A Quick Guide to Pintle Injectors in Liquid Rocket Engines
Thought about the best way to pickup information is to repeat them elsewhere, I have resorted to this medium (haha). I will first publish my articles but continue to update them over time, sorry if they’re incomplete by the time you’re reading them!
If you are new to LRE injector design, pintle injectors works by the formation of a conical propellant spray via the collision between a radial (that is typically the oxidizer)and annular sheet of fluid (fuel). A beautiful figure of a pintle injector with several key design variables labelled is shown below.
The injector features a central pintle that redirects the incoming fluid to become a radial flow, which then impinges on the incoming annular flow to form a hollow cone pattern. It’s a relatively simple design (relative to the co-axial) with good throttle ability that promotes stable combustion.
For some details related to the pintle’s advantages, we begin with recirculation zones. Due to the spray cone, there are typically two recirculation zones named the mantle recirculation and core recirculation zones if the engine is to be sized to for these zones that is. Both of these zones are advantageous.
Typically, one wants to maximize the core recirculation zone as that correspond to a better mixing and higher combustion efficiency by virtue of increased residence time. Mantle recirculation zone is useful in the fact that most of it is unburnt propellant which you can think of behaves like a “shield” or a protective buffer between the hot core flame and the chamber walls. It reduces the thermal loads on the injector overall.
Large-scale engines that have used a pintle injector include SpaceX’s Merlin series (1A to 1D that provided up to ~850 kN @ sea level w/ RP-1/LOX), to the Apollo Lunar Module Descent Engine (LMDE with ~45 kN w/ Aerozine50/N2O4).
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Currently, I am in my process of trying to better understand the optimization algorithms so won’t be able to elaborate much there. Though I can tell you about the variables that you should optimize and tune in those processes. Those variables are:
- L_open, D_pt, δ_sleeve, θ_pt, L_min, and A_min
Which correspond to the pintle opening distance, pintle tip diameter, pintle sleeve thickness, pintle tip angle, lower limit of the pintle opening distance, and the minimum area between the sleeve and pintle tip. For the details I recommend to just go through the paper:
A Numerical Approach to Optimize the Design of a Pintle Injector for LOX/GCH4 Liquid-Propellant Rocket Engine by Jihyoung Cha, Erik Andersson, and Alexis Bohlin https://www.mdpi.com/2226-4310/10/7/582
Do note that these variables and equations you find in the paper tells you how to find the numbers geometrically, but choking conditions etc you do have to evaluate yourselves. Anyways, here’s how to determine if your injector is actually “good.” There are three primary things you can look at.
- Sauter Mean Diameter (SMD): This is one of the most important number when it comes to defining the effectiveness of an injector. When the propellant is sprayed, droplets vary in size, so an average is needed but not a simple one. Since combustion depends on surface area, SMD gives more weight to both droplet volume and surface area. It represents the diameter of a droplet that has the same volume-to-surface-area ratio as the entire spray which makes it a more meaningful average for droplet size determination.
- Vaporization Distance: This is the distance liquid droplets takes to vaporize after it passes through the injector. A shorter vaporization is preferred as it allows for better mixing and longer residence time.
- There is also the spray cone angle which is pretty explanatory. This number do proceed with caution because it alters the heat needed to be managed by your LRE.
For details related to throttling, there are two primary ways. The most obvious way, is to move the pintle. This is achieved by adding some sort of actuator that extends/contracts the length of the pintle tip and thereby adjust the length open (pintle opening distance). The obvious downside is that you may only change the flow rate of what the central fluid may be. This can alter your O/F ratio if that is a concern. Perhaps you are trying to avoid a oxidizer-rich burn that higher the critical heat flux (CHF) you’re trying to manage.
The second way is to adjust the length of the sleeve. See the diagram and you should be able to understand. You can maintain the O/F ratio by modifying the sleeve-annular angle, though the downside is of course that it’s harder to manufacture.
But of course, all injectors have its limitations. The largest when it comes to pintles is non-uniform heat flux. Think about it like this, you have pintle that produces radially symmetric spray pattern, but due of nature of that spray and impingement you are likely to get localized thermal stress on the chamber wall that either requires you to increase the overall cooling capacity or complicate the regen cooling layout for those specific hotspots. There is also tip erosion that needs to be cared for as it’s directly exposed to the chamber heats.
It is also not as efficient in mixing and atomization when compared to multi-element coaxial that are designed to maximize specific impulse. NASA also reports that pintles show a lower combustion efficiency (though can still reach as high as 92%).
I’ll be back soon, hopefully.
