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Flow Field Measurements Around Isolated, Staggered, and Tandem Piers on a Rigid Bed Channel


Experimental investigations are presented on the characterization of flow turbulence and velocity fields around circular piers placed in isolated, tandem, and staggered arrangements in a rigid bed channel with identical flow conditions. Instantaneous velocity measurements are undertaken using a 16 MHz micro down-looking Acoustic Doppler Velocimeter (ADV) at different grid points along the flow depth. The streamline pattern obtained from the velocity fields is presented on vertical planes around the piers. Further, the resultant contours of vortices are plotted for all three types of arrangements, i.e., isolated, tandem, and staggered arrangements, to understand the strength of the vortices around the piers. Apart from the above investigations, the turbulence characteristics such as turbulence intensities, turbulent kinetic energy, velocity power spectra and Reynolds shear stresses at different planes are also presented for all three configurations of piers. The turbulence characteristics are used to identify the influence of one pier over others in the tandem and staggered arrangements compared to that of the isolated piers. The horseshoe vortex system, quantified by its vorticity and strength, is found to be predominant in the staggered configuration. A horseshoe vortex is formed at 0.36d, 0.9d and 0.35d (d is the diameter of the pier) upstream of the isolated pier, front piers of the tandem and front piers of the staggered case, respectively. A zone of recirculation is formed just upstream of the rear pier in the tandem case. The Reynolds shear stresses near the bed, turbulent kinetic energy and turbulence intensities are also found to be quite significant downstream of the front pier in the staggered arrangement compared to those in the isolated and tandem arrangements. The turbulent kinetic energy at the mid-flow depth is found to be 2.5 times higher than that near the bed. The velocity power spectra reveals that the strength of wake vortices is 2.5 times greater for the front piers of the staggered case than that of the tandem front piers with Strouhal numbers, \({S}_{t}\) = 0.26 and 0.112 for the staggered and tandem cases, respectively, near the bed. The present study enhances the understanding of the flow structure around isolated, tandem and staggered bridge piers.

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X :

Streamwise direction

Y :

Transverse direction

Z :

Vertical direction

d :

Diameter of pier (cm)

R e :

Flow Reynolds number

F r :

Froude number

ν :

Kinematic viscosity of the fluid (106 m2/s)

\(\rho\) :

Mass density of water (103 kg/m3)

δ :

Viscous sublayer thickness (mm)

U :

Approaching mean flow velocity (cm/s)

u :

Instantaneous velocity in X- direction (cm/s)

v :

Instantaneous velocity in Y- direction (cm/s)

w :

Instantaneous velocity in Z- direction (cm/s)

u 0 :

Time averaged velocity in X- direction (cm/s)

v 0 :

Time averaged velocity in Y- direction (cm/s)

w 0 :

Time averaged velocity in Z- direction (cm/s)

u :

Fluctuation velocity component in X- direction (cm/s)

v :

Fluctuation velocity component in Y- direction (cm/s)

w :

Fluctuation velocity component in Z- direction (cm/s)

U c :

Critical velocity of the flow (cm/s)

U * :

Shear velocity (cm/s)

Z 0 :

Approach flow depth (cm)

U + :

Non-dimensional time averaged velocity in X- direction

V + :

Non-dimensional time averaged velocity in Y- direction

W + :

Non-dimensional time averaged velocity in Z- direction

\(-\rho \overline{{u }{^{\prime}}{v}{^{\prime}}, } -\rho \overline{{v }{^{\prime}}{w}{^{\prime}}, } -\rho \overline{{u }^{{\prime}}{w}^{{\prime}}}\) :

Reynolds shear stresses (N/m2)

k :

Turbulence kinetic energy (cm2/s2)

f :

Frequency (Hz)

\({S}_{t}\) :

Strouhal number

\(\overrightarrow{V}\) :

Velocity vector

\(\overrightarrow{ds}\) :

Differential displacement vector over a closed curve

\(\overline{\omega }\) :

Vorticity (1/s)

\(\Gamma\) :

Circulation (m2/s)


Radial planes with respective to flow axis

\(f.{P}_{u}\left(f\right)\) :

Streamwise velocity power spectra (cm2/s2)

\(f.{P}_{v}\left(f\right)\) :

Transverse velocity power spectra (cm2/s2)

\(f.{P}_{w}\left(f\right)\) :

Vertical velocity power spectra (cm2/s2)

a :

Point of separation from pier boundary

A :

Area enclosed between vorticity contours

P :

Centre to centre distance between piers with incident angle α


Acoustic Doppler Velocimeter


Particle Image Velocimeter


Laser Doppler Velocimeter


Signal to Noise Ratio


Acoustic Doppler Velocity Profiler


Supervisory control and data acquisition


Variable Frequency Drive


Phase Space Threshold De-spiking


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Authors are thankful to the Centre of Excellence (CoE) on “Water Resources and Flood Management”, of SVNIT Surat funded under TEQIP-II, Ministry of Education (MoE), Government of India, necessary infrastructure support for conducting the experiments. The authors are thankful to the Editor, Associate Editor and anonymous Reviewers for their constructive comments and suggestions which improved the readability of the manuscript.

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Correspondence to Prafulkumar Vashrambhai Timbadiya.

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Pasupuleti, L.N., Timbadiya, P.V. & Patel, P.L. Flow Field Measurements Around Isolated, Staggered, and Tandem Piers on a Rigid Bed Channel. Int J Civ Eng (2021).

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  • Tandem and staggered piers
  • ADV
  • Vorticity
  • Velocity power spectra
  • Vortex shedding