Modem SRM ignition transient modeling. V - Prospective developments in CFD simulation

The current state-of-the-art in solid rocket motor (SRM) ignition transient prediction is reviewed. Although the foundation of the computational fluid dynamics (CFD) approach to SRM ignition transient predictions was laid more than a quarter century ago by Peretz, Kuo, Caveny, and Summerfield, rapid advances have been made only recently. Three-dimensional (3-D) prediction tools are being developed and may require the usage of parallel computing systems to alleviate displeasingly long computer run times. In this paper, a quasi-3D CFD approach is presented as an alternative cost-saving method for 3-D ignition transient flow predictions. Justifications and limitations are discussed. The approach is applied to two generic SRMs to illustrate: (1) 3-D flow phenomena that can not be obtained by using a 1-D or 2-D approach and (2) an easy route that leads to parallel CFD. Introduction Depending on the application objective, solid rocket motor (SRM) ignition transient phenomena can be analyzed using methods with different degrees of computational sophistication. Currently, the analytic tools available for practical applications range from the simple volume-filling method to the complicated multi-disciplinary axisymmetric computational fluid dynamics (CFD) codes. The volume-filling method is a simple procedure for obtaining a transient chamber pressure and can be used for motor casing preliminary design. The method had been considered appropriate only for motors of small length-todiameter (L/D) ratios. However, it was reported recently by Luke et al that the volume-filling method was applied to compute the chamber pressure of the Space Shuttle's Redesigned Solid Rocket Motor (RSRM), which has a very large L/D ratio. The RSRM was modeled as two inter-connected volumes with the volume-filling method applied accordingly. The predicted chamber pressure rise rate was in good agreement with that obtained by using a 1-D CFD code. If the details of flow physics are needed, such as in the Senior Engineering Specialist Copy right © 2001 by The Aerospace Corporation. Published by the American Institute of Aeronautics and Astronautics, Inc. with Permission (c)2001 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization. case of dealing with the effects of propellant cracks on the SRM performance, then a flowfield solution coupled with heat transfer and ignition is required. The foundation for CFD flowfield approaches to the SRM ignition transient prediction was laid by Peretz, Kuo, Caveny, and Summer-field more than a quarter century ago. However, rapid advances have been made only recently. In the 1970s and 1980s, the progress of analytical predictions of SRM ignition transients was hampered by the lack of a reliable computational method for solving compressible flow equations and the insufficiency of available computing power. As will be illustrated later in this paper, the SRM ignition transient flowfields are dominated by the compressible flow wave interactions. The singular nature of the strong compressions and shocks in the compressible flow equations has impeded the progress of CFD to a very large extent until the TVD (total-variation-diminishing) algorithms were developed in the late 1980s and early 1990s. As a result, accurate numerical methods were available to resolve the complex wave interactions in multi-dimensional flows. At the same time, giga-flop computing powers also became available for computational fluid dynamics (CFD) simulations. Therefore, many SRM ignition transient CFD simulations were published in the 1990s.' " Prediction methodologies have been also extended to include the coupling of flowfield and propellant deformation." However, most of the developments in this field are still based on the work of Peretz, et al. with the heat fluxes being computed by using a variety of semiempirical formulas. It is fair to say that, at the present, progress is hindered by the lack of reliable physical models for heat transfer. Fortunately, as indicated by Wang et al and demonstrated later in this paper, the computation of heat transfer in a CFD code can be conducted separately in a subroutine which can be replaced or updated without the need to change other parts of the code. Due to the progress in the performance enhancement of space launch systems, starand fin-shape propellant grain designs are now being used frequently. Therefore, there is an urgent need to replace 1-D and 2-D approaches by 3-D methodologies. Recently, funded by DOE's Accelerated Strategic Computing Initiative (ASCI) project, the University of Illinois has established a Center for Simulation of Advanced Rockets (CSAR). The goal of the center is to develop "an integrated rocket simulation tool capable of detailed, whole-system simulation of solidpropellant rockets under both normal and abnormal operating conditions." A report on the Center's progress was presented by Alvilli et al. With today's computing power, enhanced by visualization software, 3-D simulations of the SRM ignition transient are tractable. However, depending on the size of the burning area to be simulated and the computational grid resolution used, it could be very time consuming. The reason is that the mass injection on the burning surface belongs to a subsonic inflow boundary condition in CFD. An iteration procedure is therefore required, which is time consuming due to the non-linear (c)2001 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization. coupling of the equations. For the simulations presented in this paper, a quasi-3D approach is applied. Each case takes 36 CPU-hours on a Cray-SVl. This running time is considerably less than what is expected for a full 3-D simulation. The computation can be sped up by using parallel computing systems. As an example of speed-up, super parallel computers have been applied by Wang and Taylor 13 to simulate the transonic flowfield over a complete plume-on Delta II 7925, which has one core vehicle plus 9 strap-on SRM boosters. Using 506 nodes of an Intel's Paragon, a converged solution can be obtained in 48 hours. It was estimated that it would have required at least three months for the simulation if it had been done on a vector machine, CrayYMP. There is no doubt that future 3-D SRM ignition transient simulations will rely on super parallel computers. As reported by Alvi et al, super parallel computers are being used in CSAR at the University of Illinois. However, at present, full 3-D CFD simulations using parallel computers are still not popular. Furthermore, to convert an existing 3-D CFD code to run on a parallel computing system is not an easy task. A quasi-3D approach may be considered as an alternative cost-saving approach. In this paper, the physical models currently used in CFD for SRM ignition transient are reviewed. A quasi-3D flowfield simulation methodology for SRMs with large numbers of fins will be presented. The first objective is to show the 3-D phenomena in the flowfield that could not be simulated using a 1-D or 2-D CFD approach. The second objective is to illustrate an easy procedure that could lead to parallel CFD implementation. In this quasi-3D approach, an axi-symmetric system of equations is applied to the bore and a 2-D Cartesian system of equations to the fins. The fundamental assumption is that the circumferential, 0-component, velocity in the bore region, and the wcomponent velocity, which is normal to the fin surface, in the fin region are negligible. The justification is that, as the number of fins increases, the planes of symmetry increase and the momenta associated with these velocity components cancelled each other on the plane of symmetry. In this paper, the flow will be assumed inviscid and the simplest heat transfer and ignition models will be applied. Since the purpose of this paper is to illustrate the methodology and the flow physics that the present approach can bring forth, generic SRMs will be used.