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Investigating the characteristic of hydraulic T-jump on rough bed based on experimental and numerical modeling

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Abstract

Hydraulic jumps are recognized as inevitable phenomena that form when the supercritical flow induced by hydraulic structures transmits to the subcritical downstream flow. One of the common approaches to controlling the energy generated by hydraulic jumps is to expand the section of the stilling basin. The present paper aims to investigate the main characteristics of the gradual expanding T-jump on the rough bed open-channel. In this regard, a range of Froude numbers between 3 and 14, four diverging angles of transition (θ = 15, 22.5, 30, and 60º), and five rough beds (Ks = 2, 3, 4, 5, and 6 mm) were selected. Experimental results reveal when the height of the bed roughness is increased, it reduces the length of the T-jump, roller jump, and the secondary depth of the T-jump. Likewise, the same result is unfolded for the increase of divergence angle of the transition. The normalized length of the T-jump in terms of sequent depth of classical jump Lj/y*2 is estimated at around 3.73, confirming that the length of the gradual expanding T-jump on the rough bed is smaller than the classic jump and the smooth bed. The average amount of secondary depth reduction is accounted at approximately 30.51%, indicating that the tail-water depth required to form a T-jump is remarkably smaller than those corresponding quantities in the classic jump and the smooth bed. In addition, the results of simulated T-jumps demonstrate good agreements with the experimental ones. Numerical quantities show the secondary depths of the T-jumps on a rough bed experience approximately 12.9% and 16.8% reductions compared to the smooth bed. Besides, 2D variations of flow velocity illuminate the role of the dead zone areas that reduce the total length of the T-jumps. The findings of the present research would be of prominent importance in designing stilling basins to control significant energy induced by hydraulic jumps.

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Abbreviations

B :

Diverging ratio, where B = b1/b2

b 1 :

Width of narrow section (upstream)

b 2 :

Width of the channel (downstream)

D :

Dimensionless depth deficit parameter (y*2 − y2)/y*2

Fr1 :

Froude number in the initial section of the jump v1/ (gy1)0.5

g :

Gravitational acceleration

K s :

Height of bed roughness

L j :

Length of hydraulic jump

L r :

Length of roller jump

L T :

Length of the Transition

Re1 :

Reynolds number v1y1/ν

v 1 :

Average velocity in the initial section of the jump

X :

Longitudinal distance between the gate and the beginning of the expansion section

y 1 :

Supercritical depth of T-jump

y 2 :

Subcritical sequent depth of T-jump

y * 2 :

Subcritical sequent depth of classical jump

ν :

Kinematic viscosity of the fluid

ρ :

Density of the fluid

θ :

Diverging angle of the transition

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Acknowledgements

This experimental research was performed at the hydraulic laboratory of Gorgan University of Agricultural Sciences and Natural Resources, Iran, with financial support from Dr. Mehdi Meftah's grant. The first writer appreciates Dr. Amirahmad Dehghani, who solidified his enthusiasm to compile the aforesaid article. The writers acknowledge the worthwhile comments from the reviewers.

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Authors and Affiliations

  1. Department of Water and Hydraulic Engineering, Gorgan University of Agricultural Sciences and Natural Resources, Gorgan, Iran

    Emad Khanahmadi, Amir Ahmad Dehghani & Mehdi Meftah Halaghi

  2. Department of Civil Engineering, Mirdamad Institute of Higher Education, Gorgan, Iran

    Esmaeil Kordi

  3. Hydraulic Engineering IRPI-CNR (Consiglio Nazionale Delle Ricerche, Via Madonna Alta 126, 06128, Perugia, Italy

    Farhad Bahmanpouri

Authors
  1. Emad Khanahmadi
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  2. Amir Ahmad Dehghani
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  3. Mehdi Meftah Halaghi
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  4. Esmaeil Kordi
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  5. Farhad Bahmanpouri
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Correspondence to Farhad Bahmanpouri.

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Appendix

Appendix

The entire investigative quantities that were measured and plotted in the aforesaid study are presented in the following table. In case you need to access detailed data, please do not hesitate to contact the corresponding author. See Table 5 .

Table 5 Experimental observations
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Khanahmadi, E., Dehghani, A.A., Halaghi, M.M. et al. Investigating the characteristic of hydraulic T-jump on rough bed based on experimental and numerical modeling. Model. Earth Syst. Environ. 8, 5695–5712 (2022). https://doi.org/10.1007/s40808-022-01434-2

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