The current research lines of the CFD-MS group deal with the development and application of macroscopic and mesoscopic particle models for complex flow processes. Parallelization and optimization of the Lagrangian schemes is obtained by adopting routines for large-scale particle simulations, including the Particle- Particle-Mesh libraries (PPM) http://www.ppm-library.org/. Here is a list of research topics:

**CFD of viscoelastic fluids and elastic turbulence**

The continuum flow of polymeric liquids through complex geometries is of paramount importance in many areas of engineering such as composite-polymer manufacturing, extrusion processes, lubrication, enhanced oil recovery but also for several biomedical applications. In most of these processes the appearance of non-linear instabilities of the complex fluid might affect drastically the dynamics, eventually leading to a chaotic unsteady state even in the absence of fluid inertia (zero Reynolds number): a phenomenon denoted as â€śelastic turbulenceâ€ť. In the area of biomicrofluidics, elastic instabilities triggering micro-turbulence have been recently exploited for the design of novel mixing devices operating with biological liquids, whereas in manufacturing engineering (e.g. polymer extrusion) elastic instabilities represent a source of artifacts to be avoided. Despite the large technological importance of the problem, the flow of highly elastic liquids through complex geometries remains controversial. The main issue is related to a typical sudden large increase in the flow resistance and unsteadiness which cannot be predicted based on existing models. SPH-based CFD computations of viscoelastic liquids [1] through a periodic channel flow have provided evidence of unsteady elastic behaviour and enhanced resistance, in quantitative agreement with experimental observations and theoretical predictions of the energy spectrum [2]. Simulations indicate that for a sufficiently large level of fluid elasticity, a chaotic self-sustained state corresponding to inhomogeneous near-wall structures of polymer over/under-extension (Fig. 1, top/right), can be established where enhanced mixing of mass takes place (Fig.1, bottom). The objective of this research direction is to explore novel strategies to control micro-mixing based on elastic turbulence.

*Fig. 1: Viscoelastic flow through a periodic array of cylinders. Top: a) steady mean velocity field (streamwise direction x); b) steady mean polymer conformation tensor (xx); c) Reynolds stress (xx); d) snapshot main unsteady mode conformation tensor (xx) obtained via Dynamic Mode Decomposition analysis Bottom: space-time diagram of mass mixing in the top near-wall layer with no elastic instability (left) and with instability (right) [2].*

**
Computational Micro-Fluidics (CÂµF)
**

The increasing technological need to create and manipulate structures on micrometer scales and smaller has triggered the development of many numerical techniques for simulating flow problems at microscales. An emerging area is represented by bio-microfluidics where a single or a collection of molecules are actuated by accurate control of very small amounts of liquid (<ml) flowing through complex micro-devices. A challenging aspect in the modelling of complex fluids on these micro-scales (<<mm) is that no scale separation is present between the size of the suspended microstructure (e.g. the polymer molecule, colloid, cell etc.) and the external device, in such a way that no continuum model based on set of PDEs can be used. Instead, direct modelling of the microstructure, i.e. the dispersed phase, is required.

In our group we have developed a coarse-grained polymer-molecule model (Fig.2 left) where the Brownian solvent is described by the Smoothed Dissipative Particle Dynamics methods (SDPD) [3] which is a "thermodynamic-consistent" mesoscopic particle model of fluctuating hydrodynamics.

The current research direction is addressing virtual microfluidics-based rheometry (Fig. 2, right), where our recent mesoscopic simulations have allowed to clarify the link between the spatial flow relaxation of the complex liquid occurring along the channel with the microstructural relaxation processes of the single suspended polymers [4].

*Figure 2: Top: mesoscopic model of a single polymer molecule suspended in a thermal solvent: microstructural properties [3]. Bottom: microfluidics-based rheometer: a polymeric fluid is injected into the left chamber and undergoes a sudden contraction. Mesoscopic simulations have been carried out to understand the link between microstructure changes and evolution of the macroscopic flow [4].*

**CFD and rheology of complex particulate systems**

Accurate prediction of the dynamics and mechanical properties of micro/nano-particle suspensions interacting with complex media and under complex micro-flow conditions is critical for many industrial processes ranging from transport of slurries, seabed sediments to the design of hybrid particle-based fluids with enhanced shock-absorption performance, so called â€śshear-thickening fluidsâ€ť. In our group we have developed a new massively parallel mesoscopic particle simulation platform to characterize thermal and rheological properties of complex particulate systems based on SPH and SDPD. Starting from our validated mesoscopic models for colloidal and non-colloidal structures [5] suspended in simple Newtonian [6] (fig. 3: left) or viscoelastic matrices [7] (fig. 3, right), we are currently exploring the possibility to perform virtual rheology by means of direct numerical simulations (DNS) of new particle formulations, that is, by precise characterization of their input microstructure (particle shape, suspending medium rheology, microscopic inter-particle interactions etc.) to study quantitatively the corresponding bulk mechanical/thermal response. In particular, the main current focus is on shear-thickening fluids for novel hybrid fluid-solid materials with improved absorption properties.

*Fig. 3: Direct numerical simulation (DNS) of particle suspension rheology/dynamics. Left (top/bottom): suspension with a simple Newtonian solvent [6]. Right: suspension with a complex viscoelastic matrix (trace polymer conformation tensor shown).*

**Multiscale CFD modelling of biomedical flows**

In many biological processes it is critical to predict accurately the cellular transport and deposition close to vessel walls in presence of a complex, unsteady flow. This is important to control drug delivery but also for the understanding of several cardiovascular diseases. Atherosclerosis, for example, is a degenerative disease of the arterial wall that is thought to be initiated due to inflammation of the arterial endothelium, promoting the over-deposition of white blood cells (WBCs). This anomalous WBC accumulation is site-specific and can lead to initial stage lesions or, on a long-term timescale, atherosclerotic plaques. To study these problems, we have recently developed a multiscale transport model for leukocytes [8] and coupled it to an endothelial cell receptor binding model in order to link the transport and surface biology [9]. The large-scale separation existing between biological components (order of microns) and typical vessel size in the macrovascular network (order of cm) prevents the use of detailed mesoscopic particle methods. The multiscale Lagrangian Particle Tracking (LPT) strategy proposed in [6] is based on a continuum viewpoint coupled with a discrete representation of the leukocytes as "test particles" rather than real cells. Leukocyte dynamics is handled based on a continuum advection-diffusion equation for a concentration field in the bulk domain, whereas discrete cells interacting with hydrodynamic and biological adhesion-mediated forces are considered in proximity of the vessel walls. The reduced number of tracked test particles which can be achieved by distributing them within a thin near-wall region only (Fig. 4 top) allow considerable speed-up of simulation for these systems, preserving the accuracy of the deposition profiles [9].

In [9] the multiscale model has been tested against in-vitro data from a 3D geometry with a stenosis and sudden expansion (Fig. 4 bottom). In both steady and pulsatile flow conditions, results show close agreement with the experimental ones considering a class of WBCs (U937 monocytic human cells) on a E-selectin-coated geometry. Future directions include the application of the current multiscale approach to in-vivo conditions such as the carotid bifurcations and other patient-specific flows.

*Fig. 4: Multiscale Lagrangian Particle Tracking (LPT) scheme for leukocytes in flow: (Top) leukocyte dynamics in the bulk is described by a continuum concentration field governed by an advection-diffusion equation; near-wall layer is filled with test particles undergoing detailed LPT with realistic lubrication and biologically-derived adhesionforces [8]. Bottom: comparison of cell adhesion data between simulation and the experimental data for U937 cells and E-selectin coated device surfaces to replicate mechano-chemical environment.*

**BBIPED: CFD Industrial Platform for Engineering Design**

BBIPED (BCAM-Baltogar Industrial Platform for Engineering Design) is an engineering simulation software for fluid dynamics industrial applications [10]. BBIPED can handle a wide range of engineering applications in sectors such as turbomachinery, aeronautics, renewable energy, biosciences, advanced manufacturing, automotive, water and heat management; providing ad-hoc solutions for specific industry needs.

*Fig. 5: BBIPED Platform Schema. The BBIPED Platform is composed by 3 main blocks (from left to right): CAD/Mesh generation, Solver configuration and simulation, and Post-processing. Each of the blocks are integrated through a common interface, the so-called BBIPED Graphical Interface(BBIPED GUI).*

The BBIPED Graphical User Interface allows an automated CFD simulation process from CAD generation, meshing, solving and post-processing (Fig.5). The idea of developing this platform was proposed by BCAM and Baltogar, who joined efforts to overcome current industrial challenges in turbomachinery design by means of extensive research. This work has been developed within the research project "Development of an efficient, flexible and innovative CFD Computational Platform to optimally simulate and design industrial products and processes", co-funded by the Department of Economic Promotion of the Biscay Foral Council and the Department of Education, Language Policy and Culture of the Basque Government. In the recent project FRACTAL in collaboration with ETXE-TAR a CFD simulation of beam deposition process for a control laser device was performed [3]. The BBIPED Software was used to design and optimize a Laser-feeder cladding system and minimize lost material and processing time.

**References**

- [1] Ellero, M. and R. Tanner (2005). SPH simulations of transient viscoelastic flows at low Reynolds number. Journal of Non-Newtonian Fluid Mechanics 132(13), 61 â€“72.
- [2] Grilli, M., A. Vazquez-Quesada, and M. Ellero (2013). Transition to Elastic Turbulence and Mixing in a Periodic Channel Flow. Phys. Rev. Lett. 110, 174501(5).
- [3] Litvinov, S., M. Ellero, X. Hu, and N. A. Adams (2008). Smoothed dissipative particle dynamics model for polymer molecules in suspension. Phys. Rev. E 77 (6), 066703.
- [4] Litvinov, S., X. Hu, M. Ellero, and N. A. Adams (2014). Mesoscopic simulations of the transient behaviour of semi-diluted polymer solutions in microchannel following extensional flow. Microfluids and Nanofluidics 16(1), 257â€“264.
- [5] Bian, X., S. Litvinov, R. Qian, M. Ellero, and N. A. Adams (2012). Multiscale modeling of particle in suspension with smoothed dissipative particle dynamics. Physics of Fluids 24(1), 012002, 012002.
- [6] Vazquez-Quesada and M. Ellero (2016). Rheology and microstructure of non-colloidal suspensions under shear studied with Smoothed Particle Hydrodynamics. Journal of Non-Newtonian Fluid Mechanics 233, 37â€“47.
- [7]Vazquez-Quesada, A. and M. Ellero (2017). SPH modelling and simulation of spherical particles interacting in a viscoelastic matrix. Physics of Fluids 29, 121609â€“12.
- [8] Gholami, B., A. Comerford, and M. Ellero (2014). â€ťA SPH multiscale particle model of the near-wall dynamics of leukocites in flowâ€ť. Int. J. Num. Meth. Biomed. Engng. 30, 83â€“102.
- [9] Gholami, B., A. Comerford, and M. Ellero (2015). SPH simulations of WBC adhesion to the endothelium: the role of haemodynamics and endothelial binding kinetics. Biomechanics and Modeling in Mechanobiology 14(6), 1317â€“1333.
- [10] Carmen Alonso-Montes, I Garcia, A Ramezani, L Remaki (2014) BBIPED: BCAM-Baltogar Industrial Platform for Engineering Design International Conference on Circuits, Systems, Communications and Computers (CSCC 2014); Advances in Engineering Mechancis and Materials, Proc. the International Conference on Industrial Engineering (INDE 2014).