In some previous posts, I have added some Isp’s and, if you have been looking closely, they seem a little lower than expected. This is because I have been looking at gas generator cycles and in these cycles some small percentage of the flow goes thru a gas generator and does not go through the main engine. Due to a bunch of reasons like not wanting to burn the pump up in seconds and needing pressure to drive the turbines, the flow is at a much lower temperature and pressure than the main engine. To account for this we need to:
Estimate the amount of flow in the Turbine – This is a simple energy balance equation that usually comes down to around 3% for a 1000 psi LOX RP-1 engine.
Calculate the Isp from the Engine (easy, lets assume 270 s SL) and the turbopump. Now for temperature ~1000 F and low pressure, ~40 psia, so they have Isp’s of around 80 seconds.
So now you throw them into the equations:
Isptot = (1-%turbine) * IspMainEngine + (%turbine) * IspTurbine.
Or, for our example, = (0.97 * 270 + 0.03 * 80) = 264 s.
As you can easily see, Isp is significantly lower ~2.5% and this is with fairly moderate pressure. As you can image for a certain cycle, there is an optimum pressure; higher isn’t always better as far as gas generator cycles are concerned. This being said, for LOX RP-1, the tipover point with reasonable efficiencies is about 1500-2000 psi PC, so if you look around you see a lot of engines and studies for GG at around 1200 psi. Higher than this requires multiple impellers and isn’t worth the extra complexity for the very negligible gains of the next couple hundred psi.