Logarithmic Velocity Profile for Turbulent Flow in Straight Rough Pipe and Evaluation of Karman Constant with Boundary Layer Reynolds Number- A Complete Solution

2016 ◽  
Vol 7 (2) ◽  
pp. 157-162
Author(s):  
Tapan Kumar Ghosh
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Velocity Profile ◽  
Turbulent Flow ◽  
Complete Solution ◽  
Logarithmic Velocity Profile

scholarly journals Featuresof velocity distribution in a turbulent flow

Vestnik MGSU ◽  
2015 ◽  
pp. 103-109
Author(s):  
Valeriy Stepanovich Borovkov ◽  
Valeriy Valentinovich Volshanik ◽  
Irina Aleksandrovna Rylova
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Velocity Profile ◽  
Turbulent Flow ◽  
Velocity Distribution ◽  
Drag Coefficient ◽  
Viscous Flow ◽  
Measured Velocity ◽  
Displacement Thickness ◽  
Logarithmic Velocity Profile

In this article the questions of kinematic structure of steady turbulent flow near a solid boundary are considered. It has been established that due to friction the value of the local Reynolds number decreases and always becomes smaller than the critical value of the Reynolds number, which leads to formation of viscous flow near a wall. Velocity profiles for the area of viscous flow with constant and variable shear stress are obtained. The experimental investigations of different authors showed that in this area the flow is of unsteady character, where viscous flow occurs intermittently with turbulent flow. With increasing distance from the wall the flow becomes fully turbulent. In the area where generation and dissipation of turbulence are very intensive, there is a developed turbulent flow with increasing distance from the wall. Dissipation of turbulence is an action of viscous force. The logarithmic velocity profile was obtained by L. Prandtl disregarding the viscous component and the linear variation of the shear stress in the depth flow. The profile parameters C and k were determined from Nikuradze’s experiments. The detailed investigations of Nikuradze’s experiments established the part of the flow where the logarithmic velocity profile is correctly confirmed.This part of the flow was called “Prandtl layer”. The measured velocity distribution above this layer deviates in the direction of greater values. Processing of experimental data revealed that the thickness of the “Prandtl layer”, normalized to the radius of a pipe, depend on a drag coefficient. The formula for determining the thickness of the “Prandtl layer” with the known value of the drag coefficient is obtained. It is shown that the thickness of “Prandtl layer” almost coincides with the boundary layer displacement thickness formed on the wall of the pipe.

A Second Turbulent Regime When a Fully Developed Axial Turbulent Flow Enters a Rotating Pipe

2016 ◽  
Author(s):  
Ferdinand-J. Cloos ◽  
Anna-L. Zimmermann ◽  
Peter F. Pelz
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Velocity Profile ◽  
Turbulent Flow ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Circumferential Velocity ◽  
Turbulent Regime ◽  
Self Similarity ◽  
Flow Number

When a fluid enters a rotating circular pipe a swirl boundary layer with thickness of δ̃s appears at the wall and interacts with the axial momentum boundary layer with thickness of δ̃. We investigate a turbulent flow applying Laser-Doppler-Anemometry to measure the circumferential velocity profile at the inlet of the rotating pipe. The measured swirl boundary layer thickness follows a power law taking Reynolds number and flow number into account. A combination of high Reynolds number, high flow number and axial position causes a transition of the swirl boundary layer development in the turbulent regime. At this combination, the swirl boundary layer thickness as well as the turbulence intensity increase and the latter yields a self-similarity. The circumferential velocity profile changes to a new presented self-similarity as well. We define the transition inlet length, where the transition appears and a stability map for the two regimes is given for the case of a fully developed axial turbulent flow enters the rotating pipe.

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.

Turbulence in transient channel flow

2013 ◽  
Vol 715 ◽  
pp. 60-102 ◽  
Author(s):  
S. He ◽  
M. Seddighi
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Turbulent Flow ◽  
Channel Flow ◽  
Flow Rate ◽  
Bypass Transition ◽  
Turbulent Structures ◽  
Turbulent Spots ◽  
Transient Channel ◽  
Transitional Phase

AbstractDirect numerical simulations (DNS) are performed of a transient channel flow following a rapid increase of flow rate from an initially turbulent flow. It is shown that a low-Reynolds-number turbulent flow can undergo a process of transition that resembles the laminar–turbulent transition. In response to the rapid increase of flow rate, the flow does not progressively evolve from the initial turbulent structure to a new one, but undergoes a process involving three distinct phases (pre-transition, transition and fully turbulent) that are equivalent to the three regions of the boundary layer bypass transition, namely, the buffeted laminar flow, the intermittent flow and the fully turbulent flow regions. This transient channel flow represents an alternative bypass transition scenario to the free-stream-turbulence (FST) induced transition, whereby the initial flow serving as the disturbance is a low-Reynolds-number turbulent wall shear flow with pre-existing streaky structures. The flow nevertheless undergoes a ‘receptivity’ process during which the initial structures are modulated by a time-developing boundary layer, forming streaks of apparently specific favourable spacing (of about double the new boundary layer thickness) which are elongated streamwise during the pre-transitional period. The structures are stable and the flow is laminar-like initially; but later in the transitional phase, localized turbulent spots are generated which grow spatially, merge with each other and eventually occupy the entire wall surfaces when the flow becomes fully turbulent. It appears that the presence of the initial turbulent structures does not promote early transition when compared with boundary layer transition of similar FST intensity. New turbulent structures first appear at high wavenumbers extending into a lower-wavenumber spectrum later as turbulent spots grow and join together. In line with the transient energy growth theory, the maximum turbulent kinetic energy in the pre-transitional phase grows linearly but only in terms of ${u}^{\ensuremath{\prime} } $, whilst ${v}^{\ensuremath{\prime} } $ and ${w}^{\ensuremath{\prime} } $ remain essentially unchanged. The energy production and dissipation rates are very low at this stage despite the high level of ${u}^{\ensuremath{\prime} } $. The pressure–strain term remains unchanged at that time, but increases rapidly later during transition along with the generation of turbulent spots, hence providing an unambiguous measure for the onset of transition.

scholarly journals On the identification of well-behaved turbulent boundary layers

2017 ◽  
Vol 822 ◽  
pp. 109-138 ◽  
Author(s):  
C. Sanmiguel Vila ◽  
R. Vinuesa ◽  
S. Discetti ◽  
A. Ianiro ◽  
P. Schlatter ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Velocity Profile ◽  
Skin Friction ◽  
Boundary Layers ◽  
Shape Factor ◽  
Outer Region ◽  
The Other ◽  
Diagnostic Plot ◽  
Other Hand

This paper introduces a new method based on the diagnostic plot (Alfredsson et al., Phys. Fluids, vol. 23, 2011, 041702) to assess the convergence towards a well-behaved zero-pressure-gradient (ZPG) turbulent boundary layer (TBL). The most popular and well-understood methods to assess the convergence towards a well-behaved state rely on empirical skin-friction curves (requiring accurate skin-friction measurements), shape-factor curves (requiring full velocity profile measurements with an accurate wall position determination) or wake-parameter curves (requiring both of the previous quantities). On the other hand, the proposed diagnostic-plot method only needs measurements of mean and fluctuating velocities in the outer region of the boundary layer at arbitrary wall-normal positions. To test the method, six tripping configurations, including optimal set-ups as well as both under- and overtripped cases, are used to quantify the convergence of ZPG TBLs towards well-behaved conditions in the Reynolds-number range covered by recent high-fidelity direct numerical simulation data up to a Reynolds number based on the momentum thickness and free-stream velocity $Re_{\unicode[STIX]{x1D703}}$ of approximately 4000 (corresponding to 2.5 m from the leading edge) in a wind-tunnel experiment. Additionally, recent high-Reynolds-number data sets have been employed to validate the method. The results show that weak tripping configurations lead to deviations in the mean flow and the velocity fluctuations within the logarithmic region with respect to optimally tripped boundary layers. On the other hand, a strong trip leads to a more energized outer region, manifested in the emergence of an outer peak in the velocity-fluctuation profile and in a more prominent wake region. While established criteria based on skin-friction and shape-factor correlations yield generally equivalent results with the diagnostic-plot method in terms of convergence towards a well-behaved state, the proposed method has the advantage of being a practical surrogate that is a more efficient tool when designing the set-up for TBL experiments, since it diagnoses the state of the boundary layer without the need to perform extensive velocity profile measurements.

Experience With Throat-Tap Nozzles for Accurate Flow Measurement

1972 ◽  
Vol 94 (2) ◽  
pp. 133-137 ◽  
Author(s):  
K. C. Cotton ◽  
J. A. Carcich ◽  
P. Schofield
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Turbulent Flow ◽  
Flow Measurement ◽  
Boundary Layer Analysis ◽  
The Past ◽  
Layer Analysis ◽  
Considerable Experience

During the past 10 years considerable experience has been gained in the use of ASME throat-tap nozzles for accurate flow measurement. Numerous precision calibrations have established turbulent flow coefficients up to a throat Reynolds number of 6.6 million. These results verify flow coefficients calculated from boundary-layer analysis.

Turbulent Flow in the Entry Region of a Rough Pipe

1974 ◽  
Vol 96 (1) ◽  
pp. 62-68 ◽  
Author(s):  
Jeng-Song Wang ◽  
J. P. Tullis
Keyword(s):  
Boundary Layer ◽  
Mathematical Model ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Velocity Profile ◽  
Turbulent Flow ◽  
Boundary Layer Thickness ◽  
Static Pressure ◽  
Pressure Coefficient ◽  
Reynolds Numbers

The general characteristics of mean turbulent flow in the entry region of a rough pipe are discussed. A mathematical model is presented for predicting the development of boundary layer thickness, core velocity, and pressure coefficient. Measurements were made of static pressure and velocity profiles in a 12-in. dia pipe at Reynolds numbers between 7 × 105 and 3.7 × 106. Water was used as the fluid. Data are included on the length required for the wall shear stress to become constant, for the boundary layer to reach the pipe centerline and for the velocity profile to become fully developed.

Effect of Surfactant Additives on a Boundary Layer on a Flat Plate

2005 ◽  
Author(s):  
Satoshi Ogata ◽  
Takeshi Fujita
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Velocity Profile ◽  
Flat Plate ◽  
Newtonian Fluid ◽  
Surfactant Concentration ◽  
Shape Parameter ◽  
Tap Water ◽  
Number Range ◽  
Surfactant Solutions

The effect of surfactant solutions on the boundary layer over a flat plate has been investigated in the Reynolds number range of approximately Re < 153,000. Experiments were carried out by measuring the velocity profile using a PIV system. Surfactant solutions tested were aqueous solutions of oleyl-bihydroxyethyl methyl ammonium chloride (Ethoquad O/12) in the concentration range of 50 to 500 ppm, to which sodium salicylate was added as a counterion. It was clarified that the boundary layer thickness of surfactant solutions increases significantly near the leading edge comparing with that of tap water, and parallelly develops in that obtained by the Blasius equation. For lower surfactant concentration (50 and 200 ppm) the velocity profile near the wall is distributed between that of laminar flow and turbulent flow for Newtonian fluid. When the Reynolds number increases, the velocity profile gradually increases from the outer edge of the boundary, and approaches the turbulent velocity profile of Newtonian fluid. For higher surfactant concentration (500 ppm), the velocity profile shows large S-shape. The velocity profile does not change very much, even if the Reynolds increases. The shape parameter with surfactant solutions decreases slightly comparing that of tap water at Re < 92,000, The value of shape parameter H with surfactant solution shows 1.66 < H < 2.32.

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