Hostname: page-component-6b989bf9dc-zrclq Total loading time: 0 Render date: 2024-04-13T17:34:33.875Z Has data issue: false hasContentIssue false

Stirring and scalar transfer by grid-generated turbulence in the presence of a mean scalar gradient

Published online by Cambridge University Press:  23 December 2014

S. Laizet*
Turbulence, Mixing and Flow Control Group, Department of Aeronautics, Imperial College London, London SW7 2AZ, UK
J. C. Vassilicos*
Turbulence, Mixing and Flow Control Group, Department of Aeronautics, Imperial College London, London SW7 2AZ, UK
Email addresses for correspondence:,
Email addresses for correspondence:,


The stirring of a passive scalar by grid-generated turbulence in the presence of a mean scalar gradient is studied by direct numerical simulations (DNS) for six different grids: one fractal square grid with three fractal iterations, one fractal square grid with four fractal iterations, one fractal I grid and three different regular grids. Our results can be summarised as follows. (i) For all these grids, the turbulence intensity averaged over time and over a plane parallel to the grid takes its peak value when the streamwise position of this plane is between $0.75M_{eff}$ and $1.5M_{eff}$ where $M_{eff}$ is the effective mesh size introduced by Hurst & Vassilicos (Phys. Fluids, vol. 19, 2007, 035103). (ii) Downstream of the location of this peak, the turbulence intensity averaged in this way is greatly enhanced by the fractal grids relative to the regular grids even though the fractal grids have comparable or even lower blockage ratios. The novelty of this result lies in the fact that it concerns turbulence intensities averaged over lateral planes (as well as time). (iii) The pressure drop is about the same across grids of the same blockage ratio whether fractal or not, but the pressure recovery is longer for the fractal grids. (iv) Even so, the fractal grids enhance turbulent scalar fluxes by up to an order of magnitude in the region downstream of the aforementioned peak and they also greatly enhance the streamwise growth of the fluctuating scalar variance in that region. (v) We demonstrate on a simple planar model problem that the cause of this phenomenon lies in the fractality of the grids. (vi) The turbulence scalar flux coefficient is constant far enough downstream of all the present grids and is significantly dependent on the nature and details of the turbulence-generating grid.

© 2014 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)


Coffey, C. J., Hunt, G. R., Seoud, R. E. & Vassilicos, J. C.2007 Mixing effectiveness of fractal grids for inline static mixers. In Proof of Concept Report for the Attention of Imperial Innovations, Scholar
Corrsin, S. 1952 Heat transfer in isotropic turbulence. J. Appl. Phys. 33 (1), 113118.CrossRefGoogle Scholar
D’Addio, P., Sassun, D., Flores, O. & Orlandi, P. 2014 Influence of solid boundary conditions on the evolution of free and wall-bounded turbulent flows. J. Phys.: Conf. Ser. 506 (1), 012014.Google Scholar
Ferchichi, M. & Tavoularis, S. 2002 Scalar probability density function and fine structure in uniformly sheared turbulence. J. Fluid Mech. 461, 155182.CrossRefGoogle Scholar
Gomes-Fernandes, R., Ganapathisubramani, B. & Vassilicos, J. C. 2012 PIV study of fractal-generated turbulence. J. Fluid Mech. 701, 306336.Google Scholar
Hearst, R. J. & Lavoie, P. 2014 Decay of turbulence generated by a square-fractal-element grid. J. Fluid Mech. 741, 567584.Google Scholar
Hurst, D. & Vassilicos, J. C. 2007 Scalings and decay of fractal-generated turbulence. Phys. Fluids 19, 035103.Google Scholar
Laizet, S. & Lamballais, E. 2009 High-order compact schemes for incompressible flows: a simple and efficient method with the quasi-spectral accuracy. J. Comput. Phys. 228 (16), 59896015.CrossRefGoogle Scholar
Laizet, S. & Li, N. 2011 Incompact3d, a powerful tool to tackle turbulence problems with up to $o(10^{5})$ computational cores. Intl J. Numer. Meth. Fluids 67 (11), 17351757.CrossRefGoogle Scholar
Laizet, S., Nedić, J. & Vassilicos, J. C. 2014 Influence of the spatial resolution on fine-scale features in dns of turbulence generated by a single square grid. Comput. Fluids (submitted) and arXiv:1409.3621.Google Scholar
Laizet, S. & Vassilicos, J. C. 2011 DNS of fractal-generated turbulence. Flow Turbul. Combust. 87 (4), 673705.Google Scholar
Laizet, S. & Vassilicos, J. C. 2012 The fractal space-scale unfolding mechanism for energy-efficient turbulent mixing. Phys. Rev. E 86 (4), 046302.Google Scholar
Lamballais, E., Fortune, V. & Laizet, S. 2011 Straightforward high-order numerical dissipation via the viscous term for direct and large eddy simulation. J. Comput. Phys. 230 (9), 32703275.Google Scholar
Lele, S. K. 1992 Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103, 1642.Google Scholar
Mazellier, N. & Vassilicos, J. C. 2010 Turbulence without Richardson–Kolmogorov cascade. Phys. Fluids 22, 075101.Google Scholar
Mydlarski, L. & Warhaft, Z. 1998a Passive scalar statistics in high-Péclet-number grid turbulence. J. Fluid Mech. 358, 135175.Google Scholar
Mydlarski, L. & Warhaft, Z. 1998b Three-point statistics and the anisotropy of a turbulent passive scalar. Phys. Fluids 10 (11), 28852894.CrossRefGoogle Scholar
Nagata, K., Sakai, Y., Inaba, T., Suzuki, H., Terashima, H. & Suzuki, H. 2013 Turbulence structure and turbulence kinetic energy transport in multiscale/fractal-generated turbulence. Phys. Fluids 25, 065102.Google Scholar
Nedić, J., Vassilicos, J. C. & Ganapathisubramani, B. 2013 Axisymmetric turbulent wakes with new nonequilibrium similarity scalings. Phys. Rev. Lett. 111 (14), 144503.CrossRefGoogle ScholarPubMed
Nicolleau, F., Salim, S. & Nowakowski, A. F. 2011 Experimental study of a turbulent pipe flow through a fractal plate. J. Turbul. 12, 637046.CrossRefGoogle Scholar
Parnaudeau, P., Carlier, J., Heitz, D. & Lamballais, E. 2008 Experimental and numerical studies of the flow over a circular cylinder at Reynolds number 3900. Phys. Fluids 20, 085101.CrossRefGoogle Scholar
Pumir, A. 1994 A numerical study of the mixing of a passive scalar in three dimensions in the presence of a mean gradient. Phys. Fluids 6, 21182132.Google Scholar
Seoud, R. E. & Vassilicos, J. C. 2007 Dissipation and decay of fractal-generated turbulence. Phys. Fluids 19, 105108.Google Scholar
Sirivat, A. & Warhaft, Z. 1983 The effect of a passive cross-stream temperature gradient on the evolution of temperature variance and heat flux in grid turbulence. J. Fluid Mech. 128, 323346.Google Scholar
Sreenivasan, K. R., Antonia, R. A. & Britz, D. 1979 Local isotropy and large structures in a heated turbulent jet. J. Fluid Mech. 94 (4), 745775.Google Scholar
Sullivan, P. J. 1976 Dispersion of a line source in grid turbulence. Phys. Fluids 19, 159160.Google Scholar
Suzuki, H., Nagata, K., Sakai, H. & Ukai, R. 2010 High-Schmidt-number scalar transfer in regular and fractal grid turbulence. Phys. Scr. T 142, 014069.Google Scholar
Tavoularis, S. & Corrsin, S. 1981a Experiments in nearly homogenous turbulent shear flow with a uniform mean temperature gradient. Part 1. J. Fluid Mech. 104, 311347.CrossRefGoogle Scholar
Tavoularis, S. & Corrsin, S. 1981b Experiments in nearly homogeneous turbulent shear flow with a uniform mean temperature gradient. Part 2. The fine structure. J. Fluid Mech. 104, 349367.Google Scholar
Valente, P. & Vassilicos, J. C. 2012 Universal dissipation scaling for non-equilibrium turbulence. Phys. Rev. Lett. 108, 214503.Google Scholar
Yeung, P. K. & Sreenivasan, K. R. 2014 Direct numerical simulation of turbulent mixing at very low Schmidt number with a uniform mean gradient. Phys. Fluids 26 (1), 015107.Google Scholar
Yeung, P. K., Xu, S. & Sreenivasan, K. R. 2002 Schmidt number effects on turbulent transport with uniform mean scalar gradient. Phys. Fluids 14 (12), 41784191.CrossRefGoogle Scholar
Zhou, Y., Nagata, K., Sakai, Y., Suzuki, H., Ito, Y., Terashima, O. & Hayase, T. 2014 Development of turbulence behind the single square grid. Phys. Fluids 26 (4), 045102.Google Scholar