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 Cd 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!
We intend on performing multiple water flow tests across different injector dP's to properly characterize Cd. This should be easy for the fuel manifold of the injector; for the nitrous pintle, however, we need to figure out how to fit a pressure transducer to the nitrous. Nitrous is also problematic because of its two phase flow, but we should be able to calculate its Cd based on the homogenous + spi equations we found for it in our literature review.
Our P&ID for this test is under development. We are thinking to reuse the Polaris tank because it will allow us to have pressurized gas on one side of the tank and water on the other.