Properly calculating flow rates in an engine with multiple propellants

[Nertea]

I'm trying to calculate the electric charge ratio to put in an engine cfg for an engine that has multiple propellants with varying ratios. No matter what I try my equations don't seemt o match up with what I get ingame, so I thought I'd post here. I have this easily working for a single propellant engine (like the stock ion engine) but multiple fuels stump me. I'll explain my approach.

First calculate the mass flow rate for the engine:

mass flow rate (t/s) = thrust (kN) / (specific impulse (s) * g0)

Then for each fuel (let's call them A and B), I then calculate the fractional fuel consumption for each fuel.

fuel frac A = (fuel ratio A / sum of all fuel ratios)
fuel frac B = (fuel ratio B / sum of all fuel ratios)

Then I calculate the unit flow rate for each propellant:

unit flow rate A  (u/s) = (mass flow rate (t/s) * fuel frac A ) / density A (t/u)
unit flow rate B (u/s) = (mass flow rate (t/s) * fuel frac B ) / density B (t/u)

Then I sum the fuel consumption

total flow rate (u/s) = unit flow rate A (u/s) + unit flow rate B (u/s)

Then multiply the inverse by the desired electricity consumption

charge ratio = 1 / (total flow rate (u/s)) * desired EC use (u/s)

That works well for single propellants, but for multiple propellants it really screws up - I don't even get the same unit flow rates from the math above as the VAB shows ingame. And the charge use is of course totally off. 

Any idea what I'm doing wrong? I expect it's something in how I handle the ratios between fuels but Im kinda stumped!

 

 

[blowfish]

I think the step you're missing is the mixture density, which allows you to convert from mass flow rate to unit flow rate.  The mixture density would be the weighted sum of all the propellant densities

(mixture ratio) = SUM (propellant density * propellant ratio) / SUM(propellant ratio)

If you divide the mass flow rate by the mixture ratio, you will get the unit flow rate, then you can multiply by the (normalized) propellant ratio to get the flow rate in units per second for each propellant

[Nertea]

That did the trick! Thanks @blowfish! I actually don't even need to go to the flow rate per second, I just need the unit flow rate, which I can then multiply by the sum of all fuel ratios. Dividing the Ec required by that number gets me what I want for the cfg Ec ratio. 

Edited August 2, 2016 by Nertea