Mass Transfer Number Sensitivity on the Fuel Burning Rate in Hybrid Rockets

Abstract

The simplest regression rate formula, which depends solely on oxidizer mass flux, originates from Marxman's theory introduced in the 1960s. This commonly adopted model is still widely used, even though it cannot adequately represent the important effect of thermochemical properties associated to a given specific fuel. In this study, the spacetime-averaged regression rate formula taking into account the mass transfer number B is reevaluated to highlight its relative sensitivity with respect to the commonly used simple formula even if B has been known to be a weak function on the regression rate. Polymers (High Density Polyethylene, Polymethylmethacrylate, and Polypropylene) are considered as fuel where theoretical mass flux exponent of 0.75 from the classical theory of Marxman is investigated when applied to the empirical regression rate. Besides, the effect of chamber pressure and use of motor oxidizer to fuel ratio on B sensitivity have been quantified and experimentally analyzed. It is shown that Marxman's theory is a very robust model and that its local regression rate theory extends well to the space-time-averaged experimental results for fuel lean cases. Finally, results of this study were consistent with the finding of Karabeyoglu et al., which showed that an oxidizer to fuel ratio correction is merely required for system operating under fuel lean condition. Nomenclature a = regression rate constant B = mass transfer number C f = friction factor C H = Stanton number with blowing C H o = Stanton number without blowing c p = specific heat, kJ∕kg · K f a = a∕a min , relative ratio of the regression rate constant a G = instantaneous local mass flux, kg∕m 2 · s G t = total mass flux, kg∕m 2 · s G o = oxidizer mass flux, kg∕m 2 · s h b = enthalpy at the flame, kJ∕kg h w = enthalpy at the fuel surface, kJ∕kg h v = solid fuel vaporization enthalpy, kJ∕kg K ox e = concentration of oxidizer in the freestream L = fuel length, m m = mass transfer number exponent n = mass flux exponent R 2 = adjusted R-square _ r = instantaneous local regression rate, mm∕s t b = burning time, s u b = velocity of the propellant gas at the flame, m∕s u e = velocity of the propellant gas at boundary-layer edge, m∕s x = distance along port, m ρ f = fuel density, kg∕m 3 μ = dynamic viscosity of the main stream gas, kg∕m · s Subscripts b = flame e = boundary-layer edge avg = spatially-temporally averaged w = wall stoic = stoichiometry

Role of Precombustion Chamber Design in Feed-System Coupled Instabilities of Hybrid Rockets

“…(4) was considered equal to 0.5 (n=0.5). This is a reasonable assumption since the oxidizer mass flux exponent has been observed to range from 0.5 to 0.75 regardless of the type of propellant for most hybrid propulsion systems [1,19,20]. And the time rate of change of the chamber gas volume was neglected because the fuel regression rate is on the order of a few mm/s, much slower than combustion time scales.…”