Laboratory: Convergent-divergent nozzle R2.docx DIS 1 CONVERGENT-DIVERGENT NOZZLE TEST 1. Object 1.1 To determine the performance of a convergent-divergent nozzle and compare this with theory. 2. Apparatus 3. Theory 3.1 Theoretical analysis of reversible and adiabatic flow of a perfect gas through a nozzle indicates that the rate of mass discharge is a function of the inlet stagnation conditions and the overall pressure ratio at the throat, as follows: ݉ሶඥܴܶ଴ଵ ሶ ܣ௧ܲ଴ଵ = ඩ 2ߛ (ߛ െ 1) ൬ ܲ୲ ܲ଴ଵ ൰ ଶ ఊ ቌ1 െ ൬ ܲ୲ ܲ଴ଵ ൰ ఊିଵ ఊ ቍ 3.2 The function within the square root has a maximum value when: ൬ ܲ୲ ܲ଴ଵ ൰ = ൬ 2 (1 + ߛ) ൰ ఊ (ఊିଵ) Laboratory: Convergent-divergent nozzle R2.docx DIS 2 3.3 Theory indicates that the mass flow rate will actually reduce towards zero when the downstream pressure Pt is less than the critical value for maximum discharge. 3.4 Further analysis shows that the ideal velocity of the flow reaches sonic conditions at the critical discharge. Further acceleration to supersonic flow is possible only if the nozzle profile diverges to an increased cross sectional area beyond the station at which sonic flow is established. Practical investigation of nozzle performance shows that the mass flow rate increases to the critical value as downstream pressure is reduced but remains constant if the discharge pressure is reduced further. 4. Procedure: 4.1 Set the inlet pressure to 400 kN/m (gauge) 4.2 Open the nozzle outlet valve fully and record a full set of readings (as shown on the results sheet). 4.3 Shut in the outlet valve until the back pressure increases by 50 kN/m . This can be measured on the search tube at position 26 (just at the exit from the nozzle). Record a full set of readings. 4.4 Repeat 4.3, increasing the back pressure by 50kN/m each time, until the outlet pressure is less than 50kN/m below the inlet pressure. 4.5 Plot the pressure distribution along the length of the nozzle for each set of readings. Use absolute pressures (not gauge pressures) 4.6 Calculate and plot the actual and ideal mass flow parameter against pressure ratio for each test set. 4.7 Notes: x The actual mass flow can be calculated from the orifice data collected: [P3 – P4 (mmH2O)], using standard orifice plate theory. The mass flow parameter can then be calculated as shown in 3.1 . (actual using mass flows measured and theoretical using pressure ratios) x Use ABSOLUTE pressures throughout. 5. Data 5.1 Discharge pipe diameter = 76.2mm 5.2 Orifice diameter = 41.9mm 5.3 Orifice coefficient of discharge = 0.605 5.4 Nozzle length = 50mm 5.5 Nozzle inlet convergence radius = 9.5mm 5.6 Nozzle throat diameter = 6.37mm 5.7 Nozzle probe diameter = 3.3mm 5.8 Nozzle exit diameter = 7.22mm 6. Discussion 6.1 Comment on the plots obtained. Compare theoretical results with actual and discuss differences. How might he experiment be improved? 7. Conclusion Briefly address the objective of the experiment. Laboratory: Convergent-divergent nozzle R2.docx DIS 3 8. Results Test 1 1 2 3 4 5 6 7 8 9 10 P01 (kN/m ) P2e (kN/m ) T01 (°C) P3 – P4 (cm H2O) P2 (through nozzle) (kN/m ) 1 2 3 4 5 6 7 8 9 10 (throat) 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30