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T Compressible Flow Through Converging

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T Compressible Flow Through Converging Powered By Docstoc
					ME 814.3 T2: Compressible Flow


  Instructor: Maryam Einian
  Email: mae345@mail.usask.ca
               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
   Quasi-steady process:

            unsteady continuity
                  steady energy
           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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