scholarly journals A study on the derivation of a mean velocity formula from Chiu's velocity formula and bottom shear stress

2011 ◽  
Vol 8 (4) ◽  
pp. 6419-6442 ◽  
Author(s):  
T. H. Choo ◽  
I. J. Jeong ◽  
S. K. Chae ◽  
H. C. Yoon ◽  
H. S. Son
Keyword(s):  
Shear Stress ◽  
Flow Rate ◽  
Estimation Method ◽  
Maximum Velocity ◽  
Mean Velocity ◽  
River Bed ◽  
The Mean ◽  
Bed Slope ◽  
Discharge Estimation ◽  
Discrepancy Ratio

Abstract. This study proposed a new discharge estimation method using a mean velocity formula derived from Chiu's 2D velocity formula of probabilistic entropy concept and the river bed shear stress of channel. In particular, we could calculate the mean velocity, which is hardly measurable in flooding natural rivers, in consideration of several factors reflecting basic hydraulic characteristics such as river bed slope, wetted perimeter, width, and water level that are easily obtainable from rivers. In order to test the proposed method, we used highly reliable flow rate data measured in the field and published in SCI theses, estimated entropy M from the results of the mean velocity formula and, at the same time, calculated the maximum velocity. In particular, we obtained phi(M) expressing the overall equilibrium state of river through regression analysis between the maximum velocity and the mean velocity, and estimated the flow rate from the newly proposed mean velocity formula. The relation between estimated and measured discharge was analyzed through the discrepancy ratio, and the result showed that the estimate value was quite close to the measured data.

Resistance coefficients from velocity profiles in ice-covered shallow streams

1982 ◽  
Vol 9 (2) ◽  
pp. 236-247 ◽  
Author(s):  
Darryl J. Calkins ◽  
David S. Deck ◽  
Carl R. Martinson
Keyword(s):  
Shear Stress ◽  
Fluid Shear Stress ◽  
Maximum Velocity ◽  
Velocity Profiles ◽  
Roughness Coefficient ◽  
Mean Velocity ◽  
Cross Sectional ◽  
Frazil Ice ◽  
The Mean ◽  
Resistance Coefficients

Techniques for analyzing flow velocity profiles for streams where the flow depth is less than 1 m should be employed with caution. The two procedures for calculating flow resistance based on the logarithmic law, (1) mean and maximum velocity determinations and (2) intereept evaluation of log depth – velocity plots, should yield the same results for the various resistance coefficients and shear stress values, but they do not. The former procedure generally predicts higher values than the latter and is recommended for shallow streams where the field data were collected. For a 3.8 cm diameter flow sensor, the minimum distance from a boundary to the position of maximum velocity for a good velocity profile appears to be roughly 15–20 cm.The fluid shear stress values for ice covers on this shallow stream range from 0.1 to 17 Pa, depending upon ice type and duration of the cover. The shear stress under frazil ice slush showed a drop of about one tenth the initial value over a 2-week period at one location. The measured division of flow velocities about the maximum velocity associated with the bed and ice boundaries indicated that the mean velocities were not equal but often differed by as much as 25–30%, generally being higher in the section associated with ice, i.e., a rougher ice boundary.The most consistent method of determining the resistance coefficients was to define the cross-sectional shape of the river and ice cover accurately, subdivide the flow areas, use the mean velocity data calculated from the velocity profiles, and then compute the resistance values accordingly. The sensitivity of the roughness coefficient is discussed in terms of its impact on determining the total stage of an ice-covered river.

scholarly journals Effect of the Flame Dome Depth and Improvement of the Pressure Loss in the Dump Diffuser

1998 ◽  
Author(s):  
Shinji Honami ◽  
Wataru Tsuboi ◽  
Takaaki Shizawa
Keyword(s):  
Velocity Profile ◽  
Reynolds Stress ◽  
Flow Rate ◽  
Pressure Loss ◽  
Total Pressure ◽  
Flow Behavior ◽  
Sudden Expansion ◽  
Mean Velocity ◽  
The Mean ◽  
Stress Profiles

This paper presents the effect of flame dome depth on the total pressure performance and flow behavior in a sudden expansion region of the combustor diffuser without flow entering the dome head. The mean velocity and turbulent Reynolds stress profiles in the sudden expansion region were measured by a Laser Doppler Velocitmetry (LDV) system. The experiments show that total pressure loss is increased, when flame dome depth is increased. Installation of an inclined combuster wall in the sudden expansion region is suggested from the viewpoint of a control of the reattaching flow. The inclined combustor wall is found to be effective in improvement of the diffuser performance. Better characteristics of the flow rate distribution into the branched channels are obtained in the inclined wall configuration, even if the distorted velocity profile is provided at the diffuser inlet.

scholarly journals Global energy fluxes in turbulent channels with flow control

2018 ◽  
Vol 857 ◽  
pp. 345-373 ◽  
Author(s):  
Davide Gatti ◽  
Andrea Cimarelli ◽  
Yosuke Hasegawa ◽  
Bettina Frohnapfel ◽  
Maurizio Quadrio
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Energy Dissipation ◽  
Velocity Field ◽  
Flow Control ◽  
Reynolds Shear Stress ◽  
Power Input ◽  
Energy Fluxes ◽  
Mean Velocity ◽  
The Mean

This paper addresses the integral energy fluxes in natural and controlled turbulent channel flows, where active skin-friction drag reduction techniques allow a more efficient use of the available power. We study whether the increased efficiency shows any general trend in how energy is dissipated by the mean velocity field (mean dissipation) and by the fluctuating velocity field (turbulent dissipation). Direct numerical simulations (DNS) of different control strategies are performed at constant power input (CPI), so that at statistical equilibrium, each flow (either uncontrolled or controlled by different means) has the same power input, hence the same global energy flux and, by definition, the same total energy dissipation rate. The simulations reveal that changes in mean and turbulent energy dissipation rates can be of either sign in a successfully controlled flow. A quantitative description of these changes is made possible by a new decomposition of the total dissipation, stemming from an extended Reynolds decomposition, where the mean velocity is split into a laminar component and a deviation from it. Thanks to the analytical expressions of the laminar quantities, exact relationships are derived that link the achieved flow rate increase and all energy fluxes in the flow system with two wall-normal integrals of the Reynolds shear stress and the Reynolds number. The dependence of the energy fluxes on the Reynolds number is elucidated with a simple model in which the control-dependent changes of the Reynolds shear stress are accounted for via a modification of the mean velocity profile. The physical meaning of the energy fluxes stemming from the new decomposition unveils their inter-relations and connection to flow control, so that a clear target for flow control can be identified.

Fully-Developed Laminar Flow in Sinusoidal Grooves

2001 ◽  
Vol 123 (3) ◽  
pp. 656-661 ◽  
Author(s):  
Scott K. Thomas ◽  
Richard C. Lykins ◽  
Kirk L. Yerkes
Keyword(s):  
Contact Angle ◽  
Shear Stress ◽  
Volumetric Flow Rate ◽  
Numerical Data ◽  
Mean Velocity ◽  
Constant Property ◽  
Fully Developed Flow ◽  
Vapor Interface ◽  
The Mean ◽  
Poiseuille Number

The flow of a constant property fluid through a sinusoidal groove has been analyzed. A numerical solution of the conservation of mass and momentum equations for fully developed flow is presented. The mean velocity, volumetric flow rate, and Poiseuille number are presented as functions of the groove geometry, meniscus contact angle, and shear stress at the liquid-vapor interface. In addition, a semi-analytical solution for the normalized mean velocity in terms of the normalized shear stress at the meniscus is shown to agree with the numerical data quite well.

Establishment of the Wake Behind a Disk

1964 ◽  
Vol 86 (4) ◽  
pp. 869-880 ◽  
Author(s):  
Thomas Carmody
Keyword(s):  
Shear Stress ◽  
Ambient Pressure ◽  
Continuous Distribution ◽  
Flow Characteristics ◽  
Graphical Form ◽  
Stress Distributions ◽  
Mean Velocity ◽  
Pressure Distributions ◽  
Energy Relationships ◽  
The Mean

An air-tunnel study of the establishment of the wake behind a disk at a Reynolds number of approximately 7 × 104 was undertaken. On the basis of the measured data, such a wake is fully established, that is, similarity profiles of the flow characteristics are formed, within 15 diameters of the disk, and approximately 95 percent of the transfer of energy from the mean motion to the turbulence motion takes place within 3 diameters of the disk, in the region of the mean standing eddy. The measured mean ambient-pressure and mean total-pressure distributions, mean velocity distributions, turbulence-intensity and shear-stress distributions, and the mean streamline pattern are presented in graphical form, as are the quantitative balances of the integrated momentum and mean-energy relationships. A stream function consisting of a continuous distribution of doublets is introduced to extend the radial limit of understanding of the flow characteristics to a very large if not infinite radius. Considerable attention is given to the problem of obtaining and interpreting turbulence shear-stress data immediately downstream from the point of flow separation. The applicability of a local diffusion coefficient or virtual viscosity of the Boussinesq or Prandtl type for relating the turbulence shear stress to the radial gradient of mean axial velocity is discussed. The Bernoulli sum and the energy changes along individual streamlines investigated in an associated study are incorporated herein to obtain a quantitative estimate of the local errors involved in the turbulence-shear-stress measurements.

Turbulent Vorticity Diffusion in the Stronger Wall Jet Managed by a Flat Plate Wing in the Outer Layer

2015 ◽  
Author(s):  
Takuma Katayama ◽  
Shinsuke Mochizuki
Keyword(s):  
Shear Stress ◽  
Flat Plate ◽  
Outer Layer ◽  
Large Scale ◽  
Reynolds Shear Stress ◽  
Three Dimensional ◽  
Quantitative Relationship ◽  
Wall Jet ◽  
Mean Velocity ◽  
The Mean

The present experiment focuses on the vorticity diffusion in a stronger wall jet managed by a three-dimensional flat plate wing in the outer layer. Measurement of the fluctuating velocities and vorticity correlation has been carried out with 4-wire vorticity probe. The turbulent vorticity diffusion due to the large scale eddies in the outer layer is quantitatively examined by using the 4-wire vorticity probe. Quantitative relationship between vortex structure and Reynolds shear stress is revealed by means of directly measured experimental evidence which explains vorticity diffusion process and influence of the manipulating wing. It is expected that the three-dimensional outer layer manipulator contributes to keep convex profile of the mean velocity, namely, suppression of the turbulent diffusion and entrainment.

Combined effects of flow curvature and rotation on uniformly sheared turbulence

2009 ◽  
Vol 628 ◽  
pp. 371-394 ◽  
Author(s):  
D. C. ROACH ◽  
A. G. L. HOLLOWAY
Keyword(s):  
Shear Stress ◽  
Wind Tunnel ◽  
Model Development ◽  
Three Dimensional ◽  
Simple Shear Flow ◽  
Test Case ◽  
Mean Velocity ◽  
Tunnel Section ◽  
Flow Curvature ◽  
The Mean

This paper describes an experiment in which a uniformly sheared turbulence was subjected to simultaneous streamwise flow curvature and rotation about the streamwise axis. The distortion of the turbulence is complex but well defined and may serve as a test case for turbulence model development. The uniformly sheared turbulence was developed in a straight wind tunnel and then passed into a curved tunnel section. At the start of the curved section the plane of the mean shear was normal to the plane of curvature so as to create a three-dimensional or ‘out of plane’ curvature configuration. On entering the curved tunnel, the flow developed a streamwise mean vorticity that rotated the mean shear about the tunnel centreline through approximately 70°, so that the shear was nearly in the plane of curvature and oriented so as to have a stabilizing effect on the turbulence. Hot wire measurements of the mean velocity, mean vorticity, mean rate of strain and Reynolds stress anisotropy development along the wind tunnel centreline are reported. The observed effect of the mean shear rotation on the turbulence was to diminish the shear stress in the plane normal to the plane of curvature while generating non-zero values of the shear stress in the plane of curvature. A rotating frame was identified for which the measured mean velocity field took the form of a simple shear flow. The turbulence anisotropy was transformed to this frame to estimate the effects of frame rotation on the structure of sheared turbulence.

Fractal Orifices for Flowmetering

2012 ◽  
Author(s):  
Franck C. G. A. Nicolleau ◽  
Stephen B. M. Beck ◽  
Andrzej F. Nowakowski
Keyword(s):  
Wind Tunnel ◽  
Flow Rate ◽  
Velocity Profiles ◽  
Symmetric Design ◽  
Flow Properties ◽  
Mean Velocity ◽  
Fractal Pattern ◽  
The Mean

In this article we study the return to axi-symmetry for a flow generated after fractal plates in a circular wind tunnel. We consider two sets of plates: one orifice-like and one perforated-like. The mean velocity profiles are presented at different distances from the plate and we study the convergence of a flow rate based on these profiles. The return to axi-symmetry depends on how far was the original plate from an axi-symmetric design. It also depends on the level of iteration of the fractal pattern. In line with results for other flow properties [1, 2] It seems that there is not much to be gained by manufacturing fractal plates with more than three iteration levels.

scholarly journals High-resolution velocity measurement in the inner part of turbulent boundary layers over super-hydrophobic surfaces

2016 ◽  
Vol 801 ◽  
pp. 670-703 ◽  
Author(s):  
Hangjian Ling ◽  
Siddarth Srinivasan ◽  
Kevin Golovin ◽  
Gareth H. McKinley ◽  
Anish Tuteja ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Velocity Profile ◽  
Drag Reduction ◽  
Slip Velocity ◽  
Reynolds Shear Stress ◽  
Turbulent Boundary Layers ◽  
Mean Velocity ◽  
Roughness Elements ◽  
The Mean

Digital holographic microscopy is used for characterizing the profiles of mean velocity, viscous and Reynolds shear stresses, as well as turbulence level in the inner part of turbulent boundary layers over several super-hydrophobic surfaces (SHSs) with varying roughness/texture characteristics. The friction Reynolds numbers vary from 693 to 4496, and the normalized root mean square values of roughness $(k_{rms}^{+})$ vary from 0.43 to 3.28. The wall shear stress is estimated from the sum of the viscous and Reynolds shear stress at the top of roughness elements and the slip velocity is obtained from the mean profile at the same elevation. For flow over SHSs with $k_{rms}^{+}<1$, drag reduction and an upward shift of the mean velocity profile occur, along with a mild increase in turbulence in the inner part of the boundary layer. As the roughness increases above $k_{rms}^{+}\sim 1$, the flow over the SHSs transitions from drag reduction, where the viscous stress dominates, to drag increase where the Reynolds shear stress becomes the primary contributor. For the present maximum value of $k_{rms}^{+}=3.28$, the inner region exhibits the characteristics of a rough wall boundary layer, including elevated wall friction and turbulence as well as a downward shift in the mean velocity profile. Increasing the pressure in the test facility to a level that compresses the air layer on the SHSs and exposes the protruding roughness elements reduces the extent of drag reduction. Aligning the roughness elements in the streamwise direction increases the drag reduction. For SHSs where the roughness effect is not dominant ($k_{rms}^{+}<1$), the present measurements confirm previous theoretical predictions of the relationships between drag reduction and slip velocity, allowing for both spanwise and streamwise slip contributions.

Experimental Study on Mean Velocity Profiles Under Wave-Current Interactions

2008 ◽  
Author(s):  
Jinhai Zheng ◽  
Tongfei Li ◽  
Yixin Yan ◽  
Jinchun Hu
Keyword(s):  
River Estuary ◽  
Maximum Velocity ◽  
Velocity Profiles ◽  
Yangtze River Estuary ◽  
Current Profile ◽  
Linear Superposition ◽  
Mean Velocity ◽  
The Mean ◽  
Logarithmic Law ◽  
A Current

A series of experiments are carried out in a laboratory flume for combined wave-current flows, to investigate the characteristics of vertical structure of current profile in a wave-current co-existing water areas. Changes induced in the mean velocity profiles are considered for a range of wave heights, wave periods, water depths and flow velocities which are based on those typical data in the Yangtze River Estuary, China. Preliminary tests are conducted on the unidirectional current and on the wave alone. These show that the current mean velocity profiles agree well with the logarithmic law, and that the waves are approximated closely by the Stokes’ second-order theory. For the combined wave and current tests, the mean velocity profiles generally differ from those suggested by a linear superposition of wave and current velocities. In the case of waves following a current, the velocity distributions exhibit a relatively greater velocity near the bed and a smaller velocity above a certain depth relative to the logarithmic law, and the maximum velocity is observed at a lower location. In the case of wave opposing a current, the velocity distributions depart from the logarithmic law with a relatively smaller velocity near the bed and a greater velocity above a certain depth. Experimental data can be used to validate the theoretical or mathematical models associated with the combined wave-current motions.

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