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LS6: Injector Design
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There are a few general metrics and areas that we should always take into consideration to try and evaluate both whether our design does relatively well and whether the design will work within the rest of our engine’s physical constraints. Of course, there will typically be even more metrics that are used in the research literature for different injector designs, and those which should also be considered , but are not covered here.
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But how would we find it, anyway? In some cases, we can estimate the droplet size using published empirical formulas (based on the chosen injector design/flow characteristics). We can also use computational fluid dynamics methods (abbr. CFD) to computationally model the flow and estimate it that way. CFD is a little difficult to learn and use properly, though, but it is a very popular tool for verifying flow characteristics.
Impingement distance
The impingement distance can be defined as the axial distance the propellant travels before impinging with the other propellant. This is an important metric because it tells you at about what point in the combustion chamber you can expect most mixing to begin, and subsequently, a general idea of after where combustion will happen, which is good to know for thermal analysis and making sure your injector doesn’t melt. |
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The injector gets its name from the pintle-shaped bit (that green knob thing on the far right of the figure below) that allows the central flow (the red below) to turn from going towards the nozzle exit to spraying radially, more towards the chamber walls. It then impinges directly onto the outer flow (the blue below) which is going axially down the chamber. The result of their combined flow is a cone of liquid film.
→ From feed system | → Nozzle exit |
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A few theories exist to explain this inherent combustion stability, but it is most likely due to two things: the pintle’s central position in the chamber, and its recirculation zones. These recirculation zones zones are an important characteristic of pintle injectors, and and are where uncombusted propellants form (their own respective) loops in the chamber. Here, they deflect the incoming flow, and depending on the thermal profile, can either heat or cool the pintle tip and the chamber walls (it’s kinda complicated!).
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Of course, no design has only advantages. The pintle injector design can be susceptible to undesirable heating both on the pintle tip itself and on the chamber walls. As such, the pintle injector is often complemented by a dedicated cooling system (like regenerative cooling or film cooling!).
Coaxial swirl
The coaxial swirl injector, as the name suggests, uses two coaxial tubes (called swirlers) that swirl their propellants. Once either propellant exits their its swirler, it sprays into a cone of liquid film. Depending on the desired behavior, the cones can be made to collide with each other before reaching the chamber wall or not. Check out this video to see a coldflow cold flow test of a coaxial swirl injector.
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The primary advantages of a coaxial swirl design are:
Relatively stable across a large range of mass flow rates, allowing for higher mass flow rates than other designs
This is because the mixing and atomization processes that occur in the chamber are less sensitive to any pressure fluctuations or flow velocity variations with this design , since pressure oscillations within the swirling flow itself help stabilize external oscillations
Don’t worry if that doesn’t make much sense!
Better atomization of propellants in the cone sheets leads to smaller droplet sizes which also allows for better mixing
Also, the swirling gives the propellants radial, in addition to axial, momentum, meaning they have more time to mix when they enter the chamber
Reduced worry of combustion instabilities
On the other hand, this design is not good for very viscous propellants because of the behavior of the swirlers, which reduces the atomization of these kinds of propellants. In addition, modeling the flow behavior inside the swirlers can become quite complex, especially in the inner swirler because of the presence of a central gas core that forms as the propellants swirl around.
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Inner/External Mixing A lot of design choices can be made that affect the overall behavior of this type of injector. One of the major choices is choosing whether to design for inner or external mixing. External mixing is when the inner and outer cones are able to exit directly into the combustion chamber and mix that way. Internal mixing is when the outlet for the inner swirler is recessed far back enough such that the inner cone collides with the wall of the outer swirler, pictured to the right. |
This choice primarily affects the flow behavior (internal mixing can be more difficult to model), and the resultant angle, but there isn’t very much research to back up giving a more specific description than this.
One final note: researching the coaxial swirl injector can be very difficult because a lot of the work on this type of injector was done by Soviet rocket engineers, and most of their records are no longer available , or were simply never published. For this reason, you’ll find conflicting information and many different names referring to the same thing (e.g. coax swirls are also known as bi-swirl coax, duplex, double simplexes, etc.). On the other hand, it has been used previously by NASA and notably by SpaceX’s Raptor engine, so information might be found through their organizations.
Non-primary injection
This is a very general class of injection that typically involves just designing holes or slots that serve a different purpose than the primary injector. Typically these are non-impinging holes implemented for cooling purposes within the chamber.
The most common of these is called film cooling. This is when some of the fuel or oxidizer is diverted from the main flow and injected almost parallel onto the walls of the combustion chamber. This forms a protective film of coolant along the chamber wall, which helps keep the chamber wall cool, as illustrated below.
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Upstream of the injector
What occurs upstream of the injector is very important to the design of the injector. Before the propellants enter the injector, several properties must be known in order to properly develop the geometry of the injector.
Feed system inputs
From the feed system, we must know the mass flow rate of both propellants, the total drop in pressure from their initial reservoir pressure, and the actual properties of either propellant (density, boiling point, etc.). It’s useful to be very familiar with the actual behavior of the fluids, and knowing how, for example, viscosity may play a role in the injection of the propellants can be critical.
Knowing the feed system inputs allows us to determine the desired aspects of the injector from the desired outputs of the entire engine – remember, think of the injector as the interface between the feed system and the rest of the engine.
Among the most important outputs of the system are the resulting mass flow rates, the pressure drop, and the vaporization length.
A good rule of thumb for initial injector design is that the drop in pressure across an orifice be 20% of the chamber pressure (we discuss more about on how to design for this later). This is also referred to as the stiffness of the injector. The relatively large difference in pressure forcefully pushes the propellants through the orifices with high velocity, which is vital to combustion stability. Without that high velocity out of the orifice, the propellants could be subject to flow dribble, where they tend to pool up at the orifice exit, causing poor mixing and hindering the flow into the chamber.
Pressure drop and flow rates also have some effect on combustion stability, but that’s a very difficult topic that we won’t cover very much here.
Manifold
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The manifold is a space that properly reroutes the feed system propellant flow into the injector. It can also be thought of as an interface – this time between the feed system and the injector orifices. Below is a diagram of the Pyralis injector, with the fuel manifold in orange and the oxidizer manifold in green.
These spaces are specifically designed to evenly distribute the propellants across the face of the injector, allowing them to flow properly through the orifices. The manifold can also be vital for changing some aspects of the flow. For example, introducing a constriction in the manifold (called a venturi) is often used in pintle injectors to speed up the flow before it exits the orifices.
An important consideration for both manifold and injector design is whether to have the fuel or the oxidizer be the centermost propellant on the face of the injector. This decision has 2 consequences:
Any central propellant that does not directly impinge with the other propellant will go on to collide directly with the chamber wall.
Typically, the oxidizer is at a lower temperature than the fuel (most of the time, the oxidizer is cryogenic LOX). This allows us to use that unimpinged propellant as an auxiliary coolant for the chamber walls.
The outer propellant must be routed to the injector and comes in contact with more surface of the material used to make the injector.
If this outer propellant is LOX, we have to make sure that this material is compatible with LOX. Most materials are not compatible with LOX, which means it could cause problems like autoignition (very bad!!).
This is doubly so if the outer propellant is used for regenerative cooling , because then it must flow through the entire length of the chamber, and so the entire chamber would have to be rated for LOX as well.
As such, we typically design manifolds as ox-centered, but these are this is not always the case.
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Injector Geometry
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It’s difficult to give a general overview of the geometry of the injector because it varies from design to design, but there are a couple of key principles that mostly apply to all kinds of injectors. If you begin to work with injectors more closely, you’ll find more detailed design procedures and metrics that you need to account for depending on the design that you choose.
Number of elements/orifices
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The term element usually refers to the independent set of things that make up a unit of the injector, and varies from design to design. For example, in an impinging jet doublet, a pair of holes is an element, while in a coax swirl, the entire structure is an element.
You can have more than one element, and in some cases, like the impinging jet designs, you will have several of these. Deciding how many elements your injector will have is important because it directly affects the output of the injector (in terms of mass flow, propellant spread, etc.), but also can change other aspects of the geometry of each element.
The main consideration for each element is the size of their orifices. In general, the term orifice refers to a hole, but can also refer to a slot, annulus, or any general ‘exit’ for the propellant into the combustion chamber. Having more elements typically requires each element to have smaller orifices in order to supply the same mass flow, as you will see below.
Sizing
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The sizing of orifices in any injector element typically comes from knowing the desired mass flow rate ṁ out of that orifice and the desired pressure drop Δ𝑃 across that orifice. Using the equation below, we can find 𝐴, the area needed for that orifice.
The two other variables, 𝐶d and 𝜌, are the coefficient of discharge and the density of the fluid going through the orifice, respectively.
The coefficient of discharge is a nondimensional number that tells us what fraction of mass flow going through an orifice actually ‘gets through’. We can define it as the ratio of actual mass flow to theoretical mass flow out the end of an orifice, and so is between 0 and 1. We usually take an empirical estimate of this number based on the shape of the orifice (e.g. sharp corners experience more flow loss than round corners, so have a lower 𝐶d, illustrated below).
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This equation can also be used in reverse, taking a given area (or diameter of hole) and finding the resulting mass flow through that orifice. This can be very useful if there are hard-set manufacturing limits, and is also useful for designing non-primary injection.
In general, a larger number of smaller holes will result in more spread of your propellant, and allow for better mixing and atomization throughout the combustion chamber.
Knowing this, you might wonder why we don’t just use a very large number of very small holes to achieve the best performance. In fact, if all we cared about was engine performance, we would! The reason we don’t is because we also have to make the engine ourselves, and choosing to design such precise and difficult-to-machine parts is incredibly tedious and, in some cases, impossible.
As such, always be mindful of the actual manufacturing of the injector when sizing it. Oftentimes, the part will be machined by hand, and you don’t want to be the reason someone is stuck drilling 70 very precise 0.5 mm holes the night before their midterm (and you certainly don’t want to be that person yourself!).
And another note, having a relatively large number of orifices can bring up even more concerns regarding combustion stability, due to more fine patterns causing more unstable energy/pressure fluctuations, but that’s not a topic we’ll delve into very deeply.
Angles
There are 2 important angles to keep track of in the design of the injector: the angle at which the propellant enters the combustion chamber, and the resultant angle of the fluids after impingement. Knowing the entry angle can typically get you a very good idea of the resultant angle if you also know the momentums of the two streams.
Knowing the resultant angle is critical because you want the fluids to combust axially downwards, towards the nozzle exit, and not towards the chamber walls. In some cases, it is sufficient to use this equation, derived from basic collision kinematics (from high school physics!), to find the resultant angle,
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Where ṁ is the mass flow rate, v is the velocity, the subscripts 1 and 2 refer to either propellant, and the angles are illustrated below.
In general, you want the resultant angle to be very close to zero (i.e. going straight down the chamber towards the nozzle exit). Note that we have to use ṁv, the fluid’s momentum per second (units Newtons) because the flow is a moving continuous mass.
Sometimes, though, this approximation does not match empirical data, like with pintle injectors (among other designs or variations). In these cases, there are often published empirical formulas that can be used to acquire a better approximation of the resultant angle.
Orifice length
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The actual length of the orifice, from entry to exit, is actually an important factor in determining the behavior of the fluid flow across the injector. What we want is an orifice large enough to avoid flow separation, a phenomenon we won’t really discuss but just know that it can amplify flow losses – when the flow loses energy (and thus is slower, and can sometimes cause even more problems at the orifice exit or within the stream flow into the chamber). In addition, ensuring the orifice is an adequate size helps us also better avoid the problem of flow dribble that we mentioned earlier.
Most literature agrees that a good rule of thumb (at least for simple impinging jet orifices) is that the ratio of the orifice length to the orifice diameter (its L/d) should be at least 5. Having slightly less than this is sometimes ok, but it’s best to aim for at least that, and not have an incredibly long orifice.
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Summary
If you remember nothing from above, or just don’t wanna read all that, at least remember these points!
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