Quasi-2D Model for Unsteady Flow in Pipe Networks
Publication: Journal of Hydraulic Engineering
Volume 125, Issue 7
Abstract
A quasi-two-dimensional model for unsteady-flow analysis in pipes and pipe networks is presented. The turbulence model is based on the mixing length hypothesis in the turbulent zone and on Newton's law in the viscous sublayer. An expression of the mixing length in terms of the Reynolds number and an expression of the parameter of logarithmic law of the wall in terms of the friction Reynolds number are found from Nikuradse's experimental data. An implicit numerical scheme for the integration of the equations is proposed to overcome the limitations of the explicit schemes. Uniqueness of the head and continuity of discharge are considered at the junctions. The results of both a quasi-steady 1D model and a quasi-2D model are compared with results from a laboratory network. For these experimental runs, the comparisons show that the average relative errors on the maximum head oscillations are 19.1% with the 1D model and 8.6% with the quasi-2D model; those on the minimum oscillations are 19.2% with the 1D model and 5.3% with the quasi-2D model. The latter model is in better agreement because it takes into account the velocity profile, thus allowing for a more accurate evaluation of the shear stress.
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References
1.
Betamio de Almeida, A., and Koelle, E. (1993). Fluid transients in pipe networks. Computational Mechanics Publications, Southampton, Elsevier Science, London.
2.
Bratland, O. (1986). “Frequency-dependent friction and radial kinetic energy variation in transient pipe flow.” Proc., 5th Int. Conf. on Pressure Surges, British Hydromechanics Research Association, Cranfield, U.K., 95–101.
3.
Brunone, B., Golia, U. M., and Greco, M. (1991). “Some remarks on the momentum equation for fast transients.” Proc., Int. Meeting on Hydr. Transients and Water Column Separation, Valencia, Spain, 201–209.
4.
Carstens, M. R., and Roller, J. E. (1959). “Boundary-shear stress in unsteady turbulent pipe flow.”J. Hydr. Div., ASCE, 85(2), 67–81.
5.
Daily, J. W., Hankey, W. L., Olive, R. W., and Jordaan, J. M. (1956). “Resistance coefficient for accelerated and decelerated flows through smooth tubes and orifices.” Trans., ASME, 78, 1071–1077.
6.
Eichinger, P., and Lein, G. ( 1992). “The influence of friction on unsteady pipe flow.” Unsteady flow and fluid transients, R. Bettes and J. Watts, eds., Balkema, Rotterdam, The Netherlands, 41–50.
7.
Hino, M., Sawamoto, M., and Takasu, S. (1977). “Study on the transitions to turbulence and frictional coefficient in an oscillatory pipe flow.” Trans., Japan Soc. of Civ. Engrg., Tokyo, Japan, 9, 282–285.
8.
Holmboe, E., and Rouleau, W. T. (1967). “The effect of viscous shear on transients in liquid lines.” J. Basic Engrg., 89, 174–180.
9.
Karney, B. W., and McInnis, D. (1992). “Efficient calculation of transient flow in simple pipe networks.”J. Hydr. Engrg., ASCE, 118(7), 1014-1030.
10.
Marchi, E. (1961). “Il moto uniforme delle correnti liquide nei condotti chiusi e aperti.” L'Energia Elettrica, Milan, Italy, 38(4), 289–301 (in Italian).
11.
Modica, C., and Pezzinga, G. (1992). “Un modello quasi bidimensionale per il moto vario elastico in regime turbolento.” Atti, XXIII Convegno di Idraulica e Costruzioni Idrauliche, Florence, Italy, E191–E205 (in Italian).
12.
Nikuradse, J. ( 1932). “Gesetzmäβigkeiten der turbulenten Strömung in glatten Rohren.” Forschung auf dem Gebiete des Ingenieurwesens, Forschungsheft 356. VDI Verlag, Berlin, Germany (in German).
13.
Nikuradse, J. ( 1933). “Strömungsgesetze in rauhen Rohren.” Forschung auf dem Gebiete des Ingenieurwesens, Forschungsheft 361. VDI Verlag, Berlin, Germany (in German).
14.
Richardson, E. G., and Tyler, E. (1929). “Transverse velocity gradient near the mouths of pipes in which an alternating or continuous flow of air is established.” Proc., Physics Soc., London, U.K., 42, 1–15.
15.
Sawfat, H. H., and Polder, J. (1973). “Friction-frequency dependence for oscillatory flows in circular pipe.”J. Hydr. Div., ASCE, 99(11), 1933–1945.
16.
Schlichting, H. (1979). Boundary-Layer Theory, 7th Ed., McGraw-Hill, New York.
17.
Shuy, E. B. (1995). “Approximate wall shear equation for unsteady laminar pipe flows.”J. Hydr. Res., Delft, The Netherlands, 33(4), 457–469.
18.
Silva-Araya, W. F., and Chaudhry, M. H. (1997). “Computation of energy dissipation in transient flow.”J. Hydr. Engrg., ASCE, 123(2), 108–115.
19.
Szymanski, P. (1932). “Quelques solutions exactes des equations de l'hydrodynamique du fluide visqueux dans le cas d'un tube cylindrique.” J. Mathématiques Pures et Appliquées, 11, 67–107 (in French).
20.
Trikha, A. K. (1975). “An efficient method for simulating frequency-dependent friction in liquid flow.” J. Fluids Engrg., 97, 97–105.
21.
Vardy, A. E., and Brown, J. (1995). “Transient, turbulent, smooth pipe friction.”J. Hydr. Res., Delft, The Netherlands, 33(4), 435–456.
22.
Vardy, A. E., Brown, J., and Hwang, K. (1993). “A weighting function model of transient turbulent pipe friction.”J. Hydr. Res., Delft, The Netherlands, 31(4), 533–548.
23.
Vardy, A. E., and Hwang, K. (1991). “A characteristics model of transient friction in pipes.”J. Hydr. Res., Delft, The Netherlands, 29(5), 669-684.
24.
Wylie, E. B., and Streeter, V. L. (1993). Fluid transients in systems. Prentice-Hall, Englewood Cliffs, N.J.
25.
Zielke, W. (1968). “Frequency-dependent friction in transient pipe flow.” J. Basic Engrg., 90, 109–115.
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Published In
Journal of Hydraulic Engineering
Volume 125 • Issue 7 • July 1999
Pages: 676 - 685
History
Published online: Jul 1, 1999
Published in print: Jul 1999
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