Skip to main content Accessibility help
×
Home
Hostname: page-component-59b7f5684b-vcb8f Total loading time: 0.888 Render date: 2022-10-03T15:57:28.778Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "displayNetworkTab": true, "displayNetworkMapGraph": false, "useSa": true } hasContentIssue true

Downstream decay of fully developed Dean flow

Published online by Cambridge University Press:  15 July 2015

Jesse T. Ault
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
Kevin K. Chen
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
Howard A. Stone*
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
*
Email address for correspondence: hastone@princeton.edu

Abstract

Direct numerical simulations were used to investigate the downstream decay of fully developed flow in a $180^{\circ }$ curved pipe that exits into a straight outlet. The flow is studied for a range of Reynolds numbers and pipe-to-curvature radius ratios. Velocity, pressure and vorticity fields are calculated to visualize the downstream decay process. Transition ‘decay’ lengths are calculated using the norm of the velocity perturbation from the Hagen–Poiseuille velocity profile, the wall-averaged shear stress, the integral of the magnitude of the vorticity, and the maximum value of the $Q$-criterion on a cross-section. Transition lengths to the fully developed Poiseuille distribution are found to have a linear dependence on the Reynolds number with no noticeable dependence on the pipe-to-curvature radius ratio, despite the flow’s dependence on both parameters. This linear dependence of Reynolds number on the transition length is explained by linearizing the Navier–Stokes equations about the Poiseuille flow, using the form of the fully developed Dean flow as an initial condition, and using appropriate scaling arguments. We extend our results by comparing this flow recovery downstream of a curved pipe to the flow recovery in the downstream outlets of a T-junction flow. Specifically, we compare the transition lengths between these flows and document how the transition lengths depend on the Reynolds number.

Type
Papers
Copyright
© 2015 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Present address: Department of Aerospace and Mechanical Engineering, USC, Los Angeles, CA 90089, USA.

References

Anwer, M. & So, R. M. C. 1993 Swirling turbulent flow through a curved pipe. Part I: effect of swirl and bend curvature. Exp. Fluids 14, 8596.CrossRefGoogle Scholar
Anwer, M., So, R. M. C. & Lai, Y. G. 1989 Perturbation by and recovery from bend curvature of a fully developed turbulent pipe flow. Phys. Fluids 1, 13871397.CrossRefGoogle Scholar
Atkinson, B., Brocklebank, M. P., Card, C. C. H. & Smith, J. M. 1969 Low Reynolds number developing flows. AIChE J. 15, 548553.CrossRefGoogle Scholar
Austin, L. R. & Seader, J. D. 1973 Fully developed viscous flow in coiled circular pipes. AIChE J. 19, 8594.CrossRefGoogle Scholar
Berger, S. A. & Talbot, L. 1983 Flow in curved pipes. Annu. Rev. Fluid Mech. 15, 461512.CrossRefGoogle Scholar
Chen, K. K., Rowley, C. W. & Stone, H. A. 2015 Vortex dynamics in a pipe T-junction: recirculation and sensitivity. Phys. Fluids 27 (3), 034107.CrossRefGoogle Scholar
Dean, W. R. 1927 Note on the motion of fluid in a curved pipe. Phil. Mag. 20, 208223.CrossRefGoogle Scholar
Dean, W. R. 1928 The stream-line motion of fluid in a curved pipe. Phil. Mag. 5, 673695.CrossRefGoogle Scholar
Dennis, S. C. R. & Riley, N. 1991 On the fully developed flow in a curved pipe at large Dean number. Proc. R. Soc. Lond. A 434, 473478.CrossRefGoogle Scholar
Enayet, M. M., Gibson, M. M., Taylor, A. M. K. P. & Yianneskis, M. 1982 Laser-doppler measurements of laminar and turbulent flow in a pipe bend. Intl J. Heat Fluid Flow 3, 213219.CrossRefGoogle Scholar
Fairbank, J. A. & So, R. M. C. 1987 Upstream and downstream influence of pipe curvature on the flow through a bend. Intl J. Heat Fluid Flow 8, 211217.CrossRefGoogle Scholar
Fox, R. W., Pritchard, P. J. & McDonald, A. T. 2009 Introduction to Fluid Mechanics, 7th edn. John Wiley & Sons.Google Scholar
Hellström, F. & Fuchs, L.2007 Numerical computations of steady and unsteady flow in bended pipes. In 37th AIAA Fluid Dynamics Conference and Exhibit, 25–28 June 2007, Miami, FL.Google Scholar
Hellström, L. H. O., Zlatinov, M. B., Cao, G. & Smits, A. J. 2013 Turbulent pipe flow downstream of a $90^{\circ }$  bend. J. Fluid Mech. 735, R7(1–12).CrossRefGoogle Scholar
Hunt, J. C. R., Wray, A. & Moin, P.1988 Eddies, stream, and convergence zones in turbulent flows. Tech. Rep. CTR-S88. Center for Turbulence Research.Google Scholar
Issa, R. I. 1985 Solution of the implicitly discretised fluid flow equations by operator-splitting. J. Comput. Phys. 62, 4065.CrossRefGoogle Scholar
Issa, R. I. 1986 The computation of compressible and incompressible recirculating flows by a non-iterative implicit scheme. J. Comput. Phys. 62, 6682.CrossRefGoogle Scholar
Kalpakli, A., Örlü, R., Tillmark, N. & Alfredsson, P. H. 2011 Pulsatile turbulent flow through pipe bends at high Dean and Womersley numbers. J. Phys. 318, 092023.Google Scholar
Liu, S. & Masliyah, J. H. 1996 Steady developing laminar flow in helical pipes with finite pitch. Intl J. Comput. Fluid Dyn. 6, 209224.CrossRefGoogle Scholar
Mohanty, A. K. & Asthana, S. B. L. 1978 Laminar flow in the entrance region of a smooth pipe. J. Fluid Mech. 90, 433447.CrossRefGoogle Scholar
Olson, D. E. & Snyder, B. 1985 The upstream scale of flow development in curved circular pipes. J. Fluid Mech. 150, 139158.CrossRefGoogle Scholar
Pruvost, J., Legrand, J. & Legentilhomme, P. 2004 Numerical investigation of bend and torus flows. Part I: effect of swirl motion on flow structure in U-bend. Chem. Engng Sci. 59, 33453357.CrossRefGoogle Scholar
Sakakibara, J. & Machida, N. 2012 Measurement of turbulent flow upstream and downstream of a circular pipe bend. Phys. Fluids 24, 041702.CrossRefGoogle Scholar
Singh, M. P. 1974 Entry flow in a curved pipe. J. Fluid Mech. 65, 517539.CrossRefGoogle Scholar
Smith, F. T. 1976 Fluid flow into a curved pipe. Proc. R. Soc. Lond. A 351, 7187.CrossRefGoogle Scholar
Smits, A. J., Young, S. T. B. & Bradshaw, P. 1979 The effect of short regions of high surface curvature on turbulent boundary layers. J. Fluid Mech. 94, 209242.CrossRefGoogle Scholar
So, R. M. C. & Anwer, M. 1993 Swirling turbulent flow through a curved pipe. Part II: recovery from swirl and bend curvature. Exp. Fluids 14, 169177.CrossRefGoogle Scholar
Sudo, K., Sumida, M. & Hibara, H. 2000 Experimental investigation on turbulent flow through a circular-sectioned $180^{\circ }$ bend. Exp. Fluids 28, 5157.CrossRefGoogle Scholar
Tiwari, P., Antal, S. P. & Podowski, M. l.  Z. 2006 Three-dimensional fluid mechanics of particulate two-phase flows in U-bend and helical conduits. Phys. Fluids 18, 043304.CrossRefGoogle Scholar
Tunstall, M. J. & Harvey, J. K. 1968 On the effect of a sharp bend in a fully developed turbulent pipe-flow. J. Fluid Mech. 34, 595608.CrossRefGoogle Scholar
Vigolo, D., Radl, S. & Stone, H. A. 2014 Unexpected trapping of particles at a T-junction. Proc. Natl Acad. Sci. USA 111, 47704775.CrossRefGoogle Scholar
Weller, H. G., Tabor, G., Jasak, H. & Fureby, C. 1998 A tensorial approach to continuum mechanics using object-oriented techniques. Comput. Phys. 12, 620631.CrossRefGoogle Scholar
Winters, K. H. 1987 A bifurcation study of laminar flow in a curved tube of rectangular cross-section. J. Fluid Mech. 180, 343369.CrossRefGoogle Scholar
Yao, L. S. & Berger, S. A. 1975 Entry flow in a curved pipe. J. Fluid Mech. 67, 177196.CrossRefGoogle Scholar
10
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Downstream decay of fully developed Dean flow
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

Downstream decay of fully developed Dean flow
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

Downstream decay of fully developed Dean flow
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *