Using a self pressurized system means that the pressure in the fluid is significantly below the nitrous vapor pressure. While two phase flow should not be a problem in the feed system, cavitation of nitrous oxide in the injector orifices will prevent proper impingement. See Figure 4 in Dyer, et al., 2007. This paper describes the mass flow out of the orifice as a combination of a standard incompressible model and a homogeneous equilibrium model (HEM). In reality, the mass flow is not in equilibrium, and a smaller L/d ratio can allow nitrous to flow out of the orifice in liquid phase because it does not have time to cavitate. The relative contributions from these two models is related to k, the ratio between the characteristic bubble formation time and the residence time of liquid in the injector. We calculated k to be 1.76, which means that the HEM model contributes 64% to the net mass flow rate. The model in this paper has been tested over 100 times with very successful results, so the 64% number is worrying for us because there will be significantly reduced liquid flow from the nitrous orifices to impinge with ethanol.
On the other hand, self pressurizing nitrous oxide feed systems have been used successfully many times in the past. We aren't sure how they resolved this issue. More accurate modeling of the two-phase non-equilibrium flow is very difficult, so we plan to run cold flow testing to see if this is a problem.
References:
"Modeling Feed System Flow Physics for Self-Pressurizing Propellants," AIAA 2007-5702. 43rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit. July 2007.
Ewig, R., 2009. “Vapor Pressurization (VaPak) Systems History, Concepts, and Applications.” Holder Consulting Group.
Palacz, Tomasz. (2017). Nitrous Oxide Application for Low-Thrust and Low-Cost Liquid Rocket Engine. 10.13009/EUCASS2017-474.