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# T Compressible Flow Through Converging

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```									ME 814.3 T2: Compressible Flow

Instructor: Maryam Einian
CFD lab: 1B85

1
Tests
1.   Discharge of compressed air from a tank

2. Flow through a converging-diverging nozzle

2
Discharge of compressed air
from a tank
 Fill the tank
 Discharge the tank

Observe the pressure and
temperature variation in
time

3
Formulation

1    equation
 p    2        1  
 
p                2  Kt
 1      
 i                   

1
   1   1    An   2RTi
K       
 2              Vr    1
Converging-Diverging nozzle
Application:
Propulsion and the High
speed flow of gases.

Mass Flow Rate:
Low Pressure at the back
?
More mass flow rate
5
Subsonic Flow (M<1)
1- Nozzle isn't choked

2- Accelerates through the
converging section

3- Reaches its maximum speed at
the throat.

4- Decelerates through the
diverging section.

5- Lowering the back pressure increases the
flow speed everywhere in the nozzle.
6
Sonic Flow (M=1)
1- Nozzle is choked

2- Accelerates through the
converging section

3- Reaches its maximum speed at
the throat. (M=1)

4- Decelerates through the
diverging section.

7
Supersonic Flow (M>1)
1- Nozzle is choked

2- Accelerates through the
converging section

3- Reaches its maximum speed at
the throat.

4- Accelerates through the
diverging section.

8
Shock Wave
1- Nozzle is choked

2- Accelerates through the
converging section
3- Reaches its maximum speed at
the throat.

4- Accelerates through the
diverging section.

5- Shock wave occurs.

6- Decelerates through the
diverging section.
9
Conservation
Conservation of mass       VA  constant

p   1 2
Conservation of momentum   (u  )  V  constant
 2

1 2
Conservation of energy     h  V  constant
2

10
Isentropic Flow
To        1  2
 1       M
A perfect gas            T        2 

po   To   1
    
p    T 

 1
 1                2  1
1    1M 2 

po     1  2   1       A 1  2
 1     M                                 
p   2                     A M  1   1 
*

 2             

11
Shock Wave
Highly irreversible                                         No isentropic process

  1M 12  2

2
M2
2M 1    1
2

P2 1  M 1
2


P1 1  M 2 2

 1
Po 2 M 1  2  (  1) M 1         2 (1 )
2

                                        A *1 Po 2

Po1 M 2  2  (  1) M 2 2


              A *2 Po1

12
Mass Flow Rate
k 1
1 2 2     2( k 1)   A* Po
.
m max   k        
 k 1              RTo

2            k 1 
.               k
 2k  P    P           k   AP
m          1                  o
 k  1  Po 

P            RT
  o

    

o

13
Objectives
 To obtain the pressure distribution along a
converging-diverging nozzle.

 To compare the experimental results with the
theoretical calculations.

14
Data Acquisition
Supersonic       Shock wave      Subsonic

Pos =; Ptank =, Pos =; Ptank =, Pos =; Ptank =,
Pb =; To =       Pb =; To =     Pb =; To =
x   Pressure, Ps x Pressure, Ps x Pressure, Ps

15
What Do We Require To Obtain
From The Raw Data?

P    A    .  .
,    , m, m max
Po   A*

16
Dimensions of Converging-Diverging Nozzle
17
A Summary of Important
Quantities
R       12.70 mm      0.500 in
Dt      14.78 mm      0.582 in
Dprobe   1.50 mm       0.059 in
Patm     To be
measured
k        1.40          1.40
Rair    287 J/KgK   1717 ft2/s2oR
18
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21
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23

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