On the drag of model dendrite Fragments at Low Reynolds Number

Abstract

An experimental study of low Reynolds number drag on laboratory models of dendrite fragments has been conducted. The terminal velocities of the dendrites undergoing free fall along their axis of symmetry were measured in a large Stokes flow facility. Corrections for wall interference give nearly linear drag versus Reynolds number curves. Corrections for both wall interference and inertia effects show that the dendriteStokes settling velocities are always less than that of a sphere of equal mass and voIume.In the Stokes limit, the settling speed ratio is found to correlate well with the primary dendrite arm aspect ratio and a second dimensionless shape parameter which serves as a measure of the fractal-like nature of the dendrite models.These results can be used to estimate equiaxed grain velocities and distance of travel in metal castings.The drag measurements may be used in numerical codes to calculate the movement of grains in a eonvecting melt in an effort to determine macrosegregation patterns caused by the sink/float mechanism.

Multiparticle interfacial drag in equiaxed solidification

“…Note from Eqs. [4] and [7] that the knowledge of either K or C~ is necessary to determine the interracial drag.…”

“…In the former case, An expression for C~, which encompasses both limiting cases, can simply be taken as the product C~C m. Converting to the parameter,/3~, using Eqs. [7] and [11] …”

Sedimentation speed of a free dendrite growing in an undercooled melt

“…[3,4]). Also, attempts have been made to estimate the drag force and the speed of equiaxed dendrites during their settling motion in undercooled melts [5][6][7] using mathematical models. Ahuja et.…”

“…[5] and De Groh et al [7] considered the equiaxed dendrite as a porous object to calculate the drag coefficient of settling speed. But these previous models of dendrite settling [5][6][7] did not give consideration to the growth of the dendrites as they settled in the undercooled melt. Additionally, it was assumed that a free dendrite reaches its terminal velocity almost instantaneously or at least in a time that is negligible compared to the average suspension time in any realistic casting system [5][6][7].…”

“…But these previous models of dendrite settling [5][6][7] did not give consideration to the growth of the dendrites as they settled in the undercooled melt. Additionally, it was assumed that a free dendrite reaches its terminal velocity almost instantaneously or at least in a time that is negligible compared to the average suspension time in any realistic casting system [5][6][7]. However it has recently been shown, through experimental evidence of Badillo et al [8] on settling of SCNacetone dendrites in undercooled melts that sedimenting equiaxed dendrites may not reach terminal velocity.…”