A Relatively Simple Integral Method for Turbulent Flow Over Rough Surfaces

2017 ◽  
Vol 139 (12) ◽  
Author(s):  
James Sucec
Keyword(s):  
Boundary Layer ◽  
Friction Coefficient ◽  
Rough Surfaces ◽  
Integral Form ◽  
Skin Friction Coefficient ◽  
Momentum Thickness ◽  
Law Of The Wall ◽  
Roughness Elements ◽  
Layer Flow ◽  
Sand Grain Size

The integral form of the equation for x momentum is solved for the skin friction coefficient, in external thin boundary layer flow, on surfaces whose technical roughness elements' size is given. This is done by using a “roughness depression function” in the law of the wall and wake which serves as the needed velocity profile. The method uses the equivalent sand grain size concept in its calculations. Predictions are made of the friction coefficient, Cf, as a function of momentum thickness Reynolds number and also, of Cf's dependence on the ratio of momentum thickness to the size of the technical (actual) roughness elements. In addition, boundary layer thicknesses and velocity profiles on rough surfaces are calculated and, when available, comparisons are made with the experimental data from a number of sources in the literature. Also, comparisons are made with the results of another major predictive scheme which does not use the equivalent sand grain concept.

Boundary layer flow near stagnation-points on a vertical surface with slip in the presence of transverse magnetic field

2014 ◽  
Vol 24 (3) ◽  
pp. 643-653 ◽  
Author(s):  
Ibrahim Yakubu Seini ◽  
Daniel Oluwole Makinde
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Boundary Layer ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Stagnation Point ◽  
Vertical Surface ◽  
Skin Friction Coefficient ◽  
Content Type ◽  
Layer Flow

Purpose – The purpose of this paper is to investigate the MHD boundary layer flow of viscous, incompressible and electrically conducting fluid near a stagnation-point on a vertical surface with slip. Design/methodology/approach – In the study, the temperature of the surface and the velocity of the external flow are assumed to vary linearly with the distance from the stagnation-point. The governing differential equations are transformed into systems of ordinary differential equations and solved numerically by a shooting method. Findings – The effects of various parameters on the heat transfer characteristics are discussed. Graphical results are presented for the velocity and temperature profiles whilst the skin-friction coefficient and the rate of heat transfers near the surface are presented. It is observed that the presence of the magnetic field increases the skin-friction coefficient and the rate of heat transfer near the surface towards the stagnation-point. Originality/value – The presence of magnetic field increases the skin-friction coefficient and the rate of heat transfer near the surface towards the stagnation-point.

Effects of Regular and Random Roughness on the Heat Transfer and Skin Friction Coefficient on the Suction Side of a Gas Turbine Vane

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Jason E. Dees ◽  
David G. Bogard
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Suction Side ◽  
Skin Friction Coefficient ◽  
Regular Array ◽  
Roughness Elements ◽  
Turbine Vane ◽  
Regular Roughness

Skin friction coefficients and heat transfer coefficients are measured for a range of regular and random roughnesses on the suction side of a simulated gas turbine vane. The skin friction coefficients are calculated using boundary layer data and the momentum integral method. High resolution surface temperature data measured with an IR camera yield local heat transfer values. 80 grit, 50 grit, 36 grit, and 20 grit sandpapers along with a regular array of conical roughness elements are tested. Measured skin friction coefficient data show that the conical roughness array behaves very similar to the 50 grit, 36 grit, and 20 grit sandpapers in terms of the effect of the roughness on the hydrodynamic boundary layer. In terms of heat transfer, the conical roughness array is most similar to the 80 grit sandpaper, which are both lower than the roughest sandpapers tested. These data show that the particular regular array of roughness elements tested has fundamentally different behavior than randomly rough surfaces for this position on the simulated turbine vane. In addition, this difference is in the opposite direction as seen in previous experimental studies. In order to draw a more general conclusion about the nature of random and regular roughness, a parametric study of regular roughness arrays should be performed.

Effects of Regular and Random Roughness on the Heat Transfer and Skin Friction Coefficient on the Suction Side of a Gas Turbine Vane

2007 ◽  
Author(s):  
Jason E. Dees ◽  
David G. Bogard
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Suction Side ◽  
Skin Friction Coefficient ◽  
Regular Array ◽  
Roughness Elements ◽  
Turbine Vane ◽  
Regular Roughness

Skin friction coefficients and heat transfer coefficients are measured for a range of regular and random roughnesses on the suction side of a simulated gas turbine vane. The skin friction coefficients are calculated using boundary layer data and the momentum integral method. High resolution surface temperature data measured with an IR camera yields local heat transfer values. 80 grit, 50 grit, 36 grit, and 20 grit sandpaper, along with a regular array of conical roughness elements are tested. Measured skin friction coefficient data shows that the conical roughness array behaves very similarly to the 50 grit, 36 grit, and 20 grit sandpapers in terms of the effect of the roughness on the hydrodynamic boundary layer. In terms of heat transfer, the conical roughness array is most similar to the 80 grit sandpaper, which are both lower than the roughest sandpapers tested. This data shows that the particular regular array of roughness elements tested has fundamentally different behavior than randomly rough surfaces for this position on the simulated turbine vane. In addition, this difference is in the opposite direction as seen in previous experimental studies. In order to draw a more general conclusion about the nature of random and regular roughness, a parametric study of regular roughness arrays should be performed.

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.

Unsteady MHD boundary layer flow of tangent hyperbolic two-phase nanofluid of moving stretched porous wedge

2018 ◽  
Vol 28 (11) ◽  
pp. 2567-2580 ◽  
Author(s):  
A. Mahdy ◽  
Ali J. Chamkha
Keyword(s):  
Boundary Layer ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Boundary Layer Flow ◽  
Velocity Ratio ◽  
Skin Friction Coefficient ◽  
Content Type ◽  
Mhd Boundary Layer ◽  
Layer Flow ◽  
Mhd Boundary Layer Flow

Purpose The purpose of this paper is to address the thermo-physical impacts of unsteady magneto-hydrodynamic (MHD) boundary layer flow of non-Newtonian tangent hyperbolic nanofluid past a moving stretching wedge. To delineate the nanofluid, the boundary conditions for normal fluxes of the nanoparticle volume fraction are chosen to be vanish. Design/methodology/approach The local similarity transformation is implemented to reformulate the governing PDEs into coupled non-linear ODEs of higher order. Then, numerical solution is obtained for the simplified governing equations with the aid of finite difference technique. Findings Numerical calculations point out that pressure gradient parameter leads to improve all skin friction coefficient, rate of heat transfer and absolute value of rate of nanoparticle concentration. As well as, lager values of Weissenberg number tend to upgrade the skin friction coefficient, while power law index and velocity ratio parameter reduce the skin friction coefficient. Again, the horizontal velocity component enhances with upgrading power law index, unsteadiness parameter, velocity ratio parameter and Darcy number and it reduces with rising values of Weissenberg number. Originality/value A numerical treatment of unsteady MHD boundary layer flow of tangent hyperbolic nanofluid past a moving stretched wedge is obtained. The problem is original.

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.

Influence of distributed roughness elements on boundary layer transition for NACA0012 airfoil

2018 ◽  
Vol 32 (29) ◽  
pp. 1850349 ◽  
Author(s):  
Hao Dong ◽  
Shicheng Liu ◽  
Xi Geng ◽  
Kun Zhang ◽  
Keming Cheng
Keyword(s):  
Boundary Layer ◽  
Friction Coefficient ◽  
Wind Tunnel ◽  
Skin Friction Coefficient ◽  
Boundary Layer Transition ◽  
Layer Transition ◽  
Supersonic Wind Tunnel ◽  
Oil Film ◽  
Naca0012 Airfoil ◽  
Roughness Elements

The influence of distributed cylinder roughness elements on boundary layer transition for NACA0012 airfoil at Ma = 0.6 has been investigated by subsonic/transonic/supersonic wind tunnel experiment with oil-film interferometry. Three different heights and two different distances of cylinder roughness elements on the airfoil model were used, and the skin friction coefficient was measured by the oil-film interferometry. The experimental results show that higher roughness elements promote the transition earlier. In addition, narrower distance of roughness elements can delay the transition compared with the case of wider distance.

scholarly journals Laminar Boundary Layer Flow and Heat Transfer With Favorable Pressure Gradient at Constant K Values

1992 ◽  
Author(s):  
Dadong Zhou ◽  
Ting Wang
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Friction Coefficient ◽  
Pressure Gradient ◽  
Leading Edge ◽  
Skin Friction Coefficient ◽  
Convergent Channel ◽  
Flow And Heat Transfer ◽  
Favorable Pressure Gradient ◽  
Layer Flow

Approximate algebraic correlations for the two-dimensional laminar boundary layer flow and heat transfer with favorable pressure gradient at constant K (≡vUe2dUedx) values were found by using Pohlhausen’s integral method. Two thermal boundary conditions were considered: constant wall heat flux and constant wall temperature. These correlations were tabulated and compared in the limits KRex → 0 and KRex → ∞ with the similarity solutions of the Blasius flow and the convergent-channel flow. The comparisons between these correlations and those obtained numerically from the STAN5 code were excellent. The results showed that the momentum boundary layer grows at the leading edge with an initial rate like the Blasius flow to a maximum value, then decreases and asymptotically approaches the behavior of a convergent-channel flow. As KRex increases, the skin friction coefficient decreases and approaches a constant; the Pohlhausen’s pressure gradient parameter (Λ≡δ2vdUedx) increases from zero at the leading edge and approaches a constant. While hydrodynamically asymptotical solutions were obtained, no asymptotical thermal similarity was found. Skin friction coefficient and various integral parameters could be collapsed into a corresponding single curve when suitable normalization factors were chosen. The effects of Prandtl number and unheated starting length were also analyzed.

scholarly journals Free Convection Boundary Layer Flow over a Horizontal Circular Cylinder in Al2O3-Ag/Water Hybrid Nanofluid with Viscous Dissipation

2021 ◽  
Vol 17 (1) ◽  
pp. 20-25
Author(s):  
Muhammad Khairul Anuar Mohamed ◽  
Mohd Zuki Salleh ◽  
Fadhilah Che Jamil ◽  
Huei Ruey Ong
Keyword(s):  
Boundary Layer ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Skin Friction Coefficient ◽  
Convection Boundary Layer ◽  
Hybrid Nanofluid ◽  
Convection Boundary ◽  
Layer Flow ◽  
Free Convection Boundary Layer ◽  
Horizontal Circular Cylinder

In this paper, the mathematical model of free convection boundary layer flow of horizontal circular cylinder immersed in Ag/Water nanofluid and Al2O3-Ag/Water hybrid nanofluid are considered. The governing non-linear partial differential equations are first transformed to a more convenient way before being solved numerically using the Keller-box method. The numerical values for the reduced Nusselt number and the reduced skin friction coefficient are obtained and illustrated graphically as well as temperature profiles and velocity profiles. Effects of the Prandtl number, Eckert number and nanoparticle volume fraction are analyzed and discussed. It is found that the Nusselt number for Al2O3-Ag/Water hybrid nanofluid is comparable with Ag/Water nanofluid with a reduction in skin friction coefficient. The preliminary results reports here are important as a reference in exploring the potential of hybrid nanofluid to reduce the production cost compared to the used of metal nanofluid.

Sign in / Sign up

Export Citation Format

Share Document