Computation of two-phase viscous flow in solid rocket motors using aflux-split Eulerian-Lagrangian technique

Abstract

Aside from understanding the characterization of A I 2 0 3 A time-dependenk two-dimensional or axisymmetric numerical solution technique has been developed to analyze the viscous coupled gas-particle flow in a solid rocket motor. The solution combines an implicit flux-split approximate factorization scheme with a Lagrangian analysis for the particle phase in a generalized body-fitted coordinate system. The solution allows for accurate prediction of twophase flow in all flow regimes, i.e., subsonic, transonic and supersonic. Numerical simulations are presented for several bum times of the aft segment of the Space Shuttle SRB and a single bum time of the PAM 630 space satellite launch motor. Particle flow information from these simulations has been used to estimate the slag accumulation in the Space Shuttle motor. INTRODUCTION Highly aluminized propellants are frequently used in solid rocket motors (SRM) to increase specific impulse (Iw) and, to some degree. control combustion instability. The combustion of an aluminized solid propellant produces aluminum agglomerates on the propellant burning surface which are ejected into the gaseous surrounding. Along its trajectory, the AI agglomerate is oxidized at a finite rate. Some of the resulting AI,O is shed as small particles, while the rest remains attached to the A1 agglomerate. This behavior leads to a bimodal size distribution of A 1 2 0 3 consisting of large AI/A1203 composite paniclcs and small smoke The presence of these particles in the flowfield contributes to the motor perfomance loss and possible surface damage. The thermal and velocity lag between the gas and particles result in decreased nozzle efficiency. Inside the motor, these particles are the source of slag material that may remain in the motor during firing and !hereby cause excessive heating and subsequent insulation erosion where they collect. This is primarily due to the inability of the large particles to follow the gas streamlines lhrough the nozzle. It is clear that an optimum design of any SRM will require an accurate knowledge of behavior of the particle laden gas as it moves in the motor. particle formation during combustion, there is an absolute necd for an efficient and reliable computational tool that can prcdict the two-phase flow in SRMs. Selection of an appropriate numerical model is a prerequisite to this computational capability, Crowd2] provides a review of numerical models for two-phase flows. Two broad numerical approaches are currently in wide-spread use. The first technique is the two-fluid or Eulerian-Eulerian model. where both the continuous and particulate phase arc treated as continua. This approach is useful when one is interested in resolving the gas-particle field on a scale that is large compared to the average spacing between particles. The work of Harlow et and Chang 141 are excellent examples of the use of this method. There are, however. major disadvantages with this model: namely, numerical instabilities, numerical diffusion, and large storage requirements for multiple particle sizes. An alternative approach is to treat the particles as a discrete phase and employ computational particles to represent a collection of physical particles having the same attributes. The report by Cloubnan et al!” provides a complete description of an application of this approach. This Eulerian-Lagrangian technique has received increased attention in recent years because: 1) numerical dissipation and dispersion can be eliminated; 2) since particle dynamics are described by ordinary differential equations, their integration is computationally efficient; 3) appropriate models for particle collision. agglomeration, and combustion can be easily incorporated. In this technique the influence of the particles on the gas phase is accounted for by inclusion of interphase coupling terms in the Eulerian equations for the gas. However, care must he taken in interpolating between !he Lagrangian and the Eulerian meshes. In this paper, a combined Eulcrian-Lagrangian analysis, similar to !hat of Clouman et al.[51, Dukowicz‘61 and Sabnis el al!7’, is adopted to solve for the time-dependen5 axisymmetric, viscous, compressible two-phase flow in a SRM. The gas phase solution is solved in an Eulerian curvilinear mesh using the approximate factorization method of Beam and Warming[*’. The convective flux terms of the Copyright @ Arnuiorn Imtilute of A m i u t i c s snd Aamrutics. hc.. 1989. All Rights rcsrrvcd.