A. Kosir
Fakulteta za strojnistvo
Laboratorij za dinamiko fluidov
in termodinamiko
1000 Ljubljana, Askerceva 6
B. Sarler, FS, Univerza v Ljubljani
V delu sta uporabljeni numericni metodi: metoda kontrolnih
prostornin in metoda robnih elementov z dvojno reciprocnostjo, s
katerima z iterativno implicitno shemo resimo nalogo
konvekcijsko-difuzijskega prenosa toplote v sistemu s faznim
prehodom v poljubno razseznem prostoru. Temperaturno polje je
izracunano iz tako diskretiziranih enacb, da te upostevajo mozno
nelinearno zvezo med temperaturo in specificno entalpijo pri
temperaturi faznega prehoda. Z Voller-Swaminathanovim nastavkom
pri vsaki iteraciji znotraj casovnega koraka napovemo novi
prostorninski delez trdne faze. Tocnost obeh numericnih metod
primerjamo z enorazseznim konvektivno-difuzijskim problemom, za
katerega smo nasli analiticno resitev. Predstavljeni numericni
shemi sta bili pri prikazanih primerih konvergentni.
Kljucne besede: prenos toplote, fazni prehod, strjevanje,
Stefanova naloga, gibajoci se rob, kontinuirano ulivanje,
konvekcijsko-difuzijski pojavi, metoda robnih elementov, metoda
dvojne reciprocnosti, metoda kontrolnih prostornin
Two numerical fixed grid methods, the control volume method and
the boundary element method with dual reciprocity, are presented
with an updated iterative implicit scheme to solve arbitrary
dimensional phase change problems with convection and diffusion
heat transport. The temperature field is deduced from the
resolution of the governing equations whose discretization takes
into account the highly nonlinear relation between temperature
and specific heat at the melting point. At each iteration within
one time step an updated volume fraction of solid phase is found
from the Voller-Swaminathan procedure. The accuracy of the
proposed numerical methods has been checked on one dimensional
convection-conduction test problems for which we have found an
analytical solution. For several examples presented, the
numerical schemes have demonstrated convergence properties.
Key words: heat transfer, phase change, solidification, Stefan
problem,
moving boundary, continuous casting, convective-diffusive phenomena,
boundary element method, dual
reciprocity method, control volume method