MODELING OF TWO-DIMENSIONAL SOLIDIFICATION OF A FINITE CYLINDER

Silindirik geometride sıvı fazın ergime sıcaklığında bulunduğu donma problemi katı - sıvı sınırını sabitleme yöntemi kullanılarak çözülmüştür. Dış yüzeyde ergime sıcaklığının altında olmak üzere zamana veya pozisyona göre değişken olan sıcaklık sınır koşulu tanımlanmıştır. Daha önce kartezyen koordinat sisteminde kullanılmış olan koordinat dönüşümü tekniği radyal ve eksenel yönde uygulanarak çözüm bölgesi olarak sabit bir kare elde edilmiştir. Bu dönüşüm yöntemi her çözüm adımı için yeniden çözüm ağı oluşturmayı gerektirmektedir. Koordinat dönüşümü ile elde edilen enerji denklemi sonlu farklar yöntemi ile katı fazdaki sıcaklık dağılımı ve katı - sıvı sınırının ilerlemesini belirlemek üzere çözülmüş ve yükseklik/yarıçap oranı ve dış yüzeydeki konuma göre değişen sınır koşullarının etkileri incelenmiştir.

SONLU BİR SİLİNDİRDEKİ DONMANIN İKİ BOYUTLU MODELLENMESİ

Two-dimensional solidification problem of a finite cylinder, in which the liquid phase is initially at the fusion temperature, is solved by using a front fixing approach. The external surfaces of the cylinder are subjected to a temporally or spatially varying temperature below freezing. The method employed is based on one used for the solution of a solidification problem in Cartesian domain. A coordinate transformation is applied in both radial and axial directions to obtain a square computational domain. This transformation results in a computationally intensive grid generation for every time step of solution. Finite difference form of the transformed energy equation is solved for the temperature distribution in the solid phase and the solid-liquid interface energy balance is integrated for the new position of the moving solidification front. The effect of the aspect ratio and spatially varying boundary temperatures on solidification is studied.

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