Abstract
Pressure drop measurements in the laminar and turbulent regions for water flowing through an alternating curved circular tube (x=h sin 2πz/λ) are presented. Using the minimum radius of curvature of this curved tube in place of that of the toroidally curved one in calculating the Dean number (ND=Re(D/2R c )2, it is found that the resulting Dean number can help in characterizing this flow. Also, the ratio between the height and length of the tube waves which represents the degree of waveness affects significantly the pressure drop and the transition Dean number. The following correlations have been found:
-
1.
For laminar flow:
$$F_w \left( {\frac{{2R_c }}{D}} \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} = F_s \left( {\frac{{2R_c }}{D}} \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} + 0.03,\operatorname{Re}< 2000.$$ -
2.
For turbulent flow:
$$F_w \left( {\frac{{2R_c }}{D}} \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} = F_s \left( {\frac{{2R_c }}{D}} \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} + 0.005,2000< \operatorname{Re}< 15000.$$ -
3.
The transition Dean number:
$$ND_{crit} = 5.012 \times 10^3 \left( {\frac{D}{{2R}}} \right)^{2.1} ,0.0111< {D \mathord{\left/ {\vphantom {D {2R_c }}} \right. \kern-\nulldelimiterspace} {2R_c }}< 0.71.$$
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Abbreviations
- D :
-
inner diameter of the tube
- F w :
-
friction factor in wavy tube
- F s :
-
friction factor in straight tube
- ND:
-
Dean number
- h :
-
wave height
- L :
-
tube length
- n :
-
number of waves
- R c :
-
minimum radius of curvature
- Re:
-
Reynolds number
- Recrit :
-
critical Reynolds number
- WN:
-
waveness number
- λ :
-
wave length
- ρ :
-
fluid density
- Δp :
-
pressure loss along the tube
References
Aldoss, T.K., Abou-Arab, T.W. and Khatib, A.: Experimental investigation of laminar flow in a wavy pipe using hot wire anemometry.Int. J. Eng. Fluid Mech. 2 (1989) 141.
Abou-Arab, T.W., Aldoss, T.K. and Khatib, A.: Measurements of flow pattern in wavy duct. Part II. Secondary and turbulent flow.Int. J. Eng. Fluid Mech. (in press).
Berger, S.A., Talbot, L. and Yao, L. S.: Flow in curved pipes.Ann. Rev. Fluid Mech. 15 (1983) 461.
Truesdell, L.C. and Adler, R.J.: Numerical treatment of fully developed laminar flow in helically coiled tubes.AIChE J. 16 (1970) 1010.
Wang, C.Y.: On the low-Reynolds number flow in a helical pipe.J. Fluid Mech. 108 (1981) 185.
Murata, S., Miyake, Y., Inaba, T. and Ogawa: Laminar flow in a helically coiled pipe.Bull. JSME 24 (1981) 355.
Manlapaz, R.L. and Churchill, S.W.: Fully developed laminar flow in a helically coiled tube of finite pitch.Chem. Eng. Commun. 7 (1980) 57.
Mishra, P. and Gupta, N.: Momentum transfer in curved pipes, I. Newtonian fluids.Ind. Eng. Chem. Process Des. Dev. 18 (1979) 130.
Murata, S., Miyaka, Y. and Inaba, T.: Laminar flow in a curved pipe with varying curvature.J. Fluid Mech. 79 (1976) 735.
Ito, H.: Flow in curved pipes.Int. Jour J.S.M.E. 30 (1987) 543.
Taylor, G.I.: The criterion for turbulence in curved pipes.Proc. R. Soc. Lond. A 124 (1929) 243.
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Abou-Arab, T.W., Aldoss, T.K. & Mansour, A. Pressure drop in alternating curved tubes. Appl. Sci. Res. 48, 1–9 (1991). https://doi.org/10.1007/BF01998662
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DOI: https://doi.org/10.1007/BF01998662