Calibrating the discharge coefficient (Cd) of our propellants is crucial to ensuring that mass flow rates, mixture ratio, and burn time are enforced. We intend on calculating the Cd of our fuel flow through a water flow testing campaign.
- The relation between mdot and Cd is as follows: mdot = Cd * A_inj * sqrt(2*rho*dP). If injector dP is not sufficient to choke the flow, we can assume that Cd is constant throughout a cold flow test. We can then integrate both sides of this equation, which allows us to put this equation in terms of more parameters that we know (i.e. the total mass of the water that flowed through the injector). The equation becomes m_{discharged} = C_d * A_{inj} * \sqrt(2*rho) * \int_{t_1}^{t_2} \sqrt(\Delta P) \,dt. To get deltaP, we will simply have a pressure transducer port linked to our manifold. We can then take the square root of our recorded pressure data and integrate that throughout the duration of the test. For this test, we will enforce the pressure inside the manifold to be equal to the pressure drop across the injector for hotfire, as the water will feel the ambient pressure once it leaves the injector, not the chamber pressure. This should allow us to get Cd!
This is the current test setup to obtain Cd of the fuel flow. For the first test, the film cooling holes will not be drilled yet, and so no leakage will occur unless the O-rings fail. The aluminum carrier underneath the injector is to inlet fuel and prevent that fuel from leaking; in the second image, you can see the fuel port coming from the bottom of this carrier. The port on the right in the first image will link to a pressure transducer. We intend on performing multiple water flow tests across different injector dP's to properly characterize Cd.