潘晓军, 张燕平, 陈曦, 高伟, 樊剑. 水平基底上薄膜流体的数学模型及其数值模拟[J]. 工程力学, 2018, 35(6): 24-32,41. DOI: 10.6052/j.issn.1000-4750.2017.02.0105
引用本文: 潘晓军, 张燕平, 陈曦, 高伟, 樊剑. 水平基底上薄膜流体的数学模型及其数值模拟[J]. 工程力学, 2018, 35(6): 24-32,41. DOI: 10.6052/j.issn.1000-4750.2017.02.0105
PAN Xiao-jun, ZHANG Yan-ping, CHEN Xi, GAO Wei, FAN Jian. MATHEMATICAL MODEL AND NUMERICAL SIMULATION OF THIN FILM FLOW ON HORIZONTAL SUBSTRATE[J]. Engineering Mechanics, 2018, 35(6): 24-32,41. DOI: 10.6052/j.issn.1000-4750.2017.02.0105
Citation: PAN Xiao-jun, ZHANG Yan-ping, CHEN Xi, GAO Wei, FAN Jian. MATHEMATICAL MODEL AND NUMERICAL SIMULATION OF THIN FILM FLOW ON HORIZONTAL SUBSTRATE[J]. Engineering Mechanics, 2018, 35(6): 24-32,41. DOI: 10.6052/j.issn.1000-4750.2017.02.0105

水平基底上薄膜流体的数学模型及其数值模拟

MATHEMATICAL MODEL AND NUMERICAL SIMULATION OF THIN FILM FLOW ON HORIZONTAL SUBSTRATE

  • 摘要: 以应用于车体外壳的薄膜涂层为研究对象,针对涂覆于镀膜钢板上的流体高度差分布,提出了一种独特的数值模拟方法。首先基于该应用中薄膜流体的特殊几何特征和润滑近似理论简化描述流体的经典Navier-Stokes方程,结合边界条件建立所描述的薄膜流体运动的数学模型,然后运用傅里叶伪谱法与Runge-Kutta法相结合的方法进行数据处理,并根据所建立的数学模型与选取的相关算法,采用MATLAB编程对以上所描述的薄膜流体的涂覆的均匀性进行数值模拟。最后将数值模拟结果与实验数据进行对比,验证了数学模型与计算方法的合理性。通过数值模拟与实验分析可知,随着时间的推移,薄膜流体的自由液面高度差向着均匀性发展,但发展速率有限。

     

    Abstract: A unique mathematical model is built to study the relative altitude for deposited thin liquid films on steel sheets in automobiles. The classical Navier-stokes equation is simplified based on the specialties in the dimension of thin liquid films and lubrication approximation theory. Then a model is derived after the boundary condition is taken into consideration. The pseudo-spectral method combined with Runge-Kutta scheme is implemented to solve the mathematical model. The numerical simulation on the uniformity of the deposited thin liquid films is conducted by a program written in MATLAB according to the model and algorithm illustrated in this paper. The comparison between the results from the experiment and numerical simulation proves the feasibility of the mathematical model and the algorithm. The results are concluded that the height of free surface of the thin liquid film tends to be homogeneous while the homogenization rate is limited.

     

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