Compressive Flow in Nozzles Gebdiel Medina #68182 Group #2

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

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

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

Ops. Cont.

Ops. Cont.

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

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 =0.0404 𝐴 𝑡 𝑃 𝑖 𝑇 𝑖 Then diverges 2. The velocity is the local speed of sound

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).

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.

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

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 0.00440 18.1 0.004 9.0

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

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

Results and Analysis

Results and Analysis = choked = Design pressure ratio

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