能源研究与信息  2022, Vol. 38 Issue (3): 176-180 PDF

A particle turbulence model in the gas-particle two-phase flow
ZENG Zhuoxiong, XU Xiaodong, WANG Haoyuan, CHENG Heng, GONG Xue
College of Power and Mechanical Engineering, Shanghai University of Electric Power, Shanghai 201306, China
Abstract: Particle turbulence has its own generation and dissipation. Particle turbulence model has a great impact on the prediction accuracy. So, a particle turbulence model was established in which the anisotropy and the interaction between two phases were considered, and the generation terms of both gas-particle two phases and two-phase velocity correlations were closed by the algebraic Reynolds stress model. Numerical simulation on axisymmetric swirl gas-particle flow was performed using present model and kg-εg-kp-εp-θ turbulence model. Results showed that the predicted results such as particle mean velocity and fluctuation velocity by present model were closer to the experimental ones, comparing with those by kg-εg-kp-εp-θ model. It indicated that the present model was more consistent with the inherent characteristics of particle turbulence.
Key words: gas-particle flows     swirl flow     two-scale fluctuation

1 颗粒相双尺度两相湍流模型

 $\begin{split} &\dfrac{{\partial \left( {\overline {{\alpha _{\text{p}}}} {\rho _{\text{p}}}{k_{1{\text{p}}}}} \right)}}{{\partial t}} + \dfrac{{\partial \left( {\overline {{\alpha _{\text{p}}}} {\rho _{\text{p}}}{U_{{\text{p}j}}}{k_{1{\text{p}}}}} \right)}}{{\partial {x_{j}}}} = \dfrac{\partial }{{\partial {x_{j}}}}\left[\left({\mu _{\text{p}}} + \dfrac{{{\mu _{{\text{pt}}}}}}{{{\sigma _{{\text{pk}}}}}}\right)\dfrac{{\partial {k_{1{\text{p}}}}}}{{\partial {x_{l}}}}\right] - \\ &{\rho _{\text{p}}}\overline {{\alpha _{\text{p}}}}\;\overline {{u_{{\text{p}i}}}{u_{{\text{p}j}}}} \dfrac{{\partial {U_{{\text{p}i}}}}}{{\partial {x_{j}}}} - \overline {{\alpha _{\text{p}}}} {\rho _{\text{p}}}{T_{\text{p}}} + 2\beta [{k_{{\text{pg}}}} - {k_{1{\text{p}}}}]\\[-20pt] \end{split}$ (1)

 $\begin{split} & \dfrac{{\partial \left( {\overline {{\alpha _{\text{p}}}} {\rho _{\text{p}}}{k_{2{\text{p}}}}} \right)}}{{\partial t}} + \dfrac{{\partial \left( {\overline {{\alpha _{\text{p}}}} {\rho _{\text{p}}}{U_{{\text{p}j}}}{k_{2{\text{p}}}}} \right)}}{{\partial {x_{j}}}} = \dfrac{\partial }{{\partial {x_{j}}}}\left[\left({\mu _{\text{p}}} + \dfrac{{{\mu _{{\text{pt}}}}}}{{{\sigma _{{\text{pk}}}}}}\right)\dfrac{{\partial {k_{2{\text{p}}}}}}{{\partial {x_{l}}}}\right] + \\ & \overline {{\alpha _{\text{p}}}} {\rho _{\text{p}}}{T_{\text{p}}} - \overline {{\alpha _{\text{p}}}} {\rho _{\text{p}}}{\varepsilon _{\text{p}}} - \dfrac{1}{3}(1 - {e^2})\dfrac{{{k_{2{\text{p}}}}\overline {{\alpha _{\text{p}}}} {\rho _{\text{p}}}}}{{{\tau _{\text{c}}}}} - 2\beta {k_{2{\text{p}}}} \\[-20pt] \end{split}$ (2)

 $\begin{split} &\dfrac{{\partial \left( {\overline {{\alpha _{\text{p}}}} {\rho _{\text{p}}}{T_{\text{p}}}} \right)}}{{\partial t}} + \dfrac{{\partial \left( {\overline {{\alpha _{\text{p}}}} {\rho _{\text{p}}}{U_{{\text{p}j}}}{T_{\text{p}}}} \right)}}{{\partial {x_{j}}}} = \dfrac{\partial }{{\partial {x_{j}}}}\left[\left({\mu _{\text{p}}} + \dfrac{{{\mu _{{\text{pt}}}}}}{{{\sigma _{{\text{p}}\varepsilon }}}}\right)\dfrac{{\partial {T_{\text{p}}}}}{{\partial {x_{l}}}}\right] + \dfrac{{{T_{\text{p}}}}}{{{k_{1{\text{p}}}}}}\\ &({C_{{\text{p}}1}}{P_{\text{p}}} - {C_{{\text{p}}2}}\overline {{\alpha _{\text{p}}}} {\rho _{\text{p}}}{T_{\text{p}}} + {C_{{\text{p}}3}}{G_{1{\text{p}},{\text{pg}}}}) + {C_{{\text{p}}4}}\overline {{\alpha _{\text{p}}}} {\rho _{\text{p}}}\dfrac{{{P_{\text{p}}}^2}}{{{k_{1{\text{p}}}}}} \\[-20pt] \end{split}$ (3)

 $\begin{split} &\dfrac{{\partial \left( {\overline {{\alpha _{\text{p}}}} {\rho _{\text{p}}}{\varepsilon _{\text{p}}}} \right)}}{{\partial t}} + \dfrac{{\partial \left( {\overline {{\alpha _{\text{p}}}} {\rho _{\text{p}}}{U_{{\text{p}j}}}{\varepsilon _{\text{p}}}} \right)}}{{\partial {x_{j}}}} = \dfrac{\partial }{{\partial {x_{j}}}}\left[\left({\mu _{\text{p}}} + \dfrac{{{\mu _{{\text{pt}}}}}}{{{\sigma _{{\text{p}}\varepsilon }}}}\right)\dfrac{{\partial {\varepsilon _{\text{p}}}}}{{\partial {x_{l}}}}\right] + \\ &\dfrac{{{\varepsilon _{\text{p}}}}}{{{k_{2{\text{p}}}}}}({C_{\varepsilon {\text{p}}1}}\overline {{\alpha _{\text{p}}}} {\rho _{\text{p}}}{T_{\text{p}}} - {C_{\varepsilon {\text{p}}2}}\overline {{\alpha _{\text{p}}}} {\rho _{\text{p}}}{\varepsilon _{\text{p}}} + {C_{\varepsilon {\text{p}}3}}{G_{2{\text{p}},{\text{pg}}}}) +\\ & {C_{\varepsilon {\text{p}}4}}\dfrac{{{T_{\text{p}}}^2}}{{{k_{2{\text{p}}}}}}\overline {{\alpha _{\text{p}}}} {\rho _{\text{p}}}\\[-20pt] \end{split}$ (4)

 $\begin{split} &\dfrac{\partial {k_{{\text{pg}}}} }{{\partial t}} + \left( {{U_{{\text{g}j}}} + {U_{{\text{p}j}}}} \right)\dfrac{\partial {k_{{\text{pg}}}} }{{\partial {x_{j}}}} = \dfrac{\partial }{{\partial {x_{j}}}}\left[ {({\upsilon _{{\text{ge}}}} + {\upsilon _{{\text{pe}}}})\dfrac{{\partial {k_{{\text{pg}}}}}}{{\partial {x_{j}}}}} \right] - \dfrac{1}{2}\\ &\left( {\overline {{u_{{\text{g}i}}}{u_{{\text{p}j}}}} \dfrac{{\partial {U_{{\text{p}i}}}}}{{\partial {x_{j}}}} + \overline {{u_{{\text{p}i}}}{u_{{\text{g}j}}}} \dfrac{{\partial {U_{{\text{g}i}}}}}{{\partial {x_{j}}}}} \right) + \dfrac{\beta }{{\overline {{\alpha _{\text{g}}}} {\rho _{\text{g}}}\overline {{\alpha _{\text{p}}}} {\rho _{\text{p}}}}}[\overline {{\alpha _{\text{p}}}} {\rho _{\text{p}}}{k_{\text{p}}} + \overline {{\alpha _{\text{g}}}} {\rho _{\text{g}}}{k_{\text{g}}} -\\ & (\overline {{\alpha _{\text{g}}}} {\rho _{\text{g}}} + \overline {{\alpha _{\text{p}}}} {\rho _{\text{p}}}){k_{{\text{pg}}}}] - \dfrac{{{\varepsilon _{\text{g}}}}}{{{k_{\text{g}}}}}{k_{{\text{pg}}}}\\[-20pt] \end{split}$ (5)

 $\begin{split} \overline {{u_{{\text{p}i}}}{u_{{\text{g}j}}}} =& - \dfrac{{\overline {{\alpha _{\text{g}}}} {\rho _{\text{g}}}\overline {{\alpha _{\text{p}}}} {\rho _{\text{p}}}}}{{\beta \left(\overline {{\alpha _{\text{g}}}} {\rho _{\text{g}}} + \overline {{\alpha _{\text{p}}}} {\rho _{\text{p}}}\right)}}\left(\overline {{u_{{\text{p}i}}}{u_{{\text{g}l}}}} \dfrac{{\partial {U_{{\text{g}j}}}}}{{\partial {x_{l}}}} + \overline {{u_{{\text{g}j}}}{u_{{\text{p}l}}}} \dfrac{{\partial {U_{{\text{p}i}}}}}{{\partial {x_{l}}}}\right) + \\ &\left(\dfrac{{\overline {{\alpha _{\text{g}}}} {\rho _{\text{g}}}}}{{\overline {{\alpha _{\text{g}}}} {\rho _{\text{g}}} + \overline {{\alpha _{\text{p}}}} {\rho _{\text{p}}}}}\overline {{u_{{\text{g}i}}}{u_{{\text{g}j}}}} + \dfrac{{\overline {{\alpha _{\text{p}}}} {\rho _{\text{p}}}}}{{\overline {{\alpha _{\text{g}}}} {\rho _{\text{g}}} + \overline {{\alpha _{\text{p}}}} {\rho _{\text{p}}}}}\overline {{u_{{\text{p}i}}}{u_{{\text{p}j}}}} \right) - \\ & \dfrac{{2{\text{ }}\overline {{\alpha _{\text{g}}}} {\rho _{\text{g}}}\overline {{\alpha _{\text{p}}}} {\rho _{\text{p}}}}}{{\beta \left(\overline {{\alpha _{\text{g}}}} {\rho _{\text{g}}} + \overline {{\alpha _{\text{p}}}} {\rho _{\text{p}}}\right)}}\dfrac{{{k_{{\text{pg}}}}}}{{{k_{\text{g}}}}}{\varepsilon _{\text{g}}}{\delta _{{ij}}}\\[-20pt] \end{split}$ (6)

 $\begin{split} \overline {{u_{{\text{p}i}}}{u_{{\text{p}j}}}} = & - \lambda \dfrac{{{k_{\text{p}}}}}{{{\varepsilon _{\text{p}}}}}\left(\overline {{u_{{\text{p}i}}}{u_{{\text{p}l}}}} \dfrac{{\partial {U_{{\text{p}j}}}}}{{\partial {x_{l}}}} + \overline {{u_{{\text{p}j}}}{u_{{\text{p}l}}}} \dfrac{{\partial {U_{{\text{p}i}}}}}{{\partial {x_{l}}}}\right) +\\ & \dfrac{{\beta {k_{\text{p}}}}}{{{c_1}\overline {{\alpha _{\text{p}}}} {\rho _{\text{p}}}{\varepsilon _{\text{p}}}}}\left(\overline {{u_{{\text{p}i}}}{u_{{\text{g}j}}}} + \overline {{u_{{\text{g}i}}}{u_{{\text{p}j}}}} - 2\overline {{u_{{\text{p}i}}}{u_{{\text{p}j}}}} \right) + \\ &\left(1 - \lambda \right)\dfrac{2}{3}{k_{\text{p}}}{\delta _{{ij}}} \end{split}$ (7)

 $\begin{split} \overline {{u_{{\text{g}i}}}{u_{{\text{g}j}}}} = & - \lambda \dfrac{{{k_{\text{g}}}}}{{{\varepsilon _{\text{g}}}}}\left(\overline {{u_{{\text{g}i}}}{u_{{\text{g}l}}}} \dfrac{{\partial {U_{{\text{g}j}}}}}{{\partial {x_{l}}}} + \overline {{u_{{\text{g}j}}}{u_{{\text{g}l}}}} \dfrac{{\partial {U_{{\text{g}i}}}}}{{\partial {x_{l}}}}\right) +\\ &\dfrac{{\beta {k_{\text{g}}}}}{{{c_1}\overline {{\alpha _{\text{g}}}} {\rho _{\text{g}}}{\varepsilon _{\text{g}}}}}\left(\overline {{u_{{\text{p}i}}}{u_{{\text{g}j}}}} + \overline {{u_{{\text{g}i}}}{u_{{\text{p}j}}}} - 2\overline {{u_{{\text{g}i}}}{u_{{\text{g}j}}}} \right) +\\ &\left(1 - \lambda \right)\dfrac{2}{3}{k_{\text{g}}}{\delta _{{ij}}} \end{split}$ (8)

2 旋流室内气固两相流动的数值计算

 图 1 旋流室示意图 Fig.1 Geometry of the swirl chamber

 图 2 网格无关性验证 Fig.2 Grid independence verification

 图 3 气体、颗粒两相平均速度分布 Fig.3 Mean velocity of the gas and particles

 图 4 气体、颗粒两相脉动速度分布 Fig.4 Fluctuation velocity distribution of the gas and particles
3 结　论

（1）建立了颗粒相双尺度模型及两相关联湍动能方程相结合的颗粒相湍流模型，本模型同时考虑了脉动各向异性以及两相湍流间相互作用。

（2）利用本模型以及kg−εg−kp−εp−θ五方程模型对旋流两相流动进行了数值计算，并对比了两种模型下两相平均速度及脉动速度的分布。

（3）总体而言，本模型的模拟结果比kg−εgkpεpθ五方程模型的模拟结果与实验数据更吻合。

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