Turbulence modulation in thermally expanding and contracting flows

We present direct numerical simulations of developing turbulent channel flows subjected to thermal expansion or contraction downstream of a heated or cooled wall. Using different constitutive relations for viscosity we analyse the response of variable property flows to streamwise acceleration/deceleration by separating the effect of streamwise acceleration/deceleration from the effect of wall-normal property variations. We demonstrate that, beyond a certain streamwise location, the flow can be considered in a state of ‘quasi-equilibrium’ regarding semilocally scaled variables. As such, we claim that the development of turbulent quantities due to streamwise acceleration/deceleration is localized to the region of impulsive heating/cooling, while changes in turbulence occurring farther downstream can be attributed solely to property variations. This finding allows us to study turbulence modulation in accelerating/decelerating flows using the semilocal scaling framework. By investigating the energy redistribution among the turbulent velocity fluctuations, we conclude that a change in bulk streamwise velocity has a non-local effect which originates from the change in mean shear and modifies the energy pathways through velocity-pressure-gradient correlations. On the other hand, the wall-normal property gradients have a local effect and act through the modification of the viscous dissipation. We show that it is possible to superimpose and compare the two different effects when using the semilocal scaling framework.

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Phase Locked Analysis of a Simplified Car Geometry Wake Flow Control Using Synthetic Jet

Volume 2: Fora ◽

10.1115/fedsm2006-98469 ◽

2006 ◽

Cited By ~ 4

Author(s):

Ce´dric Leclerc ◽

Euge´nie Levallois ◽

Quentin Gallas ◽

Patrick Gillie´ron ◽

Azeddine Kourta

Keyword(s):

Boundary Layer ◽

Turbulent Boundary Layer ◽

Drag Reduction ◽

Vortex Shedding ◽

Aerodynamic Drag ◽

Streamwise Velocity ◽

Local Effect ◽

Synthetic Jet ◽

Wake Flow ◽

Synthetic Jet Actuator

This paper presents a numerical unsteady analysis of a SJA impact on a car wake flow. First, for the optimal reduced frequency F+, the influence of the Cμ on the mean aerodynamic drag reduction 〈Cd〉 is observed. A spectral analysis of the vortex shedding coming from the upper and the lower part of the car and of the drag coefficient is then presented for different Cμ values. Preliminary results suggest that maximum drag reduction is obtained when most energy in the wake comes from the actuator forcing frequency rather than the natural vortex shedding frequencies of the two contributions. This work is completed by a phase locked analysis of the synthetic jet actuator local effect on the turbulent boundary layer just before the flow separation. For the fixed optimal F+, different Cμ values are compared. The streamwise velocity profiles seem to show that maximal efficiency of the control is obtained when the synthetic jet injected momentum is introduced in the logarithmic sub-layer part of the turbulent boundary layer.

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A Reduced-Order Model of the Mean Properties of a Turbulent Wall Boundary Layer at a Zero Pressure Gradient

Journal of Fluids Engineering ◽

10.1115/1.4026418 ◽

2014 ◽

Vol 136 (3) ◽

Cited By ~ 1

Author(s):

Lei Xu ◽

Zvi Rusak ◽

Luciano Castillo

Keyword(s):

Boundary Layer ◽

Shear Stress ◽

Reynolds Shear Stress ◽

Streamwise Velocity ◽

Similarity Function ◽

Mixing Length ◽

Flow Properties ◽

Normal Coordinate ◽

Streamwise Location ◽

The Mean

A novel two-equations model for computing the flow properties of a spatially-developing, incompressible, zero-pressure-gradient, turbulent boundary layer over a smooth, flat wall is developed. The mean streamwise velocity component inside the boundary layer is described by the Reynolds-averaged Navier–Stokes equation where the Reynolds shear stress is given by an extended mixing-length model. The nondimensional form of the mixing length is described by a polynomial function in terms of the nondimensional wall normal coordinate. Moreover, a stream function approach is applied with a leading-order term described by a similarity function. Two ordinary differential equations are derived for the solution of the similarity function along the wall normal coordinate and for its streamwise location. A numerical integration scheme of the model equations is developed and enables the solution of flow properties. The coefficients of the mixing-length polynomial function are modified at each streamwise location as part of solution iterations to satisfy the wall and far-field boundary conditions and adjust the local boundary layer thickness, δ99.4, to a location where streamwise speed is 99.4% of the far-field streamwise velocity. The elegance of the present approach is established through the successful solution of the various flow properties across the boundary layer (i.e., mean streamwise velocity, viscous stress, Reynolds shear stress, skin friction coefficient, and growth rate of boundary layer among others) from the laminar regime all the way to the fully turbulent regime. It is found that results agree with much available experimental data and direct numerical simulations for a wide range of Reθ based on the momentum thickness (Reθ) from 15 up to 106, except for the transition region from laminar to turbulent flow. Furthermore, results shed light on the von Kármán constant as a function of Reθ, the possible four-layer nature of the mean streamwise velocity profile, the universal profiles of the streamwise velocity and the Reynolds shear stress at high Reθ, and the scaling laws at the outer region.

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Zum Materialgesetz eines elastischen Mediums mit Momentenspannungen

Zeitschrift für Naturforschung A ◽

10.1515/zna-1965-0303 ◽

1965 ◽

Vol 20 (3) ◽

pp. 336-359 ◽

Cited By ~ 1

Author(s):

F. Hehl ◽

E. Kröner

Keyword(s):

Constitutive Relations ◽

Short Review ◽

Local Effect ◽

Classical Elasticity ◽

Couple Stresses ◽

State Of Stress ◽

Order Of Magnitude ◽

Non Local ◽

Peierls Model ◽

Edge Dislocations

If through an element of area of a continuum there acts not only a force but also a couple, we have to introduce besides the force-stresses the so-called couple-stresses. In this article we emphasize the importance of couple-stresses in dislocated solids.—§ 2 gives a short review of the present state of the theory of couple-stresses. In classical elasticity couple-stresses are to be interpreted as a non-local effect intimately connected with the range of the atomic forces. The couplestresses are of a higher order in this range than force-stresses and can therefore usually be neglected.In the field theory of dislocations couple-stresses generally are of the same order of magnitude as force-stresses, however. Hence they cause considerable effects. In § 3 we determine the macroscopic observable couple-stresses of homogeneously distributed screw and edge dislocations through averaging over their microscopic fluctuating stress field. With the PEIERLS model we show in § 4 that the core of a dislocation produces an asymmetric state of stress and for that reason also couple-stresses, which are negligibly small under certain circumstances. Introducing a simple polycrystal model we derive in § 5 the constitutive relations for couple-stresses and dislocation density in an isotropic form. The results are discussed in § 6.

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Measurements in the near-wall region of a boundary layer over a wall with large transverse curvature

Journal of Fluid Mechanics ◽

10.1017/s0022112010003770 ◽

2010 ◽

Vol 664 ◽

pp. 33-50 ◽

Cited By ~ 4

Author(s):

M. H. KRANE ◽

L. M. GREGA ◽

T. WEI

Keyword(s):

Boundary Layer ◽

Direct Determination ◽

Streamwise Velocity ◽

Wall Region ◽

Wall Velocity ◽

Transverse Curvature ◽

Spatially Resolved ◽

Streamwise Location ◽

Image Velocimetry ◽

Near Wall

Measurements of the near-wall velocity field of the flow over cylinders aligned with a uniform flow are presented. The broader objective of this investigation was to quantify and understand the role of transverse curvature in the limit as cylinder diameter approaches zero. The specific goal was to begin with a turbulent boundary layer over a larger radius cylinder and see what happens as the radius is reduced. Spatially and temporally resolved digital particle image velocimetry (DPIV) measurements were made on three different radius cylinders, 0.14 cm ≤ a ≤ 3.05 cm, extending along the length of a large free-surface water tunnel. Mean and fluctuating profiles are presented at a fixed streamwise location and free-stream speed. For the first time, spatially resolved measurements were made very close to the wall, permitting direct determination of wall shear stress, i.e. uτ, from near-wall velocity profiles. The measurements revealed a region close to the wall for small radii where the mean streamwise velocity profile is inflectional. This has significant implications on assumptions regarding what happens in the limit of a vanishing cylinder radius.

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