Accuracy and applicable range of a reconstruction technique for hybrid rockets

Accuracy of a reconstruction technique assuming a constant characteristic exhaust velocity ($c^*$) efficiency for reducing hybrid rocket firing test data was examined experimentally. To avoid the difficulty arising from a number of complex chemical equilibrium calculations, a simple approximate expression of theoretical $c^*$ as a function of the oxidizer to fuel ratio (${\xi}$) and the chamber pressure was developed. A series of static firing tests with the same test conditions except burning duration revealed that the error in the calculated fuel consumption decreases with increasing firing duration, showing that the error mainly comes from the ignition and shutdown transients. The present reconstruction technique obtains ${\xi}$ by solving an equation between theoretical and experimental $c^*$ values. A difficulty arises when multiple solutions of ${\xi}$ exists. In the PMMA-LOX combination, a ${\xi}$ range of 0.6 to 1.0 corresponds to this case. The definition of $c^*$ efficiency necessary to be used in this reconstruction technique is different from a $c^*$ efficiency obtained by a general method. Because the $c^*$ efficiency obtained by average chamber pressure and ${\xi}$ includes the $c^*$ loss due to the ${\xi}$ shift, it can be below unity even when the combustion gas keeps complete mixing and chemical equilibrium during the entire period of a firing. Therefore, the $c^*$ efficiency obtained in the present reconstruction technique is superior to the $c^*$ efficiency obtained by the general method to evaluate the degree of completion of the mixing and chemical reaction in the combustion chamber.