Instability mechanisms for thermocapillary flow in an annular pool heated from inner wall. (December 2018) - Liu, Hao; Zeng, Zhong; Yin, Linmao; Qiao, Long; Zhang, Liangqi
Highlights: The SEM ensure the higher accuracy of the present results. The influence of Prandtl number on the flow instability is investigated by LSA. Three types of instabilities are found and the energy analysis reveals the different instability mechanisms. Abstract: The linear stability analysis of thermocapillary flow in an annular pool heated from inner wall was performed by using spectral element method. The physical instability mechanisms for different Prandtl numbers ( Pr ) ranging from 0.001 to 1.4 were studied by energy analysis under critical mode. We observed three instability types: (i) the Hopf (oscillatory) bifurcation with wavenumber k  = 18 for Pr  < 0.02, and the corresponding neutral mode is amplified due to the basic shear flow; (ii) the stationary instability with k  = 3 or k  = 2 for 0.02 <  Pr  < 0.6; (iii) the Hopf bifurcation again with k  = 3 for 0.6 <  Pr  < 1.4. In both Prandtl number ranges of 0.02 <  Pr  < 0.6 and 0.6 <  Pr  < 1.4, thermocapillary force induced by the disturbance temperature field drives primarily the flow instability.