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/(Injector stiffness is controlled by two equations: mdot = p_c * A_t / cstar, and mdot = Cd * A_inj ))^2 / * sqrt(2 * rho )) for an incompressible flow)*dP). The first equation tells us that if mdot decreases by a factor of 2, p_c also decreases by a factor of two. The second equation tells us that if mdot decreases by a factor of two, dP decreases by a factor of four. This means that as mass flow decreases, the injector stiffness will decrease until it drops below the critical limit.
The way we plan on controlling our engine's mass flow rate is by placing ball valves upstream of the combustion chamber that will regulate the mass flow into the combustion chamber. But wait, you may say – isn't the mass flow rate set by the injector? Well, yes, but the mass flow rate that the injector outputs is dependent on the pressure drop across the injector. An upstream valve will create a pressure drop across itself, which will decrease the injector manifold pressure. This will decrease the dP, which will decrease the mass flow of the injector. When the mass flow decreases, the chamber pressure will decrease proportionally. Thus, the main challenge with throttling is relating ball valve pulse width to mass flow reduction.
For regenerative cooling, however, another a 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 fuel (and ox) 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.
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