an introduction and guidelines

(and way more details on how I designed an injector than you probably ever need, all in the the context of Herald’s development) By Max Oberg

Warning: This was written in the context of Caltech’s PARSEC Rocketry Group’s work, and was meant to be an introductuory resource for brand new members who wanted to learn more. I tried to make it as least jargony as possible, and make it (to the degree I could possible) the least worst to read. There will be bad joke attempts scattered through out, and it was written as informally as a mildly composed text message. It also uses old images of hardware designs, and things that I have long since changed, but until I have the time to go back over this, I’m presenting it as is. With that context: enjoy……

The original PDF link can be found here/on my github

Warning 2 : Units are everywhere. I may be referring to kg in one section, and lbs in the next. I wish it wasn’t this way but someone decided to ignore the French in the 1800s and now it’s out of my hands. Screw you 1950s paper on annular orifice discharge coefficients specifically. (And for future reference, Herald is an engine developed by the Parsec team at Caltech)

Nomenclature

ṁ = mass flow rate ⍴ = density 𝑢 = velocity Cd = Discharge Coefficient V̇ = volumetric flow rate A = area ΔP = pressure difference/stiffness N = number of central pintle shaft orifices d = diameter BF = Blockage Factor

(1950s paper terms below)

G = mass flow rate through an orifice, ṁ/area μ = fluid absolute viscosity CC = coefficient of stream contraction in an orifice F = fraction of maximum pressure recovery due to stream expansion from the vena contracta to full annulus area actually recovered in an orifice 𝑓𝑝 = friction factor for flow between parallel plates of

infinite width Z = concentric annular length-to-width ratio L = orifice thickness/length

Subscripts

exp = expected
ideal = value dealing with ideal flow
fuel = value dealing with fuel characteristics
ox = value dealing with oxidizer characteristics
p = dealing with pintle shaft
oa = outer annular orifice

Introduction

Every rocket engine will typically have a few preset parameters before you approach the design
of an injector, fuel/oxidizer choice, mixture ratio and mass flow rates of your propellants, and the chamber
pressure of your engine.
Before we use these values however, some aspects of fluids need to be discussed. Injectors on a
fundamental level are plates of metal with holes in them. One of the only questions that needs to be
asked is how big to make said holes. With a certain set mass flow rate, density, and injection velocity, one
can calculate an ideal area for which the hole (or orifice) should be ideally sized. This can be seen below.

I have not finished converting this to a markdown format and will return to finish this.