Whenpo pr. there is no flow in the nozzle (Fig. 3). When po is reduced below...
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Whenpo pr. there is no flow in the nozzle (Fig. 3). When po is reduced below pr. subsonic flow is induced through the nozzle, with pressure decreasing to the throat, and then increasing in the diverging portion of the nozzle (see Fig. 3). When the back pressure is lowered to that of curve 4, sonic flow occurs at the nozzle throat Further reductions in back pressure can induce no more flow through the nozzle (the nozzle is said to be chocked). As the back pressure is reduced below that of curve 4, a normal shock appears in the nozzle downstream of the throat (curves a and b) until for a low enough back pressure, the normal shock positions itself at the nozzle exit (curve c). As the back pressure is lowered below that of curve c. an oblique shock wave inclined at an angle to the flow appears at the exit plane of the nozzle. Further reductions in back pressure cause the angle between the shock and the flow to decrease, thus decreasing the shock strength, until the isentropic case, curve 5, is reached. Curve 5 corresponds to the design condition in which the flow is perfectly expanded in the nozzle to the back pressure. For back pressures below that of curve 5, exit plane pressure is greater than the back pressure. A pressure decrease (expansion) occurs outside the nozzle in the form of expansion waves. A converging-diverging nozzle is designed to operate with an exit Mach mmber of 22 The nozzle is supplied from an air reservor at 5 MPa Assuming 1-D flow and y=1.4, calculate the following: 1. Calculate the maximum back pressure at which M= at the throat (curve 4). Hint: Use isentropic flow table to figure 4/4* and p/p*. For converging-divergingnozzle, plot the normalized mass flow (m-dot m-dot-maximum) versus back pressure (see Figure 2 for analogy). Mark schematically Fig.3 cases 1.2.3.4.5. a.b.c.dem this graph to categorize chocked (m-dot/m-dot-maximum=1) and non-chocked cases. 2. Calculate the back pressure over which a normal shock will appear at the nozzle exit plane (curve c). Hint: use normal shock wave table. Recall that the exit Mach number upstream of the shock wave is 2.2 (the same as for the isentropic design case). 3. Calculate the back pressure over whicha normal shock will appear at the nozzle plane at which Mach is 1.6 upstream of the shock wave (curve b). Hints: use isentropictable upstream and downstream the shock wave and normal shock wave table across the shock wave. Recall that downstream of the shock wave the flow is isentropic and subsonic till the nozzle exit, with increasing static pressure. 4. Calculate the back pressure for the flow through nozzle to be isentropic (without shock wave) expanded to the design supersonic Machnumber (curve 5). Hint: Use isentropic flow table. Whenpo pr. there is no flow in the nozzle (Fig. 3). When po is reduced below pr. subsonic flow is induced through the nozzle, with pressure decreasing to the throat, and then increasing in the diverging portion of the nozzle (see Fig. 3). When the back pressure is lowered to that of curve 4, sonic flow occurs at the nozzle throat Further reductions in back pressure can induce no more flow through the nozzle (the nozzle is said to be chocked). As the back pressure is reduced below that of curve 4, a normal shock appears in the nozzle downstream of the throat (curves a and b) until for a low enough back pressure, the normal shock positions itself at the nozzle exit (curve c). As the back pressure is lowered below that of curve c. an oblique shock wave inclined at an angle to the flow appears at the exit plane of the nozzle. Further reductions in back pressure cause the angle between the shock and the flow to decrease, thus decreasing the shock strength, until the isentropic case, curve 5, is reached. Curve 5 corresponds to the design condition in which the flow is perfectly expanded in the nozzle to the back pressure. For back pressures below that of curve 5, exit plane pressure is greater than the back pressure. A pressure decrease (expansion) occurs outside the nozzle in the form of expansion waves. A converging-diverging nozzle is designed to operate with an exit Mach mmber of 22 The nozzle is supplied from an air reservor at 5 MPa Assuming 1-D flow and y=1.4, calculate the following: 1. Calculate the maximum back pressure at which M= at the throat (curve 4). Hint: Use isentropic flow table to figure 4/4* and p/p*. For converging-divergingnozzle, plot the normalized mass flow (m-dot m-dot-maximum) versus back pressure (see Figure 2 for analogy). Mark schematically Fig.3 cases 1.2.3.4.5. a.b.c.dem this graph to categorize chocked (m-dot/m-dot-maximum=1) and non-chocked cases. 2. Calculate the back pressure over which a normal shock will appear at the nozzle exit plane (curve c). Hint: use normal shock wave table. Recall that the exit Mach number upstream of the shock wave is 2.2 (the same as for the isentropic design case). 3. Calculate the back pressure over whicha normal shock will appear at the nozzle plane at which Mach is 1.6 upstream of the shock wave (curve b). Hints: use isentropictable upstream and downstream the shock wave and normal shock wave table across the shock wave. Recall that downstream of the shock wave the flow is isentropic and subsonic till the nozzle exit, with increasing static pressure. 4. Calculate the back pressure for the flow through nozzle to be isentropic (without shock wave) expanded to the design supersonic Machnumber (curve 5). Hint: Use isentropic flow table.
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Related Book For
Engineering Fluid Mechanics
ISBN: 9781118880685
11th Edition
Authors: Donald F. Elger, Barbara A. LeBret, Clayton T. Crowe, John A. Robertson
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