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Research Papers: Fundamental Issues and Canonical Flows

Wall Pressure in Developing Turbulent Pipe Flows

[+] Author and Article Information
Kamal Selvam

Laboratoire Ondes et Milieux Complexes,
CNRS & Université Le Havre Normandie,
Le Havre 76600, France

Emir Öngüner

Department of Aerodynamic and
Fluid Mechanics,
BTU Cottbus–Senftenberg,
Cottbus 03046, Germany

Jorge Peixinho

Laboratoire Ondes et Milieux Complexes,
CNRS & Université Le Havre Normandie,
Le Havre 76600, France
e-mail: jorge.peixinho@univ-lehavre.fr

El-Sayed Zanoun

Department of Aerodynamics and
Fluid Mechanics,
BTU Cottbus–Senftenber,
Cottbus 03046, Germany;
Benha Faculty of Engineering,
Benha University,
Benha 13512, Egypt

Christoph Egbers

Department of Aerodynamics and
Fluid Mechanics,
BTU Cottbus–Senftenberg,
Cottbus 03046, Germany

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received August 21, 2017; final manuscript received December 15, 2017; published online March 29, 2018. Assoc. Editor: Sergio Pirozzoli.

J. Fluids Eng 140(8), 081203 (Mar 29, 2018) (7 pages) Paper No: FE-17-1518; doi: 10.1115/1.4039294 History: Received August 21, 2017; Revised December 15, 2017

Velocity fluctuations are widely used to identify the behavior of developing turbulent flows. The pressure on the other hand, which is strongly coupled with the gradient of the mean velocity and fluctuations, is less explored. In this study, we report the results of wall pressure measurements for the development of pipe flow at high Reynolds numbers along the axial direction. It is found that the pressure fluctuations increase exponentially along the pipe with a self-similarity scaling. The exponential growth of the pressure fluctuations along the pipe saturates after reaching a critical position around 50 diameters from the inlet. It qualitatively agrees with the critical position usually adopted for fully developed turbulence, which was obtained from earlier velocity fluctuations at various locations along the pipe centerline. Results also show that the exponential growth of the pressure fluctuations is weakly affected by the presence of ring obstacles placed close to the pipe inlet. Finally, it is found that the pressure fluctuations decrease as a function of Reynolds number, contrary to the boundary layer flow.

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Figures

Grahic Jump Location
Fig. 2

Friction factor, λ, in fully developed turbulent flow. (a) λ as a function of Re. The lines represent the Hagen–Poiseuille (laminar), the Prandtl, and the Blasius laws described in the text. (b) λ−1/2 as a function of Re×λ1/2. The bottom line is the Prandtl fit for Ref. [21] smooth pipe data and the top line is a fit to the present experiments.

Grahic Jump Location
Fig. 5

Wall pressure fluctuations at Re≃300,000 along the pipe for different ring disturbances. The lines are exponential fits.

Grahic Jump Location
Fig. 1

(a) Schematic of the pipe test section. The inset shows a detailed view of the ring perturbation. (b) Mean velocity profiles normalized by the centerline velocity, Uc, at the inlet (x/D=0) and downstream at x/D=110 for different Reynolds numbers. The velocity profiles at x/D=110 are fitted with a log law fit: u¯/Uc=0.092 ln(y/R)+1.0, where Uc is the centerline mean velocity, y the position from the wall, and R the radius of the pipe.

Grahic Jump Location
Fig. 4

Wall pressure fluctuations, p′/Δp, along the pipe, x/D, for different Re with ring perturbations at 1.3D from the inlet. The perturbation makes a area obstruction of (a) 10, (b) 20, (c) 30, and (d) 40%. The insets are sketches of the ring obstruction. The shaded area marks the position of local effects of the rings.

Grahic Jump Location
Fig. 6

Wall pressure fluctuations as a function of the Reynolds number in the saturated region for different ring disturbances. (a) p′/Δp versus Re and (b) p′+ versus Reτ in linear scale. The inset is also p′+ versus Reτ in log scale.

Grahic Jump Location
Fig. 3

Wall mean pressure and fluctuations along the pipe without ring: (a) p¯−p¯e, (b) p′/Δp, (c) p′+, and (d) p′+/α versus x/D for different Reynolds numbers

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