连铸结晶器内高温熔体多相流模型化研究进展

刘中秋, 李宝宽, 肖丽俊, 干勇

Modeling Progress of High-Temperature Melt Multiphase Flow in Continuous Casting Mold

LIU Zhongqiu, LI Baokuan, XIAO Lijun, GAN Yong

表1 3种湍流数值模拟方法的基本方程和特点

Table 1 Basic equations and characteristics of the three turbulent numerical methods

Method	Continuity	Momentum equation	Solvable scale	Model	Computation
	equation				requirement
DNS	$\frac{\partial u_{i}}{\partial x_{i}} = 0$	$\frac{\partial u_{i}}{\partial t} + u_{j} \frac{\partial u_{i}}{\partial x_{j}} =$	Eddies of all scales	No	Huge
		$- \frac{1}{ρ} \frac{\partial p}{\partial x_{j}} + υ \frac{\partial^{2} u_{i}}{\partial x_{j} \partial x_{j}} + f_{i}$
LES	$\frac{\partial {\bar{u}}_{i}}{\partial x_{i}} = 0$	$\frac{\partial {\bar{u}}_{i}}{\partial t} + u_{j} \frac{\partial \bar{u_{i} u_{j}}}{\partial x_{j}} =$	Eddies of large scales	Subgrid scale model	High
		$- \frac{1}{ρ} \frac{\partial \bar{p}}{\partial x_{j}} + υ \frac{\partial^{2} {\bar{u}}_{i}}{\partial x_{j} \partial x_{j}} + {\bar{f}}_{i}$
RANS	$\frac{\partial 〈u_{i}〉}{\partial x_{i}} = 0$	$\frac{\partial 〈u_{i}〉}{\partial t} + \frac{\partial 〈u_{i} u_{j}〉}{\partial x_{j}} =$	Eddies of average scale	Time-averaged turbulence model	Low
		$- \frac{1}{ρ} \frac{\partial 〈p〉}{\partial x_{j}} + υ \frac{\partial^{2} 〈u_{i}〉}{\partial x_{j} \partial x_{j}} + 〈f_{i}〉$