Pressure dependence of hybrid fuel regression rates.

Abstract

Previously published data for nonmetalized and metalized fuels exhibited a strong dependence on oxidizer flow rate and burner pressure. In this study, the observed pressure dependence was investigated further. Butyl rubber, lithium hydride, and polyurethane fuels were investigated using a laboratory slab burner; the gaseous oxidizers were fluorine, oxygen, and nitrogen. Using oxygen or nitrogen as a diluent, the partial and total pressures of fluorine were varied independently from 4 to 130 psi and 20 to 165 psi, respectively, and the flow rate was varied from 0.014 to 0.21 lb/in. 2 -sec. Measured rates were independent of total pressure for all flow rates; they increased with increasing oxidizer pressure for the higher flow rates but were nearly independent of the partial pressure, while increasing with flow rate for the lower flow rates. Dilution of fluorine with oxygen or nitrogen gave essentially the same results, indicating that oxygen acted only as a diluent. Partial pressure and flow-rate dependence were correlated with a simple model based on turbulent transport processes competing with fluorine kinetic processes.Nomenclature BI = blowing parameter, B\ = rp//(GC/ 0 /2) Cf 0 = friction coeff without blowing, (7/ 0 G = total specific flow rate through port, lb/in. 2 -sec k c = local mass transfer coeff, in./sec k = kinetic rate const, sec" 1 Poo = total gas pressure in freestream, psia P 0oo = partial oxidizer pressure in freestream, psia Pow = partial oxidizer pressure at the wall, psia r = regression rate, in./sec R = specific gas const, in.-lbf/lbm-°R Re = Reynolds number, (GaoX/n) Sc = Schmidt number T = gas temperature, °R C/oo = freestream velocity, in./sec x = distance from leading edge of grain, in. X = weight fraction of gaseous products from wall decompositionPresented as Preprint 66-113 at the AIAA 3rd Aerospace

Solid-Fuel Regression Rate Modeling for Hybrid Rockets

“…Although their early studies showed an enhancement of the regression rate with increasing pressure (assuming a fixed value of the local mass flow), the authors failed to find a satisfactory theoretical explanation for the results. In a subsequent work [4], the authors conjectured that this cause was to be found in the presence of oxygen at the solid surface. That led to the occurrence of heterogeneous reactions between the solid fuel and the surrounding gaseous oxygen, making the solid interface more reactive.…”

“…One of the major conclusions was that the assumed dependence on the chamber pressure, increased as the local specific mass flux increased. However, even though several arguments were proposed in favor of this hypothesis [4], a proved explanation for the witnessed behavior was still missing. One of the rejected explanations regarded the radiative heat flux increase with pressure.…”

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

“…This effort entailed the development of an analytical expression for the regression rate as a function of several kinetic parameters and length-scales. Miller [20] developed a model that incorporated both the fuel diffusion rate and the chemical reaction rates, which he used to successfully correlate data taken by Smoot and Price [21][22][23]. Kosdon and Williams [24] later noted that Miller's analysis was only applicable to systems with low pressure and moderate oxidizer fluxes and derived a new expression that incorporated a flame zone of finite thickness.…”

“…Another group of researchers focused more on heterogeneous surface reactions as the source of kinetics dependence. Smoot and Price [21][22][23] performed numerous tests using a slab burner and found that, above a threshold value of G, the regression rate became nearly independent of G and instead varied with P and the oxidizer composition. These researchers defined a low mass flux regime where the normal G 0.8 dependence held, an intermediate mass flux regime where both P and G played a role, and a third regime at very high mass fluxes where the regression rate varied with pressure, as in the case of a solid rocket propellant; namely,ṙ ∝ P n .…”

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

“…The fuel regression rate referred to as the rate the fuel surface recedes is a key parameter for the hybrid rocket motor design. A lot of research efforts [1][2][3][4][5][6][7] have been conducted to find out the optimum expression for the regression rate. Among such efforts, Marxman et al [8][9][10] derived a functional relation commonly known as the "local regression rate law" for the hybrid rocket combustion.…”