Nozzles

Gas flow through nozzles - sonic chokes

The maximum gas flow through a nozzle is determined by the critical pressure.

• The critical pressure ratio is the pressure ratio which will accelerate the flow to a velocity equal to the local velocity of sound in the fluid.

Critical flow nozzles are also called sonic chokes. By establishing a shock wave the sonic choke establish a fixed flow rate unaffected by the differential pressure, any fluctuations or changes in downstream pressure. A sonic choke may provide a simple way to regulate a gas flow.

The ratio between the critical pressure and the initial pressure for a nozzle can expressed as

p_c / p₁ = ( 2 / (n + 1) )^{n / (n - 1)}         (1)

where

p_c = critical pressure (Pa)

p₁ = inlet pressure (Pa)

n = index of isentropic expansion or compression - or polytropic constant

For a perfect gas undergoing an adiabatic process the index - n - is the ratio of specific heats - k = c_p / c_v. There is no unique value for - n. Values for some common gases are

• Steam where most of the process occurs in the wet region : n = 1.135
• Steam superheated : n = 1.30
• Air : n = 1.4
• Methane : n = 1.31
• Helium : n = 1.667

Example - Air Nozzles and Critical Pressure Ratios

The critical pressure ratio for an air nozzle can be calculated as

p_c / p₁ = ( 2 / (1.4 + 1) )^{1.4 / (1.4 - 1)}

    = 0.528

Critical pressures for other values of - n: 

n	1.135	1.300	1.400	1.667
pc / p1	0.577	0.546	0.528	0.487

Mass Flow through Nozzles

The mass flow through a nozzle with sonic flow where the minimum pressure equals the critical pressure can be expressed as

m_c = A_c (n p₁ ρ₁)^1/2 (2 / (n + 1))^{(n + 1)/2(n - 1)}          (2)

where

m_c = mass flow at sonic flow (kg/s)

A_c = nozzle area (m²)

ρ₁ = initial density (kg/m³)

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