A. Kluwick et S. Scheichl, ON THE EVOLUTION OF UNSTEADY DISTURBANCES IN CONTINUOUS STRIP CASTINGPROCESSES, Physics of fluids, 9(12), 1997, pp. 3697-3706
Continuous solidification processes in thin layers of molten metal are
of central importance in many fields of modern metallurgical engineer
ing. This paper deals with unsteady disturbances possibly emerging at
the free surface or the phase boundary within the solidification zone
of a horizontal strip casting process. Assuming that the wave lengths
of the disturbances are large compared to the characteristic depth of
the melt, we can apply governing equations for one-dimensional flow. F
urthermore, we assume the amplitudes of the disturbances to be so smal
l that their evolution can be regarded as weakly nonlinear. Since unst
eady wave propagation phenomena can arise from temperature variations
as well as from the excitation of waves at the free surface or the sol
idification front, both mechanisms will be studied in the following. I
n the latter case the disturbances at the surface are found to be gove
rned by the inviscid Burgers equations with varying coefficients and w
ill then, in general, develop shock discontinuities. (C) 1997 American
Institute of Physics. [S1070-6631(97)02112-0].