Review of Classical Diffusion-Limited Regression Rate Models in Hybrid Rockets

Abstract

In this article, we undertake a concise review of several milestone developments in classical regression rate models of hybrid rocket motors. After a brief description of the physical processes entailed in hybrid rocket combustion, Marxman's diffusion-limited theory is re-constructed and discussed. Considerations beyond the scope of basic convection-driven models, which address disparate forms of the blowing correction, variable fluid properties, and pressure and radiation effects, are also given. Finally, a selection of kinetically-limited models is presented, with the aim of comparing the characteristics of several competing theories that become applicable under particular circumstances.

Nano-Sized and Mechanically Activated Composites: Perspectives for Enhanced Mass Burning Rate in Aluminized Solid Fuels for Hybrid Rocket Propulsion

“…In hybrid rockets, the flame has a diffusive nature, and it is set in the boundary layer generated by the oxidizer flow over the grain surface. Fundamentals of the HRE combustion mechanism were reviewed by Chiaverini [4] and Marquardt and Majdalani [5]. A survey on solid fuel thermal decomposition (a phenomenon playing a central role in HRE combustion) was given by Lengellé [60].…”

“…The effects of radiation are due to gas radiation (playing a minor role), to soot, and (if present) to radiating metal particles [1][2][3][4][5]20,[61][62][63]. Under the influence of radiation heat transfer, r f may exhibit p c dependence [4,20], and the r f (G) power law approximation shows n r < 0.8 [1][2][3][4][5]20,[61][62][63]. Liquefying fuels show a regression rate dependence on G similar to the polymeric formulations, although their r f exhibits percentage increases of 300-400% with respect to reference HTPB [7,8].…”

“…Data sampling extended until the end of the combustion (depending on visualization quality). Diameter sampling was performed with the maximum possible frequency (5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20) Hz under the investigated conditions, with higher frequencies in the earlier phases of the burning process). During the combustion, central port diameter was sampled along different radial directions (depending on combustion uniformity).…”

“…Al → Al 2 O 3 conversion factor, % ∆m 0 mass change before the first intense oxidation onset temperature, % ∆m(T) mass change at the temperature T, % µAl micron-sized Al powder ρ Al Al density, kg/m 3 ρ f fuel density, kg/m 3 a D pre-exponential coefficient in diameter change power law fitting, mm/s nD a r pre-exponential coefficient in regression rate power law approximation, mm/s/(kg/(m 2 ·s)) nr a s particle size derived from the specific surface area, nm C Al active Al content, wt.% D (0.1) particle diameter below which 10% of the particles lay, µm D (0. 5) particle diameter below which 50% of the particles lay, µm D (0. 9) particle diameter below which 90% of the particles lay, µm D 32 surface-based mean particle diameter, µm D 43 volume-based mean particle diameter, µm D i i-th sampled port diameter, mm data fitting parameter r f solid fuel regression rate, mm/s (m/s in Equation (4)…”

“…Hybrid rocket engines (HREs) feature a diffusion-limited combustion process between the atomized liquid (or gaseous) oxidizer and the pyrolyzed/vaporized solid fuel. The turbulent boundary layer combustion is ruled by convective heat transfer, with the r f showing relatively strong dependence on G [1][2][3][4][5]. In the complex boundary layer combustion mechanism, oxidizer-lean conditions are encountered in the region extending from the regressing surface to the flame.…”