Turbulent boundary layers with large streamline curvature effects

So, R. M. C.; Mellor, George L.

doi:10.1007/bf01797303

Cited by 16 publications

(7 citation statements)

References 25 publications

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“…Wall shear stress was inferred from a Clauser plot, but the turbulent shear stress profile was not measured close enough to the wall to check all values by extrapolation. The accuracy of the shear stress measurements very near the wall has been questioned lately by So (1978).…”

Section: Introductionmentioning

confidence: 99%

Turbulent boundary-layer flow and structure on a convex wall and its redevelopment on a flat wall

1983

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Two experiments (δ/R = 0.05 and 0.10) were performed to determine how boundary-layer turbulence is affected by strong convex curvature. The flow passed from a flat surface, over convex surface with 90° of turning, and then onto a flat recovery surface. The pressure gradient along the test surface was forced to be zero.After the sudden introduction of curvature, the shear stress in the outer part of the boundary layer is sharply diminished. The wall shear also drops off quickly downstream. When the surface suddenly becomes flat again, the wall-shear and the shear-stress profiles recover very slowly towards flat-wall conditions. The shear-stress profiles in the curved region for both experiments collapse when $-\overline{uv}/u^2_{\tau}$ is plotted vs. distance from the wall normalized on wall radius, n/R. The strong-curvature data of So & Mellor also fall on the same curve. Thus suggests an asymptotic state for the shear-stress profiles of strongly curved boundary layers where R rather than boundary-layer thickness controls the active turbulence lengthscales. In this asymptotic region, the active shear-layer thickness is less than its initial value at the start of curvature. In the recovery region, the width of the active shear layer regrows slowly within the original velocity-gradient boundary layer, like a developing boundary layer under a free stream with a velocity gradient normal to the wall.

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Section: Introductionmentioning

confidence: 99%

Turbulent boundary-layer flow and structure on a convex wall and its redevelopment on a flat wall

1983

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“…These simplified equations are algebraic in nature and the stress components can be solved in terms of the mean flow properties. This approach has been used by So [26], and So and Mellor [33] to estimate small and large streamline curvature effects on boundary layers, respectively. It has also been applied to estimate the effect of swirl on turbulence velocity scales [27].…”

Section: Modelling Assumptions and The Simplified Transport Equationsmentioning

confidence: 99%

“…The effect of streamline curvature on 2-D flows due either to surface curvature, system rotation, separately or in combination, have been investigated by So [26,31], and So and Mellor [33]. The governing equations for the present analysis can be deduced from those given in [30] or directly from Equations ( 18)- (24).…”

Section: Case Ii-curved Flowmentioning

confidence: 99%

“…If Ri B 1, then to the first approximation, the modifying function Z(Ri B ) given in Equation (82) can be simplified to 1) works well in the simulations of a wide range of turbulent mixing flows and boundary layers even though it is derived using atmospheric boundary layer data [4][5][6][7][8][9][10][11][12][13][14]. For very small Ri B , Equation (85) essentially reduces to Equation (1) or Equation (33). This indicates that if Ri B is indeed very small, the simple turbulent flow and the atmospheric boundary layer behaves similarly and can be analyzed using Equation (1) or its equivalent.…”

Section: Case V-atmospheric Boundary Layermentioning

confidence: 99%

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An Analytically Derived Shear Stress and Kinetic Energy Equation for One-Equation Modelling of Complex Turbulent Flows

2021

Symmetry

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The Reynolds stress equations for two-dimensional and axisymmetric turbulent shear flows are simplified by invoking local equilibrium and boundary layer approximations in the near-wall region. These equations are made determinate by appropriately modelling the pressure–velocity correlation and dissipation rate terms and solved analytically to give a relation between the turbulent shear stress τρ and the kinetic energy of turbulence (k =q22). This is derived without external body force present. The result is identical to that proposed by Nevzgljadov in A Phenomenological Theory of Turbulence, who formulated it through phenomenological arguments based on atmospheric boundary layer measurements. The analytical approach is extended to treat turbulent flows with external body forces. A general relation τρ = a11 - AFRiFq22 is obtained for these flows, where FRiF is a function of the gradient Richardson number RiF, and a1 is found to depend on turbulence models and their assumed constants. One set of constants yields a1= 0.378, while another gives a1= 0.328. With no body force, F ≡ 1 and the relation reduces to the Nevzgljadov equation with a1 determined to be either 0.378 or 0.328, depending on model constants set assumed. The present study suggests that 0.328 is in line with Nevzgljadov's proposal. Thus, the present approach provides a theoretical base to evaluate the turbulent shear stress for flows with external body forces. The result is used to reduce the k–e model to a one-equation model that solves the k-equation, the shear stress and kinetic energy equation, and an e evaluated by assuming isotropic eddy viscosity behavior.

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“…The flow over curved surfaces is experienced in many practical situations such as is reduced com pared to a flat surface which implies that convex surface curvature exerts a stabilizing influence on the boundary layer (So and M ellor, 1978;G owda and N arayana, 1980). Such stabilizing influence o f stream wise curvature in shear layers developing on convex-shaped walls is well established (Gillis and Johnston, 1983), and is the result o f the radial equilibrium that exists between w all-norm al pressure gradients and the centrifugal force acting on the fluid particles due to their centripetal acceleration.…”

Section: Effect Of Streamwise Convex Surface Curvature On Turbulent Bmentioning

confidence: 99%

A DNS study on the effects of streamwise convex surface curvature on coherent structures in turbulent boundary layers

Dave¹

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Turbulent boundary layers with large streamline curvature effects

Cited by 16 publications

References 25 publications

Turbulent boundary-layer flow and structure on a convex wall and its redevelopment on a flat wall

Turbulent boundary-layer flow and structure on a convex wall and its redevelopment on a flat wall

An Analytically Derived Shear Stress and Kinetic Energy Equation for One-Equation Modelling of Complex Turbulent Flows

A DNS study on the effects of streamwise convex surface curvature on coherent structures in turbulent boundary layers

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