Closure to “Discussion of ‘Reynolds Number Dependence of Skin Friction and Other Bulk Flow Variables in Two-Dimensional Rectangular Duct Flow’” (1978, ASME J. Fluids Eng., 100, p. 377)

1978 ◽  
Vol 100 (3) ◽  
pp. 377-377 ◽  
Author(s):  
R. B. Dean
Keyword(s):  
Reynolds Number ◽  
Skin Friction ◽  
Bulk Flow ◽  
Two Dimensional ◽  
Duct Flow ◽  
Rectangular Duct ◽  
Flow Variables ◽  
Reynolds Number Dependence

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).

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

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.

scholarly journals Localized turbulence structures in transitional rectangular-duct flow

2015 ◽  
Vol 782 ◽  
pp. 368-379 ◽  
Author(s):  
Keisuke Takeishi ◽  
Genta Kawahara ◽  
Hiroki Wakabayashi ◽  
Markus Uhlmann ◽  
Alfredo Pinelli
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Plane Channel ◽  
Transitional Flow ◽  
Spanwise Direction ◽  
Duct Flow ◽  
Rectangular Duct ◽  
Turbulent Spots ◽  
Number Range ◽  
Turbulence Structures

Direct numerical simulations of transitional flow in a rectangular duct of cross-sectional aspect ratio $A\equiv s/h=1$–9 ($s$ and $h$ being the duct half-span and half-height, respectively) have been performed in the Reynolds number range $\mathit{Re}\equiv u_{b}h/{\it\nu}=650$–1500 ($u_{b}$ and ${\it\nu}$ being the bulk velocity and the kinematic viscosity, respectively) in order to investigate the dependence on the aspect ratio of spatially localized turbulence structures. It was observed that the lowest Reynolds number $\mathit{Re}_{T}$, estimated in a specific way, for localized (transiently sustaining) turbulence decreases monotonically from $\mathit{Re}_{T}=730$ for $A=1$ (square duct) with increasing aspect ratio, and for $A=5$ it nearly attains a minimal value $\mathit{Re}_{T}\approx 670$ that is consistent with the onset Reynolds number of turbulent spots in a plane channel ($A=\infty$). Turbulent states consist of localized structures that undergo a fundamental change around $A=4$. At $\mathit{Re}=\mathit{Re}_{T}$ turbulence for $A=1$–$3$ is streamwise-localized similar to turbulent puffs in pipe flow, while for $A=5$–9 turbulence at $\mathit{Re}=\mathit{Re}_{T}$ is also localized in the spanwise direction, similar to turbulent spots in plane channel flow. This structural change in turbulent states at $\mathit{Re}=\mathit{Re}_{T}$ is attributed to the exclusion of turbulence from the vicinity of the duct sidewalls in the case of a wide duct with $A\gtrsim 4$: here the friction length on the sidewalls is so long that the size (around 100 times the friction length) of a self-sustaining minimal flow unit of streamwise vortices and streaks is larger than the duct height and, therefore, it cannot be accommodated.

scholarly journals Lattice gas automaton modelling of a vortex flow meter: Strouhal–Reynolds number dependence

2017 ◽  
Vol 56 (4) ◽  
pp. 191-199
Author(s):  
Vaidas Juknevičius ◽  
Jogundas Armaitis
Keyword(s):  
Reynolds Number ◽  
Strouhal Number ◽  
Vortex Shedding ◽  
Vortex Flow ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Dimensional Structure ◽  
Two Dimensional ◽  
Flow Meter ◽  
Reynolds Number Dependence

Motivated by recent experimental and computational results concerning a three-dimensional structure of vortices behind a vortex shedding flow meter [M. Reik et al., Forsch. Ingenieurwes. 74, 77 (2010)], we study the Strouhal–Reynolds number dependence in the vortex street in two dimensions behind a trapezoid-shaped object by employing two types of Frisch–Hasslacher–Pomeau (FHP) models. Our geometry is intended to reproduce the operation of a vortex shedding flow meter in a two-dimensional setting, thus preventing the formation of a three-dimensional vortex structure. In particular, we check if the anomalous Reynolds–Strouhal number dependence reported for three dimensions can also be found in our two-dimensional simulation. As we find that the Strouhal number is nearly independent of the Reynolds number in this particular setup, our results provide support for the hypothesis that three-dimensional flow structures are responsible for that dependence, thus hinting at the importance of the pipe diameter to the accurate operation of industrial vortex flow meters.

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