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Isentropic flow through Nozzles
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One-Dimensional Isentropic Flow Variation of Fluid Velocity with Flow Area
• This is an important relationship
– For Ma < 1, (1 - Ma2) is positive
dA and dP have the same sign and dV has opposite sign. • Pressure of fluid must increase as the flow area of the duct
increases, and must decrease as the flow area decreases
– For Ma > 1, (1 - Ma2) is negative dA and dP have opposite signs and dV has same sign. • Pressure must increase as the flow area decreases, and must
decrease as the area increases
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Comparison of flow properties in subsonic and supersonic nozzles and diffusers
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Subsonic -Subsonic Subsonic- Subsonic (Chocked)
Subsonic – Supersonic (Chocked) Supersonic-Supersonic (chocked)
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Supersonic – Subsonic (Chocked) Supersonic-supersonic (not-choked)
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Isentropic Flow Through Nozzles Converging Nozzles
• Under steady flow conditions, mass flow rate is constant
• Substituting T and P from the expressions on slides 23 and 24 gives – Mass flow rate is a function of stagnation properties, flow
area, and Ma
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Isentropic Flow Through Nozzles Converging Nozzles
• The maximum mass flow rate through a nozzle with a given throat area A* is fixed by the P0 and T0 and occurs at Ma = 1
• This principal is important for chemical processes, medical devices, flow meters, and anywhere the mass flux of a gas must be known and controlled.
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Isentropic Flow Through Nozzles Converging-Diverging Nozzles
• The highest velocity in a converging nozzle is limited to the sonic velocity (Ma = 1), which occurs at the exit plane (throat) of the nozzle
• Accelerating a fluid to supersonic velocities (Ma > 1) requires a diverging flow section – Converging-diverging (C-D) nozzle
– Standard equipment in supersonic aircraft and rocket propulsion
• Forcing fluid through a C-D nozzle does not guarantee supersonic velocity – Requires proper back pressure Pb
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Isentropic Flow Through Nozzles Converging-Diverging Nozzles
P0 > Pb > Pc
– Flow remains subsonic, and mass flow is less than for choked flow. Diverging section acts as diffuser
Pb = PC
– Sonic flow achieved at throat. Diverging section acts as diffuser. Subsonic flow at exit. Further decrease in Pb has no effect on flow in converging portion of nozzle
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