Time-Resolved Fuel-Grain Regression Measurement in Hybrid Rockets

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This paper presents a novel technique for determining the instantaneous spatially-averaged port diameter of solid-fuel grains in hybrid rocket motors. This technique requires measurement of the frequency of the bulk-mode oscillation of the motor and is based on the principle that this frequency is inversely proportional to the square-root of the chamber volume. This technique was applied to a hybrid rocket motor burning paraffin wax with gaseous oxygen. The calculated variation of port diameter agreed well with the correlation for average regression rate, determined from mass loss during operation. A major advantage is that the only instrumentation required for implementing this technique is a high-speed pressure transducer or a photo-multiplier. Nomenclature a = fuel regression rate law coefficient A = throat area c = speed of sound D = port diameter of the fuel grain f = bulk-mode frequency G = oxidizer mass flux through the port k = ratio of specific heats l = effective length of the throat l’ = length of the throat L = length of the fuel grain & m = oxidizer mass flow rate & M = fuel mass flow rate n = fuel regression rate law exponent OFR = oxygen-to-fuel ratio & r = fuel regression rate R = gas constant t = time T = temperature V = chamber volume V’ = post-combustion chamber volume ρ = fuel density Subscripts 0 = initial 1 = at time of first frequency measurement (t = 0.5 s) f = final s-ave = spatially-averaged t-ave = time-averaged tot = total Introduction The most important measurement in characterising a hybrid rocket propellant is the spatially-averaged burning, or regression, rate of the solid-fuel grain. Usually the regression rate is determined as an time-averaged value from the mass lost from the grain during the burn, with corrections for the ignition and shutdown transients. A series of over seventy tests, using paraffin wax and gaseous oxygen, showed that the average fuel regression rate determined in this manner was related to the oxidizer mass flux by the expression: & . r a G t ave t ave n − − = (1) 39th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit 20-23 July 2003, Huntsville, Alabama AIAA 2003-4595 This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States. 2 where a and n were 0117 10 3 . × − (m/s)(kg/ms) and 0.62, respectively. These regression rates are around three to five times that of traditional hybrid fuels such as High-Density Poly-Ethylene (HDPE), Poly-Methyl Methacrylate (PMMA) and HydroxilTerminated Poly-Butadine (HTPB). In solid propellant motors the fuel regression rate is dependant on the chamber pressure. In contrast, fuel regression rate in hybrids is dependant on the oxidizer mass flux through the port as indicated by empirical correlation (1) and is independent of pressure. Therefore, as the port diameter changes during the burn, so do the instantaneous mass flux and regression rate. Due to its transient nature, a time-resolved measurement of regression is desirable and would eliminate the uncertainties associated with the ignition and shutdown transients. A time-resolved measurement would also provide a means for obtaining multiple data points from a single test, thus reducing the time and cost involved with testing. Time-resolved regression of conventional hybrid fuel grains has been measured previously in motors using ultrasound, but this method was not practical with fuels in which there are large acoustic losses, such as paraffin. Time-resolved regression has also been measured with x-ray radiography, though this technique required that the fuel grain be in the form of a slab, instead of the more practical annular configuration of the present experiments. Further, these methods provide local measurements and thus require multiple transducers to provide a spatiallyaveraged value. This paper presents a novel method for estimating the instantaneous spatially-averaged port diameter of the grain from analysis of a high-speed pressure transducer signal. It is based on the principle that the frequency of the bulk-mode oscillation decreases in a predictable manner as the port diameter of the grain increases during the burn. The technique is applied to a hybrid rocket burning paraffin wax with gaseous oxygen and the results are compared with the following expression for instantaneous port diameter: