High Performance Computing
Turbulence is the usual state of motion of fluids except at low Reynolds numbers. Understanding its physics is essential in a wide range of scientific disciplines, including engineering, progress in renewable energy, aerodynamics, astrophysics, geology or weather prediction.
The governing equations for both laminar and turbulent flows are the same (the NavierStokes equations), but the complexity of turbulent flows is very high so huge computational resources are needed to proceed to their direct solution without any model.
This approach is known as Direct Numerical Simulation (DNS). DNS is important for shedding light into the complex physics of turbulent flows, as well as to provide data for the development and validation of turbulence models (both Large Eddy Simulation (LES) and Reynolds Averaged NavierStokes (RANS) models) and also to be directly applied to certain types of flows.
CTTC has developed parallel high performance software, that can run efficiently on thousands of processors, and used it to carry out several large scale DNS and LES simulations, such as the examples presented in this page.
References
[2] E. Schillaci, O. Antepara, O. Lehmkuhl, N. Balcázar, A. Oliva. Effectiveness of adaptive mesh refinement strategies in the DNS of multiphase flows. Turbulence, Heat and Mass Transfer 8. 2015.
[3] O. Antepara, R. Borrell, O. Lehmkuhl, A. Oliva. Parallelization strategy for the adaptive refinement of threedimensional structured meshes and its application in turbulent flows. 26th International Conference on Parallel Computational Fluid Dynamics. Norway. 2014.
[4] F. Favre, O. Antepara, O. Lehmkuhl, R. Borrell, A. Oliva. On the fast transient spoiler deployment in a NACA0012 profile using LES techniques combined with AMR and IMB methods. Joint WCCM – ECCM – ECFD 2014 Congress, 6th. European Conference on Computational Fluid Dynamics (ECCOMAS ECFD VI). Spain. 2014.
[5] O. Antepara, R. Borrell, O. Lehmkuhl, I. Rodríguez, A. Oliva. Parallel adaptive mesh refinement of turbulent flow around simplified car model using an immerse boundary method. Joint WCCM – ECCM – ECFD 2014 Congress, 6th. European Conference on Computational Fluid Dynamics (ECCOMAS ECFD VI). Spain. 2014.
[7] O. Antepara, O. Lehmkuhl, A. Oliva, F. Favre. LargeEddy Simulations of turbulent flow around a wallmounted cube using an adaptive mesh refinement approach. 14Th European Turbulence Conference, 2013
[8] O. Antepara, R. Borrell, O. Lehmkuhl, A. Oliva. Parallel mesh multiplication and adaptation technique for turbulent flow simulation using unstructured meshes. 27th International Conference on Parallel Computational Fluid Dynamics. Canada. 2015
[9] E. Schillaci, O. Lehmkuhl, O. Antepara and A. Oliva. Direct numerical simulation of multiphase flows with unstable interfaces. 7th European ThermalSciences Conference (Eurotherm 2016). KrakowPoland, June 1923, 2016. https://doi.org/10.1088/17426596/745/3/032114(link is external)
Direct Numerical Simulation of BuoyancyDriven turbulent flows.
Direct Numerical Simulation of BuoyancyDriven turbulent flows.  
Buoyancydriven flows in enclosed cavities have been the subject of numerous experimental and numerical studies in the last decades. They model many engineering applications such as ventilation of rooms, cooling of electronics devices or air flow in buildings. Despite the great effort devoted there are still many questions that remain open. Firstly, significant discrepancies are still observed between numerical and experimental studies. They are strongly connected with the role of the transitional thermal boundary layer: numerical results provide strong evidences that the flow structure cannot be capture well unless the transition point at the vertical boundary is correctly located [1]. At relatively high Rayleigh numbers, LES models have consistently failed on accurately predicting the transition of the vertical boundary layer for an airfilled differentially heated cavity (DHC) of aspect ratio 5 and Ra=4.5e10. Actually, for this configuration, DNS results carried out at the CTTC have revealed that the transition of the vertical boundary layer occurs at more downstream positions than those observed in the experiments [2]. Another important issue that has remained open is the thermal stratification in the core of the cavity. Comparison between numerical and experimental results for a wide range of width/height aspect ratios give completely different results. Experimental studies yield a dimensionless stratification of about 0.5 while numerical simulations predict values of about 1. In this regard, a set of five DNS simulations of an airfilled DHC of aspect ratio 4 (Rayleigh numbers based on the cavity height 6.4e8, 2e9, 1e10, 3e10 and 1e11) were presented in [3,4]. Significant changes were observed for the two highest Ra for which the transition point at the boundary layers clearly moves upstream. Such displacement increases the top and bottom regions of disorganization shrinking the area in the cavity core where the flow is stratified. Consequently, thermal stratification values are significantly greater than unity (1.25 and 1.41, respectively).

Fig. 4: DNS of an airfilled Differentially Heated Cavity at Ra=1e11 and height aspect ratio 4.  
Direct Numerical Simulation of turbulent flows in bodies of revolution using unstructured meshes. Flow past a sphere at subcritical Reynolds numbers
The Direct Numerical Simulation (DNS) of a flow past a sphere at different subcritical Reynolds numbers of Re=3700 and Re=10000 (based on the freestream velocity and the sphere diameter) are performed. As the threedimensional and time depending flow behavior demands the use of fine grids and large integration times, there is still a lack of detailed information about turbulent statistics in the wake of the sphere. A parallel unstructured symmetrypreserving formulation has been used for simulating the flow. Computations have been carried out on unstructured grids obtained by the constantstep rotation about the axis of a twodimensional grid. With this discretisation, the Poisson equation has been solved by means of a Fourier diagonalisation method. DNSs carried out have allowed the validation of the numerical methodology used and the CFD code developed. In this sense, the main objectives of the study are: (i) to investigate the characteristics of turbulent flow over the sphere and the vortical structures associated and, (ii) to provide useful information about turbulent statistics for the assessment of turbulence models. The latter is of relevance for the prediction of flows with massive separation in many engineering and industrial applications. The main features of the flow including power spectra of a set of selected monitoring probes at different positions have been described and discussed in detail. Detailed information about turbulent statistics has also been provided. Computational grids of 9.5 and 18 million of control volumes have been used for Re=3700 and 10000, respectively. 
Projects related: FI200930011 and FI201020018 I. Rodríguez, O. Lehmkuhl, R. Borrell, A. Oliva, and C.D. PérezSegarra. Direct numerical simulation of turbulent wakes: Flow past a sphere at Re= 5000. In V European Conference on Computational Fluid Dynamics ECCOMAS, Lisbon, Portugal, 2010. I. Rodríguez, R. Borrell, O. Lehmkuhl, A. Oliva, and C.D. PérezSegarra. Direct numerical simulation of the flow over a sphere at re = 3700. In Turbulence, Heat and Mass Transfer, 2009. 
Direct Numerical Simulation of turbulent flows in complex geometries using unstructured meshes. Flow around a circular cylinder at subcritical Reynolds numbers
Direct Numerical Simulations (DNS) of the flow past a circular cylinder have been carried out at Reynolds numbers of Re=3900 and 10000. To do these simulations, the governing equations have been discretised on a collocated unstructured grid arrangement, by means of secondorder symmetrypreserving schemes. Such schemes are conservatives, i.e., they preserve the symmetry properties of the continuous differential operators, and ensure both stability and conservation of the global kineticenergy balance on any grid. For the temporal discretisation of the momentum equation a twostep linear explicit scheme on a fractionalstep method has been used for the convective and diffusive terms, while for the pressure gradient term an implicit firstorder scheme has been used. To carrying out these simulations, computational meshes up to 20 million of control volumes have been used. One of the outcomes of these simulations has been the identification of a modulation frequency of the vortex formation zone which produces an alternating enlargement and shrinking of this zone. This frequency, lower than that of the vortex shedding has been identified thanks to the large computation time considered in these simulations (about 850 vortex shedding cycles have been simulated).
Projects related: FI201120016 and FI201130003 Total hours awarded: 250 000 core hours at Marenostrum supercomputer and 156 000 core hours at Magerit CesVima supercomputer through RES – Spanish Network of Supercomputing I. Rodríguez, O. Lehmkuhl, R. Borrell, A.Oliva. Direct numerical simulation of a NACA0012 airfoil with massive separation. In Direct and Large Eddy Simulation (DLES9) Workshop. Dresden. 2013. O Lehmkuhl, I. Rodriguez, A. Baez, A. Oliva and C.D. PerezSegarra. On the LargeEddy Simulations for the flow around aerodynamic profiles using unstructured grids. Computers&Fluids. 2013. O Lehmkuhl, I. Rodríguez, R. Borrell, A. Oliva. HighPerformance computing of flows with massive separation: flow past a NACA 0012. ParCFD 2012. I.Rodríguez, J. Calafell, O. Lehmkuhl, R. Borrell, Direct numerical simulation of a NACA0012 in full stall. Conference on Modelling Fluid Flow (CMFF’12). 2012 O. Lehmkuhl, J. Calafell, I. Rodríguez and A. Oliva. LargeEddy Simulations of wind turbine dedicated airfoils at high Reynolds numbers. EUROMECH Colloquium 528. 2012. I. Rodríguez, O. Lehmkuhl, A. Baez and C.D. PérezSegarra. On LES assessment in massive separated flows: flow past a NACA airfoil at Re = 50000. EUROMECH Colloquium 528. 2012. A. Baez, O. Lehmkuhl, I. Rodríguez and C. D. PérezSegarra (2011) Direct Numerical Simulation of the turbulent flow around a NACA 0012 airfoil at different angles of attack. In Parallel CFD 2011. Barcelona. O. Lehmkuhl, A. Baez, I. Rodríguez and C.D. PérezSegarra (2011). Direct numerical simulation and largeeddy simulations of the turbulent flowaround a NACA0012 airfoil. In ICCHMT 7. Turkey. 
Direct numerical simulation of a turbulent plane impinging jet
Direct numerical simulation of a turbulent plane impinging jet 
Impinging jets are frequently found in several industrial applications because of their highly localized heat and mass transfer, compared with those achieved for the same amount of fluid flowing parallel to the object surface. Thus, impinging jets are used in heating or drying processes for production of paper, textile, glass, annealing of metal sheets, cooling of turbine blades and electronic components, etc. Most of the applications of interest are in turbulent regime with complex flow characteristics even in a relatively simple geometry, involving stagnation, recirculation and adverse pressure zones. Impinging jets also present a normal straining due to the nearly irrotational behavior of the flow in the stagnation region. Therefore, a correct prediction of heat transfer in impinging situations is of great importance in many industrial applications. Moreover, an accurate prediction of this quantity requires a good prediction and a detailed understanding of the characteristics and the structure of the flow. In this context, our study [1] focused on a Reynolds number 20000 (based on the bulk inlet velocity and the nozzle width, B) and dimensionless jettosurface spacing 4. As a first step, a reliable direct numerical simulation (DNS) was performed. Then, the DNS results were used as reference solution to assess the performance of several turbulence models [1,2]. Regarding the DNS results significant discrepancies have been observed respect to the experimental works presented in the literature. They are mainly attributed to the effect of the outflow boundary conditions usually located at x/B = ±10 ∼ 15, whereas the main recirculating region extends clearly to more downstream locations. Timeaveraged DNS results have revealed that the main recirculating flow cannot be captured well unless the outflow is placed at least at 40B from the jet centreline approximately. This suggests that previous experimental data may not be adequate to study the flow configuration far from the jet. 
Fig. 1: Instantaneous kinetic energy distribution. 
Supersonic Turbulent Flow Past a Circular Cylinder
Shockshock and shockvortex interactions are of vital importance in the simulation of compressible turbulent flows for engineering applications. For instance, the interaction of shocks with solid obstacles can occur in several applications including highspeed flows with particles, hypervelocity impact and penetration, and hypersonic propulsion flow paths. These phenomena have received significant attention in the past and yet remain as an active field of research and development. This problem involves basic structures of shock waves interacting with obstacles (such as cones, circular cylinders, spheres etc.), thus consisting of incident shock, direct or inverse Mach reflections, transmitted and reflected shocks, triple points and slip lines [1]. In order to evaluate such phenomena, the 2D viscous flow of a calorically perfect gas at Re = 10000 and M = 3.5 over a circular cylinder was simulated. Flow motion is represented by the compressible NavierStokes equations, and they are solved with Finite Volume techniques [2]. Among the different approaches existing in the literature for the numerical fluxes discretization, a hybrid methodology is preferred [3]. This type of numerical schemes preserve kinetic energy of turbulent scales, while introducing numerical diffusion only near discontinuities via a shock sensor [4]. The simulation would test the ability of the hybrid scheme to robustly and reliably capture and resolve shockshock and shockvortex interactions. Three unstructured meshes were tested: a coarse grid (100k cv), a medium grid (400k cv) and a fine grid (800k cv). Averaged density profiles are presented in Figures 1 and 2 and results are compared against reference data [5]. The time evolution of the density gradient field is presented in figure 3. Results show good convergence to reference data when the grid is refined, and the hybrid methodology has proved to be suitable for shockvortex interaction since the shock detector is only activated in flow discontinuities, leaving turbulent scales free form artifitial diffusion. This is a key aspect when solving compressible turbulent flows by means of DNS or LES (where the amount of numerical dissipation is given by the turbulence model). Other aspects concerning compressible flows in which our group is involved are: turbulence modeling of compressible flows (RANS/LES), ShockBoundary layer interaction (key aspect in applications such as transonic airfoils and wings, supersonic engine intakes, diffusers of centrifugal compressors and turbomachinery cascades) [6], aeroacoustics problems, etc. 
Fig. 1: Density profiles at y = 0. 
Fig. 2: Density profiles at x = 5. 
Fig. 3: Time evolution of the density gradient field. 
References 2. R. LeVeque. Finite Volume Methods for Hyperbolic Problems. Cambridge University Press, 2002. 3. A. Baez, J. B. Pedro, O. Lehmkuhl, I. Rodriguez, and C.D. PerezSegarra. Comparing Kinetic Eenergy Preserving and Godunov schemes on the flow around a NACA0012., 2014. 6. J. B. Pedro, A. Baez, O. Lehmkuhl, C. D. Perez Segarra, and A. Oliva. On the extension of RANS/LES methods from incompressible to compressible transonic turbulent flows with SBLI., 2015. 