Abstract
To obtain results for the title problem, the time-dependent Navier-Stokes equations have been solved numerically. Axial-velocity profiles at various distances from the entrance of the channel are shown for a number of points in time during one period of oscillation. Further some results for the time-dependent inlet length are presented.
Similar content being viewed by others
References
Atabek, H. B. and Chang, C. C.,Oscillatory flow near the entry of a circular tube. Z. angew. Math. Phys.12, 185–201 (1961).
Caro, C. G. Pedley, T. J., Schroter, R. C. and Seed, W. A.,The Mechanics of the Circulation, Oxford University Press, Oxford 1978.
Chang, C. C. and Atabek, H. B.,The inlet length for oscillatory flow and its effect on the determination of the rate of flow in arteries. Physics Med. Biol.6, 303–317 (1961).
Creff, R., Andre, P., and Batina, J.,Dynamic and convective results for a developing laminar unsteady flow. Int. J. Num. Methods in Fluids5, 745–760 (1985).
Friedmann, M., Gillis, J. and Liron, N.,Laminar flow in a pipe at low and moderate Reynolds numbers. Appl. Sci. Res.19, 426–438 (1968).
Krijger, J. K. B., Hillen, B. and Hoogstraten, H. W.,Mathematical models of the flow in the basilar artery. J. Biomech.22, 1193–1202 (1989).
Lew, H. S. and Fung, Y. C.,Entry flow into blood vessels at arbitrary Reynolds number. J. Biomech.3, 23–38 (1970).
Le Bail, R. L.,Use of fast Fourier transforms for solving partial differential equations in physics. J. Comp. Phys.9, 440–465 (1972).
Lugt, H. J. and Ohring, S.,Efficiency of numerical methods in solving the time-dependent Navier-Stokes equations. InNumerical Methods in Fluid Dynamics, eds. Brebbia, C. A. and Connor, J. J., Pentech Press, London 1973, pp. 65–83.
Morihara, H. and Cheng, R. T.,Numerical solution of the viscous flow in the entrance region of parallel plates. J. Comp. Phys.11, 550–572 (1973).
Peyret, R. and Taylor, T. D.,Computational Methods for Fluid Flow. Springer Ser. in Computational Phys., Springer Verlag, Berlin/New York 1983.
Pedley, T. J.,The Fluid Mechanics of Large Blood Vessels. Cambridge University Press, Cambridge 1980.
Pickering, M.,An Introduction to Fast Fourier Transform Methods for Partial Differential Equations with Applications. Wiley, New York 1986.
Ta Phuoc Loc,Numerical analysis of unsteady secondary vortices generated by an impulsively started circular cylinder. J. Fluid Mech.100, 111–128 (1980).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Krijger, J.K.B., Hillen, B. & Hoogstraten, H.W. Pulsating entry-flow in a plane channel. Z. angew. Math. Phys. 42, 139–153 (1991). https://doi.org/10.1007/BF00962064
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00962064