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

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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.
Original languageEnglish
Article number311
Number of pages15
JournalFluids
Volume6
Issue number9
DOIs
Publication statusPublished - 1 Sep 2021

Keywords

  • thermovibrational convection;
  • viscoelastic fluid
  • numerical simulation
  • patterning behavior

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