Nonlinear features of laminar liquid flows on Earth and in microgravity

Fluid, gas and plasma mechanics


Fedyushkin A. I.1*, Puntus A. A.2**

1. Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, 101-1, prospekt Vernadskogo, Moscow, 119526, Russia
2. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia



The article presents the numerical modeling results of hydrodynamics and heat and mass transfer and discusses the non-linear features of laminar flows. It considers numerical simulation results of hydrodynamics and heat and mass transfer and discusses the laminar flows features at moderate Rayleigh and Reynolds numbers in the following problems:

  1. On the impact of natural-convective flow on formation of various stationary convective flow structures and occurrence of countercurrents to the main flow in long horizontal layers.

  2. The problem of the symmetry violation of a steady flow in a plane diffuser.

  3. The effect of controlled vibrations on heat and mass transfer in the melt, the shape of the crystallization front and the thickness of the boundary layers and on the shape of the crystallization front.

  4. Interface location changing under the impact of thermocapillary convection.

The results based on the numerical solution of the Navier-Stokes equations for a viscous incompressible fluid for flow regimes studying in a flat diffuser with a small angle and opening are presented. Flow regimes transition in a diffuser from a symmetric stationary regime to asymmetric stationary one and then to asymmetric non-stationary regime in their dependence on the Reynolds number is demonstrated. The values of Reynolds number defining the ranges of a given regime existence are pointed out.

The impact of controlled vibrations on the heat-mass transfer and, in particular, on temperature boundary layers in the melt for crystal growth processes were studied. Analysis of the controlled vibrations effect on hydrodynamics and heat-mass transfer for the microgravity and normal gravity conditions was performed. The of numerical simulations results revealed that vibrations can enhance heat and mass transfer and mix the melt, as well as reduce dynamic, thermal and concentration boundary layers. Vibration can also increase the temperature gradient of the solidification front, which, in its turn, can increase the rate of crystal growth. The numerical simulations results demonstrated that vibrations can make the crystallization front shape flatter.

In zero gravity, while lateral heating of the two-layer system “air-liquid” in the volume with free walls, the interface due to thermo-capillary convection and small perturbations can be rotated by 90° and assume a stable position parallel to the heated wall.

Gravitational convection (even in the presence of thermocapillary convection) is a stabilizing factor for the horizontal position of the interface.


numerical modeling, convection, flow symmetry, laminar flows peculiarities


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