The effect of pressure gradient on the law of the wall in turbulent flow

McDonald, H.

doi:10.1017/s0022112069001133

Cited by 56 publications

(30 citation statements)

References 12 publications

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“…These terms may be important in a strong APG flow as was noted by Rotta (1962). A third complication is the non-linear inertia terms, which can influence the total shear stress as argued by McDonald (1969). However, in the present simulations these two terms are not important and will be disregarded in the following.…”

Section: The Inner Regionmentioning

confidence: 81%

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Direct numerical simulation of a separated turbulent boundary layer

2002

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Direct numerical simulation of two turbulent boundary layer flows has been performed. The boundary layers are both subject to a strong adverse pressure gradient. In one case a separation bubble is created while in the other the boundary layer is everywhere attached. The data from the simulations are used to investigate scaling laws near the wall, a crucial concept in turbulence models. Theoretical work concerning the inner region in a boundary layer under an adverse pressure gradient is reviewed and extended to the case of separation. Excellent agreement between theory and data from the direct numerical simulation is found in the viscous sub-layer, while a qualitative agreement is obtained for the overlap region.

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Section: The Inner Regionmentioning

confidence: 81%

“…Mellor (1966) arrived at a similar expression as Townsend. The work of Townsend was later reviewed by McDonald (1969) who included non-linear inertia effects in the expression for the velocity profile. Afzal (1996) obtained similar expressions for the velocity profile as Townsend by using asymptotic matching.…”

Section: Theoretical Investigationsmentioning

confidence: 99%

Direct numerical simulation of a separated turbulent boundary layer

2002

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“…Variations of this analysis have been made by Patel (1973), McDonald (1969, Townsend (1961), and Mellor (1966).…”

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confidence: 99%

Near-Wall Similarity in a Pressure-Driven Three-Dimensional Turbulent Boundary Layer

Pierce

McAllister

1983

Journal of Fluids Engineering

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Interim 14. IX Supplementary Notes_16. "Exte n sive measurements of the mean velocity, wall pressure and wall shear stress fields were Meade in a three-dimensional pressure-driven turbulent boundary layer created by a cylinder with trailing edge placed normal to a flat plate floor.The direct force wall shear stress measurements were made with a unique, floating element direct force sensing shear mater that responded to both the magnitude and direction of the local wall shear stress.These data were used to test the ability of ten near-wall similarity models proposed in the literature to describe the near-wall velocity field for the measured flow under a wiee range of skewing conditions and a variety of pressure gradient and wall shear vector orientations. S. Performing Organization Report Number. Insect if perfotming organization wishes to assign this number.9. Performing Organization Name and Mailing Address. Give name, street, city, state, and zip code. List no more than two levels of an organizational hierarchy. Display the name of the organization exactly as it should appear in Government indexes such as Government Reports Index (GRI).10. Project/ Took/Work Unit Number. Use the project, task and work unit numbers under which the report was prepared.11. Contract/Grant Number. Insert contract or grant number under which report was prepared.12. Sponsoring Agency Name and Mailing Address. Include zip code. C:-e main sponsors.13. Since the majority of documents are multidisciplinary in nature, the primary Field/Group assignment(s) will be the specific discipline, area of human endeavor, or type of physical object. The application(s) will be cross-referenced with secondary Field/Group assignments that will follow the primary posting(s).18. Distribution Statement. Denote public relessabilicy, for example " Release unlimited", or limitation for reasons other than security. Cite any availability to the public, other than NTIS, with address, order number and price, if known. These three-dimensional velocity field, wall pressure field, and wall shear field results were used to test the ability of ten near-wall similarity models proposed in the literature for three-dimensional turbulent boundary layers to describe the near-wall velocity field. Six of these ten models are scalar, treating some form of an equivalent velocity component. Three of the remaining four more complex models are twocomponent vector models and the last is a scalar model which recognizes the vector nature of the near-wall flow by way of a developed velocity.All. of the ten models tested find their origin, directly or indirectly, in an equilibrium boundary layer hy pothesis using a mixing length. there is the problem of fixing a lower y + limit below which data could not be used.If one were to use these three more complex models in a computational scheme replacing the no slip wall boundary condition at the wall with a match to a similarity model near the wall, then for the flows described above, such a match should be made in a range of about 50 < y ...

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“…A wall law for u + can be derived based on Equation (4) together with the eddy-viscosity assumption and a mixing-length ansatz, see [11], or by matching arguments between inner and outer scaling, see [22,23]. Using the latter argument, the diagnostic function (2) should show a plateau in case that the underlying wall law for u + is satisfied.…”

Section: Classical Theorymentioning

confidence: 99%

“…Some publications propose a functional dependence on the so-called pressure gradient parameter p + x = ν/(ρu 3 τ )dp/dx, see [7,8]. The third hypothesis by (amongst others) [9][10][11] is that the pressure gradient causes '[...] a change in the character of the velocity distribution over the entire region [...]' occupied by the log-law in a ZPG flow, see [12], which is called a 'general breakdown' of the log-law in the entire inner part of the boundary layer in [12].…”

Section: Introductionmentioning

confidence: 99%

Investigation of scaling laws in a turbulent boundary layer flow with adverse pressure gradient using PIV

Knopp

Buchmann

Schanz

et al. 2015

Journal of Turbulence

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We present an experimental investigation and data analysis of a turbulent boundary layer flow at a significant adverse pressure gradient at Reynolds number up to Re θ = 10, 000. We combine large-scale particle image velocimetry (PIV) with microscopic PIV for measuring the near wall region including the viscous sublayer. We investigate scaling laws for the mean velocity and for the total shear stress in the inner part of the boundary layer. In the inner part the mean velocity can be fitted by a log-law. In the outer part of the inner layer the log-law ceases to be valid. Instead, a modified log-law provides a good fit, which is given in terms of the pressure gradient parameter and a parameter for the mean inertial effects. Finally we describe and assess a simple quantitative model for the total shear stress distribution which is local in wall-normal direction without streamwise history effects.

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The effect of pressure gradient on the law of the wall in turbulent flow

Cited by 56 publications

References 12 publications

Direct numerical simulation of a separated turbulent boundary layer

Direct numerical simulation of a separated turbulent boundary layer

Near-Wall Similarity in a Pressure-Driven Three-Dimensional Turbulent Boundary Layer

Investigation of scaling laws in a turbulent boundary layer flow with adverse pressure gradient using PIV

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