Turbulence statistics of flow causing scour around circular and oblong piers

Abstract

In this study, experimental investigations of the flow pattern around an oblong pier (OP) mounted on a rigid flat surface are carried out in a laboratory flume and the results are compared with that of a circular pier (CP) for better understanding of the flow hydrodynamics applicable to scour. The novelty of this work is the study of turbulence characteristics such as mean velocities, Reynolds stresses, turbulent kinetic energy and the contributions of burst-sweep cycles to the total Reynolds shear stresses along the oblong and the circular piers and their inter-comparison, which have not been previously addressed. Application of power spectral analysis suggests that the peak values of vortex shedding frequency for OP are higher than those of CP, indicating lower wake instabilities for OP. The influence of perturbed flow around the CP is considerably higher than that of OP, resulting in more scour around the CP, under identical flow conditions.

Keywords:

• Burst-sweep cycle
• circular and oblong piers
• scour structure
• shear stress
• spectral analysis
• Strouhal number
• turbulence

Acknowledgements

The authors would like to acknowledge the technical staff of the Hydraulics Laboratory, IIT Bombay for their assistance in carrying out the experiments. The authors would like to express their gratitude to Jayasankar, Aslam, Jisha and Kalpesh for their help rendered at various stages of data processing and Dr Haradhan Maity and Dr Sayahnya Roy for the fruitful input during the preparation of the manuscript. Authors are thankful to the anonymous reviewers and Editors for their suggestions, which improved the quality of the manuscript significantly.

Notation

ADV	=	acoustic Doppler velocimeter (–)
CL	=	centreline (–)
CP	=	circular pier (–)
d50	=	mean diameter of bed material (mm)
d	=	diameter of pier (m)
dsc	=	scour depth (m)
F	=	Froude number (–)
fvs,cp	=	vortex shedding frequency due to circular pier (Hz)
fvs,op	=	vortex shedding frequency due to oblong pier (Hz)
FFT	=	fast Fourier transform (–)
g	=	acceleration due to gravity (m s−2)
h	=	depth of flow (m)
H	=	hole size (–)
Ii,H	=	indicator function for the ith quadrant (–)
Iu, Iv, Iw	=	turbulence intensities with respect to u, v, w (m s−1)
l	=	length of pier (m)
L	=	characteristic length (m)
n	=	number of observations (–)
OP	=	oblong pier
psd	=	power spectral density (m2 s−1)
Q	=	flow discharge (m3 s−1)
Qi	=	ith quadrant (–)
Re =	=	Reynolds number (–)
Si,H	=	stress fraction (–)
St =	=	Strouhal number (–)
TKE	=	turbulent kinetic energy (m2 s−2)
$u_{\ast }$ =	=	shear velocity (m s−1)
uin, vin, win	=	instantaneous streamwise, transverse and vertical velocity components (m s−1)
u, v, w	=	time-averaged velocity components y components (m s−1)
$u^{\mathrm{\prime }}$,$v^{\mathrm{\prime }}$,$w^{\mathrm{\prime }}$	=	velocity fluctuations in streamwise, transverse and vertical directions (m s−1)
u+, v+, w+	=	normalized intensities in streamwise, transverse and vertical directions (–)
uv+, vw+, uw+	=	normalized Reynolds shear stress components (–)
$\overline{u^{\mathrm{\prime }}{v}^{\mathrm{\prime }}}$,$\overline{v^{\mathrm{\prime }}{w}^{\mathrm{\prime }}}$, $\overline{u^{\mathrm{\prime }}{w}^{\mathrm{\prime }}}$	=	average Reynolds shear stress components (m2 s−2)
$u^{\mathrm{\prime }}{v}^{\mathrm{\prime }}$,$v^{\mathrm{\prime }}{w}^{\mathrm{\prime }}$, $u^{\mathrm{\prime }}{w}^{\mathrm{\prime }}$	=	covariance terms (m2 s−2)
U	=	depth-averaged velocity (m s−1)
x, y, z	=	coordinate system (m)
ρ	=	density of fluid (kg m−3)
ν	=	kinematic viscosity (m2 s−1)