Full Text:   <2212>

Summary:  <807>

CLC number: TH117.2

On-line Access: 2014-03-04

Received: 2013-10-10

Revision Accepted: 2013-12-20

Crosschecked: 2014-02-20

Cited: 3

Clicked: 5100

Citations:  Bibtex RefMan EndNote GB/T7714

-   Go to

Article info.
Open peer comments

Journal of Zhejiang University SCIENCE A 2014 Vol.15 No.3 P.172-184

http://doi.org/10.1631/jzus.A1300328


An efficient adaptive finite element method algorithm with mass conservation for analysis of liquid face seals*


Author(s):  Xiang-kai Meng, Shao-xian Bai, Xu-dong Peng

Affiliation(s):  . Institute of Chemical Process Machinery, Zhejiang University of Technology, Hangzhou 310032, China

Corresponding email(s):   mengxk@zjut.edu.cn

Key Words:  Cavitation, Finite element method (FEM), End face seals, Streamline upwind/Petrov-Galerkin (SUPG), Mass conservation


Xiang-kai Meng, Shao-xian Bai, Xu-dong Peng. An efficient adaptive finite element method algorithm with mass conservation for analysis of liquid face seals[J]. Journal of Zhejiang University Science A, 2014, 15(3): 172-184.

@article{title="An efficient adaptive finite element method algorithm with mass conservation for analysis of liquid face seals",
author="Xiang-kai Meng, Shao-xian Bai, Xu-dong Peng",
journal="Journal of Zhejiang University Science A",
volume="15",
number="3",
pages="172-184",
year="2014",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.A1300328"
}

%0 Journal Article
%T An efficient adaptive finite element method algorithm with mass conservation for analysis of liquid face seals
%A Xiang-kai Meng
%A Shao-xian Bai
%A Xu-dong Peng
%J Journal of Zhejiang University SCIENCE A
%V 15
%N 3
%P 172-184
%@ 1673-565X
%D 2014
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A1300328

TY - JOUR
T1 - An efficient adaptive finite element method algorithm with mass conservation for analysis of liquid face seals
A1 - Xiang-kai Meng
A1 - Shao-xian Bai
A1 - Xu-dong Peng
J0 - Journal of Zhejiang University Science A
VL - 15
IS - 3
SP - 172
EP - 184
%@ 1673-565X
Y1 - 2014
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.A1300328


Abstract: 
To improve lubrication effect and seal performance, complicated geometrical hydrodynamic grooves or patterns are often processed on end faces of liquid lubricated mechanical seals. These structures can lead to difficulties in precisely estimating the seal performance. In this study, an efficient adaptive finite element method (FEM) algorithm with mass conservation was presented, in which a streamline upwind/Petrov-Galerkin (SUPG) weighted residual FEM and a fast iteration algorithm were applied to solve the lubrication equations (Reynolds equation). A mesh adaptation technique was utilized to refine the computation domain based on a residual posterior error estimator. Validation, applicability, and efficiency were verified by comparison among different algorithms and by case studies on seals’ faces with different groove structures. The study investigated the influence of the order of shape function and the mesh number on the leakage balance. Mesh refinement occurred mainly in cavitation zones when cavitation happened, otherwise it occurred in regions with a high pressure gradient. Numerical experiments verified that the proposed algorithm is a fast, effective, and accurate method to simulate lubrication problems in the engineering field apart from end face seals.

液体润滑端面密封质量守恒自适应有限元算法

研究目的:为液体润滑端面密封空化问题的数值模拟提供一种高效精确的计算方法。
创新要点:1.采用流线迎风SUPG有限元法求解具有对流扩散特征的控制方程;2. 针对未知量的互补关系提出了一种高效的数值迭代技术;3.提供了针对润滑液膜空化问题的网格自适应技术。
重要结论:1.相比文献算法,本文算法具有计算速度快,计算精度高的优点;2.空化区域和大压力梯度区域的计算网格得到加密。

关键词:空化;有限元法;端面密封;流线迎风伽辽金法SUPG法;质量守恒

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

References

[1] Ausas, R.F., Ragot, P., Leiva, J., 2007. The impact of the cavitation model in the analysis of microtextured lubricated journal bearings. ASME Journal of Tribology, 129(4):868-875. 


[2] Ausas, R.F., Jai, M., Buscaglia, G.C., 2009. A mass-conserving algorithm for dynamical lubrication problems with cavitation. ASME Journal of Tribology, 131(3):031702


[3] Bayada, G., Chambat, M., Alaoui, M.E., 1990. Variational formulations and finite element algorithms for cavitation problems. ASME Journal of Tribology, 112(2):398-403. 


[4] Bayada, G., Chambat, M., Vazquez, C., 1998. Characteristics method for the formulation and computation of a free boundary cavitation problem. Journal of Computational and Applied Mathematics, 98(2):191-212. 


[5] Bayada, G., Martin, S., Vazquez, C., 2006. Micro-roughness effects in (elasto)hydrodynamic lubrication including a mass-flow preserving cavitation model. Tribology International, 39:1707-1718. 


[6] Boedo, S., Booker, J.F., 1995. Cavitation in normal separation of square and circular plates. ASME Journal of Tribology, 117:403-409. 


[7] Bonneau, D., Guines, D., Frene, J., 1995. EHD analysis, including structural inertia effects and a mass-conserving cavitation model. ASME Journal of Tribology, 117(3):540-547. 


[8] Brewe, D.E., 1986. Theoretical modeling of the vapor cavitation in dynamically loaded journal bearings. ASME Journal of Lubrication Technology, 108(4):628-638. 


[9] Cioc, S., Keith, T.G., 2003. Application of the CE/SE method to two-dimensional flow in fluid film bearings. International Journal of Numerical Methods for Heat & Fluid Flow, 13(2):216-243. 


[10] Cioc, S., Florin, F., Keith, T.G., 2003. Application of the CE/SE method to wave journal bearings. STLE Tribology Transactions, 46(2):179-186. 


[11] Durany, J., Garcia, G., Vasquez, C., 1997. An elasto-hydrodynamic coupled problem between a piezoviscous Reynolds equation and a hinged plate model. Modlisation Mathmatique et Analyse Numrique, (in French),31(4):495-516. 

[12] Durany, J., Pereira, J., Varas, F., 2006. A cell-vertex finite volume method for thermohydrodynamic problems in lubrication theory. Computer Methods in Applied Mechanics and Engineering, 195(44-47):5949-5961. 


[13] Elrod, H.G., 1981. A cavitation algorithm. Journal of Lubrication Technology, 103(3):350-354. 


[14] Elrod, H.G., Adams, M.L., 1975. A computer program for cavitation and starvation problems. , Proceedings of 1st Leeds-Lyon Symposium on Tribology, New York, 37-42. :37-42. 

[15] Etsion, I., Michael, O., 1994. Enhancing sealing and dynamic performance with partially porous mechanical face seals. Tribology Transactions, 37(4):701-710. 


[16] Etsion, I., Burstein, L., 1996. A model for mechanical seals with regular micro-surface structure. Tribology Transactions, 39(3):677-683. 


[17] Etsion, I., Kligerman, Y., Halperin, G., 1999. Analytical and experimental investigation of laser-textured mechanical seal faces. Tribology Transactions, 42(3):511-516. 


[18] Evans, L.C., 1997. Partial Differential Equations. , American Mathematical Society, Berkeley, USA, 398-431. :398-431. 

[19] Fatu, A., Hajjam, M., Bonneau, D., 2005. An EHD model to predict the interdependent behavior of two dynamically loaded hybrid journal bearings. ASME Journal of Tribology, 127(2):416-424. 


[20] Giacopini, M., Fowell, M.T., Dini, D., 2010. A mass-conserving complementarity formulation to study lubricant films in the presence of cavitation. ASME Journal of Tribology, 132:041702


[21] Hajjam, M., Bonneau, D., 2004. Elastohydrodynamic analysis of lip seals with microundulations. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 218(1):13-21. 


[22] Hajjam, M., Bonneau, D., 2007. A transient finite element cavitation algorithm with application to radial lip seals. Tribology International, 40:1258-1269. 


[23] Ito, K., Kunisch, K., 2003. Semi-smooth Newton methods for variational inequalities of the first kind. ESAIM: Mathematical Modelling and Numerical Analysis, 37(1):41-62. 


[24] Jakobsson, B., Floberg, L., 1957. The finite journal bearings considering vaporization. Transactions of Chalmers University of Technology, 190:1-116. 

[25] Kumar, A., Booker, J.F., 1991. A finite element cavitation algorithm. ASME Journal of Tribology, 113(2):276-286. 


[26] Kumar, A., Booker, J.F., 1994. A mass and energy conserving finite element lubrication algorithm. ASME Journal of Tribology, 116(4):667-671. 


[27] Murty, K.G., 1988.  Linear Complementarity, Linear and Nonlinear Programming. Heldermann Verlag,Berlin, Germany :361-377. 

[28] Nilsson, B., Hansbo, P., 2007. Adaptive finite element methods for hydrodynamic lubrication with cavitation. International Journal for Numerical Methods in Engineering, 72(13):1584-1604. 


[29] Olsson, K.O., 1965. Cavitation in dynamically loaded bearing. Transactions of Chalmers University of Technology, 308:1-59. 

[30] Optasanu, V., Bonneau, D., 2000. Finite element mass-conserving cavitation algorithm in pure squeeze motion. validation/application to a connecting-rod small end bearing. ASME Journal of Tribology, 122:162-169. 


[31] Payvar, P., Salant, R.F., 1992. Computational method for cavitation in a wavy mechanical seal. ASME Journal of Tribology, 114(1):199-204. 


[32] Qiu, Y., Khonsari, M.M., 2009. On the prediction of cavitation in dimples using a mass-conservative algorithm. ASME Journal of Tribology, 131(4):041702


[33] Schweizer, B., 2009. Numerical approach for solving Reynolds equation with JFO boundary conditions incorporating ALE techniques. ASME Journal of Tribology, 131(1):011702


[34] Shi, F., Salant, R.F., 1999. A mixed soft elastohydrodynamic lubrication model with interasperity cavitation and surface shear deformation. ASME Journal of Tribology, 122(1):308-316. 


[35] Shi, F., Paranjpe, R., 2002. An implicit finite element cavitation algorithm. CMES, 3:507-515. 


[36] Vijayaraghavan, D., Keith, T.G., 1990. An efficient, robust, and time accurate numerical scheme applied to a cavitation algorithm. ASME Journal of Tribology, 112(1):44-51. 


[37] Vijayaraghavan, D., Keith, T.G., 1990. Grid transformation and adaption techniques applied in the analysis of cavitated journal bearings. ASME Journal of Tribology, 112(1):52-59. 


[38] Vijayaraghavan, D., Keith, T.G., 1990. Analysis of a finite grooved misaligned journal bearing considering cavitation and starvation effects. ASME Journal of Tribology, 112(1):60-67. 


[39] Vijayaraghavan, D., Keith, T.G., Brewe, D.E., 1991. Extension of transonic flow computational concepts in the analysis of cavitated bearings. ASME Journal of Tribology, 113(3):539-546. 


[40] Yu, Q., Keith, T.G., 1995. Prediction of cavitation in journal bearings using a boundary element method. ASME Journal of Tribology, 117:411-421. 


[41] Zienkiewicz, O.C., Taylor, R.L., 2000.  The Finite Element Method. Nutterworth-Heinemann,Oxford, England :15-23. 


Open peer comments: Debate/Discuss/Question/Opinion

<1>

Please provide your name, email address and a comment





Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - Journal of Zhejiang University-SCIENCE