Max Kwon, Hope Fu, John Posada
Created: 12/7/2020
Last Modified: 12/7/2020
This document outlines our research on injector design during the Fall 2020 semester.
Our main topic is Unlike Doublet Impinging Injector Design.
Injector Basics
What is an injector?
An injector is essentially a device designed to optimally allow the flow of the fuel and oxidizer in a bipropellant rocket engine to enter the combustion chamber and combust. Without the injector, the propellants would not mix well, hindering engine performance, and could lead to severe risk of damage to parts and personnel.
Fig. 1: Top-down view of the Helios injector.
The Helios injector has two manifolds, which are the two machined grooves seen in Fig. 1. Each manifold has orifices for one of either the fuel or oxidizer, which is where the propellants pass through from the feed system to the combustion chamber.
Why do we need an injector?
The injector serves many purposes, and a few very important ones are outlined below.
To optimize the flow of the propellants into the combustion chamber
The geometry of the injector is designed to optimize the flow of the fuel and oxidizer into the combustion chamber, where they will collide, mix, and combust. In this document, we look at one specific injector design: the Unlike Doublet Impinging, where there are pairs of fuel and oxidizer orifices which are angled to collide with each other. The Helios injector is also of this design. There are several other designs that may be considered depending on the needs of the mission, but we will not discuss them in this document. We will also look at other stream parameters which are dependent on the injector, like droplet size and mixture ratio.
Fig. 2: Unlike doublet impinging injector design.
To ensure the sustainability of the combustion chamber
The positioning and orientation of the injector orifices is important to ensure that the resulting combustion flames and exhaust do not melt or deteriorate the chamber walls. This also has to do with other parameters of the engine design, like the mixture ratio of the propellants, the mass flow rates, etc. Without the injector, or with a poorly designed injector, we risk destroying the combustion chamber. Here, it is vital that our resultant stream is angled either parallel to the chamber wall, or slightly towards the central axis.
Another consideration is that cryogenic propellants (like the very common LOX) may provide minor film cooling for the chamber walls. This can be done by positioning the oxidizer orifices on the inner manifold angled towards the chamber walls.
To ensure combustion stability
This ties into the second point, but is different. The injector is designed so that the flow of the propellant streams is manageable and combusts in a way we are prepared for (with the design of the rest of the rocket). An unstable combustion would result in an unstable rocket which is typically not something you want.
How does an injector work?
Recall that injectors are utilized in bipropellant engines, where a fuel and an oxidizer are mixed at high velocities so they can combust and release exhaust through the rocket nozzle to propel the rocket. The fuel and oxidizer (often referred to as fuel/ox, or simply O/F) are propelled from their respective storage tanks towards the combustion chamber, often by a gas propellant. They travel through the feed system until they reach the injector plate.
Fig. 3: Helios engine layout.
Upon reaching their respective injector plate manifolds, the flow of the propellants is split between the orifices. Depending on the specific geometry and design of the injector, the propellants undergo a certain pressure drop while crossing into the combustion chamber. This pressure drop is chosen to both optimize engine performance and to prevent combustion instabilities. A low pressure drop increases performance, while a high pressure drop decreases the risk of combustion instabilities. Pressure drop is discussed further in this document.
For an unlike doublet injector, the propellants enter the combustion chamber, mix, combust, and are propelled on a resultant trajectory down the nozzle. The injector ensures this process is tuned to certain specifications, and achieves its other purposes outlined above. Other injector designs achieve their purpose in a different way.
General Injector Design Parameters
Flow Parameters Summary
Mass Flow Rate
The orifices of the injector will be sized such that the desired mass flow rate [kg/s] of the oxidizer and fuel enter the combustion chamber. These mass flow rates will be derived from a systems flow level. The thrust is dependent on total mass flow rate and the ratio between the fuel and oxidizer mass flow rates is dependent on the desired O/F ratio needed for a desired combustion.
Pressure Drop
For the oxidizer and fuel to flow across the injector and into the combustion chamber, there needs to be a drop in pressure across the injector. In other words, the pressure behind the injector must be greater than the pressure of the combustion chamber. The recommended pressure drop across the injector is around 15-25% of the combustion chamber pressure. If the pressure drop is too low, the velocity of the stream will not be high enough for good mixing and will kill combustion. Higher pressure drop, however, will lead to increased resistance to some combustion instabilities.
Injector Geometry Summary
Oxidizer/ Fuel Angle
The oxidizer angle and fuel angle are the angles between the respective fluid streams to a normal line of the injector plate, as shown in Fig. 4. These angles are calculated by balancing each of the stream’s lateral momentums to achieve a desired resultant angle. For a resultant angle of 0, the angles would be chosen such that each stream had the same (but opposite) momentums. They are also constrained by specifying a desired impingement angle.
Fig. 4: Definitions of injector geometry parameters.
Fig. 5: Momentum balance equation that calculates a center line angle gamma that can be used to derive both orifice angles. This calculates a gamma for a 0 degree resultant (beta).
Impingement Angle
The impingement angle is the angle between the fuel and oxidizer streams. In our research we found that 60 degrees is the optimal impingement angle [citation1].
Resultant Angle (beta)
The resultant angle is the angle between the resultant fluid stream and the normal line of the injector plate. A positive resultant angle is towards the centerline of the injector. From experimental results, some papers have suggested that a resultant angle of 0 degrees allows for the best mixing of fuel and oxidizer [citation]. However, in our design, we also need to consider not to exceed the heat capacity of the combustion chamber wall, so we would prefer a slightly positive resultant angle. The resultant angle and impingement angle has the following relationship, where v is the velocity of the fluids, alpha is the oxidizer/fuel angle and q is the mass flow rate.
Number of Orifices
In principle, a larger number of orifices will allow for better atomization of the liquids. But in reality, we also need to consider ease of manufacture in the design process.
Impingement Distance
The impingement distance is the distance from the bottom of the injector plate to the point of impingement of the oxidizer and fuel stream. From a NASA paper, the recommended range of the ratio of impingement distance to average orifice diameter is 3 to 7 [citation]. In our design, we used a typical impingement distance of 5 times the average orifice diameter.
Total Orifice Area
In our design, we modeled both the fuel and the oxidizer as compressible fluids. The total fuel area can thus be determined from the respective inputs of mass flow rate, fluid density, and pressure drop. We also note that the discharge coefficient (Cd) for a square hole is about .7. This total orifice area can then be divided by the number of orifices to find the area per orifice. Angles between the oxidizer and fuel orifices remain constant with the number of orifices as the momentum will scale with area.
Orifice Distance
The orifice distance is the distance between the fuel and oxidizer orifice on the bottom of the injector plate. This distance depends on the impingement distance (di) that we have chosen and the calculated impingement angles (theta) in the following way:
Plate Thickness at Orifices
The plate thickness at the orifice depends on the orifice length, which has an effect on the spray characteristics of the liquids since too short of an orifice will not result in a steady stream. From our research, resources have suggested that the recommended ratio between orifice length and orifice diameter is between 4 and 10 [citation]. In our design, we chose the recommended value of 5 times the respective orifice diameter for orifice length.