de Laval nozzle
Similar flow properties have been applied to jet streams within astrophysics.
[2] Later, Swedish engineer Gustaf de Laval applied his own converging diverging nozzle design for use on his impulse turbine in the year 1888.
[3][4][5][6] Laval's convergent-divergent nozzle was first applied in a rocket engine by Robert Goddard.
Most modern rocket engines that employ hot gas combustion use de Laval nozzles.
Its operation relies on the different properties of gases flowing at subsonic, sonic, and supersonic speeds.
At the "throat", where the cross-sectional area is at its minimum, the gas velocity locally becomes sonic (Mach number = 1.0), a condition called choked flow.
As the nozzle cross-sectional area increases, the gas begins to expand, and the flow increases to supersonic velocities, where a sound wave will not propagate backward through the gas as viewed in the frame of reference of the nozzle (Mach number > 1.0).
A de Laval nozzle will choke at the throat only if the pressure and mass flow through the nozzle is sufficient to reach sonic speeds; otherwise no supersonic flow is achieved, and it will act as a Venturi tube.
In addition, the pressure of the gas at the exit of the expansion portion of the exhaust of a nozzle must not be too low.
Because pressure cannot travel upstream through the supersonic flow, the exit pressure can be significantly below the ambient pressure into which it exhausts, but if it is too far below ambient, then the flow will cease to be supersonic, or the flow will separate within the expansion portion of the nozzle, forming an unstable jet that may "flop" around within the nozzle, producing a lateral thrust and possibly damaging it.
The analysis of gas flow through de Laval nozzles involves a number of concepts and assumptions: As the gas enters a nozzle, it is moving at subsonic velocities.
From there the throat the cross-sectional area then increases, allowing the gas to expand and the axial velocity to become progressively more supersonic.
As an example calculation using the above equation, assume that the propellant combustion gases are: at an absolute pressure entering the nozzle p = 7.0 MPa and exit the rocket exhaust at an absolute pressure pe = 0.1 MPa; at an absolute temperature of T = 3500 K; with an isentropic expansion factor γ = 1.22 and a molar mass M = 22 kg/kmol.
By Newton's third law of motion the mass flow rate can be used to determine the force exerted by the expelled gas by:
