Alternate Scales for Turbulent Flow in Transitional Rough Pipes: Universal Log Laws

2006 ◽  
Vol 129 (1) ◽  
pp. 80-90 ◽  
Author(s):  
Noor Afzal ◽  
Abu Seena
Keyword(s):  
Reynolds Number ◽  
Velocity Profile ◽  
Turbulent Flow ◽  
Friction Factor ◽  
Friction Velocity ◽  
Strong Support ◽  
Reynolds Numbers ◽  
Momentum Theory ◽  
The Mean ◽  
Pipe Roughness

In transitional rough pipes, the present work deals with alternate four new scales, the inner wall transitional roughness variable ζ=Z+∕ϕ, associated with a particular roughness level, defined by roughness scale ϕ connected with roughness function ▵U+, the roughness friction Reynolds number Rϕ (based on roughness friction velocity), and roughness Reynolds number Reϕ (based on roughness average velocity) where the mean turbulent flow, little above the roughness sublayer, does not depend on pipes transitional roughness. In these alternate variables, a two layer mean momentum theory is analyzed by the method of matched asymptotic expansions for large Reynolds numbers. The matching of the velocity profile and friction factor by Izakson-Millikan-Kolmogorov hypothesis gives universal log laws that are explicitly independent of pipe roughness. The data of the velocity profile and friction factor on transitional rough pipes provide strong support to universal log laws, having the same constants as for smooth walls. There is no universality of scalings in traditional variables and different expressions are needed for various types of roughness, as suggested, for example, with inflectional-type roughness, monotonic Colebrook-Moody roughness, etc. In traditional variables, the roughness scale, velocity profile, and friction factor prediction for inflectional pipes roughness are supported very well by experimental data.

Numerical and Experimental Analysis of Turbulent Flow in Corrugated Pipes

2010 ◽  
Vol 132 (7) ◽  
Author(s):  
Henrique Stel ◽  
Rigoberto E. M. Morales ◽  
Admilson T. Franco ◽  
Silvio L. M. Junqueira ◽  
Raul H. Erthal ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Pressure Drop ◽  
Turbulent Flow ◽  
Friction Factor ◽  
Turbulence Models ◽  
Reynolds Numbers ◽  
Velocity Magnitude ◽  
Geometric Configurations ◽  
Corrugated Surfaces ◽  
Friction Factors

This article describes a numerical and experimental investigation of turbulent flow in pipes with periodic “d-type” corrugations. Four geometric configurations of d-type corrugated surfaces with different groove heights and lengths are evaluated, and calculations for Reynolds numbers ranging from 5000 to 100,000 are performed. The numerical analysis is carried out using computational fluid dynamics, and two turbulence models are considered: the two-equation, low-Reynolds-number Chen–Kim k-ε turbulence model, for which several flow properties such as friction factor, Reynolds stress, and turbulence kinetic energy are computed, and the algebraic LVEL model, used only to compute the friction factors and a velocity magnitude profile for comparison. An experimental loop is designed to perform pressure-drop measurements of turbulent water flow in corrugated pipes for the different geometric configurations. Pressure-drop values are correlated with the friction factor to validate the numerical results. These show that, in general, the magnitudes of all the flow quantities analyzed increase near the corrugated wall and that this increase tends to be more significant for higher Reynolds numbers as well as for larger grooves. According to previous studies, these results may be related to enhanced momentum transfer between the groove and core flow as the Reynolds number and groove length increase. Numerical friction factors for both the Chen–Kim k-ε and LVEL turbulence models show good agreement with the experimental measurements.

Turbulent flow in smooth and rough pipes

2007 ◽  
Vol 365 (1852) ◽  
pp. 699-714 ◽  
Author(s):  
J.J Allen ◽  
M.A Shockling ◽  
G.J Kunkel ◽  
A.J Smits
Keyword(s):  
Reynolds Number ◽  
Friction Factor ◽  
Outer Layer ◽  
Strong Support ◽  
Reynolds Numbers ◽  
Mean Velocity ◽  
Number Range ◽  
Princeton University ◽  
Smooth Pipe ◽  
Logarithmic Region

Recent experiments at Princeton University have revealed aspects of smooth pipe flow behaviour that suggest a more complex scaling than previously noted. In particular, the pressure gradient results yield a new friction factor relationship for smooth pipes, and the velocity profiles indicate the presence of a power-law region near the wall and, for Reynolds numbers greater than about 400×10 3 ( R + >9×10 3 ), a logarithmic region further out. New experiments on a rough pipe with a honed surface finish with k rms / D =19.4×10 −6 , over a Reynolds number range of 57×10 3 –21×10 6 , show that in the transitionally rough regime this surface follows an inflectional friction factor relationship rather than the monotonic relationship given in the Moody diagram. Outer-layer scaling of the mean velocity data and streamwise turbulence intensities for the rough pipe show excellent collapse and provide strong support for Townsend's outer-layer similarity hypothesis for rough-walled flows. The streamwise rough-wall spectra also agree well with the corresponding smooth-wall data. The pipe exhibited smooth behaviour for , which supports the suggestion that the original smooth pipe was indeed hydraulically smooth for Re D ≤24×10 6 . The relationship between the velocity shift, Δ U / u τ , and the roughness Reynolds number, , has been used to generalize the form of the transition from smooth to fully rough flow for an arbitrary relative roughness k rms / D . These predictions apply for honed pipes when the separation of pipe diameter to roughness height is large, and they differ significantly from the traditional Moody curves.

scholarly journals Experimental and theoretical studies of dissolution roughness

1974 ◽  
Vol 65 (4) ◽  
pp. 735-751 ◽  
Author(s):  
Paul N. Blumberg ◽  
Rane L. Curl
Keyword(s):  
Mass Transfer ◽  
Reynolds Number ◽  
Turbulent Flow ◽  
Friction Factor ◽  
Flow Structure ◽  
Friction Velocity ◽  
Theoretical Studies ◽  
Average Mass ◽  
Characteristic Wavelength ◽  
Experimental And Theoretical Studies

Periodic dissolution patterns that result from the interaction of a soluble surface and an adjacent turbulent flow have been investigated experimentally and theoretically. They occur at a Reynolds number based on a characteristic wavelength and friction velocity of about 2200. Experimental results for the stable geometry, propagation, mass-transfer distribution, average mass-transfer correlation and friction factor are presented. An interpretation based upon the repetitive transitional nature of the flow structure is advanced to explain aspects of the origin and behaviour of this type of roughness.

Roughness effects of commercial steel pipe in turbulent flow: universal scaling

2013 ◽  
Vol 40 (2) ◽  
pp. 188-193 ◽  
Author(s):  
Noor Afzal
Keyword(s):  
Surface Roughness ◽  
Velocity Profile ◽  
Turbulent Flow ◽  
Friction Factor ◽  
Steel Pipe ◽  
Roughness Effects ◽  
Universal Scaling ◽  
Commercial Steel ◽  
The Mean ◽  
Grain Roughness

The mean turbulent flow over a transitional rough commercial steel pipe is considered in terms of alternate inner roughness variables. The matching of inner layer and outer layer in the overlap region leads to the universal log laws for velocity profile and friction factor, explicitly independent of surface roughness of all kinds. The roughness function, for commercial steel pipe differs from inflectional (sand grain) roughness. The traditional wall law and friction factor depends on type of surface roughness.

Some Deductions from Bowen's Non-Newtonian Turbulent Correlation

1967 ◽  
Vol 9 (5) ◽  
pp. 414-416
Author(s):  
J. Harris
Keyword(s):  
Reynolds Number ◽  
Velocity Profile ◽  
Turbulent Flow ◽  
Friction Factor ◽  
Effective Viscosity ◽  
Empirical Correlation ◽  
Dynamic Similarity ◽  
Flow Through

Starting from Bowen's empirical correlation for non-Newtonian turbulent flow through pipes, deductions are made about the form of the velocity profile, the effective viscosity, the Reynolds number for dynamic similarity and finally the associated form of the friction factor-Reynolds number correlation.

Turbulent Flow in D-Type Corrugated Pipes: Flow Pattern and Friction Factor

2012 ◽  
Vol 134 (12) ◽  
Author(s):  
H. Stel ◽  
A. T. Franco ◽  
S. L. M. Junqueira ◽  
R. H. Erthal ◽  
R. Mendes ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Flow Pattern ◽  
Friction Factor ◽  
Reynolds Numbers ◽  
Important Change ◽  
Groove Width ◽  
Simple Method ◽  
Pressure Drag ◽  
Aspect Ratios

Turbulent flow in d-type corrugated pipes of various aspect ratios has been numerically investigated in terms of flow pattern and friction factor, for Reynolds numbers ranging from 5000 to 100,000. The present numerical model was verified by comparing the friction factor with experimental and numerical results from the literature. The numerical analysis suggested that d-type behavior exists for groove aspect ratios up to w/k = (groove width/rib height) = 2 independent of the pitch. However, for a ratio of w/k = 3 an important change in the flow pattern occurs so that the pressure drag exerted by the groove walls becomes important. It is shown that the friction factor is independent of the groove height as long as the flow is similar to a flow in a d-type corrugated pipe. Moreover, the friction factor curve for d-type pipes shows a logarithmic behavior as function of the Reynolds number, so that a simple method can be used to derive an expression for the friction factor as a function of the Reynolds number and the relative groove width only. The results may be useful to engineering projects that require a better prediction of the friction factor in d-type corrugated pipes.

Mean-flow scaling of turbulent pipe flow

1998 ◽  
Vol 373 ◽  
pp. 33-79 ◽  
Author(s):  
MARK V. ZAGAROLA ◽  
ALEXANDER J. SMITS
Keyword(s):  
Friction Factor ◽  
Friction Velocity ◽  
Outer Region ◽  
Reynolds Numbers ◽  
Velocity Profiles ◽  
Mean Velocity ◽  
Velocity Scale ◽  
The Mean ◽  
Log Law ◽  
High Reynolds

Measurements of the mean velocity profile and pressure drop were performed in a fully developed, smooth pipe flow for Reynolds numbers from 31×103 to 35×106. Analysis of the mean velocity profiles indicates two overlap regions: a power law for 60<y+<500 or y+<0.15R+, the outer limit depending on whether the Kármán number R+ is greater or less than 9×103; and a log law for 600<y+<0.07R+. The log law is only evident if the Reynolds number is greater than approximately 400×103 (R+>9×103). Von Kármán's constant was shown to be 0.436 which is consistent with the friction factor data and the mean velocity profiles for 600<y+<0.07R+, and the additive constant was shown to be 6.15 when the log law is expressed in inner scaling variables.A new theory is developed to explain the scaling in both overlap regions. This theory requires a velocity scale for the outer region such that the ratio of the outer velocity scale to the inner velocity scale (the friction velocity) is a function of Reynolds number at low Reynolds numbers, and approaches a constant value at high Reynolds numbers. A reasonable candidate for the outer velocity scale is the velocity deficit in the pipe, UCL−Ū, which is a true outer velocity scale, in contrast to the friction velocity which is a velocity scale associated with the near-wall region which is ‘impressed’ on the outer region. The proposed velocity scale was used to normalize the velocity profiles in the outer region and was found to give significantly better agreement between different Reynolds numbers than the friction velocity.The friction factor data at high Reynolds numbers were found to be significantly larger (>5%) than those predicted by Prandtl's relation. A new friction factor relation is proposed which is within ±1.2% of the data for Reynolds numbers between 10×103 and 35×106, and includes a term to account for the near-wall velocity profile.

scholarly journals Aerodynamics of smooth and rough square-section prisms at incidence in very high Reynolds-number cross-flows

2021 ◽  
Vol 62 (3) ◽  
Author(s):  
Nils Paul van Hinsberg
Keyword(s):  
Reynolds Number ◽  
Cross Sections ◽  
Reynolds Numbers ◽  
Circular Cylinders ◽  
Surface Boundary ◽  
Experimental Proof ◽  
Surface Boundary Layer ◽  
Pitch Moment ◽  
The Mean ◽  
High Reynolds

Abstract The aerodynamics of smooth and slightly rough prisms with square cross-sections and sharp edges is investigated through wind tunnel experiments. Mean and fluctuating forces, the mean pitch moment, Strouhal numbers, the mean surface pressures and the mean wake profiles in the mid-span cross-section of the prism are recorded simultaneously for Reynolds numbers between 1$$\times$$ × 10$$^{5}$$ 5 $$\le$$ ≤ Re$$_{D}$$ D $$\le$$ ≤ 1$$\times$$ × 10$$^{7}$$ 7 . For the smooth prism with $$k_s$$ k s /D = 4$$\times$$ × 10$$^{-5}$$ - 5 , tests were performed at three angles of incidence, i.e. $$\alpha$$ α = 0$$^{\circ }$$ ∘ , −22.5$$^{\circ }$$ ∘ and −45$$^{\circ }$$ ∘ , whereas only both “symmetric” angles were studied for its slightly rough counterpart with $$k_s$$ k s /D = 1$$\times$$ × 10$$^{-3}$$ - 3 . First-time experimental proof is given that, within the accuracy of the data, no significant variation with Reynolds number occurs for all mean and fluctuating aerodynamic coefficients of smooth square prisms up to Reynolds numbers as high as $$\mathcal {O}$$ O (10$$^{7}$$ 7 ). This Reynolds-number independent behaviour applies to the Strouhal number and the wake profile as well. In contrast to what is known from square prisms with rounded edges and circular cylinders, an increase in surface roughness height by a factor 25 on the current sharp-edged square prism does not lead to any notable effects on the surface boundary layer and thus on the prism’s aerodynamics. For both prisms, distinct changes in the aerostatics between the various angles of incidence are seen to take place though. Graphic abstract

scholarly journals Plunging Airfoil: Reynolds Number and Angle of Attack Effects

Aerospace ◽  
2021 ◽  
Vol 8 (8) ◽  
pp. 216
Author(s):  
Emanuel A. R. Camacho ◽  
Fernando M. S. P. Neves ◽  
André R. R. Silva ◽  
Jorge M. M. Barata
Keyword(s):  
Reynolds Number ◽  
High Performance ◽  
Angle Of Attack ◽  
Systems Design ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Low Reynolds Numbers ◽  
Operational Conditions ◽  
Naca0012 Airfoil ◽  
The Mean

Natural flight has consistently been the wellspring of many creative minds, yet recreating the propulsive systems of natural flyers is quite hard and challenging. Regarding propulsive systems design, biomimetics offers a wide variety of solutions that can be applied at low Reynolds numbers, achieving high performance and maneuverability systems. The main goal of the current work is to computationally investigate the thrust-power intricacies while operating at different Reynolds numbers, reduced frequencies, nondimensional amplitudes, and mean angles of attack of the oscillatory motion of a NACA0012 airfoil. Simulations are performed utilizing a RANS (Reynolds Averaged Navier-Stokes) approach for a Reynolds number between 8.5×103 and 3.4×104, reduced frequencies within 1 and 5, and Strouhal numbers from 0.1 to 0.4. The influence of the mean angle-of-attack is also studied in the range of 0∘ to 10∘. The outcomes show ideal operational conditions for the diverse Reynolds numbers, and results regarding thrust-power correlations and the influence of the mean angle-of-attack on the aerodynamic coefficients and the propulsive efficiency are widely explored.

Heat Transfer and Flowfield Measurements in the Leading Edge Region of a Stator Vane Endwall

1999 ◽  
Vol 121 (3) ◽  
pp. 558-568 ◽  
Author(s):  
M. B. Kang ◽  
A. Kohli ◽  
K. A. Thole
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Secondary Flows ◽  
Edge Region ◽  
Leading Edge Vortex ◽  
Stator Vane ◽  
Edge Vortex ◽  
The Mean

The leading edge region of a first-stage stator vane experiences high heat transfer rates, especially near the endwall, making it very important to get a better understanding of the formation of the leading edge vortex. In order to improve numerical predictions of the complex endwall flow, benchmark quality experimental data are required. To this purpose, this study documents the endwall heat transfer and static pressure coefficient distribution of a modern stator vane for two different exit Reynolds numbers (Reex = 6 × 105 and 1.2 × 106). In addition, laser-Doppler velocimeter measurements of all three components of the mean and fluctuating velocities are presented for a plane in the leading edge region. Results indicate that the endwall heat transfer, pressure distribution, and flowfield characteristics change with Reynolds number. The endwall pressure distributions show that lower pressure coefficients occur at higher Reynolds numbers due to secondary flows. The stronger secondary flows cause enhanced heat transfer near the trailing edge of the vane at the higher Reynolds number. On the other hand, the mean velocity, turbulent kinetic energy, and vorticity results indicate that leading edge vortex is stronger and more turbulent at the lower Reynolds number. The Reynolds number also has an effect on the location of the separation point, which moves closer to the stator vane at lower Reynolds numbers.

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