Reynolds Number Dependence of Skin Friction and Other Bulk Flow Variables in Two-Dimensional Rectangular Duct Flow

1978 ◽  
Vol 100 (2) ◽  
pp. 215-223 ◽  
Author(s):  
R. B. Dean
Keyword(s):  
Reynolds Number ◽  
Skin Friction ◽  
Bulk Flow ◽  
Two Dimensional ◽  
Duct Flow ◽  
Rectangular Duct ◽  
Flow Parameters ◽  
Log Law ◽  
Flow Variables ◽  
Reynolds Number Dependence

The Reynolds number dependence of Cf, Uo, H and other bulk flow parameters in “two dimensional” (high aspect ratio) rectangular duct flow is explored and the empirical relations Cf = 0.073 Re−1/4 and Uo/U¯ = 1.28 Re−0.0116 are presented. The values A = 2.12 and K = 0.41 for the log-law constants and Π = 0.14 for Coles’ wake parameter are derived and are shown to be independent of Re. The integration of Dean’s formula for the complete velocity profile provides close agreement with all parameters when these values of A, K and Π are used and is shown to coincide with the “optimum log-law” for skin friction (which contains Π).

Power Law Velocity Profile in the Turbulent Boundary Layer on Transitional Rough Surfaces

2007 ◽  
Vol 129 (8) ◽  
pp. 1083-1100 ◽  
Author(s):  
Noor Afzal
Keyword(s):  
Boundary Layer ◽  
Functional Equation ◽  
Reynolds Number ◽  
Turbulent Boundary Layer ◽  
Velocity Profile ◽  
Skin Friction ◽  
Power Law ◽  
Wall Roughness ◽  
Closure Model ◽  
Log Law

A new approach to scaling of transitional wall roughness in turbulent flow is introduced by a new nondimensional roughness scale ϕ. This scale gives rise to an inner viscous length scale ϕν∕uτ, inner wall transitional variable, roughness friction Reynolds number, and roughness Reynolds number. The velocity distribution, just above the roughness level, turns out to be a universal relationship for all kinds of roughness (transitional, fully smooth, and fully rough surfaces), but depends implicitly on roughness scale. The open turbulent boundary layer equations, without any closure model, have been analyzed in the inner wall and outer wake layers, and matching by the Izakson-Millikan-Kolmogorov hypothesis leads to an open functional equation. An alternate open functional equation is obtained from the ratio of two successive derivatives of the basic functional equation of Izakson and Millikan, which admits two functional solutions: the power law velocity profile and the log law velocity profile. The envelope of the skin friction power law gives the log law, as well as the power law index and prefactor as the functions of roughness friction Reynolds number or skin friction coefficient as appropriate. All the results for power law and log law velocity and skin friction distributions, as well as power law constants are explicitly independent of the transitional wall roughness. The universality of these relations is supported very well by extensive experimental data from transitional rough walls for various different types of roughnesses. On the other hand, there are no universal scalings in traditional variables, and different expressions are needed for various types of roughness, such as inflectional roughness, monotonic roughness, and others. To the lowest order, the outer layer flow is governed by the nonlinear turbulent wake equations that match with the power law theory as well as log law theory, in the overlap region. These outer equations are in equilibrium for constant value of m, the pressure gradient parameter, and under constant eddy viscosity closure model, the analytical and numerical solutions are presented.

Visualization and Analysis of Flow in an Offset Channel

1992 ◽  
Vol 114 (4) ◽  
pp. 819-826 ◽  
Author(s):  
J. A. Walter ◽  
C.-J. Chen
Keyword(s):  
Reynolds Number ◽  
Velocity Field ◽  
Nuclear Power ◽  
Flow Direction ◽  
Symmetry Plane ◽  
Two Dimensional ◽  
Plant Design ◽  
Duct Flow ◽  
Inlet Channel ◽  
Cross Sectional

This paper investigates flow characteristics for a benchmark experiment that is important for thermal hydraulic phenomena in nuclear power plant design. The flow visualization experiment is carried out for flow in a rectangular offset channel covering both the laminar and turbulent flow regimes. The Reynolds number, based on the inlet velocity and the height of the inlet channel, ranges from 25 to 4600. The offset channel is an idealized thermal hydraulic geometry. Duct flow expands in a rectangular chamber and exits to a duct that is offset from the entrance duct. The offset geometry creates zones of recirculation for thermal-hydraulic mixing. Flow patterns are visualized by a laser light sheet in the symmetry plane of the primary flow direction and in three cross-sectional planes. A charge-coupled device (CCD) images the flow field, simplifying the experimental process and subsequent image analyses. The flow pattern and size of the recirculation zones change dramatically with Reynolds number until the flow is fully turbulent. While the velocity field itself is predominantly two dimensional, it is shown that the walls of the chamber produce a fully three-dimensional flow that could not be predicted properly by a two-dimensional calculation. Quantitative measurements of particle pathlines from several images are superimposed to give a composite view of the velocity field at one of the Reynolds numbers examined.

1105 Reynolds number dependence of fluttering frequency in two-dimensional jet(2)

2006 ◽  
Vol 2006 (0) ◽  
pp. _1105-1_-_1105-4_
Author(s):  
Ken HIRASHITA ◽  
Shouichiro IIO ◽  
Toshihiko IKEDA
Keyword(s):  
Reynolds Number ◽  
Two Dimensional ◽  
Reynolds Number Dependence

Static Pressure Distributions Over 2D Mast/Sail Geometries

1989 ◽  
Vol 26 (04) ◽  
pp. 333-337
Author(s):  
Stuart Wilkinson
Keyword(s):  
Reynolds Number ◽  
Static Pressure ◽  
Incidence Angle ◽  
Flow Regimes ◽  
Two Dimensional ◽  
Test Program ◽  
Flow Parameters ◽  
Pressure Distributions

A variable-camber aerofoil with integral pressure tappings has been built to investigate the nature of the flows around two-dimensional, highly cambered, sail-like aerofoil sections with circular masts. Data have been obtained in the form of static pressure distributions over representative ranges of Reynolds number, camber ratio, incidence angle, mast diameter/chord ratio and mast angle. Two sail shapes—based on the NACA a = 0.8 and NACA 63 mean-line camber distributions—were involved in the test program. All flow regimes present have been identified and related to the salient model and flow parameters.

Collision statistics of inertial particles in two-dimensional homogeneous isotropic turbulence with an inverse cascade

2014 ◽  
Vol 745 ◽  
pp. 279-299 ◽  
Author(s):  
Ryo Onishi ◽  
J. C. Vassilicos
Keyword(s):  
Reynolds Number ◽  
Isotropic Turbulence ◽  
Particle System ◽  
Stochastic Simulations ◽  
Collision Kernel ◽  
Inertial Particles ◽  
Two Dimensional ◽  
Homogeneous Isotropic Turbulence ◽  
Local Flow ◽  
Reynolds Number Dependence

AbstractThis study investigates the collision statistics of inertial particles in inverse-cascading two-dimensional (2D) homogeneous isotropic turbulence by means of a direct numerical simulation (DNS). A collision kernel model for particles with small Stokes number ($\mathit{St}$) in 2D flows is proposed based on the model of Saffman & Turner (J. Fluid Mech., vol. 1, 1956, pp. 16–30) (ST56 model). The DNS results agree with this 2D version of the ST56 model for $\mathit{St}\lesssim 0.1$. It is then confirmed that our DNS results satisfy the 2D version of the spherical formulation of the collision kernel. The fact that the flatness factor stays around 3 in our 2D flow confirms that the present 2D turbulent flow is nearly intermittency-free. Collision statistics for $\mathit{St}= 0.1$, 0.4 and 0.6, i.e. for $\mathit{St}<1$, are obtained from the present 2D DNS and compared with those obtained from the three-dimensional (3D) DNS of Onishi et al. (J. Comput. Phys., vol. 242, 2013, pp. 809–827). We have observed that the 3D radial distribution function at contact ($g(R)$, the so-called clustering effect) decreases for $\mathit{St}= 0.4$ and 0.6 with increasing Reynolds number, while the 2D $g(R)$ does not show a significant dependence on Reynolds number. This observation supports the view that the Reynolds-number dependence of $g(R)$ observed in three dimensions is due to internal intermittency of the 3D turbulence. We have further investigated the local $\mathit{St}$, which is a function of the local flow strain rates, and proposed a plausible mechanism that can explain the Reynolds-number dependence of $g(R)$. Meanwhile, 2D stochastic simulations based on the Smoluchowski equations for $\mathit{St}\ll 1$ show that the collision growth can be predicted by the 2D ST56 model and that rare but strong events do not play a significant role in such a small-$\mathit{St}$ particle system. However, the probability density function of local $\mathit{St}$ at the sites of colliding particle pairs supports the view that powerful rare events can be important for particle growth even in the absence of internal intermittency when $\mathit{St}$ is not much smaller than unity.

Experimental Investigation of Vortex Structure in the Corrugated Channel

2013 ◽  
Author(s):  
Efe Unal ◽  
Hojin Ahn ◽  
Esra Sorguven ◽  
M. Zafer Gul
Keyword(s):  
Reynolds Number ◽  
Flow Field ◽  
Vortex Structure ◽  
Low Reynolds Number ◽  
Bulk Flow ◽  
Two Dimensional ◽  
Mean Flow ◽  
Cross Sectional ◽  
Corrugated Channel ◽  
Low Reynolds

Vortex structure in a corrugated channel has been studied with a PIV system measuring two-dimensional velocity fields at different locations and Reynolds numbers. The geometry of corrugation under investigation is the two-dimensional reflection of the circular cross-sectional stainless-steel flex pipe. The results show that turbulence caused by the corrugated wall affects the whole flow field in the channel even at low Reynolds number. The bulk flow field is rather chaotic in the entire channel. Moreover, the velocity vectors show significant interaction between the flow in the groove and the bulk flow. Vortex generated from the groove is very unstable and intermittent, and the vortex is not confined within the groove even at low Reynolds number. Vortex in the groove either migrates out of the groove without breaking up, or causes bursting flow from the groove to the bulk. In addition, intermittent and time-mean flow reversals are observed near the crest of the corrugation at low Reynolds number. Though the channel design is intended to be two-dimensional, flow structures in the groove appear to be three-dimensional at high Reynolds number while two-dimensional at low Reynolds number.

Experimental Study on the Helical Flow in a Concentric Annulus With Rotating Inner Cylinder

2005 ◽  
Vol 128 (1) ◽  
pp. 113-117 ◽  
Author(s):  
Nam-Sub Woo ◽  
Young-Ju Kim ◽  
Young-Kyu Hwang
Keyword(s):  
Experimental Study ◽  
Reynolds Number ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Flow Regime ◽  
Rotational Speed ◽  
Skin Friction Coefficient ◽  
Bulk Flow ◽  
Concentric Annulus ◽  
Flow Reynolds Number

This experimental study concerns the characteristics of vortex flow in a concentric annulus with a diameter ratio of 0.52, whose outer cylinder is stationary and inner one is rotating. Pressure losses and skin friction coefficients have been measured for fully developed laminar flows of water and of 0.4% aqueous solution of sodium carboxymethyl cellulose, respectively, when the inner cylinder rotates at the speed of 0-600rpm. The results of the present study show the effect of the bulk flow Reynolds number Re and Rossby number Ro on the skin friction coefficients. They also point to the existence of a flow instability mechanism. The effect of rotation on the skin friction coefficient depends significantly on the flow regime. In all flow regimes, the skin friction coefficient is increased by the inner cylinder rotation. The change in skin friction coefficient, which corresponds to a variation of the rotational speed, is large for the laminar flow regime, whereas it becomes smaller as Re increases for transitional flow regime and, then, it gradually approaches to zero for turbulent flow regime. Consequently, the critical bulk flow Reynolds number Rec decreases as the rotational speed increases. The rotation of the inner cylinder promotes the onset of transition due to the excitation of Taylor vortices.

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