Viscoelastic thermovibrational flow driven by sinusoidal and pulse (square) waves

Lappa, Marcello and Boaro, Alessio (2021) Viscoelastic thermovibrational flow driven by sinusoidal and pulse (square) waves. Fluids, 6 (9). 311. ISSN 2311-5521

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    Abstract

    The present study aims to probe the role of an influential factor heretofore scarcely considered in earlier studies in the field of thermovibrational convection, that is, the specific time-varying shape of the forcing used to produce fluid motion under the effect of an imposed temperature gradient. Towards this end, two different temporal profiles of acceleration are considered, namely, a classical (sinusoidal) and a pulse (square) wave. Their effects are analyzed in conjunction with the ability of a specific category of fluids to accumulate and release elastic energy, i.e. that of Chilcott–Rallison finitely extensible nonlinear elastic (FENE-CR) liquids. Through solution of the related governing equations in time-dependent, three-dimensional and non-linear form for a representative set of parameters (generalized Prandtl number Prg = 8, normalized frequency Ω = 25, solvent-to-total viscosity ratio ξ = 0.5, elasticity number θ = 0.1, and vibrational Rayleigh number Raω = 4000), it is shown that while the system responds to a sinusoidal acceleration in a way that is reminiscent of modulated Rayleigh-Bénard (RB) convection in a Newtonian fluid (i.e. producing a superlattice), with a pulse wave acceleration, the flow displays a peculiar breaking-roll mode of convection that is in-between classical (un-modulated) RB in viscoelastic fluids and purely thermovibrational flows. Besides these differences, these cases share important properties, namely, a temporal subharmonic response and the tendency to produce spatially standing waves.

    ORCID iDs

    Lappa, Marcello ORCID logoORCID: https://orcid.org/0000-0002-0835-3420 and Boaro, Alessio ORCID logoORCID: https://orcid.org/0000-0002-8603-0109;