Analytical Solution for the Viscous Flow of Small Reynolds Numbers in Rough Pipes

XU Zhimin; SONG Siyuan; XIN Fengxian; YANG Xiaohu; LU Tianjian

doi:10.21656/1000-0887.380223

Volume 39 Issue 2

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Article Navigation > Applied Mathematics and Mechanics > 2018 > 39(2): 123-136

XU Zhimin, SONG Siyuan, XIN Fengxian, YANG Xiaohu, LU Tianjian. Analytical Solution for the Viscous Flow of Small Reynolds Numbers in Rough Pipes[J]. Applied Mathematics and Mechanics, 2018, 39(2): 123-136. doi: 10.21656/1000-0887.380223

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Analytical Solution for the Viscous Flow of Small Reynolds Numbers in Rough Pipes

doi: 10.21656/1000-0887.380223

¹MOE Key Laboratory for Multifunctional Materials and Structures, Xi’an Jiaotong University, Xi’an 710049, P.R.China;²State Key Laboratory for Strength and Vibration of Mechanical Structures (Xi’an Jiaotong University), Xi’an 710049, P.R.China;³School of Human Settlements and Civil Engineering, Xi’an Jiaotong University, Xi’an 710049, P.R.China

Funds: The National Natural Science Foundation of China（11761131003；51528501；11772248；U1737107）

Received Date: 2017-08-04
Rev Recd Date: 2017-09-11
Publish Date: 2018-02-15

Abstract

Abstract

In view of the viscous flow fields of small Reynolds numbers in rough circular tubes and petal circular tubes, the rough surface in the tube was considered as a smooth surface subjected to small disturbance. The perturbation method was used to expand the perturbation of fluid parameters under small disturbance. The boundary conditions with complex morphologies were expanded into the Taylor series, and the smooth boundary conditions were approximately obtained. Then the fluid mechanics equations were solved simultaneously to give the approximate solution of the pressure gradient under the premise of the 1storder perturbation expansion, and the static flow resistance and tortuosity of the pipeline were obtained. The results show that the fluid parameters determined with the modified perturbation method agree very well with those through numerical simulation, and the theoretical approximate solution of the flow field in the rough pipe is validated.
- rough surface,
- small disturbance,
- perturbation method,
- static flow resistance,
- tortuosity

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References(15)

References

[1]	BARNARD A C L, LOPEZ L, HELLUMS J D. Basic theory of blood flow in capillaries[J]. Microvascular Research,1968,1(1): 23-34.
[2]	ACHDOU Y, AVELLANEDA M. Influence of pore roughness and pore-size dispersion in estimating the permeability of a porous medium from electrical measurements[J]. Physics of Fluids A: Fluid Dynamics,1992,4(12): 2651-2673.
[3]	DARCY H. Recherches Expérimentales Relatives au Mouvement de L’Eau Dans les Tuyaux [M]. Mallet-Bachelier, 1857.
[4]	VON MISES R. Elemente der technischen hydromechanik[J]. Monatshefte für Mathematik und Physik,1915,26(1): A27-A28.
[5]	COLEBROOK C F, WHITE C M. Experiments with fluid friction in roughened pipes[J]. Proceedings of the Royal Society of London (Series A): Mathematical and Physical Sciences,1937,161(906): 367-381.
[6]	COLEBROOK C F, BLENCH T, CHATLEY H, et al. Turbulent flow in pipes, with particular reference to the transition region between the smooth and rough pipe laws[J]. Journal of the Institution of Civil Engineers,1939,12(8): 393-422.
[7]	NIKURADSE J. Laws of flow in rough pipes[R]. Technical Report Archive & Image Library, 1950: 1-63.
[8]	MOODY L F. Friction factors for pipe flow[J]. Asme Trans V,1944,66: 671-684.
[9]	POZRIKIDIS C. The flow of a liquid film along a periodic wall[J]. Journal of Fluid Mechanics,2006,188: 275-300.
[10]	QU Weilin, MALA G M, LI Dongqing. Pressure-driven water flows in trapezoidal silicon microchannels[J]. International Journal of Heat & Mass Transfer,2000,43(3): 353-64.
[11]	SCHMITT D J, KANDLIKAR S G. Effects of repeating microstructures on pressure drop in rectangular minichannels[C]//ASME 3rd International Conference on Microchannels and Minichannels . Toronto, Ontario, Canada, 2005: 281-289.
[12]	DHARAIYA V V, KANDLIKAR S G. A numerical study on the effects of 2D structured sinusoidal elements on fluid flow and heat transfer at microscale[J]. International Journal of Heat & Mass Transfer,2013,57(1): 190-20 [13]SIDDIQA S, HOSSAIN M A, GORLA R S R. Natural convection flow of viscous fluid over triangular wavy horizontal surface[J]. Computers & Fluids,2015,106: 130-134.
[13]	KANDLIKAR S G, SCHMITT D, CARRANO A L, et al. Characterization of surface roughness effects on pressure drop in single-phase flow in minichannels[J]. Physics of Fluids,2005,17(10): 100606. DOI: 10.1063/1.1896985.
[14]	American Society for Testing and Materials. Standard test method for airflow resistance of acoustical materials: ASTM C522-03[S]. 2016.
[15]	LANDAU L D, LIFSHITZ E M. Course of Theoretical Physics [M]. Elsevier, 2013.