Production of longitudinal vortices in the boundary layer along a concave wall

Tani, Itirô

doi:10.1029/jz067i008p03075

Cited by 216 publications

(96 citation statements)

References 3 publications

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“…He attributes this to the possible presence of counter rotating streamwise vortices of the Görtler (1940) type, which is an open flow extension of Taylor vortices. It was known at that time that Görtler vortices could also be present in turbulent boundary layers over concave walls (Tani 1962;So & Mellor 1975) and that there is a case for the existence of such vortices in supersonic turbulent boundary layers (Girgis & Liu 2000) comes as no surprise. McCormack et al (1970) measured significant increases in surface heat transfer rates over that of the flat plate under Görtler vortices in the downstream region.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear instability of developing streamwise vortices with applications to boundary layer heat transfer intensification through an extended Reynolds analogy

Liu

2008

Phil. Trans. R. Soc. A.

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The intent of the present contribution is to explain theoretically the experimentally measured surface heat transfer rates on a slightly concave surface with a thin boundary layer in an otherwise laminar flow. As the flow develops downstream, the measured heat transfer rate deviates from the local laminar value and eventually exceeds the local turbulent value in a non-trivial manner even in the absence of turbulence. While the theory for steady strong nonlinear development of streamwise vortices can bridge the heat transfer from laminar to the local turbulent value, further intensification is attributable to the transport effects of instability of the basic steady streamwise vortex system. The problem of heat transport by steady and fluctuating nonlinear secondary instability is formulated. An extended Reynolds analogy for Prandtl number unity, PrZ1, is developed, showing the similarity between streamwise velocity and the temperature. The role played by the fluctuation-induced heat flux is similar to momentum flux by the Reynolds shear stress. Inferences from the momentum problem indicate that the intensified heat flux developing well beyond the local turbulent value is attributed to the transport effects of the nonlinear secondary instability, which leads to the formation of 'coherent structures' of the flow. The basic underlying pinions of the non-linear hydrodynamic stability problem are the analyses of J. T. Stuart, which uncovered physical mechanisms of nonlinearities that are crucial to the present developing boundary layers supporting streamwise vortices and their efficient scalar transporting mechanisms.

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Section: Introductionmentioning

confidence: 99%

Nonlinear instability of developing streamwise vortices with applications to boundary layer heat transfer intensification through an extended Reynolds analogy

Liu

2008

Phil. Trans. R. Soc. A.

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“…Clearly, there is no dearth of fundamental problems that remain in the choice of intensification of mixing that minimizes the impact of the mixer, such as the present wavy mixer in the absence of explicit vortex generators, including the integration of the parabolized scalar transport problem for a liquid system at large Prandtl and Schmidt numbers. Tani (1962) noted that Görtler vortices can persist well into the turbulent boundary layer region. As such, these large-scale streamwise vortices are but another class of large-scale coherent structures in free turbulent shear flows and would be worthy of study for the intensification of mixing in a stimulated turbulent shear flow such as that described for predominantly spanwise-oriented structures (Liu 1988) …”

Section: Discussionmentioning

confidence: 99%

“…They point out that salient features of Görtler vortices strongly resemble that of the turbulent boundary layer. Tani (1962) points out that Görtler vortices are sustainable even in a turbulent boundary layer. Molecular transport effects considered here could be interpreted as that of fluid viscosity in the transitional range or, with an extended imagination, the qualitative effect of eddy viscosity of the eddies of much small scales.…”

Section: Appendix a Parameters Of The Problemmentioning

confidence: 99%

An extended Reynolds analogy for excited wavy instabilities of developing streamwise vortices with applications to scalar mixing intensification

Liu

2007

Proc. R. Soc. A.

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Studies are presented to elucidate the role of steady streamwise vortex structures, initiated upstream from weak Görtler vortices in the absence of explicit vortex generators, and their excited nonlinear wavy instabilities in the intensification of scalar mixing in a spatially developing mixing region. While steady streamwise vortex flow gives rise to significant mixing enhancement, the excited nonlinear wavy instabilities, which in turn modify the basic three-dimensional streamwise vortices, give rise to further mixing intensification which is quantitatively assessed by a mixedness parameter. Possibility of similarity between the dimensionless streamwise momentum and scalar transport problems leading to an extended Reynolds analogy is sought. This similarity is shown earlier to hold for the steady streamwise vortex flow in the absence of nonlinear wavy instabilities (Liu & Sabry 1991 Proc. R. Soc. A 432, 1-12). In this paper, the momentum conservation equations for the nonlinear wavy or secondary instabilities together with the advected fluctuation scalar problems are examined in detail. The presence of the streamwise fluctuation pressure gradient, which prevents the similarity, is estimated in terms of the fluctuation dynamical pressure and its relative importance to advective transport. It is found from scaling that the fluctuating streamwise pressure gradient, though not completely negligible, is sufficiently unimportant so as to render similarity between fluctuation streamwise velocity and fluctuation temperature and concentration a distinct possibility. The scalar fluctuations are then inferable from the fluctuation streamwise velocity and that the Reynolds stresses of the nonlinear fluctuations and the scalar fluxes are also similar. The nonlinear instabilitymodified mean streamwise momentum and the modified mean heat and mass transport problems are also similar, thus providing a complete 'Reynolds analogy', rendering possible the interpretation of the scalar mixedness for a gaseous medium for which the Prandtl and Schmidt numbers are near unity. It is found that the nonlinearity of the wavy instability, which induces scalar fluxes modifying the mean scalar transport, further intensifies scalar mixedness over a significant streamwise region which is well above that achieved by the steady, unmodified streamwise vortices alone for the numerical example corresponding to the most amplified wavy-sinuous mode.

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“…When planning the simulations, we deliberately used a small spanwise domain to allow for the highest possible resolution of the spanwise scales for a given number of grid points (to reduce the cost of the simulations). This was justified, as the consensus from previous experimental evidence of other investigations was that Görtler-type vortices did not play an important role in turbulent boundary layers [18,19]; the exception being the paper by Tani [33]. The rationale for this conjecture was based on the assumption that turbulent diffusion would not allow the development of strong coherent longitudinal motion or that turbulent diffusion would destroy such coherent vortices when somehow already established (by upstream history or artificial vortex generators).…”

Section: Introductionmentioning

confidence: 99%

Longitudinal Vortices in Turbulent Boundary Layers Subjected to Wall Curvature and Strong Adverse Pressure Gradients: Numerical Investigations Using LES and DNS

Fasel¹,

Groß²,

Postl³

2001

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Production of longitudinal vortices in the boundary layer along a concave wall

Cited by 216 publications

References 3 publications

Nonlinear instability of developing streamwise vortices with applications to boundary layer heat transfer intensification through an extended Reynolds analogy

Nonlinear instability of developing streamwise vortices with applications to boundary layer heat transfer intensification through an extended Reynolds analogy

An extended Reynolds analogy for excited wavy instabilities of developing streamwise vortices with applications to scalar mixing intensification

Longitudinal Vortices in Turbulent Boundary Layers Subjected to Wall Curvature and Strong Adverse Pressure Gradients: Numerical Investigations Using LES and DNS

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