When throttling an engine, the main limiting factor is injector stiffness, or the ratio of injector pressure drop to chamber pressure. A rule of thumb is that injector stiffness should be above 15% to avoid combustion instabilities. When you throttle down, mass flow through the engine decreases. This decreases the engine chamber pressure linearly (since p = mdot*cstar/A_t) but decreases the injector pressure drop nonlinearly (dP = (mdot/(Cd*A_inj))^2 / (2*rho)) for an incompressible flow). This means that as mass flow decreases, the injector stiffness will decrease until it drops below the critical limit.
For regenerative cooling, however, another limiting factor is cooling efficiency, which is what we aim to get valuable data on for our research. When an engine throttles down, there is less massflow, which means less fuel in the regenerative channels cooling the engine walls. We aim to characterize the effect of less fuel flow on the cooling efficiency of our engine.
Our plan to successfully throttle Hephaestus hinges on a significant amount of cold-flow testing to obtain a flow curve that we will use to calibrate our throttle valves. However, cold-flow testing at nominal pressures will result in inaccurate data because there is no chamber pressure, which would result in a much larger dP across the injector than there would be during hotfire. To accurately characterize flow response, we need to enforce the same flow through the system during a cold flow test as there will be during a hotfire.
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