Turbulence behavior of artificially generated vorticity

Abstract

Longitudinal vortices and hairpin-like structures are generated in an open loop flow by a row of vortex generators inserted on the inner wall of a circular pipe; the vortex generator row is made up of four diametrically opposed trapezoidal tabs tilted from the wall. Steady counter-rotating vortex pairs and periodic hairpin-like structures develop downstream from each tab. The flow pattern of these vortical structures has been studied extensively [D. Dong and H. Meng, Flow past a trapezoidal tab, J. Fluid Mech. 510 (2004), pp. 219–242]; nevertheless, the specific contributions of these structures to the mixing process have not yet been elucidated, especially with regard to global improvement of the transfer coefficients compared to a straight pipe. This study aims at exploring the turbulent mixing mechanisms caused by artificially generated vorticity, especially at the different mixing scales (macro-, meso- and micro-mixing), using both numerical simulations and laboratory experiments. Instantaneous velocities and spectral analysis using Laser Doppler Velocimetry are carried out for axial velocity components. Numerical simulations using the Reynolds stress turbulence model are also performed to investigate the effect of the different flow structures on the averaged Reynolds stress tensor and the turbulent kinetic energy dissipation rate. The development and decay of the counter-rotating vortices are also investigated using a recent pseudo-viscous model [O. Lögdberg, J.H.M. Fransson, and P.H. Alfredsson, Streamwise evolution of longitudinal vortices in a turbulent boundary layer, J. Fluid Mech. 623 (2009), pp. 27–58]. Here we modify this model to predict the center path of the streamwise vortices in a turbulent boundary layer. It is also shown that the hairpin-like structures govern both meso- and micro-mixing mechanisms, while the counter-rotating vortices act as internal agitators in the flow by creating convective transfer between the wall region and the flow core. This investigation is fundamental for optimizing static mixers based on vortex generators and for control of separation in aerodynamic applications.

Keywords:

• longitudinal vortices
• streamwise vortices
• transverse vortices
• hairpin-like structures
• vortex generators
• turbulent mixing
• turbulent mass transfer
• multifunctional heat exchangers/reactors

Acknowledgements

The authors would like to thank Dr. E. Gadoin and Dr. H. Mohand Kaci for fruitful discussions on the numerical simulation procedures. The authors are also grateful for the technical support of the Service d’Études et de Fabrication (SEF) for LDV measurements. This work was financially supported by the Programme Interdisciplinaire Energie du CNRS, under the Multifunctional Heat Exchanger project. C. Habchi would like to acknowledge the financial support of CNRS and ADEME.