Numerical resolution of turbulent flows on complex geometries.
Authors:   , Lehmkuhl Barba Oriol 
Published: October 2023

This thesis aims at developing a numerical methodology suitable for the direct numerical simulation (DNS) and large-eddy simulation (LES) of turbulent flows in order to be used in complex flows, currently encountered in industrial application.
At the same time, the study of such turbulent flows can be an opportunity for gaining
insight into the complex physics associated with them.
To accomplish these goals, the mathematical formulation, conservative spatial discretization on unstructured grids and time- integration scheme for solving the Navier-Stokes equations are presented. The spatial discretization proposed preserves
the symmetry properties of the continuous differential operator and ensure both, stability and conservation of the global kinetic energy balance on any grid. Furthermore, the time-integration technique proposed is an efficient self-adaptive strategy, based on a one-parameter second-order-explicit scheme, which has been successfully tested on both Cartesian staggered and unstructured collocated codes, leading to CPU cost reductions of up to 2.9 and 4.3, respectively.
After presenting the general methodology for computing flows in complex geometries with unstructured grids, different LES models and regularization models suitable for these kind of meshes are presented and assessed by means of the analysis
of different flows. First, regularization models are tested by means of the simulation of different cases with different level of complexity of the mesh. From a structured grid to a very complex mesh, with zones composed of prism and tetrahedral control
volumes. It has been shown, that regularization models are very dependent on the quality of the filtering process. Although good results can be obtained with structured or smooth unstructuredmeshes, their performance is affected under fully irregular unstructured grids. A possible remedy to circumvent this issue is also presented. The main idea is to formulate the C4 model within a LES template. Although preliminary results are promising, further testing is still required.
After regularization model assessment, LES models are also tested in a natural convection flow. It is shown that, although first order statistics are well solved for most of the models tested (with the exception of the Smagorinsky model), QR- and
dynamic-Smagorinsky models present a better prediction of the second-order statistics. However, if CPU time is considered, then QR model is the best alternative.
The second part of the thesis is devoted to the study of turbulent flows past bluff bodies. The cases studied are: the flow past a sphere, the flow past a circular cylinder and the flow past a NACA 0012 airfoil. All these cases shares some characteristics
encountered in turbulent flows with massive separations, i.e., flow separation, transition to turbulence in the separated shear-layers and turbulent wakes with periodic shedding of vortices. However there are intrinsic characteristics of the turbulence in
each of them, which make them interesting for the studying of the turbulence. Furthermore, the results presented for the flow past a sphere at Re = 3700 and 10000, together with the flow past a NACA 0012 at Re=50000 and AoA = 8 are the first
DNS results presented in the literature for both flows.
Conclusions drawn from the good results obtained point out that the use of the conservative formulation presented in this thesis, is one of the keys for the success of the SGS models used. This formulation, together with the use of unstructured grids might be a step towards the use of LES models for solving industrial flows on complex geometries at high Reynolds numbers.

La present tesi proposa una metodologia apte per a realitzar simulacions directes de la turbulència (DNS) i simulacions de les grans escales (LES) de fluxos turbulents en geometries complexes. Tanmateix també s'estudia detalladament els mecanismes bàsics de funcionament dels fluxos turbulents en diferents situacions d'interès industrial i acadèmic.

Per acomplir aquest objectiu s'ha desenvolupat una innovadora formulació matemàtica que permet conservar discretament les propietats continues de les equacions governants en malles no estructurades. La formulació proposada preserva la simetries originals dels operadors diferencials, assegurant així l'estabilitat i la conservació de l'energia cinètica turbulent en qualsevol mallat. Posteriorment s'ha proposat una metodologia d'integració temporal basada en una formulació explicita de segon ordre. Aquesta nova tècnica ha demostrat ser entre 2.9 i 4.3 més rapida que les tècniques anteriorment utilitzades per la comunitat.

Un cop presentada la formulació per a simular fluxos turbulents en geometries complexes, s'han validat diferents models LES adaptats a malles no estructurades. Els models s'han testejat usant diferents solucions de referencia de la literatura i simulacions d'alt nivell generades en el context de la present tesi. Finalment s'ha conclòs que la conjunció de la formulació bàsica proposada amb alguns del models LES sorgits en els darrers anys es molt efectiva per a simular fluxos turbulents en situacions complexes, essent el Variational Multiscale WALE i el model QR els més adequats per a simular situacions de interes industrial.

La segona part de la tesi es dedicada a l'estudi aerodinàmic del flux turbulent al voltant de diferents perfils. El perfils seleccionats son: el flux al voltant d'una esfera, flux al voltant d'un cilindre i flux al voltant d'un perfil NACA 0012. Els tres casos comparteixen fenomenologies com ara separació massiva de capes límits, esteles turbulentes i desprendiment periòdic de remolins. Tot i així cadascun d'ells es comporta diferent a nivell turbulent així que es d'interès estudiar-los i entendre quins son les causes de les diferencies físiques que es troben. Cal recordar que la física estudiada es la que es pot trobar posteriorment en ales d'avió, perfils de turbines de vent, aerodinàmica de cotxes, etc. Finalment recalcar que els resultats DNS del flux al voltant de l'esfera a Re=3700 i Re=10000 conjuntament amb els DNS del flux al voltant del perfil NACA a Re=50000 i AoA =8 son els primers presentats en la literatura internacional en el seu àmbit.

Finalment es pot concloure que la formulació conservativa presentada en la tesis juntament amb els diferents models LES d'última generació testejats en la tesis, han demostrat ser una eina eficaç tan per a resoldre fluxos turbulents d'interès acadèmic com per simular situacions d'interès industrial.