Active control of a global thermocapillary instability

Active control was applied to oscillatory thermocapillary flow in an open cylindrical container filled with Silicone oil. Thermocapillary convection was driven by imposing a radial temperature gradient on a flat free surface. This is an extension of the previous work by Shiomi et al. who applied proportional feedback control by locally heating the surface at a single position using the local temperature signal at a different position fed back through a simple algorithm. Although significant attenuation of the oscillation was detected, an uncertainty remained if global stabilization was achieved. In the present paper, two sensor/heater pairs were installed to achieve the global suppression of the oscillation. Successful global stabilization of the oscillation was achieved in a range of Marangoni number, with the best performance in the weakly nonlinear regime. Using a reliable temperature measurement method, quantitative analysis is carried out to quantify the performance of the control. The optimal values of gain and relative position of sensor/heater pairs were identified.