mae 278 intro to flight(5&6 - rev a)

7/17/2019 MAE 278 intro to flight(5&6 - Rev A)

1/15

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


2/15

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

,

,


3/15

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


4/15

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+ = + = + =

+


5/15

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#


6/15

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

=

= + +

= + +

= + +

=

?


7/15

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=

@


8/15

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


9/15

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


10/15

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


11/15

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


12/15

MAE 278

9anometers

>idely used pressure instruments

Common manometer fluids 9ercury: A+=*? lbDft3

>aterE: ?*+3 lbDft3

&lcoholE: =*= lbDft3 E&T T ) F C


13/15

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


14/15

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

+


15/15

MAE 278

Pitot-Static !nstallations

Pitot-static locations are different for each airplane

PITOT HEADS

P-80A P-40N

NF-104A

=

mae 278 intro to flight(5&6 - rev a)

Documents

b7172019 mae

v37172019 mae

adiabatic flow

isentropic flow

supersonic flow

dimensional flow

uation of state

subsonic transonic flow