fifth workshop on research in turbulence and transition

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FIFTH WORKSHOP ON RESEARCH IN TURBULENCE AND TRANSITION

E. T. S. Enginyeria Química Universitat Rovira I Virgili Tarragona October 29th, 2010 Iberian-East ERCOFTAC Pilot Centre

FOREWORD These pages bring together the abstracts of the communications presented at the Fifth Workshop on Research in Turbulence and Transition, held at E.T.S. Enginyeria Química, in Tarragona on October 29th, 2010. The first edition of this Workshop was held on February 6, 2003 at the International Centre for Numerical Methods in Engineering at the Technical University of Catalonia, the second was held at the School of Aeronautical Engineering at the Technical University Madrid on February 12 of 2004, and the third one took place in the College of Engineering at the University of Seville on October 17, 2008, and the fourth was held in Instituto Superior Técnico, in Lisbon on October 16th, 2009. These Workshops have been conducted at the initiative of CIMNE, Iberian-East and Iberian-West Pilot Centres of the European Research Community on Flow, Turbulence and Combustion (ERCOFTAC), and is a Europe-wide organization that promotes research on topics related to fluid dynamics, turbulence and combustion, and their industrial applications. More information can be found at www.ercoftac.org . The aim of this Workshop is to contribute to a better knowledge of the activities carried out by various Iberian research groups in any field relevant to the turbulence or/and Transition. The organizers of the Workshop want to thank the E.T.S. Enginyeria Química and the Department of Mechanical Engineering of the Universitat Rovira I Virgili for their support.

THE ORGANIZING COMMITTEE Vassilis Theofilis

School of Aeronautics, Universidad Politécnica de Madrid

Roberto Castilla

Universidad Politécnica de Catalunya – Barcelona

Anton Vernet

ETSEQ – Universitat Rovira i Virgili – Tarragona

09:30 10:00

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10:40 11:00 11:30

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17:20 17:40 18:00

Wellcome POD and Fuzzy clustering as an alternative to phase averaging: Vortex modes in the wake of an oscillating cylinder F.J. Huera-Huarte and A. Vernet Numerical simulation of the turbulent flow in the suction chamber of an external gear pump including cavitation effects D. Del Campo, R. Castilla and E. Codina Flow structures in PCB enclose model: Experimental study S. Varela, A. Vernet, J.A. Ferré Coffee break Characteristics and dynamics of the intense vorticity structures near the turbulent/nonturbulent interface in a jet Carlos B. da Silva and Ricardo J. N. dos Reis Time-resolved Evolution of the Wall-bounded Vorticity Cascade Adrián Lozano-Durán and Javier Jiménez Direct Simulation of a Separated Boundary Layer Under the Influence of Large-scale Forcing Ayse G. Gungor, Mark P. Simens and Javier Jiménez High-order methods with LES model for incompressible flows A. Montlaur; S. Rebay , S. Fernández-Méndez, A. Huerta Lunch Estudio de estabilidad del flujo de capa límite laminar oblicuo entorno a la línea de estancamiento. J.M. Pérez & V. Theofilis Experimental Study of the Vortex Wake on a HAWT A. Villegas , Y. Cheng , V. Del Campo , F. J. Díez Experimental axial evolution of the wing-tip vortex in the near field of a NACA0012 airfoil C. del Pino, R. Fernandez-Prats, L. Parras, J.M. López-Alonso, R.Fernandez-Feria Numeric simulation to optimize the hemodynamics of a bypass implant Juanjo Rivera, Gerber van der Graaf, Fausto Arias. Coffee break Dynamic nonlinear stabilization: energy transfer, dissipative structure and turbulence modeling J. Principe and R. Codina A multiple-scales theoretical approach for instability analysis of compressible flows over complex geometries Pedro Paredes, Daniel Rodíıguez, Vassilis Theofilis Maximum Propulsive Swimming Wakes R. Arellano, J.M. Redondo Jet Structure and Mixing E. Sekula, P. L. Gonzalez-Nieto, J.M. Redondo Vortices in 2D and 3D Stratified Conditions A. Matulka, J.M. Redondo

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Final discussion and Conclusions

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Break

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Dinner (if enough people join it)

POD and Fuzzy clustering as an alternative to phase averaging: Vortex modes in the wake of an oscillating cylinder F.J. Huera-Huarte* and A. Vernet Department of Mechanical Engineering, Universitat Rovira i Virgili, 43007 Tarragona, Spain. ERCOFTAC 5th Workshop on Research in Turbulence and Transition, Tarragona, 29/10/2010

ABSTRACT A method combining Proper Orthogonal Decomposition (POD) and Fuzzy Clustering (FC) is used as a pattern recognition technique, in order to identify vortex modes in digital particle image velocimetry (DPIV) data, obtained in the wake of a long flexible circular cylinder undergoing vortex-induced vibrations. The POD allows a low dimensional description of the wake, and the fuzzy c-means algorithm can be used for clustering in a reduced order problem. The output is a set of well defined flow clusters representing the vortex patterns found in the wake. This methodology provides an alternative, easier to automate when dealing with large amounts of data, to instantaneous or phase averaged representations of vortex wakes. Phase averaging becomes difficult and tedious when applied as in this case, to wakes of bluff bodies undergoing non-periodic motions. The DPIV data was obtained at two elevations along the length of a long flexible circular cylinder model, which had an aspect ratio (length over diameter) of about 94. The experiments were carried out in a water channel with flow speeds up to 0.75 m/s, giving Reynolds numbers, based on the external diameter of the cylinder, in the range from 1200 to 12000. The set up allowed changes in the fundamental natural frequencies, which resulted in reduced velocities based on that frequency (velocity divided by frequency and external diameter), up to 15. The mass ratio of the model (mass divided by mass of displaced fluid) was around 1.8. A detailed analysis of the response of the models and the DPIV data obtained in those experiments appears in.1–3 Different vortex modes have been observed in the wake of rigid oscillating (free or forced) cylinders depending on flow parameters and structural parameters.4 The determination of the structure in the wake has been traditionally done by observing instantaneous or phase averaged flow fields. In forced or harmonic motions phase averaging is very successful but in free vibrations, phase averaging sometimes becomes not useful at all. The technique proposed in this communication shows how the main structure in all the experiments, carried out with flexible cylinders free to vibrate in any direction, is the 2S vortex mode with a single vortex shed at each side of the cylinder’s wake per cycle. A detailed analysis appears in.5 An example of one of the most than 80 runs analysed appears in 1. The data is validated against another set of well established set of data coming from a forced vibration experiment with a rigid cylinder,6 in which 2P structures (2 pairs of vortices at each side of the wake of the cylinder per cycle) were observed. Keywords: Vortex-induced vibrations, vortex structures, cylinder wake, coherent structures, proper orthogonal decomposition, Fuzzy clustering

Acknowledgements FJHH gratefully acknowledges his Marie Curie IOF actions for individuals (PIOF-GA-2008-219429). * email: [email protected]

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ζ (x,y) − cluster 1, V1=5.45

ζ (x,y) − cluster 2, V1=5.45

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ζ (x,y) − cluster 4, V1=5.45

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Figure 1. Example of results. Clusters resulting from the POD+Fuzzy clustering analysis on one of the experiments

REFERENCES 1. F. J. Huera-Huarte and P. W. Bearman, “Wake structures and vortex-induced vibrations of a long flexible cylinder - part 1: Dynamic response,” Journal of Fluids and Structures 25, pp. 969–990, 2009. 2. F. J. Huera-Huarte and P. W. Bearman, “Wake structures and vortex-induced vibrations of a long flexible cylinder - part 2: Drag coefficients and vortex modes,” Journal of Fluids and Structures 25, pp. 991–1006, 2009. 3. F. J. Huera-Huarte and P. W. Bearman, “Dpiv in the wake of a tandem arrangement of two flexible circular cylinders,” Journal of Visualization 13, pp. 195–202, 2010. 4. C. H. K. Williamson and A. Roshko, “Vortex formation in the wake of an oscillating cylinder,” Journal of Fluids and Structures 2, pp. 355–381, 1988. 5. F. J. Huera-Huarte and A. Vernet, “Vortex modes in the wake of an oscillating long flexible cylinder combining pod and fuzzy clustering,” Experiments in Fluids DOI 10.1007/s00348-009-0786-3, 2009. 6. D. Jeon and M. Gharib, “On circular cylinders undrgoing two-degree-of-freedom forced motions,” Journal of Fluids and Structures 15, pp. 533–541, 2001.

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NUMERICAL SIMULATION OF THE TURBULENT FLOW IN THE SUCTION CHAMBER OF AN EXTERNAL GEAR PUMP INCLUDING CAVITATION EFFECTS D. Del Campo, R. Castilla and E. Codina The flow in the suction chamber of an external gear pump is numerically analysed at different rotational speeds using the commercial computational fluid dynamics (CFD) solver FLUENT® 12.0.16. A 2D model with a total contact ratio of 1 (only one contact point in the gearing line) is used. Despite the complex evolution of the boundaries, a laplacian smoothing technique makes it possible to keep the mesh skewness limited along several gearing cycles. The contact point is simulated by means of continuously adjusting the viscosity value in a small neighbourhood of the theoretical contact point position. Standard k−ε turbulence model has been used as it showed to be a good approach in previous studies. All equations are solved using a second-order upwind sheme with a node-based calculation of the gradients. In order to model the pressure terms, the body-force-weighted scheme, which computes the face pressure by assuming that the normal gradient of the difference between pressure and body forces is constant, is used. For rotational speeds above 300 rpm cavitation effects appear, therefore reducing the volumetric effectiveness of the pump. In order to take this into account, a multiphase mixture model (single-phase approach) with no slip velocity has been adopted. To model the phase transfer mechanism, the Schnerr and Sauer cavitation model has been used. Volumetric effectiveness is affected by several other factors (even in 2D cases) as backlash flow, compressibility, or leakage through radial gaps, which, in turn depend on the rotational speed and the pressure jump. Therefore, in order to isolate the contribution of cavitation, simulations have also been run disabling the cavitation model. The effect of cavitation in volumetric efficiency and in the pressure ripple in inlet and outlet will be analysed in the range of 1000 - 6000 rpm.

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Flow structures in PCB enclose model: Experimental study S. Varela1, A. Vernet2, J.A. Ferré 3 Departament d’Enginyeria Mecànica, Universitat Rovira i Virgili Av. Països Catalans 26, 43007, Tarragona, Spain. 1

[email protected] [email protected] [email protected]

The main objective of this work is to study velocity fields in complex domains like those encountered in computers or other electronics refrigerated subsystems with printed circuit board (PCB). Particle Image Velocimetry (PIV) has been used to obtain the velocity field in a simplified model of a PCB (Fig. 1). In order to simultaneously analyze two parallel planes in the PCB, a method to generate and record these two planes has been implemented [1]. PIV analysis technique is applied separately to each plane to obtain the two simultaneous velocity fields. Consecutive measurements changing only the distance between laser sheets allows to observe the space and time evolution of the dynamic structures of the flow. The technique will also be modified to have two parallel light-sheets that will allow measuring these two planes simultaneously. In this study the light-sheets have been generated from a single DPPSL 532 nm pulsed laser, polarized in both directions. The images have been obtained with two CMOS cameras working at 500 images per second. Figure 2 shows the experimental set-up used to generate and record the two planes. Results at different Reynolds regimes will be presented.

Inlet

Beam splitter Polarizer

Laser

Cavity

Cylindrical lens Beam splitter Polarizer

Outlet Fig. 1: Model’s sketch, three dimensional view.

Cameras Fig. 2: Optical set-up

[1] J. Lobera, N. Andrés, M.P. Arroyo and M. Quintanilla. ”Dual Holographic Interferometry for measuring the three velocity components in a fluid plane”. Appl Opt; 43 (17) 3535-3542 (2004).

Characteristics and dynamics of the intense vorticity structures near the turbulent/nonturbulent interface in a jet Carlos B. da Silva and Ricardo J. N. dos Reis IDMEC/IST, Mecˆanica I, 1o andar/LASEF Universidade T´ecnica de Lisboa, Av. Rovisco Pais, 1049-001 Lisbon, Portugal e-mail: [email protected] Web page: http://www.lasef.ist.utl.pt ABSTRACT The characteristics and dynamics of the intense vorticity structures (IVS) near the turbulent/nonturbulent (T/NT) interface separating the turbulent and the irrotational flow regions [1,2,3,4] are analysed using a direct numerical simulation (DNS) of a turbulent plane jet [5,6]. The IVS are detected using a similar vortex tracking algorithm as developed in [7,8]. Deep inside the turbulent shear layer the mean radius, tangential velocity, and circulation Reynolds number are similar to the values found 1/2 in other flows: R/η ≈ 4.6, u0 /u0 ≈ 0.8, and ReΓ /Reλ ≈ 26, where η, u0 , and Reλ are the Kolmogorov micro-scale, root-mean-square of the velocity fluctuations and the Reynolds number based in the Taylor micro-scale, respectively. The number of IVS detected by the vortex tracking algorithm is approximately constant inside the shear layer but falls sharply between 5 < yI /η < 20 where yI is the distance from the T/NT interface. No IVS exist between the T/NT interface and a distance of roughly 5η into the turbulent region. The most frequent value for the distance between the axis of the detected IVS and the T/NT interface is lω ≈ λ, and this distance coincides with the mean radius of the large-scale vortices (LSV) suggesting that the T/NT interface is defined by the shape of the LSV and IVS inside the jet. Conditional statistics in relation to the distance from the T/NT interface show that the radius, tangential velocity and circulation of the IVS increases near the T/NT interface which indicates that the IVS found near the jet edge originated in this region. The axial stretching rate acting on each IVS, which is caused by the presence of the nearby vortices, is constant inside the shear layer but decreases near the T/NT interface due to the smaller number of IVS found at that location. Consequently, the equilibrium Burgers vortex, which is known to be an excellent model for the IVS in isotropic turbulence, is a less accurate representation for the IVS inside the jet, particularly in the proximity of the T/NT interface, since in this region there is no equilibrium between axial stretching and viscous diffusion of vorticity, implying that the radius of the IVS evolves downstream in the jet. Carlos B. da Silva would like to acknowledge Prof. Javier Jim´enez for interesting discussions on this theme during his visit to Madrid in March 2009 and during the visit of Prof. Javier Jim´enez to Lisbon in November of the same year. REFERENCES [1] S. Corrsin and A. L. Kistler. Free-stream boundaries of turbulent flows. Technical Report TN-1244, NACA, 1955. [2] J. Mathew and A. Basu. Some characteristics of entrainment at a cylindrical turbulent boundary. Phys. Fluids, 14(7):2065–2072, 2002. [3] D. K. Bisset, J. C. R. Hunt, and M. M. Rogers. The turbulent/non-turbulent interface bounding a far wake. J. Fluid Mech., 451:383–410, 2002. [4] J. Westerweel, C. Fukushima, J. M. Pedersen, and J. C. R. Hunt. Mechanics of the turbulentnonturbulent interface of a jet. Phys. Review Lett., 95:174501, 2005.

[5] C. B. da Silva and J. C. F. Pereira. Invariants of the velocity-gradient, rate-of-strain, and rate-ofrotation tensors across the turbulent/nonturbulent interface in jets. Phys. Fluids, 20 055101, 2008. [6] C. B. da Silva. The behavior of subgrid-scale models near the turbulent/nonturbulent interface in jets. Phys. Fluids, 21, 081702, 2009. [7] J. Jimenez, A. Wray, P. Saffman, and R. Rogallo. The structure of intense vorticity in isotropic turbulence. J. Fluid Mech., 255:65–90, 1993. [8] Jim´enez, J., & Wray, A. On the characteristics of vortex filaments in isotropic turbulence. J. Fluid Mech. 373, 255–285, 1998.

Time-resolved Evolution of the Wall-bounded Vorticity Cascade Adri´an Lozano-Dur´an and Javier Jim´enez School of Aeronautics, Universidad Polit´ ecnica de Madrid, 28040 Madrid, Spain [email protected]

We study the temporal evolution of vortex clusters in turbulent channels with Reτ = 950 and 1880, using DNS sequences with temporal separations among fields short enough for individual structures to be tracked. From the geometric intersection of structures in consecutive fields, we build temporal connection graphs of all the cluster interactions, and, from their properties, distinguish the ”trunk” of each evolution from less important ”branches”. It is found that the lifetimes of the connected families of attached clusters are proportional to the cube roots of their maximum volumes, of the order of T uτ /h = 0.25 for the largest ones, and that they move approximately with the overall advection velocity. Especial attention is paid to the origin of the attached structures, and to their relation with an inverse cascade. They tend to be born below y + = 100, and to grow upward, although a similar study of the Reynolds stresses suggests interactions in both directions. Merging of comparable clusters is common, but splitting tends to involve smaller fragments. The creation and evolution of new clusters during the bursting events of the logarithmic layer are also studied. FUNDED by CICYT

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Direct Simulation of a Separated Boundary Layer Under the Influence of Large-scale Forcing Ayse G. Gungor, Mark P. Simens and Javier Jim´enez School of Aeronautics, Universidad Polit´ ecnica de Madrid, 28040 Madrid, Spain [email protected]

The effect of large-scale forcing mimicking incoming wakes on a separated turbulent boundary layer over a flat plate is investigated by direct numerical simulation. The flow separates due to a strong adverse pressure gradient induced by suction along the upper simulation boundary, and the forcing Strouhal number St = f lx /U0 ranges from 0.25 to 2.9. The forcing, in which all the turbulent fluctuations except for the mean velocity defect are neglected, triggers the transition of the separated shear layer, and modifies the separated region. Each forcing pulse generates three roll-up vortices, which originate near the separation point and convect with approximately half the local free-stream velocity. The separation and reattachment points vary with the forcing frequency, but no other significant variations of the mean boundary layer properties are observed unless the separation bubble is allowed to fully reform. The separation lengths of the periodic cases can be estimated from a single recovery experiment in which the forcing is suddenly removed. FUNDED by CICYT and CONSOLIDER

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HIGH-ORDER METHODS WITH LES MODEL FOR INCOMPRESSIBLE FLOWS A. Montlaur1,2 , S. Rebay 3 , S. Fern´andez-M´endez1,4 , A. Huerta1,4 1:Laboratori de C`alcul Num`eric (LaC`aN), Universitat Polit`ecnica de Catalunya, Jordi Girona 1-3, 08034 Barcelona, Spain e-mail: {adeline.de.montlaur, sonia.fernandez, antonio.huerta}@upc.edu 2: Escola Polit`ecnica Superior de Castelldefels 3: Dipartimento di Ingegneria Meccanica e Industriale, Universita de Brescia, Via Branze 38, 25123 Brescia, Italy, e-mail: [email protected] 4: E.T.S. d’Enginyers de Camins, Canals i Ports de Barcelona ABSTRACT Lately, wind energy has seen increasing rapidly its part in the global energy market. The development of wind industry has been possible thanks to numerous technological improvements experimented in the last years, but its future still presents technological challenges such as cost reduction, increase of efficiency, technical reliability, etc. Among the technological necessities of wind energy, an accurate analysis of the flow around a wind turbine is essential for its design. Given the high vorticity of such flow, high order simulation is an access. In this work, high order numerical methods for incompressible flows coupled with a turbulence model are presented. A new Interior Penalty Discontinuous Galerkin formulation has been developed in [1], leading to a symmetric and coercive bilinear weak form for the diffusion term, and achieving high-order spatial approximations. It is applied to the solution of the incompressible Navier-Stokes equations. The velocity approximation space is decomposed in every element into a solenoidal part and an irrotational part. This allows splitting the IPM weak form in two uncoupled problems. The first one solves for velocity and hybrid pressure, and the second one allows the evaluation of pressures in the interior of the elements. This results in an important reduction of the total number of degrees of freedom for both velocity and pressure. Pressure can then be computed as a post-process of the velocity solution. High-order time integration methods have then been proposed in [2] to solve transient incompressible problems, allowing obtaining unconditionally stable schemes with high orders of accuracy in time. For this purpose, the unsteady incompressible Navier-Stokes equations are interpreted as a system of Differential Algebraic Equations, that is, a system of ordinary differential equations corresponding to the conservation of momentum equation, plus algebraic constraints corresponding to the incompressibility condition. In this work, implicit Large Eddy Simulation (LES) model and LES/Smagorinsky eddy-viscosity model are considered. First, the influence of numerical dissipation in the convective term is checked without any LES model (implicit LES). That is, the convective numerical flux is written as a central flux plus a numerical dissipative flux, which is explicitly controlled by a dissipation parameter. The influence of the value of the dissipation parameter is studied. Then a Smagorinsky eddy-viscosity model is introduced, see [3, 4], and the influence of the tuning of the Smagorinsky parameter on the results is studied. Eventually the role of the numerical dissipation relative to the contribution from the Smagorinsky dissipation is explored. The proposed methods are investigated for the classical example of the turbulent channel flow, see [5, 6].

References [1] A. Montlaur, S. Fernandez-Mendez, J. Peraire, and A. Huerta, “Discontinuous Galerkin methods for the Navier-Stokes equations using solenoidal approximations,” Int. J. Numer. Methods Fluids, no. Accepted for publication, 2009. [2] A. Montlaur, High-order discontinuous Galerkin methods for incompressible flows. PhD thesis, Universitat Polit`enica de Catalunya, 2009. http://www.tesisenxarxa.net/TDX-0122110-183128. [3] F. van der Bos and B. Geurts, “Computational error-analysis of a discontinuous Galerkin discretization applied to large-eddy simulation of homogeneous turbulence,” Comput. Meth. Appl. Mech. Eng., vol. 199, pp. 903–915, 2010. [4] T. Hughes, L. Mazzei, and K. Jansen, “Large eddy simulation and the variational multiscale method,” Computing and Visualization in Science, vol. 3, pp. 47–59, 2000. [5] P. Majander and T. Siikonen, “Evaluation of Smagorinsky-based subgrid-scale models in a finitevolume computation,” Int. J. Numer. Methods Fluids, vol. 40, pp. 735–774, 2002. [6] V. Gravemeier, M. Gee, M. Kronbichler, and W. Wall, “An algebraic variational multiscalemultigrid method for large eddy simulation of turbulent flow,” Comput. Meth. Appl. Mech. Eng., vol. 199, no. 3, pp. 853–864, 2010.

Estudio de estabilidad del flujo de capa l´ımite laminar oblicuo entorno a la l´ınea de estancamiento. J.M. P´erez & V. Theofilis Escuela T´ecnica Superior de Ingenier´ıa Aeron´autica, Universidad Polit´ecnica de Madrid

September 24, 2010 En este trabajo presentaremos el estudio de estabilidad lineal entorno a la l´ınea de estancamiento en un flujo laminar e incompresible 3D que impacta contra la superficie de forma no ortogonal. El estudio de estabilidad se realiz´o mediante la aplicaci´on de la teor´ıa de estabilidad lineal BiGlobal [3]. En este an´alisis, partiendo de un flujo base bidimensional se superpone una perturbaci´on tridimensional de peque˜ na amplitud la cual tiene una dependencia temporal modal. Al sustituir dichas variables fluidas en las ecuaciones de Navier-Stokes incompresible, y quedarnos s´olo con los t´erminos lineales perturbativos, se obtiene un problema de autovalores. En esta formulaci´on la parte real del autovalor representa la frecuencia de la perturbaci´on mientras que la parte imaginaria representa la tasa de crecimiento de dicha perturbaci´on. La soluci´on base estacionaria se obtuvo a partir de la soluci´on de semejanza propuesta para el caso 2D por [1] a la que se le a˜ nadio la componente de la velocidad a lo largo de la envergadura (ver [3]). Dicha soluci´on 2D se basa en una combinaci´on lineal de un flujo ortogonal a la pared (flujo de Hiemenz) y otro paralelo a ´esta, es decir a lo largo de la cuerda, ver figura 1(a). Con estas consideraciones el flujo base puede escribirse como, 1/2 1 1 U (x, y) = Re u(x, y), V (y) = Re v¯(y) y W (y) = w(y) ¯ donde Re = W e∆/ν, ∆ = Sν ,y S es la magnitud del tensor de esfuerzos de la componente ortogonal de la velocidad en la capa l´ımite. Los par´ametros caracter´ısticos del problema son, a lo largo de la envergadura, el n´ umero de onda (β) y el n´ umero de Reynolds, as´ı como el ´angulo de ataque del flujo en el plano definido por la normal a la pared y la cuerda. Este problema param´etrico unido al gran tama˜ no de las matrices consideradas implico tener que incorporar distintas soluciones num´ericas con el objetivo de optimizar el proceso de c´alculo. Para ello se desarroll´o una versi´on no-densa del problema de autovalores que fue resuelto mediante la utilizaci´on de la librer´ıa MUMPS (ver [2]). El flujo base fue validado para el caso ortogonal con los resultados presentados en [3] y para el caso no-ortogonal con los par´ametros de capa l´ımite descritos en [1]. En cuanto 1

a la resoluci´on del problema de estabilidad, los resultados fueron comparados con [3] para el caso ortogonal y con un c´odigo DNS para el resto de los casos, obteni´endose en este caso las tasas de crecimiento predichas por el c´odigo de estabilidad. Para los ´angulos de ataque (60 y 90 grados) se realiz´o un estudio de convergencia de los autovalores para Reynolds y β definidos sobre la curva de m´axima amplificaci´on, ver figura 1(b). Adem´as, se estudi´o la dependencia del Reynols cr´ıtico con el ´angulo de ataque. Por u ´ltimo se obsrev´o que la distribuci´on de energ´ıa modal sigue siendo coherente con la dependencia funcional para los modos propuestos por G¨ortler-H¨ammerlin en el caso no ortogonal. −3

2 200

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Figure 1: (a) Funci´on de corriente y componente normal de la velocidad: α = 60 grados (AoA = 73.90) (b) wi vs. α para Reynolds 800 y β = 0.255

References [1] J. M. Dorrepaal. An exact solution of the navier-stokes equations which describes non-orthogonal stagnation-point flow in two dimensions. JFM, 163:141–147, 1986. [2] P. R. Amestoy et al. A fully asynchronous multifrontal solver using distributed dynamic scheduling. SIAM Journal of Matrix Analysis and Applications., 1:15–41, 2001. [3] V. Theofilis et al. The extended g¨ortler-h¨ammerlin model for linear instability of three-dimensional incompressible swept attachment-line boundary layer flow. JFM, 487:271–313, 2003.

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Experimental Study of the Vortex Wake on a HAWT

A. Villegas Rutgers, The State University of New Jersey Piscataway, NJ, USA

Y. Cheng Rutgers, The State University of New Jersey Piscataway, NJ, USA

V. Del Campo Universitat Politècnica de Catalunya ETSEIAT Terrassa, Spain

F. J. Díez Rutgers, The State University of New Jersey Piscataway, NJ, USA

[email protected]

[email protected]

[email protected]

[email protected]

ABSTRACT The understanding of the behavior of the wake of a wind turbine is of great importance when related to the performance of the turbines on a wind farm, where the turbines are disposed in rows and only the ones on the first row work in a complete undisturbed velocity field. The main objective of this work is to characterize experimentally the near wake of a horizontal axis wind turbine model via Particle Image Velocimetry (PIV). Furthermore, the velocity and vorticity field around a rotating blade element were also studied with the same methodology. The model used in the experiments was designed and optimized to work with low Reynolds numbers (Re ̴ 15000). The code implemented for the design (based on the Blade Element and Momentum Theory (BEMT)) was validated with experimental results reported by NREL. The constructed model has a 38cm diameter, two blades, GOE531 airfoil all along the blade, twist and no pitch. It was tested in a water tunnel with a test chamber of 0.9x0.55m2 and velocities ranging between 0.15m/s and 0.25m/s. The near vortex wake of the wind turbine was studied first with Time Resolved PIV (TRPIV) (1000Hz). Thus the vortex wake was characterized in correspondence with the azimuthal position of the blade. The main tip vortices of the helicoidal wake were visualized, as well as the vorticity shed by the blade just behind the rotor plane and its dissipation. On addition, the near wake was studied with conventional PIV (15Hz) in order to obtain a larger field of view. The expansion of the wake and induced velocity were characterized and compared by the cylinder vortex theory and BEMT predictions. Finally, TRPIV was also used to visualize the velocity field around a rotating airfoil. In order to avoid the shadow of the airfoil, the laser sheet was redirected by a mirror. With this solution, the whole velocity field around the airfoil was reconstructed. This is of great interest in order to calculate the loads impinged on the blade without the need of a balance or pressure tabs (especially interesting in the case of low Re). The future steps will make profit of this last approach and will apply it to the study of the effects of “dynamic stall” and “rotational augmentation” on the blades.

Experimental axial evolution of the wing-tip vortex in the near field of a NACA0012 airfoil1 C. del Pinoa , R. Fernandez-Pratsa , L. Parrasa , J.M. L´opez-Alonsoa , R. Fernandez-Feriaa a

E. T. S. Ingenieros Industriales, Universidad de M´ alaga, Campus Teatinos, 29071 M´ alaga (Spain)

Abstract Vortex meandering (or wandering) is a typical feature of wing-tip vortices that consists in a random fluctuation of its vortex centreline. This fluctuation is measured experimentally by means of the statistical treatment of the centroid in a vortex frame for different time steps and also the POD method is applied to characterize the frequency. This meandering of the vortex was originally thought to be due to free stream turbulence [1]. However, the vortex wandering phenomenon is still a subject of current research [2]-[3]. In this work we have undertaken a systematic visualization of the trailing vortex behind a NACA0012 airfoil at several distances near the wing tip for three angles of attack (6, 9 and 12 degrees) and two Reynolds numbers (23888 and 34192) to characterize the structure of the vortex meandering phenomenon as well as its frequency, wavelength, and amplitude. The technique is similar to the one used by del Pino et al. [4], but we characterize the downstream evolution of these vortex meandering up to sixteen chords. In the previous study with the same experimental set-up [4], it was proved that the Reynolds number has not a significant effect on the meandering amplitude in the near field (up to 4 chords). Thus, only two Reynolds numbers are tested in this study. The results based on the amplitude versus the angle of attack show that for the three cases of study (6, 9 and 12 degrees) there is no significant dependence on the Reynolds number from 0.5 till 6 chords. These data confirm the previous results. However, starting at 12 chords and up to 16 chords the variation of the vortex meandering amplitude depends slightly on 1

Work supported by the Junta de Andalucia (Spain) grant no. P05-TEP-170

Preprint submitted to Applied Aerodynamics 2010 Conference

December 15, 2009

the Reynolds number, so the amplitude is smaller as the Reynolds number is increased. This confirms other research studies [5]-[6], finding the same behaviour of the vortex meandering. The amplitude versus axial distance give us another feature of the wing tip vortex: it can be said that the the amplitude of the meandering vortex grows from the wing up to 12 chords, and then it remains approximately constant. This confirms that the amplitude tends towards an asymptotic value. On the other hand, small fluctuations in the amplitude are observed from 3 to 6 chords. This oscillations are due to the existence of the formation and the development region of the wing tip vortex. There is evidence that the frequency spectrum of the POD analysis is equal to the frequency spectrum analysis obtained from the temporal evolution of vortex center. Thus, it is shown that the frequency of the most energetic mode is the vortex meandering characteristic frequency. In most of the cases studied the structures agree with the most energetic modes in [4] and [5]. This mode corresponds to an azimuthal wave number m = 1. Keywords: Flight dynamics; [1] G. R. Baker, S. J. Barker, K. K. Bofah, P. G. Saffman, Laser anemometer measurements of trailing vortices in water, J. Fluid Mech. 65 (1974) 325. [2] S. I. Green, A. J. Acosta, Unsteady flow in trailing vortices, J. Fluid Mech. 227 (1991) 107. [3] D. Fabre, J. Fontane, P. Brancher, S. Le Dizs, C. Roy, T. Leweke, R. Fernandez-Feria, L. Parras, C. del Pino, Syntesis on vortex meandering, Technical Report D.1.1.1, STREP project no. AST4-CT-2005-012238 (2008) 1–18. [4] C. del Pino, J. M. Alonso-L´opez, L. Parras, R. Fernandez-Feria, Dynamics of the wing-tip vortex in the near field of a naca0012 airfoil, Proceeding paper, European Air and Space Conference (2009) ISBN 1 85768 208 4. [5] C. Roy, T. Leweke, Experiments on vortex meandering, Technical Report D.1.1.1-4, STREP project no. AST4-CT-2005-012238 (2008) 1–32. [6] W. J. Devenport, M. C. Rife, S. I. Liapis, F. G. J., The structure and development of a wing-tip vortex, J. Fluid Mech. 312 (1996) 67. 2

Numeric simulation to optimize the hemodynamics of a bypass implant Juanjo Rivera, Gerber van der Graaf, Fausto Arias. Universitat Politècnica Catalunya, Manresa

In general, the numerical analysis of biological flows also includes applications concerning problems of atherosclerosis, aneurisms, cerebro-spinal flow, urinary flow, etc. Artherosclerosis is the forming of plaques which obstruct the flow in the blood vessels. This is the principal cause of mortality in the western world. A common solution is placing a bypass to improve the hemodynamics of the vessel. Unfortunately, shortly after the surgery intervention new plaques may form again in the bypass. It has been proven that the hemodynamics play an important role in this process. In this the CFD study we have looked at different flow geometries to improve the hemodynamics and, therefore, improve the bypass durability. We have looked to the main critical flow quantities that affect the generation of plaques. These are the wall shear stress, oscilation index and input impedance.

Dynamic nonlinear stabilization: energy transfer, dissipative structure and turbulence modelling J. Principe1 and R. Codina2 1

International Center for Numerical Methods in Engineering (CIMNE) Gran Capitn s/n, 08034, Barcelona, Spain [email protected] 2

Universitat Politcnica de Catalunya Jordi Girona 1-3, Edifici C1, 08034, Barcelona, Spain [email protected]

Ercoftac, October2010

In this work we give an overview of the stabilization methods designed for nonlinear transient problems in fluid mechanics. Originally developed in the context of linear steady problems to avoid instabilities of different origins, either compatibility conditions or small perturbation parameters, stabilization techniques have been successfully applied to many nonlinear transient problems. But only in the last years these techniques have been designed taking nonlinearity and time dependency into account from the beginning. The variational multiscale method introduced in [1] is the starting point of these developments. The method is based on a decomposition of the unknown into a coarse scale resolvable part and a fine scale subgrid part which is approximated to obtain a feasible numerical method. Our approach [2,3] is to accept the multiscale decomposition with all its consequences and, in particular: to consider the subscales to be time dependent and to keep scale decomposition in all the nonlinear terms. The final discrete problem involves the solution of a finite element problem coupled to differential algebraic equation for the subscales which can now be considered what would be called internal variables in solid mechanics. Neglecting temporal derivatives these variables can be eliminated and standard stabilization methods are recovered. However keeping the time dependency of the subscales and taking them in the space orthogonal to the finite element space (in the L sense) permits us to identify the energy transfer mechanism by which a dissipation is introduced [4]. This dissipation has the correct behavior in laminar situations (in contrast to many turbulence models) and heuristic arguments permit to show that it also behaves as it is required by the Kolmogorov theory. These results, together with abundant numerical experience, indicate that it is possible to simulate turbulent flows without any modification of the Navier Stokes equations.

References 1. Hughes, T.J.R., Feijo, G.R., Mazzei, L. and Quincy, J.B. The variational multiscale method-a paradigm for computational mechanics, Comp. Meth. Appl. Mech. Eng. 166 ( 1998), 3-24.

2. Codina, R., Stabilized finite element approximation of transient incompressible flows using orthogonal subscales, Comp. Meth. Appl. Mech. Eng., 191 (2002), 4295-4321 3. Codina, R., Principe, J., Guasch, O. and Badia, S. Time dependent subscales in the stabilized finite element approximation of incompressible flow problems, Comp. Meth. Appl. Mech. Eng., 196 (2007), 2413-2430, 4. Principe J., Codina R. and Henke F., The dissipative structure of variational multiscale methods for incompressible flows, Comp. Meth. Appl. Mech. Eng., 199 (2010), 791-801

2

A multiple-scales theoretical approach for instability analysis of compressible flows over complex geometries Pedro Paredes1 , Daniel Rodr´ıguez2 , Vassilis Theofilis1 1

ETSI Aeron´auticos, Universidad Polit´ecnica de Madrid, E-28040, Spain 2 California Institute of Technology, Pasadena, USA

Introduction Parabolized Stability Equations (PSE) have opened new avenues to the analysis of the streamwise growth of linear and nonlinear disturbances in slowly varying shear flows such as boundary layers, jets, and far wakes. Growth mechanisms include both algebraic transient growth and exponential growth through primary and higher instabilities. In contrast to the eigensolutions of traditional linear stability equations, PSE solutions incorporate inhomogeneous initial and boundary conditions as does full spatial DNS. Formulation A small disturbance of frequency ω is imposed on a steady laminar flow and is denoted by q = (u, v, w, p, T )T which represent the velocities, pressure and temperature in the usual notation. In the PSE context q is written in the following way:

ˆ (x, y)exp[i q(x, y, z, t) = q

Z

α(x0 )dx0 + iβz − iωt]

(1)

x

Most of the streamwise oscillations and growth of q are absorbed by the complex wavenumber ˆ (x, y) a slowly-varying function of x. α(x), leaving q An algorithm has been developed to solve compressible flows over complex geometries. It has been validated in two well-knwon flows in the incompressible limit, Blasius boundary layer and laminar separation bubble. Flat Plate Boundary Layer The boundary-layer flow over a flat plate at zero pressure gradient is analyzed to illustrate some advantages of the PSE technique against classic linear stability theory. Boundary layers are in general not parallel. The velocity components U and W exhibit small variations in the streamwise and spanwise directions, and the component V normal to the surface is non-zero to provide the mass parameter as the displacement thickness changes. The mean flow utilized in PSE is given by solving the Blasius problem. One important result from the PSE analysis is the neutral stability curve. In the context of PSE, neutral curves mey be obtained in a straighforward manner. Figure 1 shows the neutral curve for nonparallel flow, and the result is compared with that of Gaster (1974).

1

Figure 1: Neutral curves for nonparallel Blasius flow according to PSE and Gaster (1974).

Laminar Separation Bubble Laminar separation bubbles embedded in a flat plate boundary layer can be considered as quasi-parallel flows, taking into account that reversed flow exits in a extremely narrow region adjacent to the wall and variations of the flow variables on the x-directions are negligible except in the vicinity of the separation and reattachment points. The stability of the laminar separation bubble basic flow under two- and threedimensional disturbances is analyzed here in the scope of the PSE approach. The mean flow is obtained by a parabolic integration of the boundary layer equations (see D. Rodriguez, PhD. 2010). The analyzed model separation bubble is characterized by δ¯max = 3.25 with xsep = 229.9 and xreat = 255.0. Choosing two three-dimensional Tollmien-Schlichting modes with spanwise wavenumber β = 0.15 from the BiGlobal analysis of D. Rodriguez (2010), ωA = 0.072071 − i0.001902 and ωB = 0.100265 − i0.003317, the streamwise velocity components u of the amplitude functions is plotted in Figure 2. Within the PSE procedure, the velocity profiles are analyzed in each streamwise station, obtaining the evolution in x of the ˆ (x, y). To compare with BiGlobal modes, complex wavenumber Rα(x) and the disturbances q 0 0 ˆ (x, y)exp[i x α(x )dx ] is calculated and excellent comparisons are obtained, with q(x, y) = q the added advantage that the computational cost of PSE is one order of magnitud lower than the BiGlobal analysis.

2

ω =0.07271−i0.001902

y

A

20

0.1

15

0.05

10

0

5

0

−0.05

160

180

200

220

240

260 x

280

300

320

340

360

−0.1

ω =0.100265−i0.003317

y

B

20

0.1

15

0.05

10

0

5

0

−0.05

160

180

200

220

240

260 x

280

300

320

340

360

Figure 2: Streamwise velocity components of the amplitude functions.

3

−0.1

Maximum Propulsive Swimming Wakes R. Arellano1 and J.M. Redondo2 1

2

Ciencias del Deporte, Universidad de Granada, Granada , SPAIN Dept. Fisica Aplicada, Univ. Politècnica de Catalunya, Barcelona , SPAIN

Swimming propulsion in humans is the result of the muscular force applied by the hands, arms and feet to the water and the aim in sport is to maximize effective propulsion minimizing energy. In previous studies we recorded propulsive force during tethered swimming and used bubbles to trace the water flow (Arellano et al, 2002, 2006)[1,2]. Vorticity in wakes was seen to be dominant in the best swimmers, whose circulation produced by both hands and feet (eddies or vortex structures) were more regular. When non-steady motions occur Zhukovsky’s condition is not met and unbound vortices are shed at the tips of the hands and feet in a turbulent 3D fashion forming a complex wake.

Figure 1 Development of vortex structures by movement of the hand and in underwater undulatory kicking. Thanks to the flow visualisation vortices of different sizes are detected.

Studies in the animal world show how vortices are generated during the flight of birds and the propulsion of fish or dolphins. [3-6], they show that there is a Strouhal number of 0.2 associated to usual propulsion, which could be associated to maximum efficiency. Three different vortices can be observed during the propulsion of the hands from experiments like those shown in figure 1: The starting vortex, the tip vortex and the hub vortex. The starting vortex is produced due to the acceleration. In these cases the sweep-back angle is 0º, and would also be generated during all the unsteady propulsive movements including from the changes in the sweep-back angles, and it is easily visible during suddenly changes of the hand movement after the change of the hand movement direction is detached and it keeps rotating in the water during a short time. The difference in pressure between upper and lower hand

produces vortices that are shed from the hands tips. These hand-tip vortices can be observed during real swimming when the swimmer traps bubbles during the hand entry. A line of bubbles shows the swimmer's pulling path. Hub vortices are generated in screw type or propeller motions, and are observed in small propulsive movements of the hands featured as sculling during synchronised swimming. The observations of Counsillman and others showed that lift was also important beside drag in human swimming [3-7], the role of vorticity production seems to be more important than previously thought [8-10]. We used different systems to observe vortices: a) vortices generated during ondulatory underwater swimming and breaststroke leg kicking injecting bubbles; b) vortices produced by the hand in analytical situation in the lab using reflective small particles and; c) vortices created during analytical situations in the swimming pool and in real freestyle swimming and kicking using a bubble wall. [2,8]

Plastic tubes connected from an air compressor to the body of the swimmer with the exit at the toe generate a bubble traces of the trajectory, easily observed during underwater body gliding. Without feet movement and during horizontal gliding, the bubbles draw a line parallel to body displacement until they start rising due to buoyancy. Traces are maintained for a couple of seconds while turbulent velocity components are larger and they allow to measure the extent and structure of the wake. The smaller the injected bubbles, the longer the structure of the wakes may be observed. The use of a Laser sheet or more powerful light allows to improve the wake analysis. The best swimmers generated a big vortex at the end of the downward kick. This vortex started during the initial phase of the downward vertical movement, in the wake we found the vortex seems more coherent and rotates in the same place without displacement longer than for slower swimmers.

Figure 2. Example of vortex structures in a Laser Sheet in the Laboratory.

A small aquarium was utilised in the laboratory with small reflective particles were placed in the water with density similar to the water. A .2 W solid state laser projected a parallel plane of light produced by a cylindrical lens. The plane of Laser light allowed us to observe easily the position of the pliolite and pearlescence particles. A video camera was placed perpendicular to the aquarium. The shutter speed was low to see easily the path of the particles. Attack angles between 40º - 70º were examined showing a direct relationship between the sixe of the vortex and the

angle of attack. The same system is being set up in new experiments positioned in the middle of the pool lane nearest to an underwater window. Trials and calibration with fidutial points is necessary to capture the movement of hand crossing the bubble wall in the correct moment to show the vorticity structure by means of PIV using DigImage programme as shown in figure 2. In preliminary experiments the coherence of the vortex rotation after kicks or the generation of larger vortices during the hand pull seem related to higher propulsion. This effect has been analysed by Linden and Turner [11] for a single propulsive vortex ring [2] but an statistical comparison of the momentum and vorticity in complex wakes, like in the measurements of lift and drag [9,10] seems important to understand the role of coherent vorticity in propulsive wakes.

References [1] Arellano, R., Pardillo, S., Gavilán, (2002) Underwater undulatory swimming: kinematic characteristics, vortex generation and application during the start, turn and swimming strokes. Universidad de Granada: ISBS 2002. [2] Arellano R., JM Terres-Nicol, JM Redondo (2006) Fundamental hydrodynamics of swimming propulsion Portuguese Journal of Sport Sciences, 6. Sup. 1, 13. [3] Bixler, B. and Riewald, S. (2002) Analysis of a swimmer’s hand and arm in steady flow conditions using computational fluid dynamics. Journal of Biomechanics, 35: 713-717. [4] Martin, B. (1989). Swimming: Forces on Aquatic Animals and Humans. In C. L. Vaughan (Ed.),Biomechanics of Sport (1 ed., pp. 35-51). Boca Raton, Florida: CRC Press, Inc. [5] Counsilman, J. E. (1971). The Application of Bernoulli's Principle to Human Propulsion in Water. Paper presented at the First International Symposium on "Biomechanics in Swimming, Water-Polo and Diving", Bruxelles. [6] Maglischo, C., & Maglischo, E. (1995). Biomechanics of Aquatic Activities. In M. Adrian & J. M. Cooper (Eds.), Biomechanics of Human Movement (2nd ed., pp. 447-470). Madison, Wisconsin: Brown & Benchmark. [7] Redondo, J. M. (1987). Efecto de la Velocidad de la Brazada en el Coeficiente de Arrastre de las Manos. Paper presented at the X Simposio de la Sociedad Ibérica de Biomecánica, Madrid. [8] Redondo, J. M., & Arellano, R. (1998). Flow Visualization Using Reflective Particles in Analytical Movements of the Hand in Water: A Pilot Study . Barcelona: Escuela Técnica Superior de Canales y Puertos. [9] Redondo, J. M., & Cano, J. L. (1979). Primeras Determinaciones de los Efectos de Sustentación e Impulso en Natación. Natación, Saltos y Water-Polo, 1(5 (5)), 36-46. [10] Redondo, J. M., Morris, S., & Cano, J. L. (1981). Estudio sobre la Propulsión Producida por las Manos en Natación. Natación, Saltos y Water-Polo, 3(1 (18)), 32-37. [11] Linden P.F. and Turner J.S. (2001) The formation of optimal vortex rings and the efficiency of propulsion devices. J. Fluid Mech, 427. 66-72.

Jet Structure and Mixing E. Sekula1 P. L. Gonzalez-Nieto 2 and J.M. Redondo1 1

Dept. Fisica Aplicada, Univ. Politècnica de Catalunya, Barcelona , SPAIN 2 Fac. Biologia. Univ. Complutense de Madrid, Madrid , SPAIN

We compare the different series of detailed experiments that have been performed in the Laboratory of Fluid Dynamics of the UPC on jet and wake generated turbulence and its decay. Measurements of the 3 components of turbulent velocity and their spectra are presented in order to obtain a basic understanding on local diffusion, mixing and mass transport in jets and vortices. We compare different wall and boundary effects on the structure of jets and vortices including vorticity production and decay. We present ADV velocity measurements and compare mean and fluctuating velocity components as well as their PDF’s and spectra. The turbulent interactions between the jets, vortices and the boundary layer structures generated are discussed taking into account both the inverse and direct cascades of the jets as a function of their distance to the wall.. The importance of the study of turbulence structure and its relevance in diffusion of contaminants in environmental flows self-similarity is present with very few exceptions in most environmental strongly non-homogeneous flows, both vertically and horizontally. Using the concept of Extended Self Similarity (ESS) we describe a criterion to identify the inertial range in the Kolmogorov sense as well as a methodology based on the evaluation of the spectral behavior and the structure functions of the velocity fields to determine intermittency. The statistical description of these complex environmental turbulent systems (jets and vertical structures) is performed in the framework of ESS for nonhomogeneous turbulence based on the analysis of the energy transfer hierarchy. A physical interpretation of the scale independence of the relative exponents indicates the nonhomogeneity of the turbulent field, which is characterized by non-local dynamics and not only intermittency.

Figure 1 Jet and Plume generation in quiescent and turbulent environments using an oscillating grid. The structures of a single Jet and Jet arrays were compared with flow visualisation.

an experimental model with two fluids of unequal density under an unstable density distribution. The mixing process is generated by the evolution of a bidimensional array of forced turbulent plumes, from 1 to 9 [1,2]. The conclusions of the first experiments where no Jet structure was formed, but a 2D array was used to measure mixing efficiency and the volume of the final mixed layer as functions of the Atwood

number, ( 0.010 to 0.134) was discussed by [2] The mixing efficiency has an upper limit of 0.18 compared with the maximum mixing efficiency (0.5) in comparable experiments [3-5]. An explanation to understand the smaller mixing efficiencies uses the reduction in possible mixing volume induced by the interaction of the array of plumes, and its interaction with the side walls that clearly modify the overall mixing efficiency, so it depends strongly on initial conditions and the structure of the jet entrainment boundaries [6-8]. The reduction of the overall mixing efficiency when the flow starts as an array of plumes may be explained because there is less volume where contact may exist at molecular level. The regions of higher local mixing would be the cones of the plumes - using Turners plume entrainment hypothesis-. Moreover, the outer region of the cones-plumes will never contain heavier fluid as figure 2 shows and once the potential energy is lost by a falling plume no mixing may take place locally above the Ozmidov scale. This initial dilution and the horizontal entrainment is crucial as less plumes and it affects in a non-linear fashion the overall mixing efficiency. For the different experiments the volume flux Q, the momentum flux M and the buoyancy flux B may be defined in different ways for 2D and 3D arrays. The initial conditions affect strongly the Plume to Jet lengthscales and these in turn affect the mixingefficiency.

Figure 2 Interaction of a single Jet with a wall and interaction within an array of jets/plumes, The shape and structure of the external entrainment surface is important and conditions the maximum mixing efficiency [2].

Figure 3 ADV turbulent velocity measurements as the plume traverses the probe, the spectra and the possible resonances between the grid generated turbulence will increase local mixing of the plume, the PDF of the velocity indicate the intermittency of the velocity,which is considered to be related to the fractal dimension spectra, [9-12]

The relationship between intermittency and fractal dimension spectral functions has not been developed fully, due to the different theoretical approaches between the structure functions and the fractality of the dissipation field. The difficulty of the measurements does not allow a functional dependence between both types of measurements. Nevertheless ther is a clear effect of the influence of a wall or of a source ofnon-homogeneity on the Kurthosis of the velocity field. This type of image analysis may also be used in satellite images of the ocean providing some indication of the mixing processes in the ocean as shown by [11,12].

Figure 4 Multifractal spectra measurements of the evolution of a plume in turbulent environment, the indication that the shape of D(i) reaches a uniform value for different intensity levels is consistent with a convective type of structure [9-11]. [1] [2] [3] [4] [5]

[6]

[7]

[8]

Linden, P.F. and Redondo J.M., 2005. Molecular mixing in Rayleigh-Taylor Instability, part 1, Phys Fluids ,A 3 , pp. 1269-1277. Gonzalez Nieto, P.L., 2004, PhD Thesis. Universidad Complutense, Madrid. Frisch, U.,1995. Turbulence the legacy of A. N. Kolmogorov, Cambridge University Press, 1995. Linden, P. F., Redondo, J. M. and Youngs, D. L., 1994. Molecular mixing in Rayleigh-Taylor Instability, Journal of Fluid Mechanics 265, pp. 97-124. Castilla R, Redondo J.M., Gamez P.J. and Babiano A., 2007. Coherent vortices and Lagrangian Dynamics in 2D Turbulence. Non-Linear Processes in Geophysics.14, 139. Redondo J.M. and Garzon G.,2004. Multifractal structure and intermittency in Rayleigh-Taylor Driven Fronts. Ed. S. Dalziel www.damtp.cam.ac.uk/iwpctm9/proceedings/IWPCTM9/Papers/Pr ogramme Redondo J.M. and Linden P.F.(1990) Mixing produced by Rayleigh-Taylor instabilities, Waves and Turbulence in stably stratified flows, IMA conference. Leeds. Ed. S.D. Mobbs. pp. 395-431. Baines W.D., 1975. Entrainment by a plume or jet at a density interface Jour. of Fluid Mechanics. 68, pp. 309-320.

[9]

[10]

[11]

[12]

Sekula E., Redondo J. M. (2008) “The structure of turbulent jets, vortices and boundary layer: Laboratory and field observations”, Il Nuovo Cimento, Vol. 31, N. 56, Settembre-Dicembre 2008, DOI 10.1393/ncc/i2009-10358-y, pp. 893 – 907. Sekula E., Redondo J.M. (2007) “The structure of turbulent jets”, Proceedings of Colloquium Fluid Dynamics, Institute of thermomechanics, Academy of Science of the Czech Republic, v. v. i., Prague, pp. 79-80, ISBN 978-80-87012-07-09 Platonov A., Tarquis A., Sekula E., Redondo J. M. (2007) “SAR observations of vortical structures and turbulence in the Ocean”, Models, Experiments and computation in turbulence. Eds. R. Castilla, E. Oñate and J.M. Redondo, CIMNE, Barcelona, pp. 195 -230 Platonov A., Carillo A., Matulka A., Sekula E., Grau J., Redondo J. M., Tarquis A. M. (2008) “Multifractal observations of eddies, oil spills and natural slicks in the ocean surface”, Il Nuovo Cimento, Vol. 31 C, N. 5-6, Settembre-Dicembre 2008, DOI 10.1393/ncc/i2009-10349-0, pp. 861 – 880

Vortices in 2D and 3D Stratified Conditions A. Matulka1 and J.M. Redondo1 1

Dept. Fisica Aplicada, Univ. Politècnica de Catalunya, Barcelona , SPAIN

Most predictive models fail when forcing at the Rossby deformation Radius is important and a large range of scales have to be taken into account. When mixing of reactants or pollutants has to be accounted, the range of scales spans from hundreds of Kilometres to the Bachelor or Kolmogorov sub millimetre scales. The effect of intermittent eddies and non-homogeneity of diffusion, are also key issues in the environment because both stratification and rotation body forces are important and cause anisotropy/non-homogeneity. These problems need further theoretical, numerical and observational work and one approach is to try to maximize the relevant geometrical information in order to understand and therefore predict these complex environmental dispersive flows. The importance of the study of turbulence structure and its relevance in diffusion of contaminants in environmental flows is clear when we see the effect of environmental disasters such as the Prestige oil spill or the Chernobyl radioactive cloud spread in the atmosphere. A series of Experiments have been performed on a strongly stratified two layer fluid consisting of Brine in the bottom and freshwater above in a 1 square meter tank. The evolution of the vortices after the passage of a grid is video recorded and Particle tracking is applied on small pliolite particles floating at the interface. The combination of internal waves and vertical vorticity produces two separate time scales that may produce resonances. Oceanic and atmospheric flows may be considered as turbulent motions under the constraints of geometry, stratification and rotation. At large scales these flows tend to be along isopycnal surfaces due to the combined effects of the very low aspect ratio of the flows (the motion is confined to thin layers of fluid) and the existence of stable density stratification. The effect of the Earth's rotation is to reduce the vertical shear in these almost planar flows. The combined effects of these constraints are to produce approximately two-dimensional turbulent flows termed as geophysical turbulence.

Figure 1 Parameter space covered by the rotating and stratified experiments [1,5].

The mixing across a density interface may be evaluated by a general entrainment law [1-3] as.

E=

Ue = c(Pr )⋅ Ri − n ( Ri ,Pr ) ' u

For oscillating grid experiments the entrainment velocity Ue defined as Ue = dD dt , where D is the depth of the turbulent layer, is given by a simple law of the form

E ∝ Ri − n where E, the entrainment rate is normalized by either some global or local reference velocity. The Richardson number, ( Ri ), measures the relative importance of buoyancy forces which usually act so as to stabilize the flow, and velocity fluctuations which tends to destabilize it. The experiments are parametrized by The Reynolds number, Re = u’ l / ν the Richardson number and the Rossby numer, Ro = u’ /Ω l. So in figure 1 the experiments are spread in a 3D space with axes (Re, Ri and 1/Ro ). There are several techniques that are used to track the pliolite particles and produce the velocity and vorticity plots used to calculate spatial correlations intermittency and spectra [3]. Figure 2 shows the evolution (during 1 second) of the vorticity (plane 2D) scalar field as the turbulence decays after the passage of the grid in the strongly stratified interface. The dominant vortices can be studied as they interact, merge or break up.

Figure 2. Example of 2D vorticity maps in false colour, the behaviour of the dominant vortices, seems much more complex than previously thought, showing non-local interactions

Figure 3. Example of a temperature interface evolution in the ocean. The Thermocline is marked in false colour, the interfacial mixing structures are clearly seen and are influences by the parameter conditions (Ri,Re,Ro). Image provided by Luis Gostiaux (Legi, Grenoble) One of the most important roles of Stratification and Rotation in environmental turbulence, and in general of all body forces, including magnetic fields; is to alter the simetry as well as the scale to scale equilibrium and symmetry of the Navier-Stokes

equations and thus modify the slope of the spectral energy cascade and the dominant instability [4,5]. The energy spectrum for two-dimensional N-point vortex systems is also estimated. The system in an infinite plane is considered. We focus our attention on the energy spectrum of the system “in equilibrium” in the grid oscillating experiments and “in a transient state” in the stratified decay of turbulence at a sharp density interface. For like-sign point vortex systems in a plane determined by the PIV system, we have succeeded in deriving a scaling law of the energy spectrum E(k) . The study of the decay of the numer of vortices in a plane, and the scaling law of the energy spectrum in equilibrium and in the transient state depends on the system parameters (Re,Ri,Ro), which controls the type of dominant mixing instability as well as the conditions of vortex decay. So the process does not seem universal. Another experimental and numerical observation is that while the anisotropy of the Reynolds stresses is obviously linked with the non-homogeneity taking the vertical axis (in stratified flows) and the rotation axis (in rotating flows) (It is not that clear for a magnetic field); Scalar behaviour in such flows has non-linear mixing properties Redondo et al. (2002,2004) [6,7]. There are similar effects that depart from Kolmogorov’s K41 and also for K62 theories, not just in second order structure functions (and related spectra) for spatial non-homogeneity, for anisotropy and for spatial and temporal intermittency [1] [2]

[3] [4] [5] [6]

[7]

Matulka, A. (2003), Environmental Turbulence. Effects of rotation and stratification on diffusion and mixing in geophysical flows, MSc Thesis. Tech. Univ. Warsaw. Carrillo, J.A., Redondo, J.M., Sánchez, M.A., and Platonov, A. (2001), Coastal and interfacial mixing laboratory experiments and satellite observation, Physics and chemistry of the Earth 26 (4), 305. Mahjoub, O. B., Babiano A. and Redondo, J. M., 1998. Structure functions in complex flows, Jour Flow, Turbulence and Combustion, 59, 299–313. Chandraeekhar, S. 1961. Hydrodynamic and Hydromagnetic Stability, Oxford University Press. Redondo, J.M. and Cantalapiedra I.R.,1993. Mixing in Horizontally HeterogeneousFlows. Jour. Flow Turbulence and Combustion. 51. 217-222 Redondo; J. M. (2002), Mixing efficiencies of different kinds of turbulent processes and instabilities: Applications to the environment in Turbulent mixing in geophysical flows. Eds. Linden P.F. and Redondo J.M., 131-157. Redondo, J.M. (2004), The topology of Stratified Rotating Flows in Topics in Fluid Mechanics. Prihoda & K.Kozel, CAS, Praga 129-135.