Simulations of Three-Dimensional Turbulent Mixing for Schmidt Numbers of the Order 1000
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
We report basic results from new numerical simulations of passive scalar mixing at Schmidt numbers (Sc) of the order of 1000 in isotropic turbulence. The required high grid-resolution is made possible by simulating turbulence at very low Reynolds numbers, which nevertheless possesses universality in dissipative scales of motion. The results obtained are qualitatively consistent with those based on another study (Yeung et al., Phys. Fluids 14 (2002) 4178-4191) with a less extended Schmidt number range and a higher Reynolds number. In the stationary state maintained by a uniform mean scalar gradient, the scalar variance increases slightly with Sc but scalar dissipation is nearly constant. As the Schmidt number increases, there is an increasing trend towards k −1 scaling predicted by Batchelor (Batchelor, J. Fluid Mech. 5 (1959) 113-133) for the viscous-convective range of the scalar spectrum; the scalar gradient skewness approaches zero; and the intermittency measured by the scalar gradient flatness approaches its asymptotic state. However, the value of Sc needed for the asymptotic behavior to emerge appears to increase with decreasing Reynolds number of the turbulence. In the viscous-diffusive range, the scalar spectrum is in better agreement with Kraichnan's (Kraichnan., Phys. Fluids 11 (1968) 945-953) result than with Batchelor's.
- Sreenivasan, K.R., The passive scalar spectrum and the Obukhov-Corrsin constant. Phys. Fluids 8 (1996) 189-196.
- Sreenivasan, K.R., On local isotropy of passive scalars in turbulent shear flows, In: Proceedings of the Royal Society of London,Vol. 434 (1991) pp. 165-182.
- Warhaft, Z., Passive scalars in turbulent flows. Ann. Rev. Fluid Mech. 32 (2000) 203-240.
- Batchelor, G.K., Small-scale variation of convected quantities like temperature in turbulent fluid. J. Fluid Mech. 5 (1959) 113-133.
- Antonia, R.A. and Orlandi, P., Effect of Schmidt number on passive scalar turbulence. Appl. Mech. Rev. 56 (2003) 615-632.
- Bogucki, D., Domaradzki, J.A. and Yeung, P.K., Direct numerical simulations of passive scalars with Pr >1 advected by turbulent flow. J. Fluid Mech., 343 (1997) 111-130.
- Yeung, P.K., Sykes, M.C. and Vedula, P., Direct numerical simulation of differential diffusion with Schmidt numbers up to 4.0. Phys. Fluids 12 (2000) 1601-1604.
- Yeung, P.K., Xu S. and Sreenivasan, K.R., Schmidt number effects on turbulent transport with uniform mean scalar gradient. Phys. Fluids 14 (2002) 4178-4191.
- Orlandi, P. and Antonia, R.A., Dependence of the nonstationary form of Yaglom's equation on the Schmidt number. J. Fluid Mech. 451 (2002) 99-108.
- Brethouwer, G., Hunt, J.C.R. and Nieuwstadt, F.T.M., Micro-structure and Lagrangian statistics of the scalar field with a mean gradient in isotropic turbulence. J. Fluid Mech. 474 (2003) 193-225.
- Gotoh, T., Nagaki, J. and Kaneda, Y., Passive-scalar spectrum in viscous-convective range in two-dimensional turbulence. Phys. Fluids 12 (2000) 155-168.
- Rogallo, R.S., Numerical experiments in homogeneous turbulence. NASA Tech. Memo. 81315, NASA Ames Research Center (1981).
- Eswaran, V. and Pope, S.B., An examination of forcing in direct numerical simulations of turbulence. Comput. Fluids 16 (1988) 257-258.
- Chen, S., Doolen, G., Herring, J.R. and Kraichnan, R.H., Far-dissipation range of turbulence. Phys. Rev. Lett. 70 (1993) 3051-3054.
- Yeung, P.K., Multi-scalar triadic interactions in differential diffusion with and without mean scalar gradients. J. Fluid Mech. 321 (1996) 235-278.
- Yeung, P.K. and Sawford, B.L., Random sweeping hypothesis for passive scalars in isotropic turbulence. J. Fluid Mech. 459 (2002) 129-138.
- Yeung, P.K. and Pope, S.B., Differential diffusion of passive scalars in isotropic turbulence. Phys. of Fluids A 5 (1993) 2467-2478.
- Mydlarski, L. and Warhaft, Z., Passive scalar statistics in high-Péclet-number grid turbulence. J. Fluid Mech. 358 (1998) 135-175.
- Kraichnan, R.H., Small-scale structure of a scalar field convected by turbulence. Phys. Fluids 11 (1968) 945-953.
- Monin, A.S. and Yaglom, A.M., Statistical Fluid Mechanics. Vol. II. MIT Press, Cambridge, MA (1975).
- Qian, J., Viscous range of turbulent scalar of large Prandtl number. Fluid Dynam. Res. 15 (1995) 103-112.
- Borgas, M.S., Sawford, B.L., Xu, S., Donzis, D.A. and Yeung, P.K., High Schmidt number scalars in turbulence: structure functions and Lagrangian theory. Phys. Fluids(2003) Submitted.
- Sreenivasan, K.R. and Antonia, R.A., The phenomenology of small-scale turbulence. Ann. Rev. Fluid Mech. 29 (1997) 435-472.
- Simulations of Three-Dimensional Turbulent Mixing for Schmidt Numbers of the Order 1000
Flow, Turbulence and Combustion
Volume 72, Issue 2-4 , pp 333-347
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links
- passive scalars
- schmidt number
- numerical simulation
- Industry Sectors