Finding the mass flow rate of a blowdown system?

Question

This is a rather amateur question I will admit but how does one find the mass flow rate of an engine with a given tank pressure? Is it really as simple as calculating the cross-section of all plumbing, subtracting the delta-p reductions (bends, wall friction/boundary layers, and other things) from your tank pressure, and then multiplying by the number of injectors or something of that nature?

Answer 1

There are several approaches, only differentiated by how big a budget you have and how accurate you want the answer - quite plausibly according to where you are in the programme / development proposal etc.

First iteration: Just assume the thruster nozzle governs the mass flow rate and its completely expanded to ambient and that its discharge coefficient is 1.0. Assume the tank pressure is the same as the chamber pressure.

A bit more effort: Make hand calculation estimates for the pipework manifold and injector delta-P so as to improve the chamber pressure estimate.

Have rather more time on your hands: Come up with some fancy analysis to determine which is the dominant feature amongst all of the pipework manifold, injector, nozzle elements.

Really need to know: Test it with representative components.

Details (EDIT) For the first step the simplifying assumption that the tank pressure is the same as the chamber relies on the idea that the main pressure drop is across the nozzle. Its just a way of getting started so that you can size the tank very roughly. As its a blow-down system a typical application could be a satellite with low thrust levels (<=20N) and 1/4' pipes a couple of metres long. If you really want to have high thrust, tortuously long pipe runs and narrow pipes then you'd need to work out their delta-P contribution.