User:Mbeychok/MRB's sandbox: Difference between revisions
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'''This is for developing articles and contributions.''' |
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[[Image:De laval nozzle.svg|right|thumb|250px|Diagram of a de Laval nozzle, showing approximate flow velocity increasing from green to red]] |
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'''Gas [[flow through nozzles]]''' can be greatly accelerated by using properly shaped nozzles such as a [[convergent-divergent nozzle]] also known as a [[De Laval nozzle]]. Such nozzles are used in modern [[rocket engines]] to accelerate the [[combustion]] gases, from burning [[propellants]], so that the exhaust gases exiting the nozzles are at [[supersonic]] velocities. |
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==Analysis of gas flow in rocket engine nozzles== |
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The analysis of gas flow through rocket nozzles involves a number of concepts and assumptions: |
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* For simplicity, the combustion gas is assumed to be an ''ideal gas''. |
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* The gas flow is isentropic (i.e., at constant entropy), frictionless, and adiabatic (i.e., there is little or no heat gained or lost) |
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* The gas flow is constant (i.e., steady) during the period of the propellent 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'' since the flow is at very high velocities. |
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==Maximum exhaust gas velocity== |
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As the combustion gas enters the rocket nozzle, it is traveling at subsonic velocities. At the nozzle throat, where the cross-sectional area is the smallest, the linear velocity becomes sonic. As the cross-sectional area then increases, the gas expands and the linear velocity becomes supersonic. This improves the ''thrust'' of the rocket because the higher velocities increase the the thrust. |
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The maximum linear velocity of the exiting exhaust gases can be calculated by using the following equation: |
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:<math>V_e = \sqrt{\;\frac{T\;R}{M}\cdot\frac{2\;k}{k-1}\cdot\bigg[ (1-(P_e/P)^{k/(k-1)}\bigg]} </math> |
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{| border="0" cellpadding="2" |
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|align=right|where: |
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!align=right| ''V<sub>e</sub>'' |
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|align=left|= Exhaust velocity at nozzle exit, m/s |
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!align=right| ''T'' |
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|align=left|= absolute temperature of inlet gas, K |
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!align=right| ''R'' |
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|align=left|= Universal gas law constant = 8,314.5 (N·m) / (kgmol·K) |
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!align=right| ''M'' |
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|align=left|= the gas molar mass, kg/kgmol (also known as the molecular weight) |
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!align=right| ''k'' |
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|align=left|= c<sub>p</sub>/c<sub>v</sub> = isentropic expansion factor |
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!align=right| ''c<sub>p</sub>'' |
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|align=left|= specific heat of the gas at constant pressure |
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!align=right| ''c<sub>v</sub>'' |
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|align=left|= specific heat of the gas at constant volume |
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!align=right| ''P<sub>e</sub>'' |
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|align=left|= absolute pressure of exhaust gas at nozzle exit, Pa |
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!align=right| ''P'' |
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|align=left|= absolute pressure of inlet gas, Pa |
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|}<br> |
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http://members.aol.com/ricnakk/th_nozz.html equation 12 |
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http://www.braeunig.us/space/propuls.htm#intro equation 2.22 |
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{{fluiddynamics-stub}} |
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[[Category:Fluid dynamics]] |
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