基于VOSET的黏弹性气液两相湍流直接数值模拟
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摘要
本文将相界面追踪高效方法VOSET与黏弹性减阻流体Giesekus本构关系相结合,建立了黏弹性气液两相流动的控制方程.研究发现减阻剂的存在使得计算稳定性相对于无减阻剂情况大幅下降,主要原因为相界面处引入了较大的黏弹性应变梯度,加剧了本构方程求解的不稳定性,使得可计算的顶盖拖动速度限制在1～2 m·s~(-1)的狭小范围内,影响了对黏弹性气液两相湍流特征的研究。通过用光滑的Heaviside函数对相界面附近的黏弹性应变进行插值,有效增强了数值稳定性,将可计算的顶盖拖动速度范围扩展至50 m·s~(-1)。采用改进后的方法在较宽的雷诺数范围进行了直接数值模拟,确认了减阻剂较大地抑制了液相湍流脉动,从而对气液两相湍流流动起到减阻作用,加剂后液相的平均流速增大约37%～86%。
We combine the efficient interface-tracking method VOSET and the constitutive relation Giesekus for viscoelastic drag-reducing fluid to establish governing equations of viscoelastic gas-liquid flow. It is found from the first-step study that the existence of the drag-reducing agents(DRAs) causes the numerical stability deteriorate compared with no agent case. The main reason is large viscoelastic conformation gradient introduced around the gas-liquid interface, enhancing numerical instability of the constitutive equation. As a result, applicable lid-driven velocity is limited in a narrow range(1～2 m·s~(-1)), affecting the study on characteristics of viscoelastic gas-liquid turbulent flow. To overcome this drawback, we use a smooth Heaviside function to interpolate the viscoelastic conformation near the gas-liquid interface. This improvement greatly enhances the numerical stability and extends the lid-driven velocity up to 50 m·s~(-1). Direct numerical simulation in a wider range of Reynolds number is implemented using the improved method. Numerical results confirm that drag-reducing agents largely depress turbulent fluctuations of liquid phase so that drag reduction occurs for the whole gas-liquid turbulent flow. Mean velocity of the liquid phase increases about 37%～86%.
We combine the efficient interface-tracking method VOSET and the constitutive relation Giesekus for viscoelastic drag-reducing fluid to establish governing equations of viscoelastic gas-liquid flow. It is found from the first-step study that the existence of the drag-reducing agents(DRAs) causes the numerical stability deteriorate compared with no agent case. The main reason is large viscoelastic conformation gradient introduced around the gas-liquid interface, enhancing numerical instability of the constitutive equation. As a result, applicable lid-driven velocity is limited in a narrow range(1～2 m·s~(-1)), affecting the study on characteristics of viscoelastic gas-liquid turbulent flow. To overcome this drawback, we use a smooth Heaviside function to interpolate the viscoelastic conformation near the gas-liquid interface. This improvement greatly enhances the numerical stability and extends the lid-driven velocity up to 50 m·s~(-1). Direct numerical simulation in a wider range of Reynolds number is implemented using the improved method. Numerical results confirm that drag-reducing agents largely depress turbulent fluctuations of liquid phase so that drag reduction occurs for the whole gas-liquid turbulent flow. Mean velocity of the liquid phase increases about 37%～86%.
引文
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[8] SUN Dongliang, QU Zhiguo, HE Yaling, et al. An Efficient Segregated Algorithm for Incompressible Fluid Flow and Heat Transfer Problems-IDEAL(Inner Doubly Iterative Efficient Algorithm for Linked Equations)Part I:Mathematical Formulation and Solution Procedure[J].Numerical Heat Transfer Part B, 2008, 53(1):1-17
[2]卢晓岩,孙东亮.运动界面追踪方法的研究现状及进展[J].科技信息,2011(32):482LU Xiaoyan, SUN Dongliang. Current Study and Progress on Moving Interface Tracking Method[J]. Scientific Information, 2011(32):482
[3] Sussman M, Puckett E G. A Coupled Level Set and Volume-of-Fluid Method for Computing 3D and Axisymmetric Incompressible Two-Phase Flows[J]. Journal of Computational Physics, 2000, 162(2):301-337
[4] SUN Dongliang, TAO Wenquan. A Coupled Volume-ofFluid and Level Set(VOSET)Method for Computing Incompressible Two-Phase Flows[J]. International Journal of Heat and Mass Transfer, 2010, 53(4):645-655
[5] Osher S. Level Set Methods and Dynamics Implict Surfaces[M]. Springer-Verlag New York, Inc, 2003
[6] Brackbill J U, Kothe D B, Zemach C. A Continuum Method for Modeling Surface Tension[J]. Journal of Computational Physics, 1992, 100:335-354
[7] Van L B. Upwind-Difference Methods for Aerodynamic Problems Governed by the Euler Equations[C]//LargeScale Computations in Fluid Mechanics, 1985:327-336
[8] SUN Dongliang, QU Zhiguo, HE Yaling, et al. An Efficient Segregated Algorithm for Incompressible Fluid Flow and Heat Transfer Problems-IDEAL(Inner Doubly Iterative Efficient Algorithm for Linked Equations)Part I:Mathematical Formulation and Solution Procedure[J].Numerical Heat Transfer Part B, 2008, 53(1):1-17
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