Addressing Propulsive Efficiency Drawbacks Associated with High Regression Rate Liquefying Hybrid Rocket Fuels Through the Modification of Thermal and Mechanical Properties

Paraffin-based liquefying hybrid rocket fuels have been shown to demonstrate significantly increased regression rates over traditional HTPB largely due to the formation of a hydrodynamically unstable melt layer. The rate of fuel mass entrainment in the combusting boundary layer is related to the dynamics of heat transfer in the melt layer along with its mechanical properties including viscosity and surface tension. Heat is transferred to the fuel grain via convection and radiation and is dispersed throughout the fuel itself through diffusive conduction. The balance of thermal flux at the fuel surface determines its temperature and governs fuel melting. Assuming little convective transfer through the melt layer, the rate fuel regression is proportional to powers of operating pressure and oxidizer mass flux though the port. It is inversely proportional to powers of fuel melt viscosity and surface tension and therefore the operating melt layer thickness. As a result, regression rate tends to increase as melting point and carbon chain length decrease. 

Raw paraffin is a translucent, waxy, brittle solid being easily penetrated by thermal radiation from the combustion zone. This leads to several issues with realistic implementations of paraffin-based fuels. In the worst case, thermal radiation fails to be absorbed by the relatively thin fuel grain and heats the fuel liner. This causes the fuel to begin melting form the outside in, causing the fuel grain to fail structurally and potentially eject unburned fuel. In the less exaggerated case, fuel mass injection increasingly outpaces the rate of oxidizer injection over the firing duration, harshly limiting the operating cycle of the motor. It also causes a departure from the optimal oxidizer to fuel ratio and performance. Using pure paraffin, this ratio is approximately 7.0 with respect to mass, making ideal performance levels difficult if not impossible to achieve due to limitations with the oxidizer feed system and mixing of fuel and oxidizer. Fuel and oxidizer are transported advectively into the thin combustion layer from opposite sides, making it difficult to effectively combust the fuel with large quantities of oxidizer.

The problems with oxidizer and fuel mixing can be partially solved using a high performance injector that creates a turbulent or swirling flow in the fuel port. An commercial X-form injector has been purchased and cold-flow tested with liquid nitrous oxide supplied by the completed oxidizer feed system. The resulting flow rate at a target operating pressure of 500 psi is approximately 175 g/sec. Using this configuration, an oxidizer to fuel ratio of approximately 2:1 is attainable. It would be necessary to increase the orifice area significantly in order to increase this ratio towards to optimal domain. However, significant metallization of the fuel using magnesium powder is shown to both increase performance and lower the optimal oxidizer to fuel ratio. For a magnesium loading of 40%, the injector orifice area still must be enlarged by a factor of 2. However, in smaller motors, there may be insufficient "residence time" in the combustion chamber for the magnesium to fully combust, lower the oxidizer to fuel ratio, and contribute favorably to the performance. Also, while opacifying the fuel and reflecting thermal radiation, magnesium also conducts heat into the fuel grain. An increase in regression rate beyond the optimal point or a structural failure of the fuel may result from high magnesium loadings. Several will be tested.

In order to improve the fuel's strength and mechanical properties during grain production, cellulose fibers will be added. Their effect on fuel density and regression performance will be characterized. An opaque fuel that is absorbent to thermal radiation at the surface is desired for an increased and pressure-dependent regression rate. Graphite and activated charcoal will be tested for this purpose. Graphite powder is expected to produce a fuel that absorbs thermal radiation but may conduct heat into the fuel grain. Activated charcoal presents a high degree of microporosity and may function as an insulator when used in the fuel. Its dark color will likely absorb heat similarly to graphite. Activated charcoal may lower the fuel density and thus density specific impulse. A combination of the additives discussed herein may vastly improve the fuel's performance and mechanical properties during grain production and firing.