396 J. SPACECRAFT VOL. 22, NO. 4 Recession Behavior of Graphitic Nozzles in Simulated Rocket Motors S.T. Keswani,* E. Andiroglu,t J.D. Campbell,! and K.K. KuoJ The Pennsylvania State University, University Park, Pennsylvania Abstract A STUDY has been conducted to predict nozzle recession behavior in two different rocket motors and for broad variations of propellant formulations and motor operating conditions. Results show that the recession rate is largely determined by the diffusion of the major oxidizing species (H 2 O and CO 2 ) to the nozzle surface. The free volume in the motor, the concentration of the major oxidizing species as affected by the aluminum content of the propellant, and the chamber pressure exert a strong influence on the recession rate. A correlation to predict the throat recession in terms of the above governing parameters has been developed. This correlation is in good agreement with experimental data in the two different motors considered. Contents As the rocket motor operates and propellant exhaust flows through the graphite nozzle, heterogeneous reactions between the exhaust gases and the carbon begin to occur. These reactions deplete the oxidizing species at the nozzle surface and thereby create concentration gradients in the flowfield. These gradients result in the diffusion of oxidizing species to the nozzle surface. Thus, the rate of nozzle recession depends on both the chemical kinetic rates of the heterogeneous reactions and the diffusion rate of oxidizing species to the nozzle surface. Detailed model formulation is given in Ref. 1. The major oxidizing species considered are H 2 O and CO 2 ; both of which are assumed to react with carbon at the same rate in a first-order reaction 2 to produce CO. The mass-loss rate of carbon due to reaction with component /, m it can be expressed as (1) where the activation energy E a and the pre-exponential factor A s are 41.9 kcal/mole and 2470 kg(m 2 -s-atm), respectively, as suggested by Libby and Blake. 2 Golovina 3 provides a similar expression for the reaction rate of CO 2 with carbon at high temperatures with E a and A s equal to 40.0 kcal/mole and 158 kg/(m 2 -s-atm), respectively. The theoretical model was solved to simulate the operational conditions of both the Bates motor 4 and the Materials Evaluation Research Motor (MERM). 5 ' 6 The input parameters for both the MERM and Bates motor are shown in Tables 1 and 2. Figure 1 shows the effect of aluminum content of propellant on the total recession at the nozzle throat as a Presented as Paper 83-1317 at the AIAA/SAE/ASME 19th Joint Propulsion Conference, Seattle, Wash., June 27-29, 1983; submitted July 25, 1983; synoptic submitted June 28, 1984. Copyright © American Institute of Aeronautics and Astronautics, Inc., 1983. All rights reserved. Full paper available from the AIAA Library, 555 W. 57th St., New York, NY 10019; microfiche—$4.00, hard copy—$9.00. Remittance must accompany order. * Research Assistant, Department of Mechanical Engineering. tGraduate Assistant, Department of Mechanical Engineering. JProfessor, Department of Mechanical Engineering. Associate Fellow AIAA. function of time. The recession at the throat decreases sharply with increasing aluminum content of propellant even though the flame temperature increases. Chemical kinetics have a significant influence on the recession for the lower aluminum content propellants but their influence diminishes with in- creasing aluminum content. Also shown in the figure are the experimental data of Swope and Berard. 5 Considering the reproducibility of the experimental data, the agreement between the predicted and experimentally determined recession is well within the experimental variations. Figure 2 shows the recession as a function of time for five propellants with very different compositions listed in Table 2. The total recession varies almost linearly with time except for propellant 2755R which has a relatively low flame tem- perature of 2627 K. This results in nozzle surface tem- peratures of about 2000 K. At these low temperatures, the influence of chemical kinetics is very pronounced. Hence, the predicted recession based on the two different kinetic con- stants differ by a large value. It is evident from this figure that the recession rate shows no correlation with the flame tem- perature. However, if the flame temperature is low enough, then the recession process may be strongly influenced by chemical kinetics and one may find a large effect of nozzle material reactivity as well as the flame temperature. The theoretical predictions are compared to the experimental data of Swope and Berard 5 in Fig. 2. Agreement between the predictions and data can be considered reasonable in view of the variation in experimental data for the same propellant. The preceding discussion has shown that the composition of the propellant plays an important role in determining the recession rate. In particular, the freestream concentrations of oxidizing species H 2 O and CO 2 at the nozzle throat appear to be very important. Another important parameter is the chamber pressure. The mass transfer rate of oxidizing species across the boundary layer to the nozzle surface is propor- tional to the gas-phase density and, hence the pressure. However, at similar pressures and oxidizing species con- centrations, the recession rates obtained in the Bates motor are considerably higher than those in the MERM motor. 4 ' 5 This can be explained in terms of the motor configuration and nozzle geometry. The MERM motor, as compared with the Bates motor, has a long flow development length to the nozzle throat, which results in a thicker boundary layer at the throat. The thicker boundary layer presents a greater resistance to the transverse diffusion of oxidizing species to the nozzle surface. This results in a lower recession rate. Also, the diameter of the MERM motor throat is one-fourth that of the Bates motor throat. The greater transverse curvature of the flowfield in the Table 1 Geometric parameters for simulating MERM and Bates motors Geometric parameters ^throat, inner' cm ^throat, outer' cm x f ,cm a, deg MERM 0.635 2.512 25.00 16.7 Bates 2.54 10.00 10.25 16.7 Downloaded by UNIVERSITY OF CALIFORNIA - DAVIS on February 10, 2015 | http://arc.aiaa.org | DOI: 10.2514/3.25763