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LS6: Injector Design
Send questions to Alex Koenig (koe@mit.edu)
Relevant links for further reading!
https://en.wikipedia.org/wiki/Liquid-propellant_rocket#Types_of_injectors
Why use injectors at all?
Although fuel and oxidizer could theoretically be directly piped into the combustion chamber with no special mechanisms, doing so would have disastrous consequences for both the efficiency and stability of the combustion. The purpose of the injector is to deliver fuel and oxidizer to the combustion chamber in a manner such that the propellants atomize and mix within the combustion chamber as thoroughly as possible. The more thoroughly the propellants mix, the more the propellants will actually end up combusting, so the injector is key to obtaining high engine efficiency -- any uncombusted fuel that escapes the engine is wasted, which is more likely to happen with imperfect injector designs. The droplet size of individual fuel and oxidizer particles is also ideally reduced by a good injector design, which additionally helps achieve thorough combustion.
Even if the combustion efficiency is very high, the system is of no use if the combustion becomes unstable and Something Breaks. The injector is a critical component in maintaining combustion stability. The general stability failure modes are when there is an oscillation the combustion which forces the system into a negative feedback loop -- for those of you who are in or plan to take 18.03 and/or 8.03, you’ll learn this as the concept of “resonance”. As a hopefully not-too-tangential demonstration of this concept, imagine pushing someone on a swing. Pushing them at the natural frequency the swing will move at when it is untouched results in the person ending up going higher and faster than if you push them back and forth randomly with no respect to the frequency of the swinging. Unlike with the swing, the goal of the injector is to damp action at these natural frequencies (“modes”) rather than excite or amplify them. These modes can also be reduced by introducing baffles and acoustic cavities that change the geometry and thus resonant frequencies of the chamber.
As another interesting note about injectors in liquid engines, in almost all other engine types (internal combustion engines, gas turbine engines, etc.), fuel and oxidizer enter the combustion chamber premixed. For those of you familiar with general aviation aircraft engines and older car engines, you will know the premixer as a carburetor. Bipropellant liquid rocket engines are fairly unique in that fuel and oxidizer are intended to only make contact upon entering the combustion chamber, primarily due to their volatility -- many fuel-oxidizer combinations are prone to detonation when mixed, particularly at the high pressures and velocities experienced within the fluid system upstream of the engine, so we keep them unmixed outside of the combustion chamber.
Helios injector layout
In a typical injector design, propellants first enter the manifold behind the injector, where they get evenly spread across the injector plate; then propellants are forced through small orifices (holes) in the injector plate, and become mixed inside the combustion chamber. Such is the design for the Helios engine, which is depicted in the diagrams below.
Fig. 1: a cross-section of the Helios engine. The manifold consists of two separate ring-shaped chambers, the innermost of which is filled with oxidizer, and the outermost of which is filled with fuel. The orifices direct propellant from the manifold into the combustion chamber. Note how the orifices are directed towards each other so that fuel and oxidizer impinge (collide) and thus become mixed.
Fig. 2: a top-down view of the Helios injector, more clearly showing the shape of the two ring-shaped chambers that comprise the manifold, along with the 16 orifices that allow propellant into the combustion chamber. (The large holes furthest away from the center of the injector plate are just for bolts to hold the injector plate onto the combustion chamber.)
Main categories of injection schemes
Non-impinging
In non-impinging injection schemes, propellants are sprayed into the engine but the streams do not directly collide with other propellants. In general, these injectors achieve the most stable combustion out of all categories, but are the most complex and difficult to machine.
I would be amiss not to point out the pintle injector in particular (bottom left). The pintle injector has had increasing fame in recent years for its use in the SpaceX Merlin engine, among others -- it is unique in its ability to achieve deep and fast throttling capabilities (i.e., to go from “lots of thrust” to “very little thrust”) while maintaining stable combustion. This has made it an ideal choice for propulsive landings, since when the spacecraft is about to land, it has expended almost all of its fuel and therefore has a significantly higher thrust-to-weight ratio than it needs to hover -- deep throttling allows the rocket to achieve a more appropriate level of thrust.
To point out another famous system, the Space Shuttle main engines (RS-25 engines) -- which are now in use for the Space Launch System -- employ coaxial elements (top right).
Like-impinging
In like-impinging injectors, fuel streams impinge on other fuel streams, and oxidizer streams impinge on other oxidizer streams. These are generally not quite as stable as non-impinging injectors, but are often favorable due to their relative ease to machine -- the only machining operations required are drilling small holes at angles such that the fuel and oxidizer impinges.
(Notably, used in the Rocketdyne F-1 engine of the Saturn V rockets!)
Unlike-impinging
In unlike-impinging injectors, fuel and oxidizer impinge on each other. Generally these achieve the least stable combustion compared to other injector schemes, but that does not necessarily mean that they are unstable, per se, just that it presents a greater design concern. It is also the case that these are the easiest to machine, which is why they were selected for use in the Helios engine (as well as the previous Viper engine), since Helios was intended to be the simplest possible bipropellant engine that we could make. These happen to be a more common choice for systems which use liquid oxygen as the oxidizer.
The table above gives a good overview of attributes of like- and unlike-impinging injector elements. Doublets refer to those which have 2 orifices per impingement; triplets have 3. (Like-impinging injectors have double the orifices per element because each ‘element’ consists of one fuel like-impinging injector and one oxidizer like-impinging injector, rather than one injector for both, as in the unlike-impinging system).
Injector element geometries
The following equations are referenced with regard to like and unlike doublets in particular, since those are the ones we most closely work with in liquid prop, but the same equations hold for other injector types as well.
Sizing
Where q = mass flow rate (kg/s), K = head-loss coefficient, ρ = fluid density (kg/m3), and ΔP = pressure drop (Pa). The pressure drop will be discussed more further on in this LSET; it is the primary parameter around which the injector area is changed in order to achieve a certain value (the other parameters like fluid density are typically known by the time the injector area is determined).
Note: the injector area is the sum of areas of each individual injector element. Therefore orifice diameter is as follows:
Where N is the number of orifices.
Number
One might start to wonder why we don’t use a very large number of very small orifices in order to achieve the best mixing of fuel and oxidizer in the chamber. Indeed, if designing purely for performance alone, we would! But alas, we also have to machine these parts ourselves, and the more orifices we employ, the more holes we have to drill and the longer it takes -- a consideration that might seem inconsequential until you’re the one assigned to machine it, and you have to stay up until midnight drilling holes into a chunk of steel when you still have a pset due tomorrow and a midterm the day after (do I speak from experience? No… well, maybe… ). In the Helios design, we used 8 unlike doublets, for a total of 16 orifices.
Angle
When the fuel and oxidizer streams impinge on each other, conservation of momentum implies the streams (on average) continue on their path in a certain new direction, specified by the “beta angle” of the stream. For our purposes, we try to achieve a small but non-zero beta angle so as to direct the propellants away from the chamber walls (so combustion happens away from the walls, keeping them cooler) but also so they still end up going mostly in the axial direction, further down into the chamber. The beta angle is calculated as follows:
Where β is the resultant stream angle with respect to the central axis of the combustion chamber, α is the stream angle, and v is the velocity of the fluid. The diagram below will help illustrate this equation a bit.
Note: The fuel and oxidizer streams will typically be at different angles because they each have different momentum associated with them (due to having different densities and flow velocities).
Impingement distance
The impingement distance (i.e., the distance away from the injector face that the streams impinge on each other) is a worthwhile factor to consider. For one, this distance determines how deep into the chamber mixing begins. For another, changing the distance may result in a different likelihood that the streams actually impinge even despite slight machining imperfections -- at very aggressive α angles and/or far impingement distances, one might imagine the streams are less likely to collide if the orifices are slightly askew. On both the Helios and Viper injectors, the impingement distance is on the order of 1 cm. The distance can be changed by altering the width between the orifices as well as the angle of the orifices, although the width is generally predetermined by the manifold sizing and machining capabilities.
Oxidizer vs. fuel -- outer or inner directions?
In the diagram above, one fluid stream points inward towards the central axis of the chamber, and the other points in the opposite direction towards the chamber wall. Generally, injection elements are arranged with the LOX orifices angled towards the chamber wall and ethanol orifices angled towards the central axis. This provides minor film cooling with the spray deflection on the outer ring angled back towards the chamber wall (the LOX is at cryogenic temperatures, of course, and so can cool down the chamber wall upon contact, assuming it has not yet been combusted by that point). The opposite arrangement would expose the chamber wall to oxidizer spray and contribute to corrosion and deterioration, although that consideration in particular is not a significant factor for the Helios engine since it is only designed to fire for a few seconds.
Manifold
As briefly mentioned in the Helios injector layout section, the manifold is the component upstream of the injectors which is intended to evenly distribute the flow across all the injector elements/orifices so as to achieve even combustion. In the Helios design, there is one manifold section for LOX, and one for ethanol; both are annulus-shaped cavities in the injector plate. Even distribution of propellants by the manifold generally dictates the use of large passageways, rounded corners, and smooth finishes; friction, cavitation sites, turbulence, and restrictions in the pathway are detrimental to consistent mass flow. Manifolds for different engines can take on a wide variety of forms, but for our purposes the ‘best’ designs are ones which evenly distribute propellants, are easy to manufacture, and don’t require complicated sealing mechanisms.
Pressure drops
Any fluid flow that is constricted or restrained in some way has an associated pressure drop in the fluid at the point of constriction. For injectors, this also holds true, since the injector represents a point of constriction for the flow of the fuel and oxidizer. The pressure drop can be altered by changing the orifice size, and it is important to understand how to properly size the orifices so as to achieve an appropriate pressure drop.
There are conflicting design trades associated with the amplitude of the pressure drop. A low pressure drop is desirable to minimize feed system mass and pumping power, since there is less resistance associated with forcing the liquid through the orifice. High pressure drops, on the other hand, are often used to increase a rocket engine’s resistance to combustion instabilities and to enhance atomization of the liquids, thereby improving performance. The pressure drops help prevent against the propagation of any disturbances upstream of the injectors from inducing oscillations in the combustion, which is why they assist with reducing instability. They enhance atomization of the fuel and oxidizer because greater pressure drops increase the velocity (and therefore momentum) of the fluids, thereby With regards to these conflicting design goals, a good rule of thumb is that the injection flow resistance should be 20% of the chamber pressure. For example, the Helios system is designed to achieve a chamber pressure of 500 psi, suggesting the pressure drop across the injectors should be 100 psi.
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