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On the onset of wake meandering for an axial flow turbine in a turbulent open channel flow

Published online by Cambridge University Press:  12 March 2014

Seokkoo Kang ,
Xiaolei Yang  and
Fotis Sotiropoulos
Seokkoo Kang
Affiliation:
St. Anthony Falls Laboratory, Department of Civil Engineering, University of Minnesota, 2 Third Avenue SE, Minneapolis, MN 55414, USA Department of Civil and Environmental Engineering, Hanyang University, Seoul 133-791, Republic of Korea
Xiaolei Yang
Affiliation:
St. Anthony Falls Laboratory, Department of Civil Engineering, University of Minnesota, 2 Third Avenue SE, Minneapolis, MN 55414, USA
Fotis Sotiropoulos*
Affiliation:
St. Anthony Falls Laboratory, Department of Civil Engineering, University of Minnesota, 2 Third Avenue SE, Minneapolis, MN 55414, USA
*
†Email address for correspondence: fotis@umn.edu
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Abstract

Laboratory experiments have yielded evidence suggestive of large-scale meandering motions in the wake of an axial flow hydrokinetic turbine in a turbulent open channel flow (Chamorro et al., J. Fluid Mech., vol. 716, 2013, pp. 658–670). We carry out a large-eddy simulation (LES) of the experimental flow to investigate the structure of turbulence in the wake of the turbine and elucidate the mechanism that gives rise to wake meandering. All geometrical details of the turbine structure are taken into account in the simulation using the curvilinear immersed boundary LES method with wall modelling (Kang et al., Adv. Water Resour., vol. 34(1), 2011, pp. 98–113). The simulated flow fields are in good agreement with the experimental measurements and confirm the theoretical model of turbine wakes (Joukowski, Tr. Otdel. Fizich. Nauk Obshch. Lyub. Estestv., vol. 16, 1912, no. 1), yielding a near-turbine wake that consists of two layers: the tip vortex (or outer) shear layer that rotates in the same direction as the rotor; and the inner layer counter-rotating hub vortex. Analysis of the calculated instantaneous flow fields reveals that the hub vortex undergoes spiral vortex breakdown and precesses slowly in the direction opposite to the turbine rotation. The precessing vortex core remains coherent for three to four rotor diameters, expands radially outwards, and intercepts the outer shear layer at approximately the location where wake meandering is initiated. The wake meandering manifests itself in terms of an elongated region of increased turbulence kinetic energy and Reynolds shear stress across the top tip wake boundary. The interaction of the outer region of the flow with the precessing hub vortex also causes the rotational component of the wake to decay completely at approximately the location where the wake begins to meander (four rotor diameters downstream of the turbine). To further investigate the importance of turbine geometry on far-wake dynamics, we carry out LES under the same flow conditions but using actuator disk and actuator line parametrizations of the turbine. While both actuator approaches yield a meandering wake, the actuator line model yields results that are in better overall agreement with the measurements. However, comparisons between the actuator line and the turbine-resolving LES reveal significant differences. Namely, in the actuator line LES model: (i) the hub vortex does not develop spiral instability and remains stable and columnar without ever intercepting the outer shear layer; (ii) wake rotation persists for much longer distance downstream than in the turbine-resolving LES; and (iii) the level of turbulence kinetic energy within and the overall size of the far-wake meandering region are considerably smaller (this discrepancy is even more pronounced for the actuator disk LES case) compared with the turbine-resolving LES. Our results identify for the first time the instability mechanism that amplified wake meandering in the experiment of Chamorro et al., show that computational models that do not take into account the geometrical details of the turbine cannot capture such phenomena, and point to the potential significance of the near-hub rotor design as a means for suppressing the instability of the hub vortex and diminishing the extent and intensity of the far-wake meandering region.

JFM classification

Turbulent Flows: Turbulent Flows Turbulent Flows: Turbulence simulation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 744 , 10 April 2014 , pp. 376 - 403
Copyright
© 2014 Cambridge University Press 

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References

Al-Abdeli, Y. M. & Masri, A. R. 2004 Precession and recirculation in turbulent swirling isothermal jets. Compos. Sci. Technol. 176 (5–6), 645–665.Google Scholar
Aubrun, S., España, G., Loyer, S., Hayden, P. & Hancock, P. 2012 Is the actuator disc concept sufficient to model the far-wake of a wind turbine?. In Progress in Turbulence and Wind Energy IV pp. 227–230. Springer.CrossRefGoogle Scholar
Calaf, M., Meneveau, C. & Meyers, J. 2010 Large eddy simulation study of fully developed wind-turbine array boundary layers. Phys. Fluids 22 (1), 015110.CrossRefGoogle Scholar
Chamorro, L., Hill, C., Morton, S., Ellis, C., Arndt, R. E. & Sotiropoulos, F. 2013a On the interaction between a turbulent open channel flow and an axial-flow turbine. J. Fluid Mech. 716, 658–670.CrossRefGoogle Scholar
Chamorro, L. P., Troolin, D. R, Lee, S.-J., Arndt, R. E. A. & Sotiropoulos, F. 2013b Three-dimensional flow visualization in the wake of a miniature axial-flow hydrokinetic turbine. Exp. Fluids 54 (2), 1–12.Google Scholar
Churchfield, M. J., Lee, S., Michalakes, J. & Moriarty, P. J. 2012 A numerical study of the effects of atmospheric and wake turbulence on wind turbine dynamics. J. Turbul. 13 (14), 1–32.CrossRefGoogle Scholar
Escudier, M. 1988 Vortex breakdown: observations and explanations. Prog. Aerosp. Sci. 25 (2), 189–229.Google Scholar
Espana, G., Aubrun, S., Loyer, S. & Devinant, P. 2011 Spatial study of the wake meandering using modelled wind turbines in a wind tunnel. Wind Energy 14 (7), 923–937.Google Scholar
Ge, L. & Sotiropoulos, F. 2007 A numerical method for solving the 3D unsteady incompressible Navier–Stokes equations in curvilinear domains with complex immersed boundaries. J. Comput. Phys. 225 (2), 1782–1809.CrossRefGoogle ScholarPubMed
Germano, M., Piomelli, U., Moin, P. & Cabot, W. H. 1991 A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3 (7), 1760–1765.CrossRefGoogle Scholar
Glauert, H. 1935 Airplane propellers. In Aerodynamic Theory pp. 169–360. Springer.CrossRefGoogle Scholar
Güney, M. S. & Kaygusuz, K. 2010 Hydrokinetic energy conversion systems: a technology status review. Renew. Sustain. Energy Rev. 14 (9), 2996–3004.CrossRefGoogle Scholar
Ivanell, S., Mikkelsen, R., Sørensen, J. N. & Henningson, D. 2010 Stability analysis of the tip vortices of a wind turbine. Wind Energy 13 (8), 705–715.Google Scholar
Ivanell, S., Sørensen, J. N., Mikkelsen, R. & Henningson, D. 2009 Analysis of numerically generated wake structures. Wind Energy 12 (1), 63–80.Google Scholar
Joukowski, N. E. 1912 Vortex theory of screw propeller. Tr. Otdel. Fizich. Nauk Obshch. Lyub. Estestv. 16, no. 1 (in Russian).Google Scholar
Kang, S., Borazjani, I., Colby, J. A. & Sotiropoulos, F. 2012 Numerical simulation of 3D flow past a real-life marine hydrokinetic turbine. Adv. Water Resour. 39, 33–43.CrossRefGoogle Scholar
Kang, S., Lightbody, A., Hill, C. & Sotiropoulos, F. 2011 High-resolution numerical simulation of turbulence in natural waterways. Adv. Water Resour. 34 (1), 98–113.Google Scholar
Kang, S. & Sotiropoulos, F. 2011 Flow phenomena and mechanisms in a field-scale experimental meandering channel with a pool–riffle sequence: insights gained via numerical simulation. J. Geophys. Res. 116, F03011.Google Scholar
Kang, S. & Sotiropoulos, F. 2012a Assessing the predictive capabilities of isotropic, eddy viscosity Reynolds-averaged turbulence models in a natural-like meandering channel. Water Resour. Res. 48 (6), W06505.Google Scholar
Kang, S. & Sotiropoulos, F. 2012b Numerical modeling of 3D turbulent free surface flow in natural waterways. Adv. Water Resour. 40, 23–36.Google Scholar
Khosronejad, A., Hill, C., Kang, S. & Sotiropoulos, F. 2013 Computational and experimental investigation of scour past laboratory models of stream restoration rock structures. Adv. Water Resour. 54, 191–207.CrossRefGoogle Scholar
Khosronejad, A., Kang, S., Borazjani, I. & Sotiropoulos, F. 2011 Curvilinear immersed boundary method for simulating coupled flow and bed morphodynamic interactions due to sediment transport phenomena. Adv. Water Resour. 34 (7), 829–843.Google Scholar
Khosronejad, A., Kang, S. & Sotiropoulos, F. 2012 Experimental and computational investigation of local scour around bridge piers. Adv. Water Resour. 37, 73–85.Google Scholar
Larsen, G. C., Madsen, H. A., Thomsen, K. & Larsen, T. J. 2008 Wake meandering: a pragmatic approach. Wind Energy 11 (4), 377–395.Google Scholar
Lu, H. & Porté-Agel, F. 2011 Large-eddy simulation of a very large wind farm in a stable atmospheric boundary layer. Phys. Fluids 23, 065101.CrossRefGoogle Scholar
Medici, D. & Alfredsson, P. H. 2008 Measurements behind model wind turbines: further evidence of wake meandering. Wind Energy 11 (2), 211–217.Google Scholar
Okulov, V. L. & Sørenson, J. N. 2007 Stability of helical tip vortices in a rotor far wake. J. Fluid Mech. 576, 1–25.Google Scholar
Ranga Dinesh, K. K. J. 2009 Study of jet precession, recirculation and vortex breakdown in turbulent swirling jets using LES. Comput. Fluids 38 (6), 1232–1242.Google Scholar
Sarpkaya, T. 1995 Turbulent vortex breakdown. Phys. Fluids 7 (10), 2301–2303.Google Scholar
Smagorinsky, J. S. 1963 General circulation experiments with the primitive equations. Mon. Weath. Rev. 91, 99–164.Google Scholar
Sørensen, J. N. & Shen, W. Z. 2002 Numerical modeling of wind turbine wakes. J. Fluids Engng 124 (2), 393–399.CrossRefGoogle Scholar
Syred, N. 2006 A review of oscillation mechanisms and the role of the precessing vortex core (PVC) in swirl combustion systems. Prog. Energy Combust. Sci. 32 (2), 93–161.Google Scholar
Troldborg, N., Larsen, G. C., Madsen, H. A., Hansen, K. S., Sørensen, J. N. & Mikkelsen, R. 2011 Numerical simulations of wake interaction between two wind turbines at various inflow conditions. Wind Energy 14 (7), 859–876.CrossRefGoogle Scholar
Wang, M. & Moin, P. 2002 Dynamic wall modeling for large-eddy simulation of complex turbulent flows. Phys. Fluids 14 (7), 2043–2051.Google Scholar
Wu, Y. T. & Porté-Agel, F. 2011 Large-eddy simulation of wind-turbine wakes: evaluation of turbine parametrisations. Boundary-Layer Meteorol. 138 (3), 345–366.Google Scholar
Yang, X., Kang, S. & Sotiropoulos, F. 2012 Computational study and modeling of turbine spacing effects in infinite aligned wind farms. Phys. Fluids 24 (11), 115107.Google Scholar
Yang, X., Zhang, X., Li, Z. & He, G.-W. 2009 A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations. J. Comput. Phys. 228 (20), 7821–7836.Google Scholar