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| [[Image:Nozzle de Laval diagram.svg|right|thumb|250px|Diagram of a de Laval nozzle, showing approximate flow velocity (v), together with the effect on temperature (T) and pressure (p)]]
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| A '''de Laval nozzle''' (or '''convergent-divergent nozzle''', '''CD nozzle''' or '''con-di nozzle''') is a tube that is pinched in the middle, making a carefully balanced, asymmetric hourglass-shape. It is used to accelerate a hot, pressurized [[gas]] passing through it to a [[supersonic]] speed, and upon expansion, to shape the exhaust flow so that the heat energy propelling the flow is maximally converted into directed [[kinetic energy]]. Because of this, the [[nozzle]] is widely used in some types of [[steam turbines]], and is used as a [[rocket engine nozzle]]. It also sees use in supersonic [[jet engines]].
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| Similar flow properties have been applied to [[Jet (fluid)|jet streams]] within [[astrophysics]].<ref>{{cite book| author= C.J. Clarke and B. Carswell|title=Principles of Astrophysical Fluid Dynamics|edition=1st|pages=226| publisher=Cambridge University Press|year=2007|ISBN= 978-0-521-85331-6}}</ref>
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| ==History==
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| The nozzle was developed by [[Sweden|Swedish]] inventor [[Gustaf de Laval]] in 1888 for use on a [[steam turbine]].<ref>British patent 7143 of 1889.</ref><ref>{{cite book|author=Theodore Stevens and Henry M. Hobart|title=Steam Turbine Engineering|edition=|publisher=MacMillan Company|year=1906|pages=24–27|ISBN=}} Available on-line [http://books.google.com/books?id=9ElMAAAAMAAJ&pg=PA27&lpg=PA26&ots=i9N3YYNjIF&ie=ISO-8859-1&output=html here] in Google Books.</ref><ref>{{cite book|author=Robert M. Neilson|title=The Steam Turbine|edition=|publisher=Longmans, Green, and Company|year=1903|pages=102–103|ISBN=}} Available on-line [http://books.google.com/books?id=ODhMAAAAMAAJ&pg=PA102&lpg=PA102&ots=WYaRaosiiM&ie=ISO-8859-1&output=html here] in Google Books.</ref><ref>{{cite book| author=Garrett Scaife|title=From Galaxies to Turbines: Science, Technology, and the Parsons Family|edition=|publisher=Taylor & Francis Group|year=2000|pages=197|ISBN=}} Available on-line | |
| [http://books.google.com/books?id=BeMjgxsifcQC&pg=PA197&lpg=PA197&source=bl&ots=VpRffcaLG2&sig=mNb8dGDFErN8mgmo79HN6Dpa2DM&hl=en&ei=jMkjS82WFJHIlAew4IH9CQ&sa=X&oi=book_result&ct=result&resnum=10&ved=0CCUQ6AEwCTgU here] in Google Books.</ref> | |
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| This principle was first used in a rocket engine by [[Robert Goddard (scientist)|Robert Goddard]]. Very nearly all modern rocket engines that employ hot gas combustion use de Laval nozzles.
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| ==Operation==
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| Its operation relies on the different properties of gases flowing at [[Speed of sound|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 process#Isentropic flow|isentropic]] (gas [[entropy]] is nearly constant). At subsonic flow the gas is compressible; [[sound]], a small [[longitudinal wave|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 begins 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).
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| ==Conditions for operation==
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| 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 and it will act as a [[Venturi tube]]; this requires the entry pressure to the nozzle to be significantly above ambient at all times (equivalently, the [[stagnation pressure]] of the jet must be above ambient).
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| 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.
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| 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.
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| ==Analysis of gas flow in de Laval nozzles==
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| The analysis of gas flow through de Laval nozzles involves a number of concepts and assumptions:
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| * For simplicity, the gas is assumed to be an [[ideal gas]].
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| * The gas flow is [[Isentropic process#Isentropic flow|isentropic]] (i.e., at constant [[entropy]]). As a result the flow is [[Reversible process (thermodynamics)|reversible]] (frictionless and no dissipative losses), and [[adiabatic process|adiabatic]] (i.e., there is no heat gained or lost).
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| * The gas flow is constant (i.e., steady) during the period of the [[propellant]] burn.
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| * The gas flow is along a straight line from gas inlet to exhaust gas exit (i.e., along the nozzle's axis of symmetry)
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| * The gas flow behavior is [[compressible flow|compressible]] since the flow is at very high [[velocities]] (Mach number > 0.3).
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| ==Exhaust gas velocity==
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| As the gas enters a nozzle, it is traveling at [[Speed of sound|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 [[mach number|sonic]]. From the throat the cross-sectional area then increases, the gas expands and the linear velocity becomes progressively more [[supersonic]].
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| The linear velocity of the exiting exhaust gases can be calculated using the following equation:<ref>[http://www.nakka-rocketry.net/th_nozz.html Richard Nakka's Equation 12.]</ref><ref>[http://www.braeunig.us/space/propuls.htm#intro Robert Braeuning's Equation 1.22.]</ref><ref>{{cite book|author=George P. Sutton| title=Rocket Propulsion Elements: An Introduction to the Engineering of Rockets|edition=6th|pages=636| publisher=Wiley-Interscience|year=1992|isbn=0-471-52938-9}}</ref> | |
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| :<math>v_e = \sqrt{\frac{TR}{M} \cdot \frac{2\gamma}{\gamma - 1} \cdot \left[1 - \left(\frac{p_e}{p}\right)^{\frac{\gamma - 1}{\gamma}}\right]}</math>
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| {| border="0" cellpadding="2"
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| |align=right|where:
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| !align=right|<math>v_e</math>
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| |align=left|= Exhaust velocity at nozzle exit, m/s
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| !align=right|<math>T</math>
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| |align=left|= absolute [[temperature]] of inlet gas, K
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| !align=right|<math>R</math>
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| |align=left|= [[gas constant|Universal gas law constant]] = 8314.5 J/(kmol·K)
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| !align=right|<math>M</math>
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| |align=left|= the gas [[molecular mass]], kg/kmol (also known as the molecular weight)
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| !align=right|<math>\gamma</math>
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| |align=left|= <math>\frac{c_p}{c_v}</math> = [[adiabatic index|isentropic expansion factor]]
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| !align=right|<math>c_p</math>
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| |align=left|= [[specific heat capacity|specific heat]] of the gas at constant pressure
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| !align=right|<math>c_v</math>
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| |align=left|= specific heat of the gas at constant volume
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| !align=right|<math>p_e</math>
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| |align=left|= [[pressure|absolute pressure]] of exhaust gas at nozzle exit, [[pascal (unit)|Pa]]
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| !align=right|<math>p</math>
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| |align=left|= absolute pressure of inlet gas, Pa
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| |}
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| Some typical values of the exhaust gas velocity ''v''<sub>e</sub> for rocket engines burning various propellants are:
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| * 1,700 to 2,900 m/s (3,800 to 6,500 mph) for liquid [[monopropellant]]s
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| * 2,900 to 4,500 m/s (6,500 to 10,100 mph) for liquid [[bipropellant]]s
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| * 2,100 to 3,200 m/s (4,700 to 7,200 mph) for [[solid rocket|solid propellant]]s
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| As a note of interest, '''''v<sub>e</sub>''''' 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.
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| 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<sub>e</sub>''''' = 0.1 MPa; at an absolute temperature of '''''T''''' = 3500 K; with an isentropic expansion factor of '''''γ''''' = 1.22 and a molar mass of '''''M''''' = 22 kg/kmol. Using those values in the above equation yields an exhaust velocity '''''v<sub>e</sub>''''' = 2802 m/s or 2.80 km/s which is consistent with above typical values.
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| 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<sub>s</sub>''''' which only applies to a specific individual gas. The relationship between the two constants is '''''R<sub>s</sub>''''' = '''''R/M'''''.
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| ==See also==
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| *[[Active galactic nucleus]]
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| *[[Choked flow]]
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| *[[Giovanni Battista Venturi]]
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| *[[Gustaf de Laval]]
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| *[[History of the internal combustion engine]]
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| *[[Rocket engine]]
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| *[[Rocket engine nozzles]]
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| *[[Spacecraft propulsion]]
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| *[[Twister Supersonic Separator]] for natural gas treatment
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| *[[Venturi tube]]
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| *[[Venturi effect]]
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| ==References==
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| {{Commons category|Convergent-divergent nozzles}}
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| <references />
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| [[Category:Nozzles]]
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| [[Category:Rocket propulsion]]
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| [[Category:Jet engines]]
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| [[Category:Astrophysics]]
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| [[es:Tobera#Tobera De Laval]]
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Formerly a association struggle begins, you will see The particular War Map, a good map of this showdown area area association battles booty place. Warm and friendly territories will consistently wind up being on the left, accompanied by the adversary association just in the right. Almost every boondocks anteroom on most of the war map represents some sort or other of war base.
The actual amend delivers a information of notable enhancements, arch of which could turn out to be the new Dynasty Competition Manner. In specific mode, you can designed combating dynasties and alleviate utter rewards aloft her beat.
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