1. Compressive Flow in Nozzles
Gebdiel Medina #68182
Group #2

2. Objective
To investigate compressible flow in convergent, convergent-divergent nozzles

3. Introduction
Converging-Diverging nozzles are widely use in many engineering contexts
Civil
Aerospace
Mechanical
They are designed to accelerate fluids to supersonic speeds at the nozzle
Their operation relies on the ratio between the inlet (stagnation, P0) pressure and outlet (back pressure, Pb) pressure

4. Operation
Configuration for converging-diverging (CD) nozzle is shown above
Gas flows through nozzle from region of high pressure (chamber) to low pressure (ambient)
The chamber is taken as big enough so that any flow velocities are negligible
Gas flows from chamber into converging portion of nozzle, past the throat, through the diverging portion and then exhausts into the ambient as a jet
Pressure of ambient is referred to as back pressure

5. Ops. Cont.

6. Ops. Cont.

7. Theory
Mach Number
Is a dimensionless parameter that measures the compressibility of fluid flow
Defined as the ratio between the velocity of the flowing fluid and the velocity of sound of the fluid
This non-dimensional parameter is important when discussing compressible flows, and leads to the following classifications of different flow regimes:
M < 1(subsonic flow)
M = 1(sonic flow)
M > 1(supersonic flow)
k= ratio of specific heats
R= gas constant
T= absolute temperature

8. Theory Choked Flow Critical Pressure Ratio
Choked flow of gases is useful in many engineering applications because the mass flow rate is independent of the downstream pressure
Depends only on the temperature and pressure upstream
Choked flow condition and mass flow rate
where k is the heat capacity ratio, typically k=1.4
Compressible fluid expands reversibly & adiabatically through duct
3. In converging portion, velocity will be subsonic and diverging, supersonic
4. Mass flow rate is determined by the cross section in throat and the properties of the fluid at inlet
𝑃 0 𝑃 𝑖 < 2 𝑘+1 𝑘 𝑘+1
1. Passage reduces area (converges) until
𝑃 𝑡 𝑃 𝑖 = 2 𝑘+1 𝑘 𝑘+1
𝑚 = 𝐴 𝑡 𝑃 𝑖 𝑇 𝑖
Then diverges
2. The velocity is the local speed of sound

9. Procedure Hilton Nozzle Pressure Distribution Unit F810 Nozzles
For Nozzle C & A (Shocking Effect)
With the air inlet valve closed, fitted Nozzle C or A into the unit and connected all pressure tappings, starting at position No.1.
Selected an inlet pressure Pi of around 700 kPa (gauge). Maintained the inlet pressure constant throughout the demonstration.
Closed the outlet pressure control valve (backpressure valve) until the outlet pressure was equal to the inlet pressure (Po=Pi), therefore obtaining an air flow rate of zero.
Gradually opened the outlet pressure control valve with decrements in back pressure (Po gauge) of about 100 kPa while observing the air mass flow rate meter.
At this point, recorded Po and m, at which just the mass flow rate stopped increasing.
Next changed the nozzle and repeated the procedure.
Finally used the recorded data to make the required analysis for this task. Compared the experimental Pi/Po ratio with the theoretical Pi/Po (absolute pressure ratios).

10. Procedure For Nozzle C, A & B (Constant Inlet Effect)
The procedure to perform this task was as follows:
Closed the inlet pressure control valve and fitted Nozzle C in the unit.
Opened the inlet pressure control valve until the inlet pressure gauge (P i ) read around 700 kPa (~650 Kpa, gauge).
With the outlet pressure control valve fully opened; the value for pressures, temperatures, and air mass flow rate were noted.
Partially closed the outlet pressure control valve while observing the outlet pressure increasing to around 100 kPa (gauge).
Repeat this procedure with increments of 100 kPa until the outlet pressure reached its maximum.
Repeated the procedure with Nozzle A.
Finally used the recorded data to make the required calculations in order to achieve the analysis for this task.
For Nozzle C, A & B (Constant Outlet Effect)
Closed air inlet valve and fit Nozzle A or C.
Adjusted the inlet pressure gage at 700 kPa (gauge).
Adjusted the outlet pressure gage at 50 kPa (gauge). Keep pressure constant the whole experiment.
Recorded the inlet temperature and mass flow rate at the corresponding Pi. You may record the other pressure gauges.
Reduced the inlet pressure in steps of 100 kPa decrements.
Repeated steps (d) and (e) until Pi = 100 kPa (gauge).
Repeated the before process with next nozzle.

11. What We Expected The validation of: Seeing the phenomenon of choking
Study the effect of the outlet pressure on the flow rate with constant inlet pressure
Study the effect of the inlet pressure on the flow rate with constant back pressure
Seeing the pressure distribution in nozzles

12. Results and Analysis
Table 4.1 Experiment Data for Chocking Condition
Obs
Nozzle
Maximum Air mass flow rate ṁ (kg/s)
Absolute Inlet Pressure Pi (kPa)
Absolute Outlet Pressure Po (kPa)
Experimental Chocking Condition Po/Pi
Theoretical Chocking Condition Po/Pi
% Error 1 C
0.0036
701.3
476.3
0.679
0.528
28.6 2 A
0.004
451.3
0.644
21.8
Table 4.2 Variation Air Mass Flow Rate due to Ration Po/Pi
Inlet Pressure Pi= 600 (kN/m^2)
Inlet Temperature= 300(K)
Obs
Outlet Pressure Po (kPa)
Overall Pressure Ration Po/Pi
Actual Air Mass Flow Rate ṁ (kg/s)
Nozzle A
Nozzle B
Nozzle C 1
650
1.083
0.0034
0.0030
0.0020 2
550
0.917
0.0028 3
450
0.750
0.0038
0.0040
0.0032 4
350
0.583 5
250
0.417
0.0042 6
150
0.250 7 50
0.083
Maximum Air mass flow rate ṁ (kg/s)
Theoretical Air mass flow rate ṁ (kg/s)
% Error
0.0036
18.1
0.004
9.0

13. Results and Analysis
Table 4.2 Variation Air Mass Flow Rate due to Ration Po/Pi
Inlet Pressure Pi= 600 (kN/m^2)
Inlet Temperature= 300(K)
Obs
Outlet Pressure Po (kPa)
Overall Pressure Ration Po/Pi
Actual Air Mass Flow Rate ṁ (kg/s)
Nozzle A
Nozzle B
Nozzle C 1
650
1.083
0.0034
0.0030
0.0020 2
550
0.917
0.0028 3
450
0.750
0.0038
0.0040
0.0032 4
350
0.583 5
250
0.417
0.0042 6
150
0.250 7 50
0.083

14. Results and Analysis
Table 4.3 (C) Variation of Mass Flow Rate due to Inlet Pressure
Outlet Pressure Po= 50 (kN/m^2)
Obs
Inlet Temp. (K)
Inlet Pressure (kPa)
Actual Air Mass Flow Rate ṁ (kg/s)
Theoretical Air Mass Flow Rate ṁ (kg/s) 1
293.2
600
0.0038
0.0044 2
293.4
500
0.0034
0.0037 3
293.5
400
0.0028
0.0030 4
293.7
300
0.0022 5
293.6
200
0.0016
0.0015 6
294.1
100
0.0012
0.0007 7
294.7 50
0.0000
0.0004

15. Results and Analysis

16. Results and Analysis
= choked
= Design pressure ratio

17. Conclusion The validation of: Seen the phenomenon of choking
Studied the effect of the outlet pressure on the flow rate with constant inlet pressure
Studied the effect of the inlet pressure on the flow rate with constant back pressure
Saw the pressure distribution in nozzles