Numerical resolution of turbulent flows on complex geometries.

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.Postprint (published version

Direct numerical simulation of multiphase flows with unstable interfaces

Published under licence in Journal of Physics: Conference Series by IOP Publishing Ltd. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.This paper presents a numerical model that intends to simulate efficiently the surface instability that arise in multiphase flows, typically liquid-gas, both for laminar or turbulent regimes. The model is developed on the in-house computing platform TermoFluids , and operates the finite-volume, direct numerical simulation (DNS) of multiphase flows by means of a conservative level-set method for the interface-capturing. The mesh size is optimized by means of an adaptive mesh refinement (AMR) strategy, that allows the dynamic re-concentration of the mesh in the vicinity of the interfaces between fluids, in order to correctly represent the diverse structures (as ligaments and droplets) that may rise from unstable phenomena. In addition, special attention is given to the discretization of the various terms of the momentum equations, to ensure stability of the flow and correct representation of turbulent vortices. As shown, the method is capable of truthfully simulate the interface phenomena as the Kelvin-Helmholtz instability and the Plateau-Rayleigh instability, both in the case of 2-D and 3-D configurations. Therefore it is suitable for the simulation of complex phenomena such as simulation of air-blast atomization, with several important application in the field of automotive and aerospace engines. A prove is given by our preliminary study of the 3-D coaxial liquid-gas jet.Peer ReviewedPostprint (published version

Partitioned semi-implicit methods for simulation of biomechanical fluid-structure interaction problems

This article is published under a CC BY licence. The Version of Record is available online at: http://dx.doi.org/10.1088/1742-6596/745/3/032020.This paper represents numerical simulation of fluid-structure interaction (FSI) system involving an incompressible viscous fluid and a lightweight elastic structure. We follow a semi-implicit approach in which we implicitly couple the added-mass term (pressure stress) of the fluid to the structure, while other terms are coupled explicitly. This significantly reduces the computational cost of the simulations while showing adequate stability. Several coupling schemes are tested including fixed-point method with different static and dynamic relaxation, as well as Newton-Krylov method with approximated Jacobian. Numerical tests are conducted in the context of a biomechanical problem. Results indicate that the Newton-Krylov solver outperforms fixed point ones while introducing more complexity to the problem due to the evaluation of the Jacobian. Fixed-point solver with Aitken's relaxation method also proved to be a simple, yet efficient method for FSI simulations.Peer ReviewedPostprint (published version

Parallel load balancing strategy for Volume-of-Fluid methods on 3-D unstructured meshes

© 2016. This version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/l Volume-of-Fluid (VOF) is one of the methods of choice to reproduce the interface motion in the simulation of multi-fluid flows. One of its main strengths is its accuracy in capturing sharp interface geometries, although requiring for it a number of geometric calculations. Under these circumstances, achieving parallel performance on current supercomputers is a must. The main obstacle for the parallelization is that the computing costs are concentrated only in the discrete elements that lie on the interface between fluids. Consequently, if the interface is not homogeneously distributed throughout the domain, standard domain decomposition (DD) strategies lead to imbalanced workload distributions. In this paper, we present a new parallelization strategy for general unstructured VOF solvers, based on a dynamic load balancing process complementary to the underlying DD. Its parallel efficiency has been analyzed and compared to the DD one using up to 1024 CPU-cores on an Intel SandyBridge based supercomputer. The results obtained on the solution of several artificially generated test cases show a speedup of up to similar to 12x with respect to the standard DD, depending on the interface size, the initial distribution and the number of parallel processes engaged. Moreover, the new parallelization strategy presented is of general purpose, therefore, it could be used to parallelize any VOF solver without requiring changes on the coupled flow solver. Finally, note that although designed for the VOF method, our approach could be easily adapted to other interface-capturing methods, such as the Level-Set, which may present similar workload imbalances. (C) 2014 Elsevier Inc. Allrights reserved.Peer ReviewedPostprint (author's final draft

LES study of the impact of fuel composition on a swirl spray flame approaching blow-off

The present paper focuses on the large eddy simulation (LES) of the n-heptane and n-dodecane flames of the Cambridge swirl flames data repository (Sidey et al., 2017). The applied tabulated chemistry spray combustion model reproduces well the key phenomena controlling flame dynamics. The distinct volatility of the fuels is identified as the source of main difference between the n-heptane and n-dodecane flames.We acknowledge the funding from the CoEC project through the European Union’s Horizon 2020 research and innovation programme under grant agreement No 952181. The authors thankfully acknowledge the computer resources at MareNostrum and the technical support provided by Barcelona Supercomputing Center (FI-2019-1-0045, IM-2019-3-0019, IM-2020- 1-0011, IM-2020-2-0025.)Peer ReviewedPostprint (published version

A new statistical model for subgrid dispersion in large eddy simulations of particle-laden flows

This article is published under a CC BY licence. The Version of Record is available online at: http.//dx.doi.org/10.1088/1742-6596/745/3/032115Dispersed multiphase turbulent flows are present in many industrial and commercial applications like internal combustion engines, turbofans, dispersion of contaminants, steam turbines, etc. Therefore, there is a clear interest in the development of models and numerical tools capable of performing detailed and reliable simulations about these kind of flows. Large Eddy Simulations offer good accuracy and reliable results together with reasonable computational requirements, making it a really interesting method to develop numerical tools for particle-laden turbulent flows. Nonetheless, in multiphase dispersed flows additional difficulties arises in LES, since the effect of the unresolved scales of the continuous phase over the dispersed phase is lost due to the filtering procedure. In order to solve this issue a model able to reconstruct the subgrid velocity seen by the particles is required. In this work a new model for the reconstruction of the subgrid scale effects over the dispersed phase is presented and assessed. This innovative methodology is based in the reconstruction of statistics via Probability Density Functions (PDFs).Peer ReviewedPostprint (published version

Noise radiated by an open cavity at low Mach number: Effect of the cavity oscillation mode

The present work focuses on the study of noise generation and radiation of an infinite open three-dimensional cavity at low Mach number with laminar upstream conditions that is of interest to understand noise generation mechanisms in wall-bounded separated flows. A particular feature of this configuration is the oscillatory mode: shear layer mode or wake mode. For the parameters considered in the present study it is seen that while in shear layer mode the flow shows a two-dimensional behavior, in the wake mode the flow is three-dimensional, resulting in significantly different sound sources. The influence of the acoustic feedback mechanism in the shear layer mode has also been investigated comparing the results between different momentum thickness values at the cavity inlet. This paper presents results of sound radiated by a three-dimensional infinite open cavity with aspect ratio L/D = 4 at Reynolds number based on the cavity depth of ReD = 1500 and Mach number of M = 0.15, both for shear layer (L/θ = 67) and wake (L/θ = 84) oscillation modes. To do so, Curle integral evaluated as a post-process of an incompressible solution will be used. The results are compared with the resulting Curle post-process of a two-dimensional incompressible simulationPeer ReviewedPostprint (author's final draft

Large-eddy simulations of the flow on an aerofoil with leading-edge imperfections

We performed large-eddy simulations of the flow over an aerofoil to understand the effects of leading-edge roughness designed to mimic ice accretion. The roughness elements protrude outside the boundary layer, which, near the leading edge, is very thin; thus, the configuration does not represent a classical rough-wall boundary layer, but rather the flow over macroscopic obstacles. A grid convergence study is conducted and results are validated by comparison to numerical and experimental studies in the literature. The main effect of the obstacles is to accelerate transition to turbulence. Significant variations in structure generation are observed for different roughness shapes. The three-dimensionality of the irregularities has a strong impact on the flow: it creates alternating regions of high-speed (‘peaks’) and low-speed (‘valleys’) regions, a phenomenon termed ‘channelling’. The valley regions resemble a decelerating boundary layer: they exhibit considerable wake and higher levels of Reynolds stresses. The peak regions, on the other hand, are more similar to an accelerating one. Implications of the channelling phenomenon on turbulence modelling are discussed.VK acknowledges the financial support by Mitacs, Bombardier Aerospace and CARIC/CRIAQ. UP acknowledges the support from the Natural Science and Engineering Research Council of Canada (NSERC) under the Discovery Grant program, and the Canada Research Chair program. This research was enabled in part by computational support provided by Compute Ontario (computeontario.ca) and Southern Ontario Smart Computing Innovation Platform (SOSCIP) (www.soscip.org).Peer ReviewedPostprint (author's final draft

Three dimensionality in the wake of the flow around a circular cylinder at Reynolds number 5000

The turbulent flow around a circular cylinder has been investigated at Re=5000Re=5000 using direct numerical simulations. Low frequency behavior, vortex undulation, vortex splitting, vortex dislocations and three dimensional flow within the wake were found to happen at this flow regime. In order to successfully capture the wake three dimensionality, different span-wise lengths were considered. It was found that a length LZ=2pDLZ=2pD was enough to capture this behavior, correctly predicting different aspects of the flow such as drag coefficient, Strouhal number and pressure and velocity distributions when compared to experimental values. Two instability mechanisms were found to coexist in the present case study: a global type instability originating in the shear layer, which shows a characteristic frequency, and a convective type instability that seems to be constantly present in the near wake. Characteristics of both types of instabilities are identified and discussed in detail. As suggested by Norberg, a resonance-type effect takes place in the vortex formation region, as the coexistence of both instability mechanisms result in distorted vortex tubes. However, vortex coherence is never lost within the wake.Peer ReviewedPostprint (author's final draft

On the properties of discrete spatial filters for CFD

© 2016. This version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/The spatial filtering of variables in the context of Computational Fluid Dynamics (CFD) is a common practice. Most of the discrete filters used in CFD simulations are locally accurate models of continuous operators. However, when filters are adaptative, i.e. the filter width is not constant, or meshes are irregular, discrete filters sometimes break relevant global properties of the continuous models they are based on. For example, the principle of maxima and minima reduction or conservation are eventually infringed. In this paper, we analyze the properties of analytic continuous convolution filters and extract those we consider to define filtering. Then, we impose the accomplishment of these properties on explicit discrete filters by means of constraints. Three filters satisfying the derived conditions are deduced and compared to common differential discrete CFD filters on synthetic fields. Tests on the developed discrete filters show the fulfillment of the imposed properties. In particular, the problem of maxima and minima generation is resolved for physically relevant cases. The tests are conducted on the basis of the eigenvectors of graph Laplacian matrices of meshes. Thus, insight into the relations between filtering and oscillation growth on general meshes is provided. Further tests on singularity fields and on isentropic vortices have also been conducted to evaluate the performance of filters on basic CFD fields. Results confirm that imposing the proposed conditions makes discrete filters properties consistent with those of the continuous ones.Peer ReviewedPostprint (author's final draft