Skip to main content Accessibility help
×
Home
Hostname: page-component-5d6d958fb5-x8cck Total loading time: 0.544 Render date: 2022-11-28T23:15:34.583Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "displayNetworkTab": true, "displayNetworkMapGraph": false, "useSa": true } hasContentIssue true

Asymptotic analysis of initial flow around an impulsively started circular cylinder using a Brinkman penalization method

Published online by Cambridge University Press:  27 October 2021

Y. Ueda*
Affiliation:
Department of Mechanical Engineering, Faculty of Science and Engineering, Setsunan University, 17–8 Ikeda-Nakamachi, Neyagawa, Osaka572-8508, Japan
T. Kida
Affiliation:
Professor Emeritus, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka,599-8531Japan
*
Email address for correspondence: yoshiaki.ueda@mec.setsunan.ac.jp

Abstract

The initial flow past an impulsively started translating circular cylinder is asymptotically analysed using a Brinkman penalization method on the Navier–Stokes equations. The asymptotic solution obtained shows that the tangential and normal slip velocities on the cylinder surface are of the order of $1/\sqrt {\lambda }$ and $1/\lambda$, respectively, within the second approximation of the present asymptotic analysis, where $\lambda$ is the penalization parameter. This result agrees with the estimation of Carbou & Fabrie (Adv. Diff. Equ., vol. 8, 2003, pp. 1453–1480). Based on the asymptotic solution, the influence of the penalization parameter $\lambda$ is discussed on the drag coefficient that is calculated using the adopted three formulae. It can then be found that the drag coefficient calculated from the integration of the penalization term exhibits a half-value of the results of Bar-Lev & Yang (J. Fluid Mech., vol. 72, 1975, pp. 625–647) as $\lambda \to \infty$.

Type
JFM Papers
Copyright
© The Author(s), 2021. Published by 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.)

References

REFERENCES

Abramowitz, M.A. & Stegun, A. 1954 Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover.Google Scholar
Al-Mdallal, Q.M. 2012 A numerical study of initial flow past a circular cylinder with combined streamwise and transverse oscillation. Comput. Fluids 63, 174183.CrossRefGoogle Scholar
Angot, P. 2011 On the well-posed coupling between free fluid and porous viscous flows. Appl. Maths Lett. 24, 803810.CrossRefGoogle Scholar
Angot, P., Bruneau, C.-H. & Fabrie, P. 1999 A penalization method to take into account obstacles in incompressible viscous flows. Numer. Math. 81, 497520.CrossRefGoogle Scholar
Badr, H.M. & Dennis, S.C.R. 1985 Time-dependent viscous flow past an impulsively started rotating and translating circular cylinder. J. Fluid Mech. 158, 447488.CrossRefGoogle Scholar
Bar-Lev, M. & Yang, H.T. 1975 Initial flow field over an impulsively started circular cylinder. J. Fluid Mech. 72, 625647.CrossRefGoogle Scholar
Bost, C., Cottet, G.-H. & Maitre, E. 2010 Convergence analysis of a penalization method for the three-dimensional motion of a rigid body in an incompressible viscous fluid. SIAM J. Numer. Anal. 48, 13131337.CrossRefGoogle Scholar
Carbou, G. 2004 Penalization method for viscous incompressible flow around a porous thin layer. Nonlinear Anal. 5, 815855.CrossRefGoogle Scholar
Carbou, G. 2008 Brinkmann model and double penalization method for the flow around a porous thin layer. J. Math. Fluid Mech. 10, 126158.CrossRefGoogle Scholar
Carbou, G. & Fabrie, P. 2003 Boundary layer for a penalization method for viscous incompressible flow. Adv. Diff. Equ. 8 (12), 14531480.Google Scholar
Collins, W.M. & Dennis, S.C.R. 1973 The initial flow past an impulsively started circular cylinder. Q. J. Mech. Appl. Maths 26 (1), 5375.CrossRefGoogle Scholar
Engels, T., Kolomenskiy, D., Schneider, K. & Sesterhenn, J. 2015 Numerical simulation of fluid-structure interaction with volume penalization method. J. Comput. Phys. 281, 96115.CrossRefGoogle Scholar
Feireisl, E., Neustupa, J. & Stebel, J. 2010 Convergence of a Brinkman-type penalization for compressible fluid flow. Mathematical Institute of Academy of Science of the Czech Republic, Preprint No. 2010-013.Google Scholar
Gazzola, M., Chatelain, P., van Rees, W.M. & Koumoutsakos, P. 2011 Simulations of single and multiple swimmers with non-divergence free deforming geometries. J. Comput. Phys. 230, 70937114.CrossRefGoogle Scholar
Hejlesen, M.M., Koumoutsakos, P., Leonard, A. & Walther, J.H. 2015 Iterative Brinkman penalization for remeshed vortex methods. J. Comput. Phys. 280, 547562.CrossRefGoogle Scholar
Kadoch, B., Kolomenskiy, D., Angot, P. & Schneider, K. 2012 A volume penalization method for incompressible flows and scalar advection-diffusion with moving obstacles. J. Comput. Phys. 231, 43654383.CrossRefGoogle Scholar
Kevlahan, N.K.-R. & Vasilyev, O. 2005 An adaptive wavelet collocation method for fluid-structure interaction at high Reynolds numbers. SIAM J. Sci. Comput. 26 (6), 18941915.CrossRefGoogle Scholar
Kolomenskiy, D. & Schneider, K. 2009 A Fourier spectral method for the Navier–Stokes equations with volume penalization for moving solid obstacles. J. Comput. Phys. 228, 56875709.CrossRefGoogle Scholar
Koumoutsakos, P. & Leonard, A. 1995 High-resolution simulations of the flow around an impulsively started cylinder using vortex methods. J. Fluid Mech. 296, 138.CrossRefGoogle Scholar
Koumoutsakos, P., Leonard, A. & Pépin, F. 1994 Boundary conditions for viscous vortex methods. J. Comput. Phys. 113, 5261.CrossRefGoogle Scholar
Mimeau, C., Cottet, G.-H. & Mortazavi, I. 2015 Vortex penalization method for bluff body flows. Intl J. Numer. Meth. Fluids 79, 5583.CrossRefGoogle Scholar
Mittal, H.V.R., Ray, R.K. & Al-Mdallal, Q.M. 2017 A numerical study of initial flow past an impulsively started rotationally oscilating circular cylinder using a transformation-free HOC scheme. Phys. Fluids 29 (9), 093603.CrossRefGoogle Scholar
Nguyen van yen, R., Farge, M. & Schneider, K. 2011 Energy dissipating structures produced by walls in two-dimensional flows at vanishing viscosity. Phys. Rev. Lett. 106, 184502.CrossRefGoogle ScholarPubMed
Nguyen van yen, R., Kolomenskiy, D. & Schneider, K. 2014 Approximation of the Laplace and Stokes operators with Dirichlet boundary conditions through volume penalization; a spectral viewpoint. Numer. Math. 128, 301338.CrossRefGoogle Scholar
Rasmussen, J.T., Cottet, G.-H. & Walther, J.H. 2011 A multiresolution remeshed Vortex-In-Cell algorithm using patches. J. Comput. Phys. 230, 67426755.CrossRefGoogle Scholar
Rossinelli, D., Bergdorf, M., Cottet, G.-H. & Koumoutsakos, P. 2010 GPU accelerated simulations of bluff body flows using vortex particle methods. J. Comput. Phys. 229, 33163333.CrossRefGoogle Scholar
Schneider, K. & Farge, M. 2002 Adaptive wavelet simulation of a flow around an impulsively started cylinder using penalization. Appl. Comput. Harmon. Anal. 12, 374380.CrossRefGoogle Scholar
Schneider, K. & Farge, M. 2005 Numerical simulation of the transient flow behavior in tube bundles using a volume penalization method. J. Fluids Struct. 20, 555566.CrossRefGoogle Scholar
Schneider, K., Paget-Goy, M., Verga, A. & Farge, M. 2014 Numerical simulation of flows past flat plates using volume penalization. Comput. Appl. Maths 33, 481495.CrossRefGoogle Scholar
Shiels, D. 1998 Simulation of controlled bluff body flow with a viscous vortex method. Ph.D. dissertation, Caltech.Google Scholar
Uchiyama, T., Gu, Q., Degawa, T., Iio, S., Ikeda, T. & Tamura, K. 2020 Numerical simulations of the flow and performance of a hydraulic Savonius turbine by the vortex in cell with volume penalization. Renewable Energy 157, 482490.CrossRefGoogle Scholar
Verma, S., Abbati, G., Novati, G. & Koumoutsakos, P. 2017 Computing the force distribution on the surface of complex, deforming geometries using vortex method and Brinkman penalization. Intl J. Numer. Meth. Fluids 85, 484501.CrossRefGoogle Scholar

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.

Asymptotic analysis of initial flow around an impulsively started circular cylinder using a Brinkman penalization method
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.

Asymptotic analysis of initial flow around an impulsively started circular cylinder using a Brinkman penalization method
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.

Asymptotic analysis of initial flow around an impulsively started circular cylinder using a Brinkman penalization method
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? *