# Multiphysics simulation of solid rocket motor ignition through code coupling : design of a novel strategy based on a mathematical study (Laurent François, Onera et École Polytechnique)

21.12.2021 14:00

A solid rocket motor uses the combustion of a solid material (propellant) as its energy source. A crucial stage in its operation is the ignition transient, which involves a wide variety of phenomena (compressible flow, heat transfer, pyrolysis, combustion, etc.). This multiphysical character and the associated disparities in space and time time scales make it impossible to simulate ignition using a single tool based on an exhaustive model. In particular, the propellant flame is so thin that it cannot be spatially resolved in a CFD mesh for a complete engine. Therefore, the classical approach is to use a 1D model of propellant combustion, at each boundary face of the CFD domain belonging to the propellant surface. Thus, all the physico-chemical and numerical complexities of solving this combustion are contained in a dynamic boundary condition.

This presentation will be divided into two parts. First, I will present the 1D model and the associated solver developed during my PhD thesis. Specific attention is given to the mathematical analysis of the 1D model in steady state, through the study of a travelling combustion wave, where the surface temperature appears as an eigenvalue of a nonlinear problem.

Then, the 1D model is semi-discretized in space in order to simulate unsteady combustion. The analysis of the differential-algebraic nature of the system of equations allows for the choice of high-order adaptive time integration methods.

The 1D solver is then coupled with ONERA's 3D CFD code CEDRE, in order to allow for the simulation of ignition in complete motors. This code coupling problem, via a potentially active interface, is a generic problem. For our applications, we have limited ourselves to first order accuracy in time. In order to verify the effect of the 1D representation of the flame, a more detailed approach is also developed, where the flame is solved in the CFD code itself. A comparison between the two approaches is presented on a discriminating 2D test case, and demonstrates the ability of the proposed strategy to solve the complete dynamics accurately.

In the second part, we will present an exploration of techniques to improve the temporal coupling, using error estimates to dynamically adapt both the time step and the order. This original approach is based on a time extrapolation of the coupling variables. It also has similarities with the transmission conditions found in domain decomposition methods. The benefits of this approach will be showcased on simplified test cases. This type of approach, useful for the applications targeted in the thesis, also allows for a more general look on the issue of code coupling.

### Lieu

Bâtiment: Conseil Général 7-9

Room 1-05, Séminaire d'analyse numérique

### Organisé par

Section de mathématiques### Intervenants

Laurent François , Onera et École Polytechniqueentrée libre