Diagram of a de Laval nozzle, showing approximate flow velocity increasing from green to red in the direction of flow

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. Image File history File links De_laval_nozzle. ... Image File history File links De_laval_nozzle. ... Rocket Nozzle A nozzle is a mechanical device designed to control the characteristics of a fluid flow as it exits from an enclosed chamber into some medium. ... For other uses, see Gas (disambiguation). ... A United States Navy F/A-18E/F Super Hornet in transonic flight. ... A rotor of a modern steam turbine, used in a power plant A steam turbine is a mechanical device that extracts thermal energy from pressurized steam, and converts it into useful mechanical work. ... RS-68 being tested at NASAs Stennis Space Center, note the relatively transparent exhaust, this is due to this engines use of hydrogen fuel A rocket engine is a reaction engine that takes all its reaction mass from within tankage and forms it into a high speed jet... A Pratt and Whitney turbofan engine for the F-15 Eagle is tested at Robins Air Force Base, Georgia, USA. The tunnel behind the engine muffles noise and allows exhaust to escape. ...

Similar flow properties have been applied to jet streams within astrophysics. ^[1] Spiral Galaxy ESO 269-57 Astrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties (luminosity, density, temperature, and chemical composition) of celestial objects such as stars, galaxies, and the interstellar medium, as well as their interactions. ...

History

The nozzle was developed by Swedish inventor Gustaf de Laval in 1897 for use on an impulse steam turbine.^[1] Gustaf de Laval The former De Laval steam turbine factory, now converted to a conference centre, in Nacka, outside Stockholm Gustaf Patrik de Laval (May 9, 1845 - February 2, 1913) was a Swedish engineer and inventor who made important contributions to the design of steam turbines and dairy machinery. ... A rotor of a modern steam turbine, used in a power plant A steam turbine is a mechanical device that extracts thermal energy from pressurized steam, and converts it into useful mechanical work. ...

This principle was used in a rocket engine by Robert Goddard. Walter Thiel's implementation of it made the V2 rocket possible, and very nearly all modern rocket engines that employ hot gas combustion use de Laval nozzles. Robert Goddard Robert Hutchings Goddard (October 5, 1882 – August 10, 1945) was one of the pioneers of modern rocketry. ... Walter Thiel (March 2, 1910 - August 17, 1943) was a German engineer who largely designed the rocket engine that powered the V-2 missile. ... German test launch. ...

Operation

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. 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. 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). Subsonic has two possible meanings: A speed lower than the speed of sound is called subsonic. ... A United States Navy F/A-18E/F Super Hornet in transonic flight. ... Mass flow rate is the movement of mass per time. ... An isentropic process (a combination of the Greek word iso -same- and entropy) is one during which the entropy of working fluid remains constant. ... For other uses, see: information entropy (in information theory) and entropy (disambiguation). ... This article is about audible acoustic waves. ... Longitudinal waves are waves that have vibrations along or parallel to their direction of travel. ... Choked flow is a hydrodynamic condition caused by the Venturi effect. ... An F/A-18 Hornet at transonic speed and displaying the Prandtl-Glauert singularity just before reaching the speed of sound Mach number (Ma) (generally pronounced , sometimes or ) is the speed of an object moving through air, or any fluid substance, divided by the speed of sound through that substance...

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 ideal gas.
• 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 propellant burn.
• 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 velocities.

An ideal gas or perfect gas is a hypothetical gas consisting of identical particles of zero volume, with no intermolecular forces, where the constituent atoms or molecules undergo perfectly elastic collisions with the walls of the container and each other and are in constant random motion. ... An isentropic process (a combination of the Greek word iso -same- and entropy) is one during which the entropy of working fluid remains constant. ... For other uses, see: information entropy (in information theory) and entropy (disambiguation). ... A reversible process (or reversible cycle if the process is cyclic) , in thermodynamics, is a process that can be reversed by means of infinitesimal changes in some property of the system (Sears and Salinger, 1986). ... In thermodynamics, an adiabatic process or an isocaloric process is a thermodynamic process in which no heat is transferred to or from the working fluid. ... A propellant is a material that is used to move an object by applying a motive force. ... A compressible flow is a situation in which the compressibility of a fluid must be taken into account. ... This article is about velocity in physics. ...

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. Subsonic has two possible meanings: A speed lower than the speed of sound is called subsonic. ... An F/A-18 Hornet at transonic speed and displaying the Prandtl-Glauert singularity just before reaching the speed of sound Mach number (Ma) (generally pronounced , sometimes or ) is the speed of an object moving through air, or any fluid substance, divided by the speed of sound through that substance... A United States Navy F/A-18E/F Super Hornet in transonic flight. ...

The linear velocity of the exiting exhaust gases can be calculated using the following equation:^{[1] [2] [3]}

Some typical values of the exhaust gas velocity V_e for rocket engines burning various propellants are: For other uses, see Temperature (disambiguation). ... The gas constant (also known as the molar, universal, or ideal gas constant, usually denoted by symbol R) is a physical constant which is featured in a large number of fundamental equations in the physical sciences, such as the ideal gas law and the Nernst equation. ... The molecular mass (abbreviated Mr) of a substance, formerly also called molecular weight and abbreviated as MW, is the mass of one molecule of that substance, relative to the unified atomic mass unit u (equal to 1/12 the mass of one atom of carbon-12). ... The adiabatic index of a gas, is the ratio of its specific heat capacity at constant pressure (CP) to its specific heat capacity at constant volume (CV). ... Specific heat capacity, also known simply as specific heat, is the measure of the heat energy required to increase the temperature of a unit quantity of a substance by a certain temperature interval. ... This article is about pressure in the physical sciences. ... For other uses, see Pascal. ...

• 1.7 to 2.9 km/s (3,800 to 6,500 mph) for liquid monopropellants
• 2.9 to 4.5 km/s (6,500 to 10,100 mph) for liquid bipropellants
• 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. A (usually liquid) rocket propellant that can be used by itself, without the need for a second component. ... F-1 rocket engine (The kind used by the Saturn V.) A bipropellant rocket is a rocket that uses separate fuel and oxidizer propellants. ... The Space Shuttle is initially launched with the help of solid-fuel boosters A Solid rocket or a solid fuel rocket is a rocket with a motor that uses solid propellants (fuel/oxidizer). ...

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 P_e = 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 V_e = 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 R_s which only applies to a specific individual gas. The relationship between the two constants is R_s = R/M. An ideal gas or perfect gas is a hypothetical gas consisting of identical particles of zero volume, with no intermolecular forces, where the constituent atoms or molecules undergo perfectly elastic collisions with the walls of the container and each other and are in constant random motion. ...

Examples

For example 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 article is about pressure in the physical sciences. ... A pressure gauge reading in PSI (red scale) and kPa (black scale) The pound-force per square inch (symbol: lbf/in²) is a non-SI unit of pressure based on avoirdupois units. ... For other uses, see Kelvin (disambiguation). ... Specific impulse (usually abbreviated Isp) is a way to describe the efficiency of rocket and jet engines. ...

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 disk has a similar function as the pipe, save it is not a solid wall, but itself a fluid that can contain a relativistic jet by a pressure balanced boundary. The interstellar medium (or ISM) is the name astronomers give to the tenuous gas and dust that pervade interstellar space. ... An accretion disc (or accretion disk) is a structure formed by material falling into a gravitational source. ... Relativistic Jet. ...

See also

• Spacecraft propulsion
• Rocket engine
• Rocket engine nozzles
• Choked flow
• Twister Supersonic Separator for natural gas treatment
• Active galactic nucleus

A remote camera captures a close-up view of a Space Shuttle Main Engine during a test firing at the John C. Stennis Space Center in Hancock County, Mississippi Spacecraft propulsion is any method used to change the velocity of spacecraft and artificial satellites. ... RS-68 being tested at NASAs Stennis Space Center, note the relatively transparent exhaust, this is due to this engines use of hydrogen fuel A rocket engine is a reaction engine that takes all its reaction mass from within tankage and forms it into a high speed jet... Figure 1: A de Laval nozzle, showing approximate flow velocity increasing from green to red in the direction of flow The main type of rocket engine nozzles used in modern rocket engines is the de Laval nozzle which is used to expand and accelerate the combustion gases, from burning propellants... Choked flow is a hydrodynamic condition caused by the Venturi effect. ... An active galaxy is a galaxy where a significant fraction of the energy output is not emitted by the normal components of a galaxy: stars, dust and interstellar gas. ...

References

1. ^ Fundamentals of Jet Propulsion with Applications - Cambridge University Press

1. ^{^} Clarke, C. J. & Carswell B. (2007). Principles of Astrophysical Fluid Dynamics, chpt 9.2, 1st Edition, Cambridge University Press, 226. 978-0521853316. 
2. ^{^} Richard Nakka's Equation 12
3. ^{^} Robert Braeuning's Equation 2.22
4. ^{^} Sutton, George P. (1992). Rocket Propulsion Elements: An Introduction to the Engineering of Rockets, 6th Edition, Wiley-Interscience, 636. 0471529389.