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For the sake of this discussion, we will only consider centrifugal pumps – but if you are doing rockets and not using hydrogen, that is a good assumption. The pump on a rocket is broken up into 3 main parts: the inducer, the impeller, and the volute. The inducer is a low pressure rise pump that  limits cavitation in the impeller; it is only necessary for high specific speed pumps, which is most of rocketry. The impeller is the main pumping element and is effectively a paddle wheel that takes slow moving fluid from the core and ejects it at high speed from its sides. The volute takes the high speed fluid and slows it down, converting the high speed to high pressure. All told, they make up a rocket pump, but we will just go over the basic sizing of the impeller and not worry about fun things like velocity triangles today.

All of the basics of a standard rocket pump from SP-125.
All of the basics of a standard rocket pump from SP-125.
A specific petrol impeller I did for some people from aRocket.
A specific petrol impeller I did for some people from aRocket.

Once you have done all of the basic sizing that we talked about last week, you have the basic properties of the pump system but no sizes. If you want to do a detailed pump sizing, I would recommend NASA SP-125 and SP-8109 as it is a bit more complicated than a blog post. But, today, let’s get you the two biggest pieces of information you need: outlet diameter and outlet height. These are useful to determine the mass and manufacturability of the pump, as outlet height is usually the smallest geometry and diameter of the impeller and, thus, the volute determines most of the mass properties for a pump.

The process for exit diameter is iterative and consists of the following equations (everything in ft, GPM, ft/s, and RPM):

Head_Coefficient = gravity * Head_Rise / (Tip_Velocity)^2

Specific_Diameter = Tip_Diameter * Head_Rise^0.25 / Flowrate^0.5

Tip_Diameter = Tip_Velocity / (pi * RPM)

Then use the plot below.

Head Coefficient as a function of Specific Speed and Specific Diameter (from SP 8109).
Head Coefficient as a function of Specific Speed and Specific Diameter (from SP 8109).

So now iterate on that for a bit, and we have the outlet diameter.

To find the exit height the equation is:

Exit_Height (in) = Flow_Rate(GPM) / (3.12 * pi * exit_diameter(in) * exit_radial_velocity(ft/s) * contraction_factor)

where the contraction factor is usually estimated as 0.9 and the radial velocity can be estimated by:

exit_radial_velocity = flow coefficient * tip_velocity

Flow coefficient is usually between 0.01 and 0.15 and can be found on the plow below.

Flow Coefficient plot from NASA SP-8109.
Flow Coefficient plot from NASA SP-8109.

I hope this has all been useful in determining how to size a impeller; obviously the final design is more complicated with flow angles, but these basics should point you in the correct direction.

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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.