Finite Analytic Numerical Solution of Unsteady Laminar Flow Past Disc‐Valves
Publication: Journal of Engineering Mechanics
Volume 113, Issue 8
Abstract
The unsteady flow past a disc‐type valve in an axisymmetric tube has been calculated numerically from the governing Navier‐Stokes equations. The flow is assumed to be laminar and incompressible, and the fluid possesses constant properties. Numerical solutions for unsteady flow patterns and pressure drops across the valve are obtained. The finite analytic numerical method is used to solve the Navier‐Stokes equations expressed in terms of pressure and velocities. In the present investigation, the finite analytic solution has been obtained for pulsatile flow past the disc‐type valve at a Reynolds number of 100 based on the tube diameter and the maximum mean velocity during the pulsatile flow. A comparison of the results with that for steady flow at a corresponding Reynolds number showed that, in unsteady flow, larger shear stresses at the edge of the valve ring were observed along with substantial changes in the separation characteristics downstream to the valve. The applicability of the results to delineate the effect of flow past valve prosthesis in vivo is briefly discussed.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Bruss, K. H., Reul, H., Van Gilse, J., and Knott, E. (1983). “Pressure drop and velocity fields at torn mechanical heart valve prostheses: Bjork‐Shiley standard, Bjork‐Shiley concave‐convex, Hall‐Kaster and St. Jude Medical.” Life Support Systems 1, 3–22.
2.
Chandran, K. B., Cabell, G. N., Khalighi, B., and Chen, C.‐J. (1983). “Laser anemometry measurements of pulsatile flow past aortic valve prostheses.” J. Biomech. 16, 865–873.
3.
Chandran, K. B., Cabell, G. N., Khalighi, B., and Chen, C.‐J. (1984). “Pulsatile flow past aortic valve bioprostheses in a model human aorta.” J. Biomech. 17, 609–619.
4.
Chen, C. J., and Chen, H. C. (1984). “Finite analytic numerical method for unsteady two dimensional Navier‐Stokes equations.” J. Computational Physics 54(2), 209–226.
5.
Chen, C. J., and Yoon, Y. H. (1983). “Finite analytic numerical solution of axi‐symmetric Navier‐Stokes and energy equations.” J. Heat Transfer 105, 639–645.
6.
Chen, C. J., and Cheng, W. S. (1985). “Finite analytic predictions of turbulent flow past an inclined cylinder.” Proc., 3rd Symp. on Numerical and Physical Aspects of Aerodynamic Flows, Long Beach, Calif., Jan., 1985, No. 3, 27–41.
7.
Greenfield, H., and Kolff, W. (1972). “The prosthetic heart valve and computer graphics.” JAMA, 219(1), 69–74.
8.
Harlow, R. H., and Welch, J. E. (1965). “Numerical calculation of time‐dependent viscous incompressible flow of fluid with free surface.” Physics of Fluids, 8, 2182–2189.
9.
Mazumdar, J., and Thalassoudis, K. (1983). “A mathematical model for the study of flow through disc‐type prosthetic heart valves.” Medical and Biological Engrg. and Computing, 21, 400–409.
10.
Mueller, T. J. (1974). “On the fluid dynamics of prosthetic heart valve flow—a preliminary numerical and experimental study.” Technical Note 101, VonKarman Inst. for Fluid Dynamics.
11.
Mueller, T. J. (1978). Numerical Method in Fluid Dynamics. Chap. 2, Hemisphere Publishing Corp.
12.
Mueller, T. J., Lloyd, J. R., Lower, J. L., Strouble, W. T., and Underwood, F. N. (1973). “On the separate flow produced by a fully open disc‐type prosthetic heart valve.” Biomech. Symp. ASME AMD, 2, 97–98.
13.
Patankar, S. V. (1980). Numerical Heat Transfer and Fluid Flow, McGraw‐Hill Book Co., Inc., New York, N.Y.
14.
Sator, F. (1975). “Application of the finite element method to the calculation of plane pulsatile flow through artificial heart valves.” CAMM Conf. Numer. Methods Fluid Mech., Oct. 8–10, 173–180.
15.
Skaland, E. (1971). “Analysis of plane flow through a prosthetic aortic valve,” dissertation presented to the Drexel Inst. of Tech., at Philadelphia, Pa., in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
16.
Skaland, E., and Moskowitz, G. (1972). “Plane flow through a prosthetic aortic valve.” Proc., 25th ACEMB, 272.
17.
Yang, W. J., and Wang, J. H. (1983). “Turbulent flows through a disk‐type prosthetic heart valve.” J. Biomech. Engrg., ASME, 105, 263–267.
18.
Yu, C. H. (1983). “Finite analytic solutions of laminar and turbulent flows past an axisymmetric disc valve,” dissertation presented to the University of Iowa, at Iowa City, Iowa, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 113 • Issue 8 • August 1987
Pages: 1147 - 1162
Copyright
Copyright © 1987 ASCE.
History
Published online: Aug 1, 1987
Published in print: Aug 1987
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.