×

zbMATH — the first resource for mathematics

Study on the formation of Goertler vortices in natural convection flow over a rotating concave surface. (English) Zbl 1151.74405
Summary: This paper presents a numerical study of the formation of Görtler vortices in natural convection flow over a concave surface with rotation. The onset position characterized by the Grashof number \(Gr_{\delta_{r}}\), depends on the rotational Reynolds number, the Prandtl number (\(Pr\) = 0.7 for air) and the wave number. The buoyancy force and Coriolis force are found to significantly affect the flow structure and heat transfer. However, centrifugal force has minor stabilizing effect on the flow. Positive rotation stabilizes the boundary layer flow on the concave surface. On the contrary, negative rotation destabilizes the flow. The numerical data show reasonable agreement with the experimental results in the case of zero rotation.

MSC:
74R10 Brittle fracture
76D10 Boundary-layer theory, separation and reattachment, higher-order effects
76E06 Convection in hydrodynamic stability
76E07 Rotation in hydrodynamic stability
76U05 General theory of rotating fluids
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Tani, I., Production of longitudinal vortices in the boundary layer along a concave wall, J. geophys. res., 67, 8, 3075-3080, (1962)
[2] Wortmann, F.X., Visualization of transition, J. fluid mech., 38, 473-480, (1969)
[3] H. Bippes, Experimental study of the laminar-turbulent transition of a concave wall in a parallel flow, NASA (1978) TM-75243.
[4] Winoto, S.H.; Durao, D.F.G.; Crane, R.I., Measurements within goertler vortices, ASME J. fluids eng., 101, 517-520, (1979)
[5] Swearingen, J.D.; Blackwelder, R.F., The growth and breakdown of streamwise vortices in the presence of a wall, J. fluid mech., 182, 255-290, (1987)
[6] Peerhossaini, H.; Wesfreid, J.E., On the inner structure of streamwise goertler rolls, Int. J. heat fluid flow, 9, 1, 12-18, (1988)
[7] J.F. Jean, Visualization of vortices in a rotating curved-rectangular passage, Ms. Thesis, National Tsing-Hwa University, Taiwan, ROC, 1997.
[8] Hwang, G.J.; Lin, M.H., Estimation of the onset of longitudinal vortices in a laminar boundary layer heated from below, ASME J. heat transfer, 117, 835-842, (1995)
[9] Lin, M.H., Numerical study of formation of longitudinal vortices in natural convection flow over horizontal and inclined surfaces, Int. J. heat mass transfer, 44, 1759-1766, (2001) · Zbl 1008.76083
[10] Chen, C.T.; Lin, M.H., Effect of rotation on goertler vortices in the boundary layer flow on a curved surface, Int. J. numer. methods fluids, 40, 1327-1346, (2002) · Zbl 1025.76011
[11] Mutabazi, I.; Normand, C.; Wesfreid, J.E., Gap size effects on centrifugally and rotationally driven instabilities, Phys. rev. A, 4, 6, 1199-1205, (1992) · Zbl 0825.76208
[12] Matsson, O.J.E.; Alfredsson, P.H., Experiments on instabilities in a curved channel flow, Phys. rev. A, 4, 8, 1666-1676, (1992)
[13] Selmi, A.; Nandakumar, K.; Finley, W.H., A bifurcation study of viscous flow through a rotating curved duct, J. fluid mech., 262, 353-375, (1994) · Zbl 0813.76088
[14] Matsson, O.J.E.; Alfredsson, P.H., The effect of spanwise system rotation on Dean vortices, J. fluid mech., 274, 243-265, (1994)
[15] Wang, L.; Cheng, K.C., Flows in curved channel with a low negative rotation speed, Phys. rev. E, 51, 1155-1161, (1995)
[16] Wang, L.; Cheng, K.C., Flow transitions and combined free and forced convective heat transfer in rotating curved channels: the case of positive rotation, Phys. fluids, 8, 1553-1573, (1996) · Zbl 1087.76096
[17] Wang, L., The effect of negative spanwise rotation on Dean vortices, ASME J. fluids eng., 119, 718-721, (1997)
[18] Wang, L., Buoyancy-force-driven transitions in flow structures and their effects on heat transfer in a rotating curved channel, Int. J. heat mass transfer, 40, 2, 223-235, (1997) · Zbl 0925.76883
[19] Lee, S.L., Weighting function scheme and its application on multidimensional conservation equations, Int. J. heat mass transfer, 32, 2065-2073, (1982)
[20] Incropera, F.P.; Knox, A.; Maughen, J.R., Mixed convection flow and heat transfer in the entry region of a horizontal rectangular duct, ASME J. heat transfer, 109, 434-439, (1987)
[21] Maughen, J.R.; Incorpera, F.P., Experiments on mixed convection heat transfer for airflow in a horizontal and inclined channels, Int. J. heat mass transfer, 30, 7, 1307-1318, (1987)
[22] Chou, F.C.; Han, C.S., Wall conduction effect on the onset of thermal instability in horizontal rectangular channel, Exp. heat transfer, 4, 355-365, (1991)
[23] Fujii, T.; Imura, H., Natural convection heat transfer from a plate with arbitrary inclination, Int. J. heat mass transfer, 15, 4, 755-767, (1972)
[24] Cheng, K.C.; Obata, T.; Gilpin, R.R., Buoyancy effects on forced convection heat transfer in the transition regime of a horizontal boundary layer heated from below, ASME J. heat transfer, 110, 596-603, (1988)
[25] Cheng, K.C.; Kim, Y.W., Vortex instability phenomena relating to the cooling of a horizontal isothermal flat-plate by natural and forced laminar convection flows, (), 169-182
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.