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De Laval nozzle
A de Laval nozzle (or convergent-divergent nozzle, CD nozzle or con-di nozzle) is a tube that is pinched in the middle, making an hourglass-shape. It is used as a means of accelerating the flow of a gas passing through it to a supersonic speed. It is widely used in some types of steam turbine and is an essential part of the modern rocket engine and supersonic jet engines.
The nozzle was developed by Swedish inventor Gustaf de Laval in the 19th century. Its operation relies on the different properties of gases flowing at subsonic and supersonic speeds. The speed of a subsonic flow of gas will increase if the pipe carrying it narrows because the mass flow rate is constant (grams or pounds per second). The gas flow through a de Laval nozzle is isentropic (gas entropy is nearly constant). At subsonic flow the gas is compressible; sound, a small pressure wave, will propagate through it. Near the nozzle "throat", where the cross sectional area is a minimum, the gas velocity locally becomes transonic (Mach number = 1.0), a condition called choked flow. As the nozzle cross sectional area increases the gas continues to expand and the gas flow increases to supersonic velocities where a sound wave will not propagate backwards through the gas as viewed in the rest frame of the nozzle (Mach number > 1.0).
A de Laval nozzle using hot air at a pressure of 1,000 psi (6.9 MPa or 68 atm), temperature of 1470 K, would have a pressure of 540 psi (3.7 MPa or 37 atm), temperature of 1269 K at the throat, and 15 psi (0.1 MPa or 1 atm), temperature of 502 K at the nozzle exit. The expansion ratio, nozzle cross sectional area at exit divided by area at throat, would be 6.8. The specific impulse would be 151 s (1480 N·s/kg).
This principle was used in a rocket engine by Robert Goddard. Walter Thiel's implementation of it made the V2 rocket possible.
Conditions for operation
A de Laval nozzle will only choke at the throat if the mass flow through the nozzle is sufficient, otherwise no supersonic flow is achieved.
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 ambient pressure it exhausts into, 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, possibly damaging it.
In practice ambient pressure must be no higher than roughly 2.7 times the pressure in the supersonic gas for supersonic flow to leave the nozzle.
Analysis of gas flow in de Laval nozzles
The analysis of gas flow through de Laval nozzles involves a number of concepts and assumptions:
Exhaust gas velocity
As the gas enters a nozzle, it is traveling at subsonic velocities. As the throat contracts down the gas is forced to accelerate until at the nozzle throat, where the cross-sectional area is the smallest, the linear velocity becomes sonic. From the throat the cross-sectional area then increases, the gas expands and the linear velocity becomes progressively more supersonic.
Some typical values of the exhaust gas velocity Ve for rocket engines burning various propellants are:
As a note of interest, Ve is sometimes referred to as the ideal exhaust gas velocity because it based on the assumption that the exhaust gas behaves as an ideal gas.
As an example calculation using the above equation, assume that the propellant combustion gases are: at an absolute pressure entering the nozzle of P = 7.0 MPa and exit the rocket exhaust at an absolute pressure of Pe = 0.1 MPa; at an absolute temperature of T = 3500 K; with an isentropic expansion factor of k = 1.22 and a molar mass of M = 22 kg/kmol. Using those values in the above equation yields an exhaust velocity Ve = 2802 m/s or 2.80 km/s which is consistent with above typical values.
The technical literature can be very confusing because many authors fail to explain whether they are using the universal gas law constant R which applies to any ideal gas or whether they are using the gas law constant Rs which only applies to a specific individual gas. The relationship between the two constants is Rs = R/M.
|This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "De_Laval_nozzle". A list of authors is available in Wikipedia.|