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.

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.

An Anisotropic Subgrid Model for Large Eddy Simulation of Wall Bounded Turbulent Flows

2007 ◽  
Author(s):  
Sachin S. Badarayani ◽  
Kyle D. Squires
Keyword(s):  
Reynolds Number ◽  
Large Eddy Simulation ◽  
Velocity Profile ◽  
Turbulent Flows ◽  
Model Parameters ◽  
Wall Region ◽  
Outer Flow ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Near Wall

Large Eddy Simulation (LES) of high-Reynolds-number wall-bounded turbulent flows is prohibitively expensive if the energy-containing eddies in the near-wall region are resolved. This motivates the use of wall-layer models in which an approximate solution of the near wall dynamics is bridged to an LES of the outer flow. The main interest of the present work are wall-modeling strategies based on Detached Eddy Simulation (DES). In these approaches, the near-wall solution is closed using a Reynolds-averaged Navier Stokes model with a subgrid closure applied to the outer flow. As is well known, the original DES formulation applied directly as a wall model results in a shift in the velocity profile, corresponding to an under-estimation of the skin friction. A new formulation is proposed in this contribution in which the wall-parallel components of the modeled stress are reduced in order to lower the influence of the model and increase the resolved stress. The effectiveness of the new model is evaluated via comparison against DES predictions using the original and recently-proposed versions of the method. The effect of grid resolution and model parameters are also assessed using computations of turbulent channel flow at a Reynolds number based on friction velocity and channel halfwidth of 5000. The predictions show that the anisotropic form of the model stress yields an improved prediction of the mean velocity profile in better agreement with the logarithmic law and with larger resolved stress in the near-wall region.

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.

scholarly journals INVESTIGATION OF A HYDRODYNAMIC ENTRANCE REGION FOR A POWER-LAW FLUID FLOW IN A ROUND PIPE

2020 ◽  
pp. 78-88
Author(s):  
Evgeniy I. BORZENKO ◽  
◽  
Dmitriy N. GARBUZOV ◽  
Keyword(s):  
Reynolds Number ◽  
Fluid Flow ◽  
Power Law ◽  
Simple Procedure ◽  
Mathematical Formulation ◽  
Flow Region ◽  
Inlet Section ◽  
Development Length ◽  
Flow Zone ◽  
Power Law Index

The paper presents a study of the Ostwald – de Waele fluid flow in a round pipe with a uniform velocity profile specified at the inlet section. Mathematical formulation of the problem is presented using dimensionless variables. A numerical algorithm is developed on the basis of the finite volume method and SIMPLE procedure. Parametric studies of the flow are carried out for the Reynolds number varying from 0.1 to 80 and the power-law index varying from 0.2 to 1.5. It is shown that the flow can be distinguished into a developing flow zone in the inlet boundary vicinity and a fully developed flow zone in the rest part of the flow region. Dependency diagrams are plotted for the development length depending on the power-law index and Reynolds number. The first diagram is found to be non-monotonic. The development length is shown to be almost linearly dependent on the Reynolds number in the range from 1 to 80. In the region of low Reynolds numbers, the length remains almost uniform. The agreement of the obtained numerical results with data from other studies is shown.

Investigation of the influence of the flow structure on the accuracy of flow measurement before a hydrometric structure in an open channel

2020 ◽  
pp. 41-44
Author(s):  
Anatoly Kusher
Keyword(s):  
Velocity Profile ◽  
Flow Velocity ◽  
Water Flow ◽  
Flow Measurement ◽  
Water Discharge ◽  
Critical Depth ◽  
Flow Measurements ◽  
Study Results ◽  
Flow Velocity Profile ◽  
Upstream Flow

The reliability of water flow measurement in irrigational canals depends on the measurement method and design features of the flow-measuring structure and the upstream flow velocity profile. The flow velocity profile is a function of the channel geometry and wall roughness. The article presents the study results of the influence of the upstream flow velocity profile on the discharge measurement accuracy. For this, the physical and numerical modeling of two structures was carried out: a critical depth flume and a hydrometric overfall in a rectangular channel. According to the data of numerical simulation of the critical depth flume with a uniform and parabolic (1/7) velocity profile in the upstream channel, the values of water discharge differ very little from the experimental values in the laboratory model with a similar geometry (δ < 2 %). In contrast to the critical depth flume, a change in the velocity profile only due to an increase in the height of the bottom roughness by 3 mm causes a decrease of the overfall discharge coefficient by 4…5 %. According to the results of the numerical and physical modeling, it was found that an increase of backwater by hydrometric structure reduces the influence of the upstream flow velocity profile and increases the reliability of water flow measurements.

Simulating flow separation from continuous surfaces: routes to overcoming the Reynolds number barrier

2009 ◽  
Vol 367 (1899) ◽  
pp. 2885-2903 ◽  
Author(s):  
Michael Leschziner ◽  
Ning Li ◽  
Fabrizio Tessicini
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
Major Elements ◽  
Wall Layer ◽  
Navier Stokes ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Rans Models ◽  
High Reynolds ◽  
Near Wall

This paper provides a discussion of several aspects of the construction of approaches that combine statistical (Reynolds-averaged Navier–Stokes, RANS) models with large eddy simulation (LES), with the objective of making LES an economically viable method for predicting complex, high Reynolds number turbulent flows. The first part provides a review of alternative approaches, highlighting their rationale and major elements. Next, two particular methods are introduced in greater detail: one based on coupling near-wall RANS models to the outer LES domain on a single contiguous mesh, and the other involving the application of the RANS and LES procedures on separate zones, the former confined to a thin near-wall layer. Examples for their performance are included for channel flow and, in the case of the zonal strategy, for three separated flows. Finally, a discussion of prospects is given, as viewed from the writer's perspective.

The asymptotic stage of longitudinal turbulent dispersion within a tube

1977 ◽  
Vol 80 (2) ◽  
pp. 293-303 ◽  
Author(s):  
R. Dewey ◽  
Paul J. Sullivan
Keyword(s):  
Turbulent Flows ◽  
Friction Velocity ◽  
Turbulent Dispersion ◽  
Time Interval ◽  
Longitudinal Diffusion ◽  
A Value ◽  
Discharge Velocity ◽  
Concentration Curves ◽  
Temporal Growth Rate ◽  
Short Times

This paper describes an experimental investigation of the conditions for which the asymptotic description of longitudinal dispersion given by Taylor (1954) would apply. At non-dimensional times following the release of a dye pulse that are significantly larger than those previously investigated, the integrated concentration curves were observed to be skewed. At relatively short times from release the concentration curves appear to be well described by the models presented by Sullivan (1971) and by Chatwin (1973). Some features of the asymptotic behaviour, namely the translation of the modal value of the integrated concentration curve at the discharge velocity and the constant temporal growth rate of the variance, are observed at the longest times following release. On the basis of these observations it is estimated that a non-dimensional time interval oftu*/d=O(105/R*), whereR*=u*d/v,u*is the friction velocity,vthe kinematic viscosity anddthe tube diameter, is required for the Taylor result to become applicable. Thus application of Taylor's theory is significantly restricted in turbulent flows, especially those with irregular boundaries and those that are not stationary. There the variations in the flow must be small with respect to an equivalent ‘development time’ if a value of the ‘local’ longitudinal diffusion coefficient is to have meaning.

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