Three-Dimensional Boundary-Layer Flow Across A Wedge: A Numerical Investigation
Authors
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Department of Mathematics, M.S. Ramaiah Institute of Technology (Affiliated to VTU), Bengaluru -560054 ,IN
S. Shashi Prabha Gogate -
Department of Mathematics, M.S. Ramaiah Institute of Technology (Affiliated to VTU), Bengaluru -560054 ,INM. M. Praveena
DOI:
https://doi.org/10.18311/jmmf/2023/36049Keywords:
Boundary-layer, Keller-box, Numerical Simulation, Similar Solution, Three-dimensionalAbstract
The present work investigates the flow of a continuous, laminar, 3-D boundary-layer over a fixed wedge, where the outside free-stream flows are approximately approximated by a power of distances. The controlling partial differential equations are transformed into coupled nonlinear ordinary differential equations with the necessary boundary conditions using surface similarity transformations. These equations involve two physical variables: pressure gradient and shear-to-strain rate. The resulting equations are numerically solved by the implicit finite-difference scheme known as the Keller-box approach. The obtained results are compared with those reported in the literature for a few special cases. Our numerical results indicate that the flow zone is divided into two areas: near-field (close to the wedge surface) and far-field field (mostly controlled by inviscid flow).
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References
Van Dyke M. Laminar Boundary Layers. Edited by L. ROSENHEAD. Oxford University Press, 1963. 688pp. aE4. 10s. Journal of Fluid Mechanics. 1964 Mar; 18(3):477-80. DOI: https://doi.org/10.1017/S0022112064210350
Howarth L. XXV. The boundary layer in three dimensional flow. Part I. Derivation of the equations for flow along a general curved surface. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 1951 Mar 1; 42(326):239-43. DOI: https://doi.org/10.1080/14786445108561259
Howarth L. CXLIV. The boundary layer in three dimensional flow. —Part II. The flow near a stagnation point. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 1951 Dec 1; 42(335):1433-40. DOI: https://doi.org/10.1080/14786445108560962
Weidman PD. Non-axisymmetric Homann stagnation-point flows. Journal of Fluid Mechanics. 2012 Jul; 702:460-9. DOI: https://doi.org/10.1017/jfm.2012.197
Howarth L. CXXIX. Note on the boundary layer on a rotating sphere. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 1951 Nov 1; 42(334):1308-15. DOI: https://doi.org/10.1080/14786444108561386
Davey A. Boundary-layer flow at a saddle point of attachment. Journal of Fluid Mechanics. 1961 Jun; 10(4):593-610. DOI: https://doi.org/10.1017/S0022112061000391
Libby PA. Heat and mass transfer at a general three- dimensional stagnation point. AIAA Journal. 1967 Mar; 5(3):507-17. DOI: https://doi.org/10.2514/3.4008
Davey A, Schofield D. Three-dimensional flow near a two-dimensional stagnation point. Journal of Fluid Mechanics. 1967 Apr; 28(1):149-51. DOI: https://doi.org/10.1017/S0022112067001958
Wang CY. The three‐dimensional flow due to a stretching flat surface. The physics of fluids. 1984 Aug; 27(8):1915- 7. DOI: https://doi.org/10.1063/1.864868
Devi CS, Takhar HS, Nath G. Unsteady, three-dimensional, boundary-layer flow due to a stretching surface. International Journal of Heat and Mass Transfer. 1986 Dec 1; 29(12):1996-9. DOI: https://doi.org/10.1016/0017-9310(86)90020-7
Hewitt RE, Duck PW, Stow SR. Continua of states in boundary-layer flows. Journal of Fluid Mechanics. 2002 Oct; 468:121-52. DOI: https://doi.org/10.1017/S0022112002001507
Schlichting H, Gersten K. Boundary-layer theory. Springer; 2016 Oct 4. DOI: https://doi.org/10.1007/978-3-662-52919-5
Benzi R, Ching ES, Chu VW. Heat transport by laminar boundary layer flow with polymers. Journal of fluid mechanics. 2012 Apr; 696:330-44. DOI: https://doi.org/10.1017/jfm.2012.46
Benzi R, Ching ES, Wilson CK, Wang Y. Heat transport modification by finitely extensible polymers in laminar boundary layer flow. Journal of Fluid Mechanics. 2016 Feb; 788:337-57. DOI: https://doi.org/10.1017/jfm.2015.714
Cebeci T, Bradshaw P. Momentum transfer in boundary layers. Washington. 1977.
Keller HB. Numerical methods in boundary-layer theory. Annual Review of Fluid Mechanics. 1978 Jan; 10(1):417-33. DOI: https://doi.org/10.1146/annurev.fl.10.010178.002221
Biberdrof, EA, Popova NI. Guaranteed accuracy of current methods in linear algebra. Novosibirsk, Izd-vo So RAN, 2006, 320p.
