Numerical solution to melting of a solid in a horizontal circular cylinder

Abstract

The present study could be divided into the following three parts. The transient natural convection within a horizontal circular annulus was firstly computed to examine the liquid-melt flow affectin the melting process in a horizontal tube. The governing equations were time accurately solved by an explicit Euler method and a direct solver, SEVP. To capture finely the secondary flows the spatially fourth-order accurate Arakawa scheme was adopted for convective Jacobian. Secondly, the inward melting in a horizontal circular cylinder was numerically investigated with two-dimensional assumption. Lastly, the complete threedimensional computation was performed over the above melting problem, considering the longitudinal flow instability as well as the one within the transverse plane. The three-dimensional phase change problem was successfully computed by the modificatin of a Navier-Stokes slover, pseudo-compressibility method, according to the concept of enthalpy method. For the transient natural convection in the annulus, the initial disturbance of extremely small differences was found to result in two or three bifurcating soultions:bicellular, tricellular, and quadricellular flow modes. Further, like-rotating cells were sometimes induced by hydrodynamic instability at the vertical portion of the annulus, besides counter-rotating cells developing near the thermally unstabel top region. The two-dimensional results of the melting problem showed that three drastically different melting patterns could be developed depending on the types of initial idsturbance:namely the First, Second, and Third mode of melting process were respectively accompanied with the natural convection flows of unicellular, bicellular, and tricellular form. Moreover, each of the different melting patterns agreed well with the earlier contradictory results in literature. It seems then the earlier discrepancies might be caused by the bifurcation of solution in the melting problem. From the complete ...