Research over the last week focused mainly on the methods employed by others to characterize the regression rate and performance of hybrid rocket fuels. The theory behind hybrid rocket fuel regression was also studied.
For rubberized fuels, regression proceeds through the desorption of high molecular mass particles from the fuel grain surface into a detached boundary layer in the fuel port where combustion occurs in the presence of oxidizer flow. Due to the exothermic nature of the combustion reaction, heat is released largely in this combustion zone. The desorption of fuel particles is governed largely by convective heat transfer to the fuel surface. Radiative heat transfer also plays a role. However, without convection, fuel particles are not carried into the combustion zone. Since heat is generated in the combustion zone, the regression of fuels is determined through the rate of heat transfer and convection that occurs between this boundary layer and the fuel surface within the combustion port. The effects of boundary layer growth and mass flux within the combustion port both play competing roles in the rate of convective heat transfer to the fuel. Their influence is a function of axial position within the fuel port. Near the point of oxidizer injection, the boundary layer is very thin, possessing high temperature and velocity gradients, resulting in high shear stresses and convective heat transfer to the fuel surface. As the boundary layer grows with axial distance from the injector, these effects are less pronounced and reduce the rate of regression. However, the total mass flux in the fuel port increases with axial position due to mass addition in the form of upstream fuel injection. This effect tends to increase the convective heating of the fuel surface with increasing mass flux and axial position. Regression is more sensitive to mass flux than boundary layer growth and is therefor high near the injector, decreasing to a minimum and finally increasing agin until the end of the fuel port. At high oxidizer mass fluxes and lower pressures, the effects of convection dominate radiation. However, at high pressures and low oxidizer mass fluxes, the effects of radiation become significant, increasing regression over that predicted with purely convective models. Such a scenario occurs near the end of motor burn, where the port area has widened, decreasing oxidizer flux values and pressure is high because of increased exposed fuel surface area.
When non-rubber, liquefying, fuels like paraffin are used, additional effects are present that can significantly increase rates of fuel regression. These fuels produce a liquid film of low-viscosity fuel at their surface in a combustion port. Regions of high shear stress in the boundary layer cause this film to destabilize and form ripples, from which fuel droplets are ejected and convected into the combustion zone. These effects tend to amplify the factors that effect the regression of rubberized fuels, giving liquefying fuels much higher burn rates in comparison. Additionally, Hydrogen peroxide can be decomposed in a catalyst bed into oxygen gas and water vapor; these gases, now at temperatures of roughly 800 degrees Celsius, can be used as a hypergolic oxidizer in paraffin based fuel grains. The high injection temperature of the oxidizer serves to further increase the burn rate of the fuel. This concept draws on the ideas of liquid monopropellants and is a good subject for investigation. Other oxidizers like HAN have been proposed as monopropellants and could be investigated.
Common test setups for characterizing the burn rate and performance of hybrid rocket fuels consist of a lab-scale motor with instrumentation and a test stand remotely controlled via USB standoff. A firing program is executed by a computer, which controls the timing of ignition, oxidizer flow initiation, and inert gas purge. Electrically actuated solenoid valves are used to control these events from a distance. Several pressure transducers and a load cell are used to measure the motor's performance.
Oxidizers are pressure fed using an inert gas like nitrogen or helium, regulated down from roughly 2000 psi to operating pressures. Oxidizer flow rates are measured and controlled using various types of venturies. Two that look promising are the tapped venturi with a differential transducer that measures pressure differences between an inlet and nozzle throat to find the rate of flow. Another type is the cavitating venturi. Here, the liquid oxidizer is passed through a converging passage, increasing its velocity and lowing its pressure according to continuity. The velocity is high enough after the converging section to lower the fluid's static pressure bellow its vapor pressure, limiting the flow due to the presence of a gaseous bubble in the divergent section. Thus, the flow is only dependent of a recorded upstream pressure. The cavitating venturi seems to be simpler in construction. Hybrid tests stands use the inert pressurization gas as a post-firing purge. This removes any hazardous oxidizer from the fuel port and injection system.
For a given fuel and chamber pressure, tests are run using thermodynamics software to determine the oxidizer to fuel mass ratio that produces the highest specific impulse. For tests, fuel grain length are varied to change oxidizer to fuel ratios and pressure. Nozzle throat area is varied to change chamber pressure. Lastly, oxidizer flow rate is varied to change average oxidizer mass fluxes in the fuel port. Thrust, firing time, oxidizer flow rate, chamber pressure, fuel mass differences before and after firing, and fuel port diameter changes are measured. These data allow for the calculation of specific impulse along with burn rate and its relationship with oxidizer mass flux and pressure. These experiments will serve as a model for my testing and experimental design.
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