Hydraulic analysis of free-surface flows with solidification

The paper is concerned with a one-dimensional analysis of plane open-channe l flow with continuous solidification. The process is of relevance for rece nt developments in the casting of steel and other metals. The bottom of the channel consists of a rotating casting roll and a horizontal cooling table , where the solidified material is withdrawn with given velocity. The study is restricted to the region downstream of the top of the casting roll. Sur face tension is neglected. In the main part of the analysis inviscid fluid flow is considered since th e Reynolds number is very large in the applications. It is found that the s teady-state solutions are nonunique in a certain parameter range. In additi on to a continuous solution, there are two solutions including hydraulic ju mps, with one hydraulic jump being located on the casting roll, the other o ne on the cooling table. Regarding the stability of the non unique solution s, the evolution of disturbances is investigated numerically as an initial- value problem. It is concluded that the hydraulic jump on the cooling table is unstable, while the other discontinuous solution as well as the continu ous solution are stable for sufficiently small disturbances. Which stable s olution is attained in the steady state, depends on the history of the proc ess. Friction at the liquid/solid interface is taken into account in the last pa rt of the analysis. A constant friction coefficient is assumed. It is found that the history of the process determines the steady-state solution if, a nd only if, the friction coefficient is sufficiently small. For larger valu es of the friction coefficient, the steady-state solution is unique and ind ependent of the history of the transient process. Furthermore, for sufficie ntly large friction coefficients, stable hydraulic jumps are found, in cont rast to the inviscid case, also on the cooling table.