv
v
v
P
P
v
v
P
Pv
dv
P
dP
v
dv
P
dP P
P
,
,
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7/17/2019 MAE 278 intro to flight(5&6 - Rev A)
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MAE 278
!sentropic "low #elations $%
Combinin( the e.uation of state with the inte(ration
results
#eturn to the ener(y balance e/pressed by the first lawof thermodynamics
The physical principle is:
Energy can neither be created nor destroyed
"or adiabatic $or isentropic% flow0 #ecallin( euler1s e.uation:
0 Combinin( these two e/pressions, utili2in( the fact that
= =
=
P
RT
P
P
T
T2
1
2
1
2
1
1
0== vdPdhqdP VdV =
dh VdV+ = 0
,1
=v
3
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7/17/2019 MAE 278 intro to flight(5&6 - Rev A)
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MAE 278
!nte(ratin( this ener(y-based e.uation alon( astreamline:
#ecallin( that adiabatic flow implies:
4ner(y 4.uation
dh VdV dh VdV
h h V V
h V
h V
h V
CONSTANT
h
h
V
V+ = + =
+
=
+ = + = + =
0 0
2 2 0
2 2 2
1
2
1
2
2 122
12
112
222 2
TchdTcdhvdPvdPdhq
P
P
=
====
therefore
0
c T V
c T V
c T V
CONSTANTP P P112
222 2
2 2 2+ = + = + =
+
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MAE 278
4.uation Summary
CO5T!56!T7 486&T!O5 $!5CO9P#4SS!;4%
4#5O6;;!1S 486&T!O5
CO5T!56!T7 486&T!O5 $CO9P#4SS!;4%
!S45T#OP!C #4;&T!O5S
454#
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MAE 278
Sound >aves
Consider a wave movin( at velocity, a:
9ake the wave stationary0 One dimensional flow:
0 &pply continuity
( ) ( )
( )( )
1 1 1 2 2 2
1 2
A V A V
A a d A a da
a d a da
a a ad da
a da
d
=
= + +
= + +
= + +
=
?
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MAE 278
Speed of Sound $%
&pplyin( 4uler1s 4.uation $9omentum%:
Substitutin( into the e.uation for a:
"or isentropic flow:
Substitutin( into a and usin( the e.uation of state:
dp ada da dpa
= =
a da
d d
dp
a a
dp
d= = =
2a
dp
disentropic
=
p
p
p pcons t
2
1
2
1
2
2
1
1
=
= =
tan
dp
d
d
d c c
p p
isentropic
= = = = 1 1
a dp
d
p
isentropic
=
=
a RT=
@
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MAE 278
Speed of Sound $%
Physical interpretation of speed of sound andtemperature relationship Temperature is a measure of random molecular motion
Speed of sound is a superimposed, directed motiontransmitted by molecular collisions
A
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MAE 278
9ach 5umber
9ach 5umber relates directed ener(y $kinetic ener(y% tointernal ener(y
"low re(imes
Subsonic and supersonic flow are easy to analy2e Transonic flow is the most difficult re(ime to analy2e
a
VM=a
VM=
B
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MAE 278
Transonic "low
"reestream flow is still subsonic Transonic flow is a mi/ed flow re(ime
!t is partly subsonic and partly supersonic
THE LOCAL FLOW SPEEDS UP
OVER A CURVED SURFACE
M
> 1
M < 1
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MAE 278
;ow Speed Tunnel
#earran(in( ernoulli1s 4.uation
Solvin( the Continuity 4.uation for
Substitutin( for , we (et
V A
A
V
p V p V
21
21
1 12
2 221
2
1
2
=
+ = +
( )V p p V
2
2
2 1 1
22= +
V A
A V1
2
12= ( )
=
2
1
2
21
2
1
2
A
A
ppV
( )
=
2
1
2
21
2
1
2
A
A
ppV
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MAE 278
9anometers
>idely used pressure instruments
Common manometer fluids 9ercury: A+=*? lbDft3
>aterE: ?*+3 lbDft3
&lcoholE: =*= lbDft3 E&T T ) F C
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MAE 278
Types of Pressure
Static Pressure
The force per unit area (enerated by ran-dommolecular motions*
!t e/ists even with the fluid at rest
Total Pressure
The force per unit area that would e/ist if the flowwere brou(ht to rest isentropically
!t is a thermodynamic property
yna!ic Pressure The force per unit area in a flow due to density andflow velocity
q V1
22q V
1
22
3
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MAE 278
Pitot-Static 9easurements
Pitot-static probe schematic:
'etail of typical pitot-static probe head:
FLOW WITH
VELOCITY V1
STATIC PRESSURE ORIFICE;
p IS MEASURED HERE
TOTAL
PRESSURE
MEASURED
HERE
DIFFERENTIAL
PRESSURE GAGEPITOT TUBE
TOTAL
PRESSURE
STATICPRESSURE
+
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MAE 278
Pitot-Static !nstallations
Pitot-static locations are different for each airplane
PITOT HEADS
P-80A P-40N
NF-104A
=