Analysis of a Power Law and Log Law for a Turbulent Wall Jet Over a Transitional Rough Surface: Universal Relations

2011 ◽  
Vol 133 (9) ◽  
Author(s):  
Noor Afzal ◽  
Abu Seena
Keyword(s):  
Experimental Data ◽  
Rough Surface ◽  
Power Law ◽  
Power Laws ◽  
Velocity Profiles ◽  
Wall Jet ◽  
Log Law ◽  
Jet Velocity ◽  
Turbulent Wall ◽  
Momentum Integral

The power law and log law velocity profiles and an integral analysis in a turbulent wall jet over a transitional rough surface have been proposed. Based on open mean momentum Reynolds equations, a two layer theory for large Reynolds numbers is presented and the matching in the overlap region is carried out by the Izakson-Millikan-Kolmogorov hypothesis. The velocity profiles and skin friction are shown to be governed by universal log laws as well as by universal power laws, explicitly independent of surface roughness, having the same constants as a fully smooth surface wall jet (or fully rough surface wall jet, as appropriate). The novel scalings for stream-wise variations of the flow over a rough wall jet have been analyzed, and best fit relations for maximum wall jet velocity, boundary layer thickness at maxima of wall jet velocity, the jet half width, the friction factor, and momentum integral are supported by the experimental data. There is no universality of scalings in traditional variables, and different expressions are needed for transitional roughness. The experimental data provides very good support to our universal relations proposed in terms of alternate variables.

Parametric Analysis of Turbulent Wall Jet in Still Air Over a Transitional Rough, With Asymptotes of Fully Rough and Fully Smooth Wall Jets

2013 ◽  
Vol 135 (11) ◽  
Author(s):  
Noor Afzal ◽  
Abu Seena
Keyword(s):  
Experimental Data ◽  
Reynolds Number ◽  
Rough Surfaces ◽  
Flow Direction ◽  
Wall Jet ◽  
Functional Forms ◽  
Jet Velocity ◽  
Turbulent Wall ◽  
Momentum Integral ◽  
Power Law Index

The novel scalings for streamwise variations of the flow in a turbulent wall jet over a fully smooth, transitional, and fully rough surfaces have been analyzed. The universal scaling for arbitrary wall roughness is considered in terms of the roughness friction Reynolds number (that arises from the stream wise variations of roughness in the flow direction) and roughness Reynolds number at the nozzle jet exit. The transitional rough wall jet functional forms have been proposed, whose numerical constants power law index and prefactor are estimated from best fit to the data for several variables, like, maximum wall jet velocity, boundary layer thickness at maxima of wall jet velocity, the jet half width, the friction factor and momentum integral, which are supported by the experimental data. The data shows that the two asymptotes of fully rough and fully smooth surfaces are co-linear with transitional rough surface, predicting same constants for any variable of flow for full smooth, fully rough and transitional rough surfaces. There is no universality of scalings in terms of traditional variables as different expressions are needed for each stage of the transitional roughness. The experimental data provides very good support to our universal relations.

Plane Turbulent Wall Jet Flow Development and Friction Factor

1963 ◽  
Vol 85 (1) ◽  
pp. 47-53 ◽  
Author(s):  
G. E. Myers ◽  
J. J. Schauer ◽  
R. H. Eustis
Keyword(s):  
Maximum Velocity ◽  
Velocity Profiles ◽  
Wall Jet ◽  
Shearing Stress ◽  
Integral Methods ◽  
Velocity Decay ◽  
Wall Jet Flow ◽  
Turbulent Wall ◽  
Momentum Integral ◽  
Wall Shearing Stress

An investigation of the jet development, the velocity profiles, and the wall shearing stress in a two-dimensional, incompressible, turbulent wall jet was undertaken. The maximum velocity decay, jet thickness, and the shearing stress are predicted analytically by momentum-integral methods. Experimental data concerning velocity profiles, velocity decay, and jet thickness agree well with previous investigators. The wall shearing stress was measured by a hot-film technique and the results help to resolve a wide divergence between the experimental values of other investigators.

Analysis of power law and log law velocity profiles in the overlap region of a turbulent wall jet

2005 ◽  
Vol 461 (2058) ◽  
pp. 1889-1910 ◽  
Author(s):  
Noor Afzal
Keyword(s):  
Power Law ◽  
Asymptotic Expansions ◽  
Friction Velocity ◽  
Matched Asymptotic Expansions ◽  
Large Reynolds Number ◽  
Wall Jet ◽  
Law Of The Wall ◽  
Log Law ◽  
Turbulent Wall ◽  
Overlap Region

The two-dimensional turbulent wall jet on a flat surface without free stream is analysed at a large Reynolds number, using the method of matched asymptotic expansions. The open mean equations of the turbulent boundary layer are analysed in the wall and wake layers by the method of matched asymptotic expansions and the results are matched by the Izakson–Millikan–Kolmogorov hypothesis. In the overlap region, the outer wake layer is governed by the velocity defect law (based on U m , the maximum velocity) and the inner layer by the law of the wall. It is shown that the overlap region possesses a non-unique solution, where the power law region simultaneously exists along with the log law region. Analysis of the power law and log law solutions in the overlap region leads to self-consistent relations, where the power law index, α , is of the order of the non-dimensional friction velocity and the power law multiplication constant, C , is of the order of the inverse of the non-dimensional friction velocity. The lowest order wake layer equation has been closed with generalized gradient transport model and a closed form solution is obtained. A comparison of the theory with experimental data is presented.

An Experimental Investigation of the Skin Friction in a Plane Turbulent Wall Jet Over Smooth and Rough Surfaces

2010 ◽  
Author(s):  
Noorallah Rostamy ◽  
Donald J. Bergstrom ◽  
David Sumner ◽  
James D. Bugg
Keyword(s):  
Skin Friction ◽  
Rough Surface ◽  
Smooth Surface ◽  
Rough Surfaces ◽  
Glass Plate ◽  
Power Laws ◽  
Jet Flows ◽  
Wall Jet ◽  
Friction Behavior ◽  
Turbulent Wall

Estimation of the skin friction in a turbulent wall jet flow over smooth and rough surfaces was studied experimentally. Wall jet flows can be found in many engineering applications in which knowledge of the skin friction behavior is essential for predicting the drag force as well as the heat transfer rate at the wall. Although there are many studies which consider a wall jet on a smooth surface, only a few experiments have examined wall jet flows on a rough surface. This paper reports on an experimental investigation which used a two-component laser Doppler anemometry (LDA) system to measure the mean velocity field in a plane turbulent wall jet on both smooth and transitionally rough surfaces. The Reynolds number based on the slot height and exit velocity of the jet was approximately Re = 7500. A glass plate was used for the smooth surface, while the rough surface consisted of a 36-grit sheet glued to the glass plate. The momentum-viscosity scaling originally introduced by Narasimha et al. (1973) and revisited by Wygnanski et al. (1992) can be used to construct a similarity profile for a wall jet on a smooth surface, which together with the momentum integral equation leads to a convenient expression for the friction velocity and hence skin friction coefficient Cf. This approach has been used to process the experimental results, which gives values of Cf which are consistent with the results of other methods and some existing empirical correlations. However, for rough wall flow, the friction at the wall is not only governed by viscosity, but also by surface roughness. Hogg et al. (1997) suggested that for a fully rough surface, the viscosity be replaced by the roughness parameter Uoke, where Uo and ke are the initial velocity and roughness length, respectively. Here, this approach is applied to our recent velocity measurements in a wall jet on a transitionally rough surface, where both viscous and roughness effects are present. The present results indicate that for an equivalent sand-grain roughness range of 40 < ks+ < 70, the momentum-viscosity scaling is able to capture the skin friction behavior compared to that obtained from the logarithmic and power laws. The results also show that the scalings proposed by Hogg et al. (1997) and Wygnanski et al. (1992) both result in similar values for the friction velocity. However, the values of Cf estimated by both scalings are considerably larger (approximately 47%) than those obtained from the logarithmic and power laws.

A plane turbulent wall jet on a fully rough surface

2017 ◽  
Vol 66 ◽  
pp. 258-264 ◽  
Author(s):  
Z. Tang ◽  
D.J. Bergstrom ◽  
J.D. Bugg
Keyword(s):  
Rough Surface ◽  
Wall Jet ◽  
Turbulent Wall

The asymptotic downstream flow of plane turbulent wall jets without external stream

2015 ◽  
Vol 779 ◽  
pp. 351-370 ◽  
Author(s):  
Klaus Gersten
Keyword(s):  
Experimental Data ◽  
Momentum Flux ◽  
Maximum Velocity ◽  
Jet Flow ◽  
Plane Wall ◽  
Wall Jet ◽  
Free Jet ◽  
Wall Distance ◽  
Wall Jet Flow ◽  
Turbulent Wall

The plane turbulent wall-jet flow without externally imposed stream is considered. It is assumed that the wall jet does not emerge from a second wall perpendicular to the velocity vector of the initial wall jet. The (kinematic) momentum flux $K(x)$ of the wall jet decreases downstream owing to the shear stress at the wall. This investigation is based on the hypothesis that the total friction force on the wall is smaller than the total inflow momentum flux. In other words, the turbulent wall jet tends to a turbulent ‘half-free jet’ with a non-zero momentum flux $K_{\infty }\;(\text{m}^{3}~\text{s}^{-2})$ far downstream. The fact that the turbulent half-free jet is the asymptotic form of a turbulent wall jet is the basis for a singular perturbation method by which the wall-jet flow is determined. It turns out that the ratio between the wall distance $y_{m}$ of the maximum velocity and the wall distance $y_{0.5}$ of half the maximum velocity decreases downstream to zero. Dimensional analysis leads immediately to a universal function of the dimensionless momentum flux $K(\mathit{Re}_{x})/K_{\infty }$ that depends asymptotically only on the local Reynolds number $\mathit{Re}_{x}=\sqrt{(x-x_{0})K_{\infty }}/{\it\nu}$, where $x_{0}$ denotes the coordinate of the virtual origin. When the values $K$ and ${\it\nu}$ at the position $x-x_{0}$ are known, the asymptotic momentum flux $K_{\infty }$ can be determined. Experimental data on all turbulent plane wall jets (except those emerging from a second plane wall) collapse to a single universal curve. Comparisons between available experimental data and the analysis make the hypothesis $K_{\infty }\neq 0$ plausible. A convincing verification, however, will be possible in the future, preferably by direct numerical simulations.

Effects of an Initial Gap on the Flow in a Turbulent Wall Jet

1966 ◽  
Vol 70 (666) ◽  
pp. 669-673 ◽  
Author(s):  
K. Sridhar ◽  
P. K. C. Tu
Keyword(s):  
Power Law ◽  
Nozzle Exit ◽  
Leading Edge ◽  
Wall Jet ◽  
Gap Size ◽  
Two Dimensional ◽  
Free Jet ◽  
Layer Velocity ◽  
Turbulent Wall ◽  
Gap Effects

SummaryThe flow in a two-dimensional plane wall jet with different initial gaps between the nozzle exit and the leading edge of the wall was probed at various stations along the jet. The jet slot thickness and the velocity were kept constant. It was found that the region close to the leading edge of the wall behaved like a transforming region where the type of flow changed from a free jet to a wall jet. The length of this region, which depended directly on the gap size, was so short for small gaps that the gap effects were found to be negligible. In addition, it was found that the inner layer velocity distribution of a wall jet did not follow the classic one-seventh power law.

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