Direct numerical simulation of double-diffusive convection at vibrations
DOI:
https://doi.org/10.7242/1999-6691/2023.16.3.24Keywords:
double-diffusive convection, vibration, direct numerical simulation, miscible fluidsAbstract
The problem of the evolution of double-diffusive convection in a plane layer under the action of external vibrations is solved numerically. A two-layered system of miscible fluids placed in the vertical fields of gravity and linear translational vibrations is considered. The former is the generator of convection: due to the difference in the diffusivity of the species dissolved, unstably stratified fluid regions are formed in the layer. Water is used as a continuous medium. The bottom layer is the solution of sodium chloride and it has a higher density than the top layer formed by the glucose solution. Initially, the system is stably stratified. The problem is solved in a two-dimensional transitional formulation by means of the ANSYS Fluent commercial software. The change in the behavior of fluids under the action of vibrations is studied. Convective structures and density profiles at different vibrational acceleration magnitudes, as well as the evolution of convective characteristics, are considered. Analysis of the system behavior is conducted in two aspects: global and local. Global analysis implicates the description of the processes taking place in the scale of the entire layer, and local analysis focuses on the dynamics of separate convective structures. The main vibration effect results in the convection slowdown. In the global scale, this manifests itself as a decrease in the growth rate of the convective structures; the magnitude of this effect increases (is stored) with time. In the local scale, under relatively low vibrational accelerations, the convection onset is delayed, whereas at high accelerations the growth of convective structures is reoriented along the horizontal direction. The results obtained can be used to develop vibratory control methods for diffusive-reactive systems.
Downloads
References
Wolf G.H. The dynamic stabilization of the Rayleigh–Taylor instability and the corresponding dynamic equilibrium. Z. Physik, 1969, vol. 227, pp. 291-300. https://doi.org/10.1007/BF01397662
Wolf G.H. 9.1. Dynamic stabilization of hydrodynamic interchange instabilities – a model for plasma physics. AIP Conf. Proc., 1970, vol. 1, pp. 293-304. https://doi.org/10.1063/1.2948512
Wolf G.H. Dynamic stabilization of the Rayleigh–Taylor instability of miscible liquids and the related “frozen waves”. Phys. Fluids, 2018, vol. 30, 021701. https://doi.org/10.1063/1.5017846
Gershuni G.Z., Lyubimov D.V. Thermal vibrational convection. New York, Wiley, 1998. 358 p.
Gel'fgat A.Yu. Development and instability of steady convective flows in a square cavity heated from below and a field of vertically directed vibrational forces. Fluid Dyn., 1991, vol. 26, pp. 165-172. https://doi.org/10.1007/BF01050134
Carbo R.M., Smith R.W.M., Poese M.E. A computational model for the dynamic stabilization of Rayleigh–Bénard convection in a cubic cavity. J. Acoust. Soc. Am., 2014, vol. 135, pp. 654-668. https://doi.org/10.1121/1.4861360
Swaminathan A., Garrett S.L., Poese M.E., Smith R.W.M. Dynamic stabilization of the Rayleigh–Bénard instability by acceleration modulation. J. Acoust. Soc. Am., 2018, vol. 144, pp. 2334-2343. https://doi.org/10.1121/1.5063820
Ivanova A., Kozlov V. Opyty po vibratsionnoy mekhanike [Experiments on vibrational mechanics]. Saarbrücken, Palmarium Academic Publishing, 2013. 120 p.
Nevolin V.G. Parametric excitation of waves at an interface. Fluid Dyn., 1977, vol. 12, pp. 302-305. https://doi.org/10.1007/BF01050704
Vladimirov V.A. Parametric resonance in a stratified fluid. J. Appl. Mech. Tech. Phys., 1981, vol. 22, pp. 886-892. https://doi.org/10.1007/BF00906125
Sekerzh-Zen’kovitch, S.Ya. Parametric excitation of finite-amplitude waves at the interface of two liquids with different densities. Sov. Phys. Dokl., 1983, vol. 28, p. 844.
Benielli D., Sommeria J. Excitation and breaking of internal gravity waves by parametric instability. J. Fluid Mech., 1998, vol. 374, pp. 117-144. https://doi.org/10.1017/S0022112098002602
Jalikop S.V., Juel A. Steep capillary-gravity waves in oscillatory shear-driven flows. J. Fluid Mech., 2009, vol. 640, pp. 131 150. https://doi.org/10.1017/S0022112009991509
Ivanova A.A., Kozlov V.G. Sand-fluid interface under vibration. Fluid Dyn., 2002, vol. 37, pp. 277-293. https://doi.org/10.1023/A:1015866518221
Gaponenko Y., Torregrosa M., Yasnou V., Mialdun A., Shevtsova V. Dynamics of the interface between miscible liquids subjected to horizontal vibration. J. Fluid Mech., 2015, vol. 784, pp. 342-372. https://doi.org/10.1017/jfm.2015.586
Shevtsova V., Gaponenko Y.A., Yasnou V., Mialdun A., Nepomnyashchy A. Two-scale wave patterns on a periodically excited miscible liquid–liquid interface. J. Fluid Mech., 2016, vol. 795, pp. 409-422. https://doi.org/10.1017/jfm.2016.222
Zagvozkin T., Vorobev A., Lyubimova T. Kelvin-Helmholtz and Holmboe instabilities of a diffusive interface between miscible phases. Phys. Rev. E., 2019, vol. 100, 023103. https://doi.org/10.1103/PhysRevE.100.023103
Trevelyan P.M.J., Almarcha C., De Wit A. Buoyancy-driven instabilities around miscible A + B → C reaction fronts: A general classification. Phys. Rev. E., 2015, vol. 91, 023001. https://doi.org/10.1103/PhysRevE.91.023001
Mizev A.I., Mosheva E.A., Bratsun D.A. Extended classification of the buoyancy-driven flows induced by a neutralization reaction in miscible fluids. Part 1. Experimental study. J. Fluid Mech., 2021, vol. 916, A22. http://doi.org/10.1017/jfm.2021.201
Cooper C.A., Glass R.J., Tyler S.W. Experimental investigation of the stability boundary for double-diffusive finger convection in a Hele-Shaw cell. Water Resour. Res., 1997, vol. 33, pp. 517-526. http://dx.doi.org/10.1029/96WR03811
Cooper C.A., Glass R.J., Tyler S.W. Effect of buoyancy ratio on the development of double-diffusive finger convection in a Hele-Shaw cell. Water Resour. Res., 2001, vol. 37, pp. 2323-2332. https://doi.org/10.1029/2001WR000343
Sorkin A., Sorkin V., Leizerson I. Salt fingers in double-diffusive systems. Physica A, 2002, vol. 303, pp. 13-26. https://doi.org/10.1016/S0378-4371(01)00396-X
Pringle S.E., Glass R.J., Cooper C.A. Double-diffusive finger convection in a Hele-Shaw cell: An experiment exploring the evolution of concentration fields, length scales and mass transfer. Transport in Porous Media, 2002, vol. 47, pp. 195-214. https://doi.org/10.1023/A:1015535214283
Almarcha C., R’Honi Y., De Decker Y., Trevelyan P.M.J., Eckert K., De Wit A. Convective mixing induced by acid–base reactions. J. Phys. Chem. B., 2011, vol. 115, pp. 9739-9744. https://dx.doi.org/10.1021/jp202201e
Aatif H., Allali K., El Karouni K. Influence of vibrations on convective instability of reaction fronts in porous media. Math. Model. Nat. Phenom., 2010, vol. 5, pp. 123-137. https://doi.org/10.1051/mmnp/20105508
Bratsun D.A., Stepkina O.S., Kostarev K.G., Mizev A.I., Mosheva E.A. Development of concentration-dependent diffusion instability in reactive miscible fluids under influence of constant or variable inertia. Microgravity Sci. Technol., 2016, vol. 28, pp. 575-585. https://doi.org/10.1007/s12217-016-9513-x
Mosheva E., Kozlov N. Study of chemoconvection by PIV at neutralization reaction under normal and modulated gravity. Exp. Fluids., 2021, vol. 62, 10. https://doi.org/10.1007/s00348-020-03097-0
Kozlov N. Numerical study of double-diffusive convection at vibrations. J. Phys.: Conf. Ser., 2021, vol. 1809, 012023. https://doi.org/10.1088/1742-6596/1809/1/012023
Detwiler R.L., Rajaram H., Glass R.J. Solute transport in variable-aperture fractures: An investigation of the relative importance of Taylor dispersion and macrodispersion. Water Resour. Res., 2000, vol. 36, pp. 1611-1625. http://dx.doi.org/10.1029/2000WR900036
Nield D.A., Bejan A. Convection in porous media. New-York, Springer, 2013. 778 p.
Nikol’skiy B.P. (ed.) Spravochnik khimika. Tom 3. Khimicheskoye ravnovesiye i kinetika, svoystva rastvorov, elektrodnyye protsessy [Chemist’s handbook. Vol. 3. Chemical equilibrium and kinetics, properties of solutions, electrode processes]. Moscow, Khimiya Publishing House, 1965, 1008 p.
Downloads
Published
Issue
Section
License
Copyright (c) 2023 Computational Continuum Mechanics
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.