Stabilization of a bipropellant liquid rocket motor

Abstract

The unstable burning of a bipropellant rocket combustion chamber is investigated and a study made of the requirements for an automatic closed loop control circuit to stabilize the motor. The bipropellant combustion chamber equations developed by Dr. L. Crocco(1) are utilised as the analytical description of the rocket motor burning phenomena. Equations similar to those developed by Dr. H. S. Taiga(2) are used for the oxidizer and fuel supply systems and the two closed loop stabilizing circuits. The stability or instability of the system is demonstrated by the use of a special plotting diagram in the complex plane suggested by M. Satche as a means of handling systems with time lag, and developed for this use by H. S. Tsien. This involves separating the transfer function into two parts. In the complex plane the first portion of the transfer function, the exponential variable containing the time lag, plots as a unit circle as the complex variable p is made to take a contour enclosing the positive half of the p—plane. If the remaining portion of the transfer function intersects this unit circle, the rocket motor can be unstable for large reduced time lag; if it does not intersect the unit circle, the system is generally stable, although the roots of the exponential coefficient in the positive half of the complex plane must be investigated. This latter requirement can be conveniently accomplished by the aid of a Nyquist Diagram. The equations for the feedback circuit are developed and the oxidizer and fuel transfer function requirements are determined. Two cases of stable combustion and two cases of unstable combustion are analyzed. One unstable case is stabilized by the addition of a feedback circuit.