Power Law Turbulent Velocity Profile in Transitional Rough Pipes

2005 ◽  
Vol 128 (3) ◽  
pp. 548-558 ◽  
Author(s):  
Noor Afzal ◽  
Abu Seena ◽  
Afzal Bushra
Keyword(s):  
Reynolds Number ◽  
Velocity Profile ◽  
Power Law ◽  
Roughness Parameter ◽  
Rough Wall ◽  
Wall Roughness ◽  
Velocity Shift ◽  
Normal Wall ◽  
Good Support ◽  
Grain Roughness

Alternate power law velocity profile u+=Aζα in transitional rough pipe fully turbulent flow, has been proposed, in terms of new appropriate inner rough wall variables (ζ=Z+∕ϕ, uϕ=u∕ϕ), and new parameters Rϕ=Rτ∕ϕ termed as the roughness friction Reynolds number, Reϕ=Re∕ϕ termed as the roughness Reynolds number and ϕ termed as roughness scale (along with normal wall coordinate Z=y+ϵr where ϵr is the shift of the origin of boundary layer due to the rough wall, Z+=Zuτ∕ν and u+=u∕uτ). The envelope of the power law shows that the power law constants α and A depend on the parameter Rϕ (i.e., α=α(Rϕ) and A=A(Rϕ)) but explicitly independent of the wall roughness parameter h∕δ (roughness height h in pipe of radius δ). The roughness scale ϕ has been related to the roughness function ΔU+ of Clauser representing the velocity shift caused by wall roughness. The present results of the velocity profile, just slightly above the wall roughness level h, remain valid for all types of wall roughness. The data of Nikuradse for sand-grain roughness, in transitional and fully rough pipes, has been considered, which provides good support to the predictions of an alternate power law velocity profile, based on single parameter Rϕ, the roughness friction Reynolds number.

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.

scholarly journals Turbulence Intensity Scaling: A Fugue

Fluids ◽  
2019 ◽  
Vol 4 (4) ◽  
pp. 180 ◽  
Author(s):  
Nils T. Basse
Keyword(s):  
Reynolds Number ◽  
Friction Factor ◽  
Turbulence Intensity ◽  
Pipe Flow ◽  
Rough Wall ◽  
Flow Measurements ◽  
Flow Turbulence ◽  
Intensity Scaling ◽  
Grain Roughness ◽  
Made In

We study streamwise turbulence intensity definitions using smooth- and rough-wall pipe flow measurements made in the Princeton Superpipe. Scaling of turbulence intensity with the bulk (and friction) Reynolds number is provided for the definitions. The turbulence intensity scales with the friction factor for both smooth- and rough-wall pipe flow. Turbulence intensity definitions providing the best description of the measurements are identified. A procedure to calculate the turbulence intensity based on the bulk Reynolds number (and the sand-grain roughness for rough-wall pipe flow) is outlined.

Wall Roughness Effects on Stagnation-Point Heat Transfer Beneath an Impinging Liquid Jet

1994 ◽  
Vol 116 (1) ◽  
pp. 81-87 ◽  
Author(s):  
L. A. Gabour ◽  
J. H. Lienhard
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Stagnation Point ◽  
Rough Surfaces ◽  
Roughness Parameter ◽  
Jet Impingement ◽  
Liquid Jet ◽  
Wall Roughness ◽  
Smooth Wall ◽  
Number Range

Jet impingement cooling applications often involve rough surfaces, yet few studies have examined the role of wall roughness. Surface protrusions can pierce the thermal sublayer in the stagnation region and increase the heat transfer. In this paper, the effect of surface roughness on the stagnation-point heat transfer of an impinging unsubmerged liquid jet is investigated. Experiments were performed in which a fully developed turbulent water jet struck a uniformly heated rough surface. Heat transfer measurements were made for jets of diameters 4.4–9.0 mm over a Reynolds number range of 20,000–84,000. The Prandtl number was held nearly constant at 8.2–9.1. Results are presented for nine well-characterized rough surfaces with root-mean-square average roughness heights ranging from 4.7 to 28.2 μm. Measured values of the local Nusselt number for the rough plates are compared with those for a smooth wall, and increases of as much as 50 percent are observed. Heat transfer in the stagnation zone is scaled with Reynolds number and a roughness parameter. For a given roughness height and jet diameter, the minimum Reynolds number required to increase heat transfer above that of a smooth plate is established. A correlation for smooth wall heat transfer is also given.

Steady Penetration of a Rigid Cone With a Rough Wall Into a Power-Law Viscous Solid

1991 ◽  
Vol 58 (4) ◽  
pp. 872-880 ◽  
Author(s):  
N. A. Fleck ◽  
D. Durban
Keyword(s):  
Boundary Layer ◽  
Strain Rate ◽  
Power Law ◽  
Eigenvalue Analysis ◽  
Rough Wall ◽  
Wall Friction ◽  
Stress Fields ◽  
Wall Roughness ◽  
Perfectly Plastic ◽  
Special Cases

Singular strain rate and stress fields are examined at the tip of a rigid conical indentor penetrating an incompressible viscous solid. Attention is focused on friction effects induced by wall roughness. The problem is formulated within the usual framework of eigenvalue analysis of locally singular fields. Some special cases are investigated further with emphasis on a boundary layer expansion for the rigid/perfectly plastic solid sliding along the perfectly rough wall. It has been found that the level of singularity increases as the cone becomes sharper and the wall friction decreases. Numerical results, presented for a variety of cases, suggest a boundary layer build up for sharp cones with rough walls.

scholarly journals Velocity Profile Representation for Fully Developed Turbulent Flows in Pipes: A Modified Power Law

Fluids ◽  
2021 ◽  
Vol 6 (10) ◽  
pp. 369
Author(s):  
Amgad Salama
Keyword(s):  
Reynolds Number ◽  
Velocity Profile ◽  
Turbulent Flows ◽  
Power Law ◽  
Flow Region ◽  
Design Parameters ◽  
Wall Area ◽  
A Value ◽  
Flow Velocity Profile ◽  
Two Parameters

In the design practices of many engineering applications, gross information about the flow field may suffice to provide magnitudes of the parameters that are essential to complete the design with reasonable accuracy. If such design parameters can be estimated following simpler steps, it may be possible to abandon the need to conduct expensive numerical and/or experimental works to produce them. In this work, we are interested in providing a generalized power law that depicts the velocity profile for fully developed turbulent flows. This law incorporates two fitting parameters m and n that represent the exponents of (1) a nondimensional length scale and (2) an overall exponent, respectively. These two parameters may be determined by fitting the experimental and/or computational data. In this work, fitting benchmark experimental and computational fluid dynamics (CFD) data found in the literature reveals that the parameter m changes over a relatively smaller range (between 1 and 2), while the parameter n changes over a wider range (between 1 and 12 for the range of Reynolds number considered). These two parameters (m and n) are, generally, not universal, and they depend on the Reynolds number (Re). A correlation was also developed to correlate n and Re in the turbulent flow region. In order to preserve the continuity of the derivative of the velocity profile at the centerline, a value of m equals 2 over the whole range of Re is recommended. Apart from the near wall area, the new law fits the velocity profile reasonably well. This generalized law abides to a number of favorable stipulations for the velocity profile, namely the continuity of derivatives and reduction to the laminar flow velocity profile for lower values of Re.

Improving Pin-Fin Heat Transfer Predictions Using Artificial Neural Networks

2013 ◽  
Author(s):  
Jason K. Ostanek
Keyword(s):  
Neural Network ◽  
Heat Transfer ◽  
Neural Networks ◽  
Reynolds Number ◽  
Artificial Neural Networks ◽  
Power Law ◽  
Transfer Data ◽  
Pin Fin ◽  
The Neural Network ◽  
Artificial Neural

In much of the public literature on pin-fin heat transfer, Nusselt number is presented as a function of Reynolds number using a power-law correlation. Power-law correlations typically have an accuracy of 20% while the experimental uncertainty of such measurements is typically between 5% and 10%. Additionally, the use of power-law correlations may require many sets of empirical constants to fully characterize heat transfer for different geometrical arrangements. In the present work, artificial neural networks were used to predict heat transfer as a function of streamwise spacing, spanwise spacing, pin-fin height, Reynolds number, and row position. When predicting experimental heat transfer data, the neural network was able to predict 73% of array-averaged heat transfer data to within 10% accuracy while published power-law correlations predicted 48% of the data to within 10% accuracy. Similarly, the neural network predicted 81% of row-averaged data to within 10% accuracy while 52% of the data was predicted to within 10% accuracy using power-law correlations. The present work shows that first-order heat transfer predictions may be simplified by using a single neural network model rather than combining or interpolating between power-law correlations. Furthermore, the neural network may be expanded to include additional pin-fin features of interest such as fillets, duct rotation, pin shape, pin inclination angle, and more making neural networks expandable and adaptable models for predicting pin-fin heat transfer.

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