Viscoelastic thermally-driven flows in microgravity

In the present thesis, non-linear and time-dependent numerical simulations are used to investigate the possible convective states of a specific category of non-Newtonian fluids under microgravity conditions, namely, the so-called Boger liquids. The “typical” microgravity phenomena examined include flows induced by vibrations and surfacetension in the presence of an imposed temperature gradient. The considered fluids are modelled using the classical Oldroyd-B model. However, the more sophisticated FENECR (Chilcott–Rallison finitely extensible nonlinear elastic) constitutive paradigm is also exploited to relax some of the mathematical difficulties inherent to this class of problems. A specific strategy of attack is implemented to clarify the flow dynamics, with situations of increasing complexity being analysed as the thesis progresses. First, thermovibrational flow is considered in a 2D square cavity, and it is shown that the relationship between the characteristic time scales (diffusivity, fluid elastic relaxation, and the period of vibrations) of these phenomena can lead to a kaleidoscope of states, which differ regarding the symmetry properties and the related spatiotemporal behaviours. Moreover, the fluid response in terms of hierarchy of bifurcations is extremely sensitive to the direction of vibrations. In all cases, an interesting parallelism can be drawn with respect to certain multi-component mechanical systems that undergo resonances and anti-resonances. When the constraint of two-dimensionality is removed and the flow is allowed to develop in an unbounded domain (infinite layer), very interesting patterns emerge, which are reminiscent of the superlattice structures typical of “complex order” in fluid-dynamics. The onset of thermovibrational convection in these cases occurs for values of the control parameter which are one order of magnitude smaller than the equivalent threshold to be exceeded in the companion Newtonian case, thereby lending evidence to the applicability of the concept of overstability to these circumstances. A strong decrease of the critical parameter needed to produce a bifurcation also occurs in the Marangoni (thermocapillary) flow case. Rather than being driven by a complex interplay of harmonic and sub-harmonic modes of convection found in the thermovibrational case, however, the complex hierarchy of states displayed by Marangoni flow from an initial laminar condition up to fully developed chaos depends on the interplay between transverse (two-dimensional) and longitudinal (three-dimensional) disturbances. Moreover, in this case, elastic and inertial turbulence can coexist if specific conditions are considered.In the present thesis, non-linear and time-dependent numerical simulations are used to investigate the possible convective states of a specific category of non-Newtonian fluids under microgravity conditions, namely, the so-called Boger liquids. The “typical” microgravity phenomena examined include flows induced by vibrations and surfacetension in the presence of an imposed temperature gradient. The considered fluids are modelled using the classical Oldroyd-B model. However, the more sophisticated FENECR (Chilcott–Rallison finitely extensible nonlinear elastic) constitutive paradigm is also exploited to relax some of the mathematical difficulties inherent to this class of problems. A specific strategy of attack is implemented to clarify the flow dynamics, with situations of increasing complexity being analysed as the thesis progresses. First, thermovibrational flow is considered in a 2D square cavity, and it is shown that the relationship between the characteristic time scales (diffusivity, fluid elastic relaxation, and the period of vibrations) of these phenomena can lead to a kaleidoscope of states, which differ regarding the symmetry properties and the related spatiotemporal behaviours. Moreover, the fluid response in terms of hierarchy of bifurcations is extremely sensitive to the direction of vibrations. In all cases, an interesting parallelism can be drawn with respect to certain multi-component mechanical systems that undergo resonances and anti-resonances. When the constraint of two-dimensionality is removed and the flow is allowed to develop in an unbounded domain (infinite layer), very interesting patterns emerge, which are reminiscent of the superlattice structures typical of “complex order” in fluid-dynamics. The onset of thermovibrational convection in these cases occurs for values of the control parameter which are one order of magnitude smaller than the equivalent threshold to be exceeded in the companion Newtonian case, thereby lending evidence to the applicability of the concept of overstability to these circumstances. A strong decrease of the critical parameter needed to produce a bifurcation also occurs in the Marangoni (thermocapillary) flow case. Rather than being driven by a complex interplay of harmonic and sub-harmonic modes of convection found in the thermovibrational case, however, the complex hierarchy of states displayed by Marangoni flow from an initial laminar condition up to fully developed chaos depends on the interplay between transverse (two-dimensional) and longitudinal (three-dimensional) disturbances. Moreover, in this case, elastic and inertial turbulence can coexist if specific conditions are considered