The goal of this project was to develop mathematical models and simulation tools for virtual design of exhaust systems with respect to aero-acoustic properties. The interdisciplinary project team was funded by Vinnova and the Swedish Energy Agency, and consisted of mathematicians of the KTH Computational Technology Laboratory (CTL), and engineers of the KTH Marcus Wallenberg Laboratory (MWL) and Eberspächer Exhaust Technology Sweden AB (former Swenox AB).

An exhaust system consists of flexible parts interacting with the airflow from the engine, and the problem is to predict aero-acoustic properties of such a system. The basic model is the Navier-Stokes equations describing velocity, pressure and density of the exhaust air, together with corresponding equations for the solid structures of the system. The main challenges are: (i) to model turbulent fluid flow, with several open problems with respect to the mathematics of the model and the computational cost of resolving the turbulent scales, (ii) robust coupling of the fluid and the structure models, and (iii) extraction of acoustic information from the model, in the form of very small pressure fluctuations.

The mathematical technology used in the project to simulate both the turbulent airflow and the solid structures is adaptive finite element methods. The coupling of the fluid and the structure is handled by a monolithic approach where the fluid and solid were formulated as one unified continuum. The aero-acoustic sources can then be extracted from the simulations by acoustic analogies. The algorithms are implemented in the open source software project FEniCS. To address the industrial problem of complex geometry and realistic physics, the algorithms and software had to be redesign to run efficiently on the most advanced supercomputers available in Europe.

### References

KTH Marcus Wallenberg Laboratory (MWL)

KTH Computational Technology Laboratory (CTL)

### Contact

Professor Johan Hoffman, principal investigator CTL