Accurate Computation of Grain Burning Coupled with Flow Simulation in Rocket Chamber D. Gueyffier, * F. X. Roux, † and Y. Fabignon ‡ ONERA, The French Aerospace Lab, F-91761 Palaiseau, France G. Chaineray, § N. Lupoglazoff, ¶ and F. Vuillot ** ONERA, F-92322 Châtillon, France J. Hijlkema †† ONERA, F-31410 Mauzac, France and F. Alauzet ‡‡ Institut National de Recherche en Informatique et en Automatique Paris-Rocquencourt, 78153 Le Chesnay, France DOI: 10.2514/1.B35736 In this paper, we present a novel numerical approach for predicting the fluid flow in a solid rocket motor chamber with burning propellant grain. We use a high-order technique to track the regressing grain surface. Spectral convergence toward the exact burning surface is achieved thanks to Fourier differentiation. For the computation of the internal chamber fluid flow, we make use of a body-fitted volume mesh deforming with the grain surface. We describe several methods to deform the volume mesh and to keep good mesh element quality without global remeshing. We then couple the surface and volume approaches and integrate them into a complex code for compressible, multispecies, turbulent flow simulations. Thanks to these methods, we are able to exhibit one of the first three-dimensional simulations of the internal flow in a realistic solid rocket motor coupled to complex grain surface regression. In prior work, burning grain surface methods have only been coupled with one-dimensional internal ballistics solvers. I. Introduction A SOLID rocket motor (SRM) relies on solid propellant combus- tion to create high-pressure gases in the internal rocket chamber. These combustion gases are then expelled trough the nozzle at supersonic velocity to provide thrust to the rocket. Chamber pressure and rocket thrust depend directly on the burning surface area. Various complex grain geometries are currently in use in SRMs to control the time evolution of the thrust vector. Cylindrical grain geometries are used to increase thrust with time. Star grains or finocyls are usually chosen to maintain constant thrust. Other grain geometries contain fins, holes, or grooves. The time evolution of the burning grain surface for such grain geometries can be computed using various techniques. Researchers in the aerospace community sometimes use the terminology “grain burnback analysis” and other refer to the term “grain regression anal- ysis. ” In the following, we will talk about burning grain or regressing grain as we believe the simplest terminology is often the best. A number of analytical methods have been developed to study simple two-dimensional (2-D) geometries [1–3]. For more complex grain shapes or for three-dimensional (3-D) geometries, CAD software has been used to compute the evolving surface [4,5]. A Hamilton–Jacobi problem can also be resolved to compute the time evolution of the burning surface [6–8]. The level set method, which also relies on the resolution of a Hamilton–Jacobi problem, was used in [9–12]. This method has also been applied to the simulation of grain com- bustion at small scale [13]. A review of several methods currently in use to predict grain regression can be found in [10]. To compute the time-dependent 3-D flow in solid rocket chambers together with the regression of the grain surface, one must solve a coupled problem. Doing so will help us better understand combustion instabilities and pressure oscillations in rocket chambers [14–17]. Our novel methods will also help assess the effect of erosive and dynamic burning on the internal rocket flow. Other applications include optimal grain design and computation of the multiphase flow in the chamber [18,19]. For these applications, the method has to compute the flow in a time-dependent domain, and the method has to track the grain surface with a burning rate depending on local flow properties. Resolving this coupled problem is much more difficult than only predicting the burning surface evolution. To treat deformations of the computational domain, most compu- tational fluid dynamics (CFD) codes make use of an Arbitrary Lagrangian-Eulerian (ALE) method [20]. But difficulties arise when the mesh undergoes dramatic deformations during the regression of several types of grain. The most problematic deformations occur in regions where the grain surface is initially convex toward the gas. In these regions, a geometric singularity (caustic) forms in finite time on the grain surface. As shown on Fig. 1, if no special action is taken, the neighboring mesh will quickly become invalid. Our novel approach has been designed to prevent the collapse of volume mesh elements by moving vertices away from the singularity. In addition, a large proportion of CFD codes does not handle the addition or deletion of mesh elements during computations. Our method ensures that the deforming mesh keeps the same number of elements at all times; i.e., the mesh remains homeomorphic to the initial mesh. The contributions of this paper are 1) a novel spectral method to accurately track the burning grain surface and deform the surface mesh, 2) a method that prevents volume mesh elements to become invalid in regions where singularities appear on the grain surface, 3) a tech- nique that constrains the volume mesh to keep the same connectivity during the entire burning phase, and 4) a fully coupled method that predicts the effect of grain regression on the internal fluid flow. Presented as Paper 2014-3612 at the 50th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, Cleveland, OH, 28–30 July 2014; received 20 January 2015; revision received 28 May 2015; accepted for publication 28 May 2015; published online 10 August 2015. Copyright © 2015 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code 1533-3876/ 15 and $10.00 in correspondence with the CCC. *Senior Scientist, Solid Rocket Propulsion Team. Member AIAA. † Team Leader, High Performance Computing Team. ‡ Team Leader, Solid Rocket Propulsion Team. § Scientist, Computational Fluid Dynamics Team. ¶ Scientist, Computational Fluid Dynamics Team. **Team Leader, Computational Fluid Dynamics Team. †† Scientist, Propulsion Laboratory. ‡‡ Researcher, GAMMA3 Team. 1761 JOURNAL OF PROPULSION AND POWER Vol. 31, No. 6, November–December 2015 Downloaded by UNIVERSITA DEGLI STUDI DI MILANO on November 18, 2015 | http://arc.aiaa.org | DOI: 10.2514/1.B35736