Control of oscillatory thermocapillary convection

Abstract: The possibility to stabilize the oscillatory thermocapillaryconvection is demonstrated using a proportional feedbackcontrol. This topic has a strong industrial motivation inconnection with a container-less crystal growth method calledthe floating-zone technique. The thermocapillary oscillation isknown to cause detrimental striations, microscopicinhomogeneity of the dopant distribution, in the final productof the crystal growth process. The feedback control is realizedby locally modifying the surface temperature by using the localtemperature measured at dierent locations fed back through asimple control law. Placing sensor/actuator pairs (controllers)in a strategical manner using the knowledge of the modalstructures, a simple cancellation scheme can be constructedwith only a few controllers. In this method, the state can bestabilized without altering the base flow appreciably whichcould be advantageous compared with other available controlmethods targeting the base convection.As an initial study of such kind of control method, thisthesis work explores the possibility of applying the control insimplified geometries such as the annular configuration and thehalf-zone for high Prandtl number liquids by means ofexperiments, numerical simulations, and formulation of a simplemodel equation system. Successful suppression of theoscillation was obtained especially in the weakly nonlinearregime where the control completely suppresses theoscillations. With a right choice of actuators, even with thelocal control, it was shown that it is possible to modify thelinear and weakly-nonlinear properties of the three-dimensionalflow system with linear and weakly nonlinear control. On theother hand, the method exhibits certain limitations. Dependingon the geometry of the system and actuators, the limitation canbe caused by either the enhancement of nonlinear dynamics dueto the finite size of the actuators or the amplification of newlinear modes. The former case can be attenuated by increasingthe azimuthal length of the actuators to reduce the generationof broad wavenumber waves. In the latter case, having an ideaof the structures of the newly appearing modes, thedestabilization of those modes can be delayed by optimizing theconfiguration of controllers. On the whole, the oscillation canbe attenuated significantly in a range of supercritical Maup to almost twice the critical value.Keywords:Fluid mechanics, Marangoni convection,thermocapillary convection, annular configuration, half-zone,feedback control, flow visualization, low dimensional model,bifurcation.