On nonaxisymmetric entry flow at very low Reynolds numbers. (English) Zbl 0767.76080
Summary: The eigensolutions of nonaxisymmetric entry flow of a Newtonian viscous fluid with very small Reynolds number in a semiinfinite rigid circular pipe is obtained. Leading eigenvalues are computed for steady flow and two periodic cases. The result shows that the entry length for nonaxisymmetric flows should be longer than the entry length for axisymmetric flows.
References:
| [1] | Aiello, G. A.; Trefil, J. S., The generalized entry flow problem and the establishment of Poiseuille flow in locally constricted tubes, J. Biomech., 9, 49-54 (1976) |
| [2] | Atabek, H. B.; Chang, C. C., Oscillatory flow near the entry of a circular tube, Z. Angew. Math. Phys., 12, 185-201 (1961) · Zbl 0100.22905 |
| [3] | Benson, L. H.; Trogdon, S. A., An eigenfunction solution of entry flow in a semi-infinite pipe at low Reynolds numbers, Appl. Sci. Res., 42, 347-359 (1985) · Zbl 0586.76014 |
| [4] | Burckel, R. B., (An Introduction to Classical Complex Analysis, Vol. 1 (1979), Academic: Academic New York), 227 · Zbl 0434.30002 |
| [5] | Garg, V. K., Stability of developing flow in a pipe: non-axisymmetric disturbances, J. Fluid Mech., 110, 209-216 (1981) · Zbl 0478.76049 |
| [6] | Goldberg, I. S.; Folk, R. T., Solutions for steady and nonsteady entrance flow in a semi-infinite circular tube at very low Reynolds numbers, SIAM J. Appl. Math., 48, 770-791 (1988) · Zbl 0645.76037 |
| [7] | Goldberg, I. S.; Carey, G. F.; McLay, R.; Phinney, L., Periodic viscous flow: a bench-mark problem, Int. J. Numer. Methods Fluids, 11, 87-97 (1990) · Zbl 0697.76041 |
| [8] | Huang, L. M.; Chen, T. S., Stability of developing pipe flow subjected to non-axisymmetric disturbances, J. Fluid Mech., 63, 184-193 (1974) · Zbl 0277.76037 |
| [9] | Iberall, A. S., Attenuation of oscillatory pressure in instrument lines, (Research Paper RP2115. Research Paper RP2115, J. Res., Vol. 45 (July 1950), U.S. Dept. of Commerce, National Bureau of Standards) |
| [10] | Kuchar, N. R.; Ostrach, S., Unsteady entrance flows in elastic tubes with application to the vascular system, (Tech. Rep. FTAS⧸TR67-25 (November 1967), School of Engineering, Case Western Reserve Univ.,: School of Engineering, Case Western Reserve Univ., Cleveland) · Zbl 0225.76060 |
| [11] | Lew, H. S.; Fung, Y. C., On the low-Reynolds-number entry flow into a circular cylindrical tube, J. Biomech., 2, 105-119 (1969) · Zbl 0176.54202 |
| [12] | Lew, H. S.; Miller, J., A low Reynolds number entry flow theory and its application to the motion of plasma in bolus flow, J. Biomech., 7, 113-121 (1974) |
| [13] | Marsden, J. E., Basic Complex Analysis, ((1973), Freeman: Freeman San Francisco), 319-325 · Zbl 0271.30001 |
| [14] | Mohanty, A. K.; Asthana, S. B., Laminar flow in the entrance region of a smooth pipe, J. Fluid Mech., 90, 433-447 (1978) |
| [15] | Sparrow, E. M.; Lin, S. H., Flow development in the hydrodynamic entrance region of tubes and ducts, Phys. Fluids, 7, 338-347 (1964) · Zbl 0118.20603 |
| [16] | Tanner, E. I., End effect in falling ball viscometry, J. Fluid Mech., 17, 161-170 (1963) |
| [17] | Weibel, E. R., Morphometry of the Human Lung, ((1963), Academic: Academic New York), 110-143 |
| [18] | Womersley, J. R., An elastic tube theory of pulse transmission and oscillatory flow in mammalian arteries, (W.A.D.C. Tech. Rep. T.R.56-614 (1957), Wright Air Development Center, U.S. Air Force) |
| [19] | Xue, H.; Fung, Y. C., Persistence of asymmetry in nonaxisymmetric entry flow in a circular cylindrical tube and its relevance to arterial pulse wave diagnosis, J. Biomech. Eng., 111, 37-41 (1989) |
| [20] | Zou, Q.; Chen, Y., Nonaxisymmetric wave propagation through a viscous fluid in a viscoelastic tube, Math. Biosci., 103, 275-286 (1991) · Zbl 0714.76123 |
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