Effects of convex transverse curvature on wall-bounded turbulence. Part 1. The velocity and vorticity

1994 ◽  
Vol 272 ◽  
pp. 349-382 ◽  
Author(s):  
João C. Neves ◽  
Parviz Moin ◽  
Robert D. Moser
Keyword(s):  
Turbulent Flows ◽  
Plane Channel ◽  
Axial Flow ◽  
Structural Data ◽  
Streamwise Velocity ◽  
Momentum Equation ◽  
Radius Of Curvature ◽  
Curvature Effects ◽  
Transverse Curvature ◽  
Logarithmic Region

Convex transverse curvature effects in wall-bounded turbulent flows are significant if the boundary-layer thickness is large compared to the radius of curvature (large γ = δ/a). The curvature affects the inner part of the flow if a+, the cylinder radius in wall units, is small.Two direct numerical simulations of a model problem approximating axial flow boundary layers on long cylinders were performed for γ = 5 (a+ ≈ 43) and γ = 11 (a+ ≈ 21). Statistical and structural data were extracted from the computed flow fields. The effects of the transverse curvature were identified by comparing the present results with those of the plane channel simulation of Kim, Moin & Moser (1987), performed at a similar Reynolds number. As the curvature increases, the skin friction increases, the slope of the logarithmic region decreases and turbulence intensities are reduced. Several turbulence statistics are found to scale with a curvature dependent velocity scale derived from the mean momentum equation. Near the wall, the flow is more anisotropic than in the plane channel with a larger percentage of the turbulent kinetic energy resulting from the streamwise velocity fluctuations. As the curvature increases, regions of strong normal vorticity develop near the wall.

scholarly journals A predictive inner–outer model for streamwise turbulence statistics in wall-bounded flows

2011 ◽  
Vol 681 ◽  
pp. 537-566 ◽  
Author(s):  
ROMAIN MATHIS ◽  
NICHOLAS HUTCHINS ◽  
IVAN MARUSIC
Keyword(s):  
Pressure Gradient ◽  
Turbulent Flows ◽  
Large Scale ◽  
Adverse Pressure Gradient ◽  
Reynolds Numbers ◽  
Streamwise Velocity ◽  
Gradient Flows ◽  
Streamwise Pressure Gradient ◽  
Logarithmic Region ◽  
Inner Region

A model is proposed with which the statistics of the fluctuating streamwise velocity in the inner region of wall-bounded turbulent flows are predicted from a measured large-scale velocity signature from an outer position in the logarithmic region of the flow. Results, including spectra and all moments up to sixth order, are shown and compared to experimental data for zero-pressure-gradient flows over a large range of Reynolds numbers. The model uses universal time-series and constants that were empirically determined from zero-pressure-gradient boundary layer data. In order to test the applicability of these for other flows, the model is also applied to channel, pipe and adverse-pressure-gradient flows. The results support the concept of a universal inner region that is modified through a modulation and superposition of the large-scale outer motions, which are specific to the geometry or imposed streamwise pressure gradient acting on the flow.

scholarly journals Analysis of axisymmetric boundary layers

2018 ◽  
Vol 849 ◽  
pp. 927-941 ◽  
Author(s):  
Praveen Kumar ◽  
Krishnan Mahesh
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Axial Flow ◽  
Streamwise Velocity ◽  
Skin Friction Coefficient ◽  
Radius Of Curvature ◽  
Normal Velocity ◽  
Displacement Thickness ◽  
Analytical Relations

Axisymmetric boundary layers are studied using integral analysis of the governing equations for axial flow over a circular cylinder. The analysis includes the effect of pressure gradient and focuses on the effect of transverse curvature on boundary layer parameters such as shape factor ($H$) and skin-friction coefficient ($C_{f}$), defined as $H=\unicode[STIX]{x1D6FF}^{\ast }/\unicode[STIX]{x1D703}$ and $C_{f}=\unicode[STIX]{x1D70F}_{w}/(0.5\unicode[STIX]{x1D70C}U_{e}^{2})$ respectively, where $\unicode[STIX]{x1D6FF}^{\ast }$ is displacement thickness, $\unicode[STIX]{x1D703}$ is momentum thickness, $\unicode[STIX]{x1D70F}_{w}$ is the shear stress at the wall, $\unicode[STIX]{x1D70C}$ is density and $U_{e}$ is the streamwise velocity at the edge of the boundary layer. Relations are obtained relating the mean wall-normal velocity at the edge of the boundary layer ($V_{e}$) and $C_{f}$ to the boundary layer and pressure gradient parameters. The analytical relations reduce to established results for planar boundary layers in the limit of infinite radius of curvature. The relations are used to obtain $C_{f}$ which shows good agreement with the data reported in the literature. The analytical results are used to discuss different flow regimes of axisymmetric boundary layers in the presence of pressure gradients.

Stiffness Constants for Composite Beams Including Large Initial Twist and Curvature Effects

1995 ◽  
Vol 48 (11S) ◽  
pp. S61-S67 ◽  
Author(s):  
Carlos E. S. Cesnik ◽  
Dewey H. Hodges
Keyword(s):  
Wave Length ◽  
Three Dimensional ◽  
Radius Of Curvature ◽  
Cross Sectional ◽  
Curvature Effects ◽  
Three Dimensional Representation ◽  
Stiffness Model ◽  
Sectional Analysis ◽  
Three Dimensional Elasticity ◽  
Coupling Phenomena

An asymptotically exact methodology, based on geometrically nonlinear, three-dimensional elasticity, is presented for cross-sectional analysis of initially curved and twisted, nonhomogeneous, anisotropic beams. Through accounting for all possible deformation in the three-dimensional representation, the analysis correctly accounts for the complex elastic coupling phenomena in anisotropic beams associated with shear deformation. The analysis is subject only to the restrictions that the strain is small relative to unity and that the maximum dimension of the cross section is small relative to the wave length of the deformation and to the minimum radius of curvature and/or twist. The resulting cross-sectional elastic constants exhibit second-order dependence on the initial curvature and twist. As is well known, the associated geometrically-exact, one-dimensional equilibrium and kinematical equations also depend on initial twist and curvature. The corrections to the stiffness model derived herein are also necessary in general for proper representation of initially curved and twisted beams.

Characterization of Geometrical and Temporal Properties of Large-scale Motions in Turbulent Flows

2021 ◽  
Author(s):  
Christina Tsai ◽  
Kuang-Ting Wu
Keyword(s):  
Turbulent Flow ◽  
Turbulent Flows ◽  
Coherent Structures ◽  
Large Scale ◽  
Streamwise Velocity ◽  
Turbulent Structures ◽  
Temporal Properties ◽  
Turbulent Statistics ◽  
Spatial Locations

<p>It is demonstrated that turbulent boundary layers are populated by a hierarchy of recurrent structures, normally referred to as the coherent structures. Thus, it is desirable to gain a better understanding of the spatial-temporal characteristics of coherent structures and their impact on fluid particles. Furthermore, the ejection and sweep events play an important role in turbulent statistics. Therefore, this study focuses on the characterizations of flow particles under the influence of the above-mentioned two structures.</p><div><span>With regard to the geometry of turbulent structures, </span><span>Meinhart & Adrian (1995) </span>first highlighted the existence of large and irregularly shaped regions of uniform streamwise momentum zone (hereafter referred to as a uniform momentum zone, or UMZs), regions of relatively similar streamwise velocity with coherence in the streamwise and wall-normal directions.  <span>Subsequently, </span><span>de Silva et al. (2017) </span><span>provided a detection criterion that had previously been utilized to locate the uniform momentum zones (UMZ) and demonstrated the application of this criterion to estimate the spatial locations of the edges that demarcates UMZs.</span></div><div> </div><div>In this study, detection of the existence of UMZs is a pre-process of identifying the coherent structures. After the edges of UMZs are determined, the identification procedure of ejection and sweep events from turbulent flow DNS data should be defined. As such, an integrated criterion of distinguishing ejection and sweep events is proposed. Based on the integrated criterion, the statistical characterizations of coherent structures from available turbulent flow data such as event durations, event maximum heights, and wall-normal and streamwise lengths can be presented.</div>

Direct numerical simulation of turbulent channel flow up to

2015 ◽  
Vol 774 ◽  
pp. 395-415 ◽  
Author(s):  
Myoungkyu Lee ◽  
Robert D. Moser
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Direct Numerical Simulation ◽  
Turbulent Flows ◽  
Channel Flow ◽  
Turbulent Channel Flow ◽  
Streamwise Velocity ◽  
Mean Velocity ◽  
Layer Structures ◽  
High Reynolds

A direct numerical simulation of incompressible channel flow at a friction Reynolds number ($\mathit{Re}_{{\it\tau}}$) of 5186 has been performed, and the flow exhibits a number of the characteristics of high-Reynolds-number wall-bounded turbulent flows. For example, a region where the mean velocity has a logarithmic variation is observed, with von Kármán constant ${\it\kappa}=0.384\pm 0.004$. There is also a logarithmic dependence of the variance of the spanwise velocity component, though not the streamwise component. A distinct separation of scales exists between the large outer-layer structures and small inner-layer structures. At intermediate distances from the wall, the one-dimensional spectrum of the streamwise velocity fluctuation in both the streamwise and spanwise directions exhibits $k^{-1}$ dependence over a short range in wavenumber $(k)$. Further, consistent with previous experimental observations, when these spectra are multiplied by $k$ (premultiplied spectra), they have a bimodal structure with local peaks located at wavenumbers on either side of the $k^{-1}$ range.

A Mixing-Length Model for the Prediction of Convex Curvature Effects on Turbulent Boundary Layers

1984 ◽  
Vol 106 (1) ◽  
pp. 142-148 ◽  
Author(s):  
E. W. Adams ◽  
J. P. Johnston
Keyword(s):  
Heat Transfer ◽  
Layer Thickness ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Radius Of Curvature ◽  
Data Sets ◽  
Mixing Length ◽  
Flat Wall ◽  
Curvature Effects ◽  
Layer Thickness Ratio

A mixing-length model is developed for the prediction of turbulent boundary layers with convex streamwise curvature. For large layer thickness ratio, δ/R > 0.05, the model scales mixing length on the wall radius of curvature, R. For small δ/R, ordinary flat wall modeling is used for the mixing-length profile with curvature corrections, following the recommendations of Eide and Johnston [7]. Effects of streamwise change of curvature are considered; a strong lag from equilibrium is required when R increases downstream. Fifteen separate data sets were compared, including both hydrodynamic and heat transfer results. In this paper, six of these computations are presented and compared to experiment.

scholarly journals Velocity transformation for compressible wall-bounded turbulent flows with and without heat transfer

2021 ◽  
Vol 118 (34) ◽  
pp. e2111144118 ◽  
Author(s):  
Kevin Patrick Griffin ◽  
Lin Fu ◽  
Parviz Moin
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Turbulent Flows ◽  
Viscous Sublayer ◽  
Mean Velocity ◽  
General Transformation ◽  
Law Of The Wall ◽  
Velocity Transformation ◽  
Logarithmic Region ◽  
Logarithmic Layer

In this work, a transformation, which maps the mean velocity profiles of compressible wall-bounded turbulent flows to the incompressible law of the wall, is proposed. Unlike existing approaches, the proposed transformation successfully collapses, without specific tuning, numerical simulation data from fully developed channel and pipe flows, and boundary layers with or without heat transfer. In all these cases, the transformation is successful across the entire inner layer of the boundary layer (including the viscous sublayer, buffer layer, and logarithmic layer), recovers the asymptotically exact near-wall behavior in the viscous sublayer, and is consistent with the near balance of turbulence production and dissipation in the logarithmic region of the boundary layer. The performance of the transformation is verified for compressible wall-bounded flows with edge Mach numbers ranging from 0 to 15 and friction Reynolds numbers ranging from 200 to 2,000. Based on physical arguments, we show that such a general transformation exists for compressible wall-bounded turbulence regardless of the wall thermal condition.

scholarly journals The Transient Liquid Crystal Technique: Influence of Surface Curvature and Finite Wall Thickness

2004 ◽  
Author(s):  
G. Wagner ◽  
M. Kotulla ◽  
P. Ott ◽  
B. Weigand ◽  
J. von Wolfersdorf
Keyword(s):  
Heat Transfer ◽  
Liquid Crystal ◽  
Flat Plate ◽  
Hollow Cylinder ◽  
Wall Thickness ◽  
Reduction Method ◽  
Radius Of Curvature ◽  
Test Model ◽  
Curvature Effects ◽  
Transient Liquid Crystal Technique

The transient liquid crystal technique is nowadays widely used for measuring the heat transfer characteristics in gas turbine applications. Usually, the assumption is made that the wall of the test model can be treated as a flat and semi-infinite solid. This assumption is correct as long as the penetration depth of the heat compared to the thickness of the wall and to the radius of curvature is small. However, those two assumptions are not always respected for measurements near the leading edge of a blade. This paper presents a rigorous treatment of the curvature and finite wall thickness effects. The unsteady heat transfer for a hollow cylinder has been investigated analytically and a data reduction method taking into account curvature and finite wall thickness effects has been developed. Experimental tests made on hollow cylinder models have been evaluated using the new reduction method as well as the traditional semi-infinite flat plate approach and a third method that approximately accounts for curvature effects. It has been found that curvature and finite thickness of the wall have in some cases a significant influence on the obtained heat transfer coefficient. The parameters influencing the accuracy of the semi-infinite flat plate model and the approximate curvature correction are determined and the domains of validity are represented.

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