- 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 gaspassing through it to a supersonicspeed. It is widely used in some types of steam turbineand is an essential part of the modern rocket engineand supersonic jet engines.
Similar flow properties have been applied to jet streams within
astrophysics. ref label|Clarke|1|^
The nozzle was developed by Swedish inventor
Gustaf de Lavalin 1897 for use on an impulse steam turbine. [ [http://www.cambridge.org/uk/catalogue/catalogue.asp?isbn=9780521819831&ss=exc Fundamentals of Jet Propulsion with Applications - Cambridge University Press ] ]
This principle was used in a rocket engine by Robert Goddard, and very nearly all modern rocket engines that employ hot gas combustion use de Laval nozzles.
Its operation relies on the different properties of gases flowing at
subsonicand supersonicspeeds. The speed of a subsonic flow of gas will increase if the pipe carrying it narrows because the mass flow rateis constant. The gas flow through a de Laval nozzle is isentropic (gas entropyis nearly constant). At subsonic flow the gas is compressible; sound, a small pressure wave, will propagate through it. At the "throat", where the cross sectional area is a 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 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 frame of reference of the nozzle ( Mach number> 1.0).
Conditions for operation
A de Laval nozzle will only choke at the throat if the pressure and mass flow through the nozzle is sufficient to reach sonic speeds, 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 2-3 times the pressure in the supersonic gas at the exit 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:
* For simplicity, the gas is assumed to be an
* The gas flow is isentropic (i.e., at constant
entropy). As a result the flow is reversible(frictionless and no dissipative losses), and adiabatic (i.e., there is no heat gained or lost).
* The gas flow is constant (i.e., steady) during the period of the
* The gas flow is along a straight line from gas inlet to exhaust gas exit (i.e., along the nozzle's axis of symmetry)
* The gas flow behavior is compressible since the flow is at very high
Exhaust gas velocity
As the gas enters a nozzle, it is traveling at
subsonicvelocities. 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. The linear velocity of the exiting exhaust gases can be calculated using the following equation:ref label|Nakka|1|^ ref label|Braeunig|2|^ ref label|Sutton|3|^
Some typical values of the exhaust gas velocity "V"e for rocket engines burning various propellants are:
* 1.7 to 2.9 km/s (3,800 to 6,500 mph) for liquid
* 2.9 to 4.5 km/s (6,500 to 10,100 mph) for liquid
* 2.1 to 3.2 km/s (4,700 to 7,200 mph) for solid propellants
As a note of interest, "V"e 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 gasor whether they are using the gas law constant "R"s which only applies to a specific individual gas. The relationship between the two constants is "R"s = "R"/"M".
For example a de Laval nozzle using hot air at a
pressureof 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 impulsewould be 151 s (1480 N·s/kg).
Application to celestial objects
Theoretical astrophysicists have found that pipes with the flow pattern of a De Laval nozzle have analogous phenomena in the
interstellar medium. The interior of an accretion diskhas a similar function as the pipe, save it is not a solid wall, but itself a fluid that can contain a relativistic jetby a pressure balanced boundary.
Rocket engine nozzles
Twister Supersonic Separatorfor natural gas treatment
Active galactic nucleus
History of the internal combustion engine
#note label|Clarke|1|^cite book | author= Clarke, C. J. & Carswell B. | title=Principles of Astrophysical Fluid Dynamics, chpt 9.2| edition=1st Edition | pages=226 | publisher=Cambridge University Press | year=2007| id= 978-0521853316
#note label|Nakka|2|^ [http://www.nakka-rocketry.net/th_nozz.html Richard Nakka's Equation 12]
#note label|Braeunig|3|^ [http://www.braeunig.us/space/propuls.htm#intro Robert Braeuning's Equation 2.22]
#note label|Sutton|4|^cite book | author=Sutton, George P. | title=Rocket Propulsion Elements: An Introduction to the Engineering of Rockets| edition=6th Edition | pages=636 | publisher=Wiley-Interscience | year=1992 | id= 0471529389
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