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Is there any way to know the weight of Fuel / Oxidizer consumed by just the turbo pumps of the RS-25 rocket engine?

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  • $\begingroup$ I rolled back your edits. The advice someone gave you about editing was bad, because there is already an answer here. Once answers begin to appear we don't change the questions. I think that your new question is fine as long as you add some evidence of research effort. $\endgroup$
    – uhoh
    Jan 27 at 12:59

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The RS-25 is a staged combustion engine, so the question does not really make sense. Almost all the fuel is sent to the preburners and passes through the high pressure turbines. Much of the oxygen is dumped straight into the main combustion chamber without passing through the turbines.

The preburners operate very fuel-rich so much of the hydrogen passing through them is not combusted. But all the exhaust gas from the preburners serves to drive the turbines, and then passes into the main combustion chamber. So the bulk of the hydrogen is used as hot gas to drive the turbines and is then burned in the main combustion chamber. For this kind of engine, you can't say "this amount of fuel drives the turbine and is set aside just for that."

enter image description here

(Ignore the purple arrows, that was for a different question: https://space.stackexchange.com/a/36010/6944)

The question would make more sense for a gas generator engine where a small portion of the inlet flow is dedicated to producing hot gas to drive turbine(s).

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  • $\begingroup$ Whats actually driving the pumps? $\endgroup$ Jan 27 at 12:28
  • $\begingroup$ All (most) of the h2 and some of the o2 is sent to preburners. The hot h2 rich preburner exhaust drives the high pressure turbines. $\endgroup$ Jan 27 at 12:32
  • $\begingroup$ Were still combusting H2 + O to drive them, yes? $\endgroup$ Jan 27 at 12:37
  • $\begingroup$ But uncombusted h2 flows through the turbines. It is "used by the turbopumps" $\endgroup$ Jan 27 at 12:38
  • $\begingroup$ But there still must be a molecular quantity of of H2 + O, responsible for powering them. $\endgroup$ Jan 27 at 12:40
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The easiest way to figure out the fuel used for the turbines and pumps is to base it off of the flow rate of the lean reactant. In the case of both turbines/pumps, that reactant is oxygen. Its flow rate is 68 lbs/sec for the hydrogen pump and 25 lbs/sec for the oxygen pump.

enter image description here

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We know that these pumps are operating fuel rich because the stochiometric ratio of the reaction is 2:1 hydrogen/oxygen, and Oxygen is 16 times heavier than hydrogen. So, to figure out how much fuel is used in the pre-burners, just need apply that ratio.

$$ConsumptionRate_{H2}/mass_{H2} = 2{\times}ConsumptionRate_{O2}/mass_{O2}$$

Since the reaction is fuel rich all of the O2 is consumed; therefore, $ConsumptionRate_{O2}=FlowRate_{O2}$, so...

$$ConsumptionRate_{H2} = 2{\times}FlowRate_{O2}{\times}mass_{H2}/mass_{O2}$$

The problem with this approach is that the fuel is used both to power the pumps and to heat up the reactants, so this might not be exactly what you want.

You can also work out the power extracted by the turbopumps with

$$W=m(h_{inlet}-h_{outlet})$$

Where:

$W$ is the power,

$m$ is the mass flow rate, and

$h$ is the specific enthalpy of the gas.

However, the specific enthalpy is generally a function of both temperature and pressure, and the relationships can be complex. The specific enthalpy can be obtained from thermodynamic tables or charts, or by using specialized software.

You could do this calculation over the pumps, which would enable you to use pure hydrogen or pure oxygen for your enthalpy calculations, but would neglect some energy lost to the turbine's inefficiency.

You could do this calculation over the turbine itself, which would avoid inaccuracy due to turbine inefficiency but would make it more difficult to calculate the correct inlet and outlet enthalpies of the gas.

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  • $\begingroup$ It shows how much h2 goes to the preburners on the diagram. I know how much was combusted. The point is that it all flows through the turbine, combusted or not. $\endgroup$ Jan 28 at 2:48
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    $\begingroup$ Yes, but the H2 flow rate doesn't represent how much of the H2 was combusted since it's operating fuel rich. Your answer did not explain how to figure out how much H2 is combusted in the turbine and my answer adds that information. BTW, your figure is very helpful! $\endgroup$
    – phil1008
    Jan 28 at 3:12
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    $\begingroup$ I improved the answer a bit to help to address your comment. $\endgroup$
    – phil1008
    Jan 28 at 3:26
  • $\begingroup$ I looked back and found my notes from working on the SSME model in the Shuttle Mission Simulator. The equation we derived agrees with yours. The mass flowrate of the H2 consumed burning in an excess of O2 is 0.125 * the O2 mass flowrate. So the unburned H2 out of the preburner is the H2 mass flowrate in - 0.125 * the O2 mass flowrate. $\endgroup$ Jan 29 at 18:26

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