On the occurrence of buoyancy-induced oscillatory growth instability in directional solidification of alloys

TL;DR

This study models buoyancy-induced oscillatory growth instability during directional solidification of alloys, demonstrating its occurrence across different alloys and mapping the conditions under which various oscillation behaviors emerge.

Contribution

It extends previous modeling of oscillatory growth instability from CMSX4 to other alloys like Al-4at.%Cu, providing a comprehensive map of conditions leading to different oscillation regimes.

Findings

Oscillations occur within a narrow range of cooling rates and dendrite spacings.

A minimum pulling velocity is required for oscillations to occur.

The type of oscillation correlates with the ratio of fluid velocity to pulling velocity.

Abstract

Recent solidification experiments identified an oscillatory growth instability during directional solidification of Ni-based superalloy CMSX4 under a given range of cooling rates. From a modeling perspective, the quantitative simulation of dendritic growth under convective conditions remains challenging, due to the multiple length scales involved. Using the dendritic needle network (DNN) model, coupled with an efficient Navier-Stokes solver, we reproduced the buoyancy-induced growth oscillations observed in CMSX4 directional solidification. These previous results have shown that, for a given alloy and temperature gradient, oscillations occur in a narrow range of cooling rates (or pulling velocity, $V_p$) and that the selected primary dendrite arm spacing ($\Lambda$) plays a crucial role in the activation of the flow leading to oscillations. Here, we show that the oscillatory behavior may be generalized to other binary alloys within an appropriate range of $(V_p,\Lambda)$ by reproducing it for an Al-4at.%Cu alloy. We perform a mapping of oscillatory states as a function of $V_p$ and $\Lambda$, and identify the regions of occurrence of different behaviors (e.g., sustained or damped oscillations) and their effect on the oscillation characteristics. Our results suggest a minimum of $V_p$ for the occurrence of oscillations and confirm the correlation between the oscillation type (namely: damped, sustained, or noisy) with the ratio of average fluid velocity $\overline V$ over $V_p$. We describe the different observed growth regimes and highlight similarities and contrasts with our previous results for a CMSX4 alloy.