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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.
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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. 34. 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.
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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
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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.
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Injector Flow Metrics
Combustion Stability
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Impingement Distance (Revisited)
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Pressure Drop (Revisited)
Mixture Ratio
Stream Stability
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