TED-AJ03-270 NUMERICAL ANALYSIS OF SURFACE TENSION DRIVEN CONVECTION IN A LIQUID DROPLET USING A SPECTRAL METHOD

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概要

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• A three-dimensional numerical analysis is performed to study the Marangoni convection in a spherical liquid droplet cooled uniformly from its surroundings. Like the Benard cells observed on flat liquid surfaces cooled from the surface, the convection occurs even for curved liquid surfaces under appropriate conditions. The essential physical features of the phenomenon come from the fact that surface tension is a monotonous decreasing function of temperature in most fluids. Consider a hot liquid droplet cooling from its surface. When the free surface of a fluid layer is not under a uniform temperature, surface traction from the hot areas to cold areas causes a motion within the fluid. At the hot spot on the surface, warm fluid is drawn towards the surface from the inside of the droplet, which keeps the spot being hot. And this hot fluid spreads across the surface, cooling as it goes. The decrease in temperature across the surface is accompanied by an increase in surface tension that tends to maintain the convection. This phenomenon of the surface-tension-driven convection may affect the heat and mass transport within a small droplet in spray combustion or spray drying. And it may also play an important roll within a droplet under micro-gravity condition, a droplet radiator for example, which may be used as a compact heat-releasing device for space stations. In out study, a method is developed to analyze the three-dimensional transient Marangoni convection in a spherical liquid droplet that is cooled uniformly from its surroundings. As the field is unstable and is very sensitive to the temperature gradients along the surface, it is required for the numerical scheme to be highly accurate and be free from the effects of the polar and central singularities. For the purpose, a spherical harmonic spectral method was adopted to analyze the flow and temperature fields in the droplet on the spherical coordinates. And the transports equation of rƒ (r : radius coordinate, ƒ : velocity components, pressure, temperature) is numerically solved to avoid the singularity at the center of the droplet. The validity of the numerical method is checked at first. And some calculations are carried out to study the effects of parameters, i.e., Marangoni number, Prandt1 number, on the numerical results and it is found that the net heat transport rate within the droplet is affected by the surface tension driven convection when Ma>1000.[figure]

• 一般社団法人日本機械学会の論文

著者

• KUDO Kazuhiko

  Division of Mechanical Science, Graduate School of Engineering, Hokkaido University

• Totani Tsuyoshi

  Division Of Mechanical Science Graduate School Of Engineering Hokkaido University

• Kudo Kazuhiko

  Division Of Mechanical Science Graduate School Of Engineering Hokkaido University

• Kuroda Akiyoshi

  Division Of Mechanical Science Graduate School Of Engineering Hokkaido University

• Kudo Kazuhiko

  Division Of Human Mechanical Systems And Design Graduate School Of Engineering Hokkaido University

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