Turbulent Skin-Friction Coefficient and Momentum Thickness in Adverse Pressure Gradient

1969 ◽  
Vol 6 (1) ◽  
pp. 78-78
Author(s):  
C. Y. LIU
Keyword(s):  
Friction Coefficient ◽  
Pressure Gradient ◽  
Skin Friction ◽  
Adverse Pressure Gradient ◽  
Skin Friction Coefficient ◽  
Momentum Thickness

scholarly journals Evolution Characteristics of Separated Vortices and Near-Wall Flow in a Centrifugal Impeller in an Off-Designed Condition

2020 ◽  
Vol 10 (22) ◽  
pp. 8209
Author(s):  
Shihao Zhou ◽  
Peifeng Lin ◽  
Wei Zhang ◽  
Zuchao Zhu
Keyword(s):  
Friction Coefficient ◽  
Pressure Gradient ◽  
Skin Friction ◽  
Cross Sections ◽  
Adverse Pressure Gradient ◽  
Skin Friction Coefficient ◽  
Centrifugal Impeller ◽  
Suction Surface ◽  
Pressure Surface ◽  
Evolution Characteristics

Flow separation is undesirable and lowers the efficiency of centrifugal impellers. In this study, the evolution characteristics of separated vortices in a centrifugal impeller are studied under the off-designed flow rate condition. Unsteady Reynolds-Averaged Navier–Stokes (URANS) with standard k-ε turbulent model is applied to simulate the alternating stall in the six-blade centrifugal impeller. We present and analyze the distributions of pressure gradient (either adverse or favorable) and skin friction coefficients on both sides of the blade for the stalled and unstalled passages to study the relationship between pressure gradient and separation of boundary layer flow. The evolution of skin friction coefficient is also presented at various axial cross sections. Numerical results reveal that, for the stalled passage, the increase in adverse pressure gradient on the pressure surface near the middle of the blade (S/S0 = 0.4) is much larger than that of the suction surface during a vortex formation cycle. The skin friction coefficient on the pressure surface also increases in magnitude sharply and the variation shows a peak-valley trend, while the coefficient on the suction surface increases slowly. Comparing the distribution of skin friction coefficient on the pressure surface of the same blade at different axial cross sections, it is found that the skin friction coefficient notably increases at S/S0 = 0.6 on the middle axial cross section (Z/b2 = 0.5). For the unstalled passage, both the pressure and suction surfaces produce favorable pressure gradients. The skin friction coefficient on the pressure surface shows an increasing trend around S/S0 = 0.5, and a large vortex can be seen at the exit of the impeller. The variation of skin friction coefficient on the suction surface is relatively mild; thus, the flow is relatively stable. It is clarified that the effect of adverse pressure gradient and wall shear stress jointly cause separation of the boundary layer; thus, the separated vortices are generated in the rotating impeller and deteriorate the performance of the impeller.

Experimental Investigation of Turbulent Boundary Layers Under Favorable Pressure Gradient

2010 ◽  
Author(s):  
Pranav Joshi ◽  
Joseph Katz
Keyword(s):  
Boundary Layer ◽  
Friction Coefficient ◽  
Pressure Gradient ◽  
Skin Friction ◽  
Velocity Profiles ◽  
Skin Friction Coefficient ◽  
Mean Velocity ◽  
Freestream Velocity ◽  
Favorable Pressure Gradient ◽  
The Mean

The goal of this research is to study the effect of favorable pressure gradient (FPG) on the near wall structures of a turbulent boundary layer on a smooth wall. 2D-PIV measurements have been performed in a sink flow, initially at a coarse resolution, to characterize the development of the mean flow and (under resolved) Reynolds stresses. Lack of self-similarity of mean velocity profiles shows that the boundary layer does not attain the sink flow equilibrium. In the initial phase of acceleration, the acceleration parameter, K = v/U2dU/dx, increases from zero to 0.575×10−6, skin friction coefficient decreases and mean velocity profiles show a log region, but lack universality. Further downstream, K remains constant, skin friction coefficient increases and the mean velocity profiles show a second log region away from the wall. In the initial part of the FPG region, all the Reynolds stress components decrease over the entire boundary layer. In the latter phase, they continue to decrease in the middle of the boundary layer, and increase significantly close to the wall (below y∼0.15δ), where they collapse when normalized with the local freestream velocity. Turbulence production and wallnormal transport, scaled with outer units, show self-similar profiles close to the wall in the constant K region. Spanwise-streamwise plane data shows evidence of low speed streaks in the log layer, with widths scaling with the boundary layer thickness.

An Integral Solution for Skin Friction in Turbulent Flow Over Aerodynamically Rough Surfaces With an Arbitrary Pressure Gradient

2014 ◽  
Vol 136 (8) ◽  
Author(s):  
James Sucec
Keyword(s):  
Reynolds Number ◽  
Pressure Gradient ◽  
Skin Friction ◽  
Integral Form ◽  
Skin Friction Coefficient ◽  
Momentum Equation ◽  
Data Sets ◽  
Momentum Thickness ◽  
Local Skin ◽  
Law Of The Wall

The combined law of the wall and wake, with the inclusion of the “roughness depression function” for the inner law in the “Log” region, is used as the inner coordinates' velocity profile in the integral form of the x momentum equation to solve for the local skin friction coefficient. The “equivalent sand grain roughness” concept is employed in the roughness depression function in the solution. Calculations are started at the beginning of roughness on a surface, as opposed to starting them using the measured experimental values at the first data point, when making comparisons of predictions with data sets. The dependence of the velocity wake strength on both pressure gradient and momentum thickness Reynolds number are taken into account. Comparisons of the prediction with experimental skin friction data, from the literature, have been made for some adverse, zero, and favorable (accelerating flows) pressure gradients. Predictions of the shape factor, roughness Reynolds number, and momentum thickness Reynolds number and comparisons with data are also made for some cases. In addition, some comparisons with the predictions of earlier investigators have also been made.

Measurement and Calculation of Fluid Dynamic Characteristics of Rough-Wall Turbulent Boundary-Layer Flows

1993 ◽  
Vol 115 (3) ◽  
pp. 383-388 ◽  
Author(s):  
M. H. Hosni ◽  
H. W. Coleman ◽  
R. P. Taylor
Keyword(s):  
Boundary Layer ◽  
Friction Coefficient ◽  
Turbulent Boundary Layer ◽  
Skin Friction ◽  
Rough Surface ◽  
Skin Friction Coefficient ◽  
Rough Wall ◽  
Momentum Thickness ◽  
Boundary Layer Flows ◽  
Mean Velocity

Experimental measurements of profiles of mean velocity and distributions of boundary-layer thickness and skin friction coefficient from aerodynamically smooth, transitionally rough, and fully rough turbulent boundary-layer flows are presented for four surfaces—three rough and one smooth. The rough surfaces are composed of 1.27 mm diameter hemispheres spaced in staggered arrays 2, 4, and 10 base diameters apart, respectively, on otherwise smooth walls. The current incompressible turbulent boundary-layer rough-wall air flow data are compared with previously published results on another, similar rough surface. It is shown that fully rough mean velocity profiles collapse together when scaled as a function of momentum thickness, as was reported previously. However, this similarity cannot be used to distinguish roughness flow regimes, since a similar degree of collapse is observed in the transitionally rough data. Observation of the new data shows that scaling on the momentum thickness alone is not sufficient to produce similar velocity profiles for flows over surfaces of different roughness character. The skin friction coefficient data versus the ratio of the momentum thickness to roughness height collapse within the data uncertainty, irrespective of roughness flow regime, with the data for each rough surface collapsing to a different curve. Calculations made using the previously published discrete element prediction method are compared with data from the rough surfaces with well-defined roughness elements, and it is shown that the calculations are in good agreement with the data.

The Determination of Turbulent Skin Friction by Means of Pitot Tubes

1954 ◽  
Vol 58 (518) ◽  
pp. 109-121 ◽  
Author(s):  
J. H. Preston
Keyword(s):  
Boundary Layer ◽  
Friction Coefficient ◽  
Wind Tunnel ◽  
Pressure Gradient ◽  
Skin Friction ◽  
Basic Assumption ◽  
Skin Friction Coefficient ◽  
Pitot Tube ◽  
Tunnel Wall ◽  
Local Skin

SummaryA simple method of determining local turbulent skin friction on a smooth surface has been developed which utilises a round pitot tube resting on the surface. Assuming the existence of a region near the surface in which conditions are functions only of the skin friction, the relevant physical constants of the fluid and a suitable length, a universal non-dimensional relation is obtained for the difference between the total pressure recorded by the tube and the static pressure at the wall, in terms of the skin friction. This relation, on this assumption, is independent of the pressure gradient. The truth and form of the relation were first established, to a considerable degree of accuracy, in a pipe using four geometrically similar round pitot tubes—the diameter being taken as representative length. These four pitot tubes were then used to determine the local skin friction coefficient at three stations on a wind tunnel wall, under varying conditions of pressure gradient. At each station, within the limits of experimental accuracy, the deduced skin friction coefficient was found to be the same for each pitot tube, thus confirming the basic assumption and leaving little doubt as to the correctness of the skin friction so found. Pitot traverses were then made in the pipe and in the boundary layer on the wind tunnel wall. The results were plotted in two non-dimensional forms on the basis already suggested and they fell close together in a region whose outer limit represented the breakdown of the basic assumption, but close to the wall the results spread out, due to the unknown displacement of the effective centre of a pitot tube near a wall. This again provides further evidence of the existence of a region of local dynamical similarity and of the correctness of the skin friction deduced from measurements with round pitot tubes on the wind tunnel wall. The extent of the region in which the local dynamical similarity may be expected to hold appears to vary from about 1/5 to 1/20 of the boundary-layer thickness for conditions remote from, and close to, separation respectively.

A New Integral Method for Analyzing the Turbulent Boundary Layer With Arbitrary Pressure Gradient

1969 ◽  
Vol 91 (3) ◽  
pp. 371-376 ◽  
Author(s):  
F. M. White
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Skin Friction ◽  
Shape Factor ◽  
Single Equation ◽  
Skin Friction Coefficient ◽  
New Method ◽  
Momentum Thickness ◽  
New Approach

For routine calculations of the properties of the incompressible turbulent boundary layer with arbitrary pressure gradient, the presently accepted method is the Karman integral technique, which consists of three simultaneous equations, the three unknowns being the momentum thickness, the skin friction, and the shape factor. Considerable empiricism is contained in the Karman method, so that the reliability is only fair. The present paper derives an entirely new method, based upon a suggestion of R. Brand and L. Persen. The new approach results in a single equation for the skin friction coefficient, with the only parameter being the nominal Reynolds number and the only empiricism being a single assumption about the effect of pressure gradient. No other variables, such as shape factor or momentum thickness, are needed, although they can of course be calculated as byproducts of the analysis. The new method also contains a built-in separation criterion, which was the most glaring omission of the Karman technique. Agreement with experiment is as good or better than the most reliable Karman methods in use today.

Impact of viscosity variation on oblique flow of Cu–H2O nanofluid

2017 ◽  
Vol 232 (5) ◽  
pp. 622-631 ◽  
Author(s):  
R Tabassum ◽  
Rashid Mehmood ◽  
O Pourmehran ◽  
NS Akbar ◽  
M Gorji-Bandpy
Keyword(s):  
Heat Flux ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Volume Fraction ◽  
Variable Viscosity ◽  
Solid Volume Fraction ◽  
Local Heat ◽  
Skin Friction Coefficient ◽  
Viscosity Parameter ◽  
Local Heat Flux

The dynamic properties of nanofluids have made them an area of intense research during the past few decades. In this article, flow of nonaligned stagnation point nanofluid is investigated. Copper–water based nanofluid in the presence of temperature-dependent viscosity is taken into account. The governing nonlinear coupled ordinary differential equations transformed by partial differential equations are solved numerically by using fourth-order Runge–Kutta–Fehlberg integration technique. Effects of variable viscosity parameter on velocity and temperature profiles of pure fluid and copper–water nanofluid are analyzed, discussed, and presented graphically. Streamlines, skin friction coefficients, and local heat flux of nanofluid under the impact of variable viscosity parameter, stretching ratio, and solid volume fraction of nanoparticles are also displayed and discussed. It is observed that an increase in solid volume fraction of nanoparticles enhances the magnitude of normal skin friction coefficient, tangential skin friction coefficient, and local heat flux. Viscosity parameter is found to have decreasing effect on normal and tangential skin friction coefficients whereas it has a positive influence on local heat flux.

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