块石基底路基中局部非热平衡效应研究

块石基底路基中局部非热平衡效应研究

侯彦东, 王凯歌, 雷文远, 梁澍豪, 唐东昌

Research on local thermal non-equilibrium effect in crushed rock based embankment

Yandong HOU, Kaige WANG, Wenyuan LEI, Shuhao LIANG, Dongchang TANG

表1 控制方程

Table 1 Governing equation

区域	方程类型		控制方程
空气域^［11］	质量方程		$\frac{\partial v_{x}}{\partial x} + \frac{\partial v_{y}}{\partial y} = 0$
	动量方程		$ρ_{f} \frac{\partial v_{x}}{\partial t} + ρ_{f} [\frac{\partial (v_{x} v_{x})}{\partial x} + \frac{\partial (v_{y} v_{x})}{\partial y}] = - \frac{\partial p}{\partial x} + μ (\frac{\partial^{2} v_{x}}{\partial x^{2}} + \frac{\partial^{2} v_{x}}{\partial y^{2}})$ $ρ_{f} \frac{\partial v_{y}}{\partial t} + ρ_{f} [\frac{\partial (v_{x} v_{y})}{\partial x} + \frac{\partial (v_{y} v_{y})}{\partial y}] = - \frac{\partial p}{\partial y} + μ (\frac{\partial^{2} v_{x}}{\partial x^{2}} + \frac{\partial^{2} v_{x}}{\partial y^{2}}) - ρ_{α} g$
	能量方程		$ρ_{f} c_{f} \frac{\partial T}{\partial t} = \frac{\partial}{\partial x} (λ_{f} \frac{\partial T}{\partial x}) + \frac{\partial}{\partial y} (λ_{f} \frac{\partial T}{\partial y}) - ρ_{f} c_{f} [\frac{\partial (v_{x} T)}{\partial x} + \frac{\partial (v_{y} T)}{\partial y}]$
块石^{［11，18-19］}	质量方程		$\frac{\partial v_{x}}{\partial x} + \frac{\partial v_{y}}{\partial y} = 0$
	动量方程		$\begin{array}{l} \frac{\partial p}{\partial x} = - \frac{μ}{k} v_{x} - ρ_{f} B \|v\| v_{x} \\ \frac{\partial p}{\partial y} = - \frac{μ}{k} v_{y} - ρ_{f} B \|v\| v_{y} - ρ_{f} g \end{array}$ ， $B = \frac{α (1 - ε_{p})}{d_{p} {ε_{p}}^{3}}, k = \frac{d_{p}^{2} {ε_{p}}^{3}}{180 (1 - ε_{p})^{2}}$
	能量方程	LTE	$\frac{\partial}{\partial t} [ρ_{f} c_{p, f} ε_{p} + ρ_{s} c_{p, s} (1 - ε_{p})] T + \nabla (ρ_{f} c_{p, f} u T) = \nabla (λ \nabla T)$
	能量方程	LTNE	$\{\begin{array}{l} 流体 : ρ_{f} c_{p, f} ε_{p} \frac{\partial T_{f}}{\partial t} + ρ_{f} c_{p, f} ε_{p} v \nabla T_{f} = \nabla [(ε_{p} λ_{f} + λ_{s}) \nabla T_{f}] + a_{s f} h_{s f} (T_{s} - T_{f}) \\ 固体 : \frac{\partial}{\partial t} [ρ_{s} c_{p, s} (1 - ε_{p}) T_{s}] = \nabla [(1 - ε_{p}) λ_{s} \nabla T_{s}] - a_{s f} h_{s f} (T_{s} - T_{f}) \end{array}$
土层域^［11］	能量方程		$c_{e} \frac{\partial T}{\partial t} = \frac{\partial}{\partial x} [(λ_{e} \frac{\partial T}{\partial x}) + \frac{\partial}{\partial y} (λ_{e} \frac{\partial T}{\partial y})]$
换热系数	Achenbach^［23］		$h_{s f} = \frac{λ_{f}}{d_{p}} {[(1.18 R e^{0.58})^{4} + (0.23 R e_{h}^{0.58})^{4}]}^{\frac{1}{4}}$ $R e_{h} = R e / (1 - ε_{p})$
	Wakao^［24］		$h_{s f} = \frac{λ_{f} (2 + 1.1 P r^{1 / 3} R e^{0.6})}{d_{p}}$
	Dixon等^［25］		$h_{s f} = {[\frac{d_{p} ε_{p}}{0.225 P r^{1 / 3} R e^{2 / 3} k_{f}} + \frac{d_{p}}{β k_{s}}]}^{- 1}$
	Pallares等^［26］		$h_{s f} = \frac{k_{f}}{d_{p}} \{2 [1 + \frac{4 (1 - ε_{p})}{ε_{p}}] + (1 - ε_{p})^{0.5} R e^{0.6} P r^{1 / 3}\}$
比表面积^［23］			$a = 6 (1 - ε_{p}) / d_{p}$