Denis Melnikov

Three-dimensional simulations of hydrodynamic instability in liquid bridges: Influence of temperature-dependent viscosity

The development of thermocapillary convection inside a cylindrical liquid bridge is investigated by using a direct numerical simulation of the three-dimensional (3D), time-dependent problem for a wide range of Prandtl numbers, Pr=1,3,4,5 and Pr=35. Above the critical value of temperature difference between the supporting disks, two counterpropagating hydrothermal waves bifurcate from the two-dimensional (2D) steady state. The existence of standing and traveling waves is discussed. The dependence of viscosity upon temperature is taken into account. The critical Reynolds number and critical frequency at which the system undergoes a transition from a 2D steady state to a 3D oscillatory flow decreases if the viscosity diminishes with temperature. The stability boundary is determined for Pr=3–5 with a viscosity contrast (νmax/νmin) up to a factor 10. Near the threshold of instability the flow organization is similar for the constant and variable viscosity cases despite the large difference in critical Reynolds...

Influence of vibrations on thermodiffusion in binary mixture: A benchmark of numerical solutions

Double-diffusive and vibrational convection with the Soret effect is considered in a cubic rigid cell filled with water (90%) and isopropanol (10%), subjected to a temperature difference between opposite lateral walls. Numerical simulations are carried out for g-jitter induced flow. The direction of g-jitter is the same as the residual gravity vector, which is perpendicular to the applied temperature gradient. Along with various combinations of static and oscillatory components, vibrations with two different frequencies are examined: (a) when the period of oscillations is smaller than any characteristic time (viscous, thermal, and diffusion), f=0.2Hz; (b) when the period of oscillations is comparable with viscous time, f=0.01Hz. Component separation due to the Soret effect under these driving actions is analyzed. The concept of time-averaged models is applied for the explanation of the high-frequency results. The interplay between the mean and fluctuating motions is discussed. Three research groups perfor...

Onset of temporal aperiodicity in high Prandtl number liquid bridge under terrestrial conditions

The paper presents a three-dimensional numerical study of the bifurcations and onset of chaotic regime for the thermoconvective oscillatory flow in cylindrical liquid bridge. Three-dimensional Navier–Stokes equations in Boussinesq approximation are solved numerically by finite volume method. Silicone oil 1cSt, with rather large Prandtl number, Pr=18.8, is chosen as test liquid. The simulations are done at normal gravity conditions and unit aspect ratio. The dependence of viscosity of the fluid upon temperature allows us to be close to the real phenomenon. Both spatial and temporal changes occurring in the system are analyzed. The results are compared to the experimental data. A following sequence of well-defined dynamic regimes was detected when temperature difference between the supporting disks is increasing: steady, periodic, quasiperiodic, periodic, and chaotic. The observed succession of bifurcations on the way to chaos is similar to the one coming from experiments. Except for these dynamic bifurcati...

Experimental and theoretical study of vibration-induced thermal convection in low gravity

Vibrations acting on a fluid with density gradient induced by temperature variations can cause relative flows. High-frequency vibration leads to the appearance of time-averaged (mean) flows (or streaming flows), which can essentially affect heat and mass transfer processes. This phenomenon is most pronounced in the absence of other external forces (in particular, static gravity). In this work, an extensive experimental and computational study of thermal vibrational convection in a reduced-gravity environment of a parabolic flight is performed. The transient evolution of the temperature field in a cubic cell subjected to translational vibration is investigated by optical digital interferometry. The mean flow structures previously reported in numerical studies are confirmed. The transition from four-vortex flow to a pattern with a large diagonal vortex and two small vortices is observed in the transient state. The experiments reveal a significant enhancement of heat transfer by vibrational mean flows with increasing the vibrational strength. Three-dimensional direct numerical simulation with real microgravity profile and two-dimensional numerical modelling based on averaging approach provide a very good agreement with the experimental results. The influence of residual gravity on heat transfer and bifurcation scenario is first investigated numerically and correlated with the experimental data. It is demonstrated that gravity effects on non-uniformly heated fluids can be reproduced in weightlessness by applying vibrations to the system.

IVIDIL: on-board g-jitters and diffusion controlled phenomena

The experiment IVIDIL (Influence of Vibrations on Diffusion in Liquids) has been performed in 2009-2010 onboard the ISS, inside the SODI instrument mounted in the Glovebox at the ESA Columbus module. 55 experimental runs were carried out and each of them lasted 18 hours. The objectives of the experiment were multi-fold and here we report results for one of them. After each space experiment there is a discussion about the role of onboard g-jitters. The attention is focused on reproducibility of the results, their accuracy and comparison with numerical simulations conducted in exact geometry and using the physical properties of the system. We shortly report on the results of six experiments which were performed in natural environment of the ISS without forced vibrations. Thermodiffusion process in the cells filled with binary mixtures was monitored by means of optical digital interferometry. Perturbations of the diffusion control processes by on-board g-jitters is not observed in nominal regime of the ISS. Perturbations of thermodiffusion process were observed in non-nominal regime of the ISS, e.g. attitude control maneuvers.

Synchronization of finite-size particles by a traveling wave in a cylindrical flow

Motion of small finite-size particles suspended in a cylindrical thermocapillary flow with an azimuthally traveling wave is studied experimentally and numerically. At certain flow regimes the particles spontaneously align in dynamic accumulation structures (PAS) of spiral shape. We find that long-time trajectories of individual particles in this flow fall into three basic categories that can be described, borrowing the dynamical systems terminology, as the stable periodic, the quasiperiodic, and the quasistable periodic orbits. Besides these basic types of orbits, we observe the “doubled” periodic orbits and shuttle-like particle trajectories. We find that ensembles of particles having periodic orbits give rise to one-dimensional spiral PAS, while ensembles of particles having quasiperiodic orbits form two-dimensional PAS of toroidal shape. We expound the reasons why these types of orbits and the emergence of the corresponding accumulation structures should naturally be anticipated based on the phase lock...

The Choice of the Critical Mode of Hydrothermal Instability in Liquid Bridge

The appearance and the development of thermoconvective oscillatory flows in a liquid bridge are explained. A theoretical and experimental study was conducted on a liquid bridge of aspect ratio Γ = 1.2 filled with a 10 cSt silicone oil. The experiments were carried out in terrestrial conditions for a wide range of volumes of liquid bridges. For the first time two branches of the stability diagram, (ΔT cr vs. Volume), belonging to different azimuthal wave numbers were observed. The influence of the temperature of the cold rod on the onset of instability and on the critical azimuthal wave number was experimentally studied. The experiments show that the critical temperature difference is diminished with the increase of the temperature of the cold rod. 3-D numerical simulations have been done using the parameters as close as possible to the experimental conditions. In these calculations, both thermocapillary and buoyancy mechanisms of convection are taken into account and it is seen that the numerical results agree well with the experimental ones. A key reason for the good agreement between the model and experiments is that the numerical code takes into account the dependence of the viscosity upon the temperature.

Thermocapillary convection in a liquid bridge subjected to interfacial cooling

Influence of heat loss through interface on a supercritical three-dimensional thermoconvective flow in a long liquid bridge is numerically investigated under terrestrial conditions. A flow in a high Prandtl number liquid surrounded by an ambient gas of constant temperature is simulated for the large aspect ratio, Γ=1.8. It is shown that the heat loss plays a significant role in the flow dynamics. It modifies both the flow and the liquid temperature field. Moreover, for the relatively large aspect ratio and a high Prandtl number liquid the heat loss from interface leads to destabilization of the flow.

Unstable density stratification in binary mixture

Three-dimensional numerical modelling of Soret driven convection in a cubic cell filled with a binary mixture of water (90%) and isopropanol (10%) is performed. The system is heated from above while the Soret coefficient is negative. The concentration and temperature fields are strongly coupled by Soret effect that causes concentration gradients in response to the applied temperature difference. Due to negative Soret effect the heavier liquid is accumulated on the top of the lighter one. At some moment this unstable stratification leads to appearing of motion. The transient behaviour of the velocity, temperature and concentration fields is discussed.

Development of convection in binary mixture with Soret effect

The future Space experiment IVIDIL is planned to study the influence of vibration stimuli on the measurements of diffusion and thermodiffusion coefficients. A binary mixture of water and isopropanol is chosen as a working liquid. The principle of the Space experiment and ground based research are outlined. In addition preparatory experiments might be performed during parabolic flights. Results of 3D numerical simulations of thermal vibrational convection in binary mixture at the conditions of the parabolic flight are presented. Heat and mass transport arising in the system with increasing of vibration actions is discussed.