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In some turbopump designs, propellant is burned and used to power the pumps; then it is dumped overboard. This causes a reduced specific impulse, because not all all the propellant is expelled through the nozzle in an efficient way.

However, some designs don't dump any propellant overboard; for example, in a closed expander cycle, fuel is pumped in at an extremely high pressure, then expanded using heat from the combustion chamber / nozzle (which powers the pumps), and then finally enters the combustion chamber.

What I don't understand is how this could achieve less than a perfect effiency, since all the energy consumed eventually ends up going back to the fuel; an inefficient turbopump simply heat up the fuel slightly, and an inefficent turbine powering the pump simply means that less energy is extracted from the fuel in the first place. In the end, all that energy ends up in the combustion chamber.

Obviously, this can't be right, so what am I missing?

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    $\begingroup$ The RL10 has extremely good specific impulse so I'm not sure you are really incorrect. The biggest problem with this cycle that I know of is that it's hard to scale up to big engines. $\endgroup$ – Organic Marble Mar 25 '16 at 18:45
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    $\begingroup$ I'm not sure I understand the point of the question. Some heat energy is radiated away laterally; some kinetic energy is wasted in sideways motion of the exhaust in underexpanded nozzles; some energy is locked up in molecular vibration modes that don't contribute to thrust (yarchive.net/space/rocket/fuels/fuel_ratio.html), and depending on the mixture ratio and injector efficiency, propellant may not be completely combusted. $\endgroup$ – Russell Borogove Mar 25 '16 at 23:30
  • $\begingroup$ @RussellBorogove I know its been a while but... I'm assuming radiation, sideways exhaust motion, and other vibration modes don't contribute to inefficiency that much. What DOES contribute is dumping many kilograms per second of fuel overboard, which is: not used as a reaction mass (to the extent that it could be), and also equates to megawatts of thermal energy loss in large engines. So it seems silly to design an engine that does dump propellant overboard, or maybe I am underestimating how hard it is to design a fully closed cycle engine? $\endgroup$ – BWG Apr 13 '16 at 3:16
  • $\begingroup$ That's why staged combustion (closed cycle) engines produce higher specific impulse than gas-generator (open cycle) engines, all other things being equal. Expander cycle is fairly simple, but definitely has a size limit. The WP articles on the various cycles gives a good overview of the tradeoffs. en.wikipedia.org/wiki/Gas-generator_cycle en.wikipedia.org/wiki/Staged_combustion_cycle $\endgroup$ – Russell Borogove Apr 13 '16 at 15:01
  • $\begingroup$ Note that in gas generator engines, the turbopump exhaust generally is dumped in the right direction; in cases like the F-1, it's recycled into the nozzle as a cooler curtain to protect the nozzle from the primary chamber exhaust. Getting the last of the thermal energy out of it (by combusting it at a stoichiometric ratio) would require a weightier cooling solution! $\endgroup$ – Russell Borogove Apr 13 '16 at 15:04
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The part of propellant burned in the gas generator has a lower temperature than that in the combustion chamber. When the gas from the generator passed the turbine the temperature decreases further. In the combustion chamber this gas with a lower temperature is mixed with the other hot gas, the resulting temperature is a little lower. Lower temperature means a little less pressure and little less exhaust velocity and therefore a little less efficiency. No propellant mass flow is lost for the turbo pumps, but a little heat loss means a loss of energy.

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