Instability and Transition of Nonparallel Bouyancy-Induced Flows Adjacent to an Ice Surface Melting in Water

얼음 벽면의 융해율을 고려한 비평행 자연대류에서 유동의 불안정성과 천이에 관한 연구

A set of stability equations is formulated for natural convection flows adjacent to a vertical isothermal surface melting in cold pure water. It takes account of the nonparallelism of the base flows. The melting rate is regarded as a blowing velocity at the ice surface. The numerical solutions of the linear stability equations which constitute a two-point boundary value problem are accurately obtained for various values of the density extremum parameter $R=(T_m-T_{\infty})/(T_0-T_{\infty})$ in the range $0.3{\leq}R{\leq}0.6$, by using a computer code COLNEW. The blowing effects on the base flow becomes more significant as ambient temperature ($T_{\infty}$) increases to $T_{\infty}=10^{\circ}C$. The maximum decrease of heat transfer rate is about 6.4 percent. The stability results show that the melting at surface causes the critical Grashof number $G^*$ and the maximum frequency of disturbances to decrease. In comparision with the results for the conventional parallel flow model, the nonparallel flow model has a higher critical Grashof number but has lower amplification rates of disturbances than does the parallel flow model. The spatial amplification contours exhibit that the selective frequency $B_0$ of the nonparallel flow model is higher than that of the parallel flow model and that the effects of melting are rather small. The present study also indicates that the selective frequency $B_0$ can be easily predicted by the value of the frequency parameter $B^*$ at $G^*$, which comes from the neutral stability results of the nonparallel flow model.