A mathematical model of incompressible viscous laminar flow in smooth coil tubes is proposed and the results of its numerical realization in a nonorthogonal helical coordinate system are presented. This coordinate system is free of singularities in the domain of definition of the unknown functions, that is, the pressure and the velocity components, which makes it possible to refine the existing distributions of the axial component and the secondary crossflows obtained using the well-known orthogonal coordinate system having a singularity at the center of the coil channel. The momentum transport equation is written in the projections on the axes of the natural basis of the coordinate system, which makes it possible to subdivide the system of equations into two alternately solved subsystems. The distributions of the axial and two transverse components show that at the center of coil tubes the transverse components are comparable with the axial velocity (the transverse components can be as high as half the mean-flow-rate velocity and one third of it at the center of the channel).
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
A.G. Bagoutdinova and Ya.D. Zolotonosov, “Coil Heat Exchangers and Their Mathematical Description,” Izv. Vuzov. Stroitelstvo No. 7, 44 (2015).
A.Ya. Zolotonosov, Ya.D. Zolotonosov, I.A. Knyazeva, and A.G. Bagoutdinova, “Coil Heat Exchanger. Russian Federation Patent No. 133596,” Bullet. Izobr. No. 29 (2013).
A.Ya. Zolotonosov, Ya.D. Zolotonosov, and I.A. Knyazeva,” “Coil Heat Exchanger Element. Russian Federation Patent No. 155676,” Bullet. Izobr. No. 29 (2015).
A.Ya. Zolotonosov, Ya.D. Zolotonosov, I.A. Knyazeva, A.G. Bagoutdinova, and E.K. Vachagina, “Coil Heat Exchanger. Russian Federation Patent No. 166177,” Bullet. Izobr. No. 10 (2016).
Yu.F. Gortyshev, Heat-Hydraulic Efficiency of Promising Methods of Heat Transfer Intensification in the Channels of Heat Exchange Devices [in Russian], Kazan (2009).
A.I. Leont’ev and V.V. Olimpiev, “Thermophysics and Heat Engineering of Promising Heat Transfer Intensifiers. An Overview,” Izv. Ross. Akad. Nauk. Energetika. No. 1, 7 (2011).
I.Z. Aronov, “Heat Transfer and Hydraulic Drag in Curved Pipes,” Candidate Dissertation, Kiev (1950).
V.G. Fastovskii and A.E. Rovinskii, “Investigation of Heat Transfer in a Helical Channel,” Teploenergetika No. 1, 39 (1957).
V.K. Shchukin, “Generalization of the Experimental Data on Heat Transfer in Coils,” Teploenergetika No. 2, 50 (1969).
V.K. Shchukin, “Additional Conditions of the Flow Similarity in the Field of Body Inertial Forces,” Tr. KAI No. 76, 26 (1963).
E.V. Sukhov, “Development of the Structures and the Methods of Calculation of Size-Saving Helical Coil Cooling Elements of Compressor Equipment,” Candidate Dissertation, Omsk (2012).
P. Gavade Pravin and P.R. Kulkarni, “Experimental Evaluation of Helical Coil Tube in Tube Heat Exchanger,” Int. J. Emerging Engineering Research Techn. 3 (2), 12 (2015).
V.P. Desial and S.L. Borse, “Experimental Study on Enhancement of Thermal Performance of Wire Wound Tube in Tube Helical Coil Heat Exchanger,” IJERA 3, 340 (2013).
Vinodkumar Kiran Voonna and T.K. Tharakeshwar, “Improvement of Heat Transfer Coefficients in a Shell and Helical Tube Heat Exchanger Using Water/Al2O3 Nanofluid,” IRJET 2, 213 (2015).
Y. Ma, Z. Zhou, J. Wang, Y. Liu, and J. Liang, “Design Optimization of Tube-in-Tube Helical Heat Exchanger Used in JT Refrigerator,” in: Int. Cryocooler Conf. Inc. 09–12 June 2014, Syracuse Univ., New York (2014).
E.A. Krasnoshchekov and A.S. Sukomel, Handbook on Heat Transfer [in Russian], Energetika, Moscow (1980).
M.N. Manish, G.K. Deshmukh, R.A. Patel, and R.H. Bhoi, “Parametric Analysis of Tube in Tube Helical Coil Exchanger at Constant Wall Temperature,” IJSTE 1 (10), 279 (2015).
N.M. Triloki, “Modeling and CFD Analysis of Tube in Tube Helical Coil Exchanger,” IJSR 4, 1536 (2015).
P. Deshmukh, V.D. Patil, and B. Devakant, “CFD Analysis of Heat Transfer in Helical Coil Tube Heat Exchanger,” IJIERT 3 (1), 1 (2016).
W.R. Dean and J.M. Hurst, “Note on the Motion of Fluid in a Curved Pipe,” Phil. Mag. 20 (4), 208 (1927).
W.R. Dean and J.M. Hurst, “The Streamline Motion of Fluid in a Curved Pipe,” Phil. Mag. 5 (30), 673 (1928).
H.G. Cuming, “The Secondary Flow in Curved Pipes,” Aeronautical Res. Council. Report No. 2880 (1952).
D.J. Mcconaloguanen and D.R. Srivastava, “Motion of a Fluid in a Curved Tube,” Proc. Roy. Soc. London. Ser. A 307, 37 (1968).
M. Germano, “On the Effect of Torsion on a Helical Pipe Flow,” J. Fluid Mech. 125, 1 (1982).
M. Germano, “The Dean Equations Extended to a Helical Pipe Flow,” J. Fluid Mech. 203, 289 (1989).
T.J. Hüttl, “Navier–Stokes Solutions of Laminar Flows Based on Orthogonal Helical Coordinates,” Numer. Methods in Laminar and Turbulent Flow 10, 191 (1997).
M. Vasudevaian and R. Rajalakshmi, “Flow in a Helical Pipe,” J. Appl. Math. 19, 75 (1988).
M. Vasudevaian and R. Patturaj, “Effect of Torsion in a Helical Pipe Flow,” Int. J. Math. Math. Sci. 17, 553 (1994).
D.G. Dritschel, “Generalized Helical Beltrami Flows in Hydrodynamics and Magnetohydrodynamics,” J. Fluid Mech. 222, 525 (1991).
Lei Xue, “Study on Laminar Flow in Helical Circular Pipes with Galerkin Method,” Computers Fluids 31, 113 (2002).
Z. Zapryanov, Ch. Christov, and E. Toshev, “Fully Developed Laminar Flow and Heat Transfer in Curved Tubes,” Int. J. Heat Mass Transfer 23, 873 (1980).
L.C. Truesdell, R.J. Adler, “Numerical Treatment of Fully Developed Laminar Flow in Helically Coiled Tubes,” A.I. Ch.E.J. 16, 1010 (1970).
S.V. Patankar, V.S. Pratap, and D.B. Spalding, “Prediction of Laminar Flow and Heat Transfer in Helically Coiled Pipes,” J. Fluid Mech. 62, 539 (1974).
A.N. Dravid, K.A. Smith, E.W. Merrill, and P.L.T. Brian, “Effect of Secondary Fluid Motion on Laminar Flow Heat Transfer in Helically Coiled Circular Pipes,” AIChEJ 17, 1114 (9171).
Yu.G. Namzeev, Fluid Dynamics and Heat Transfer of Swirled Flows of Rheologically Complex Media [in Russian], Energoizdat, Moscow (1996).
Original Russian Text © A.G. Bagoutdinova, E.K. Vachagina, Ya.D. Zolotonosov, 2017, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2017, No. 4, pp. 9–23.
About this article
Cite this article
Bagoutdinova, A.G., Vachagina, E.K. & Zolotonosov, Y.D. Viscous laminar flow in smooth coil tubes. Fluid Dyn 52, 468–480 (2017). https://doi.org/10.1134/S0015462817040020
- heat transfer
- fluid dynamics
- mathematical models
- coil tubes
- helical coordinate system
- metric tensor