# Multi-physics modelling

## Combustion

Chemically reacting flows with heat release, or combustion phenomena, are a found commonly in many industrial applications, involving gas turbines, internal combustion engines, boilers, etc.

Combustion phenomena, are characterised by several fundamental processes such as turbulence, heat and mass transfer, chemical reactions and radiation.

Combustion in the form of deflagration is characterised by high heat and mass transfer, causing high density variations at relatively low speeds. The low-Mach approximation to the Navier-Stokes equations offers a suitable approach to solving this phenomena.

Chemical reactions of a combustion process can span from a few species and reactions up to a few hundred species and reactions, which would require solving for a transport equation for each specie. This approach is extremely costly and models have been developed to reduce it. The flamelet model allows tabulating all chemistry effects as a function of several tabulation variables.

In order to study industry relevant phenomena, the transient turbulent Navier-Stokes equations in the low-Mach regime are solved using a Large Eddy Simulation (LES) approach. Advanced models are used to close the subgrid turbulent terms, such as the dynamic Smagorinsky or the WALE model. Combustion is modelled using the flamelet/progress-variable (FPV) model, allowing to incorporate detailed chemistry into the CFD simulations through tabulation.

Examples of performed and ongoing studies are a turbulent hydrogen enriched methane flame with a Reynolds of 15200.

## Publications

J. Ventosa, J. Muela, O. Lehmkuhl, C.D. PÃ©rez-Segarra, A. Oliva. Large Eddy Simulation of a turbulent jet diffusion flame using unstructured meshes. In Proceedings of the 8th Mediterranean Combustion Symposium, Turkey, 2013.

J. Muela, J. Ventosa, O. Lehmkuhl, C.D. PÃ©rez-Segarra, A. Oliva. Study of the autoignition of a hydrogen jet in a turbulent co-flow of heated air using LES modelling. In Proceedings of the 8th Mediterranean Combustion Symposium, Turkey, 2013.

J. Ventosa, O. Lehmkuhl, C.D. PÃ©rez-Segarra, A. Oliva. Large Eddy Simulation of a Turbulent Jet Diï¬€usion Flame Using the Flamelet-Progress Variable Model. In Proceedings of the 6th European Combustion Meeting, Lund, Sweden, 2013.

J. Muela, J. Ventosa, O. Lehmkuhl, C.D. PÃ©rez-Segarra, A. Oliva. Study of the Autoignition of a Hydrogen Jet in a Turbulent Co-flow of Heated Air Using LES Modelling. In Proceedings of the 6th European Combustion Meeting, Lund, Sweden, 2013.

J. Ventosa, J. Chiva, O. Lehmkuhl, C.D. PÃ©rez-Segarra, A. Oliva. Low Mach Navier-Stokes equations on unstructured meshes. In Proceedings of the 15th International Conference on Fluid Flow Technologies, Budapest, Hungary 2012.

J. Chiva, J. Ventosa, O. Lehmkuhl, C.D. PÃ©rez-Segarra, A. Oliva. Modelization of the low-Mach Navier-Stokes equations in unstructured meshes. In Proceedings of the 7th International Conference on Computational Heat and Mass Transfer, Istanbul, Turkey, 2011.

# Fluid Structure interaction

Fluid-structure interactions (FSI) are invited by the coupling between a fluid flow and the movement or deformation of a structure. This type of interactions can be found in a great amount of industrial applications, such as the design of aircrafts, the study of aerolastic instabilities of bridges and buildings, the optimisation of wind turbines or in bio-fluid mechanics research like heart valve development, among others. In those cases, the understanding of the fluid flow behaviour or the awareness of the dynamic action of the structure can be essential to improve engineering designs and optimisations. Therefore, accompanied by a great enhance in computational resources, in the last years the numerical simulation has become an important tool to predict FSI applications, even in turbulent regimes. As a consequence, a partitioned FSI solution coupled algorithm focused on the study of the flow phenomena in these type of problems has been implemented.

To attempt the numerical simulation of these phenomena, a robust, accurate and fast method which redistributes the computational mesh in accordance with the movement of the domain is needed. In general terms, the case is formulated as a three-field problem: the fluid domain, the structure domain and the dynamic mesh. Thus, each subdomain is solved separatly and a coupling criterion manages the transfer of information between domains. This staggered procedure allows to use the desired or most case-suitable solver for the fluid, the structure and the moving mesh, independently of the other domains.

In the fluid domain, the incompressible Navier-Stokes equations concerning dynamic mesh are solved by means of a three-dimensional explicit finite volume fractional-step algorithm formulated in a second-order, conservative and collocated unstructured grid arrangement. To compute the grid velocity considering the conservation principle and avoiding the loss of mass and momentum, the space conservation law is applied. Large-eddy simulations (LES) are performed for turbulent flows.

Referring to the dynamic mesh technique, a radial basis function (RBF) method is involved. The RBF approximation is becoming increasingly popular as a method the interpolate scattered data. In our context, the basic idea is to solve an interpolation problem in order to transfer the known displacements of a set of control points to the rest of grid points.

Different strategies have been carried out in the solid domain; for instance, a simplified model based on a steady state deformation law or a routine implying modal analysis of the solid dynamic action. Moreover, a finite volume computational structural dynamics (CSD) solver has been elaborated to solve the transient and dynamic elastic deformation of a St. Venant-Kirchhof material.

## References

O. Estruch, O. Lehmkuhl, R. Borrell, C.D. PÃ©rez-Segarra and A. Oliva. A parallel radial basis function interpolation method for unstructured dynamics meshes. Computer and Fluids, 80:44-54, 2013.

O. Estruch, O. Lehmkuhl, J. Rigola, A. Oliva and C.D. PÃ©rez-Segarra. Transient and dynamic numerical simulation of the fluid flow through valves based on large eddy simulation models. In Proceedings of the 8th International Conference on Compressors and their Systems, London, 2013.

O. Estruch, O. Lehmkuhl, J. Rigola, A. Oliva and C.D. PÃ©rez-Segarra. Large eddy simulation model assessment of the turbulent flow through dynamic compressor valves. In Proceedings of the 8th International Conference on Compressors and Coolants, CastÃ¡ Papiernicka, Slovakia, 2013.

O. Estruch, O. Lehmkuhl, R. Borrell and C.D. PÃ©rez-Segarra. Large-eddy simulation of turbulent dynamics fluid-structure interaction. In Proceedings of the 7th International Synopsium on Turbulence, Heat and Mass Transfer, Palermo, 2012.

O. Estruch, R. Borrell, O. Lehmkuhl and C.D. PÃ©rez-Segarra. A parallel Radial Basis Function Interpolation method for unstructured dynamic meshes. In Proceedings of theÂ 24th International Conference on Parallel CFD 2012, Atlanta, 2012.

O. Estruch, O. Lehmkuhl, R. Borrell and C.D. PÃ©rez-Segarra. A parallel three-dimensional Radial Basis Function Interpolation method for unstructured dynamic meshes. In Proceedings of the 23rd International Conference on Parallel CFD 2011, Barcelona, 2011.