Why maintain nominal engine inlet mixture ratio for a gas generator engine?

Question

I was reading up on gas generator cycles and came across the following paragraph talking about fuel or oxidizer rich gas generators and the different mixture ratios for the main combustion chamber versus the gas generator (from Liquid Rocket Thrust Chambers, p. 637-638):

For a fuel-rich configuration, the mixture ratio of the gas generator flow, selected to maintain acceptable turbine temperature limits, is much lower than the mixture ratio of the main chamber. To maintain a nominal engine inlet mixture ratio, the main chamber must operate above the nominal mixture ratio to compensate for the lower mixture ratio in the gas generator. Similarly, for an oxidizer-rich configuration, the mixture ratio of the main chamber must operate below the nominal mixture ratio, because the mixture ratio of the gas generator is higher. Thus, for both configurations main chamber performance is reduced because the mixture ratio is further from the peak performance value.

Why would I care about the engine inlet mixture ratio? Why not pick one that gets both the gas generator and main combustion chamber their preferred mixture ratio?

I could only see it slightly affecting tank size and thus weight, but I don't see why that would be so drastic as to warrant a sub-optimal mixture ratio for the main combustion chamber.

Answer 1

I agree with your analysis.

To maintain a nominal engine inlet mixture ratio, the main chamber must operate above the nominal mixture ratio to compensate for the lower mixture ratio in the gas generator.

This sentence makes a certain amount of sense in isolation; if the complete engine specifies a given mixture ratio, then the main chamber will be at a slightly higher ratio than that and the gas generator at a lower one.

Thus, for both configurations main chamber performance is reduced because the mixture ratio is further from the peak performance value.

This part makes no sense and suggests confusion on the part of the author. It's putting the cart before the horse. There's no reason to take the peak performance ratio for the main chamber alone as the mixture ratio for the complete engine if that reduces performance.

In fact, the paper goes on to say (SciHub link):

To minimize the impact of this mixture ratio shift, the vehicle tanks can be designed to operate at a "system" or engine inlet mixture ratio that is somewhat reduced. This works better for nonhydrogen fueled engines, where the fuel density is nearer to the density of the oxidizer and mixture ratio selection has minimal impact on the stage tank weight and volume.

All of this just seems like sloppy thinking. The proper mixture ratio is that which provides the best overall system performance, taking into account tankage size, gas generator ratio and flowrate, and main chamber performance from the start. The ideal main chamber ratio (itself possibly constrained by thermal considerations as well as pure specific impulse) i a fine starting point for the solution search space, but there are a number of reasons it might not be the optimum.