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Characteristics of Hydraulic Jump in U-Shaped Channels

  • Research Article - Civil Engineering
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Abstract

A hydraulic jump is the rapid transition from a supercritical to subcritical flow. This transition is characterized by large-scale turbulence and energy dissipation. Despite the importance of understanding the hydraulic jump to design hydraulic structures, few studies have aimed on hydraulic jumps in U-shaped channels. In this paper, the 3D pattern of hydraulic jumps in U-shaped channels is studied numerically. The variations of the flow free surface are predicted using the volume of fluid scheme. Also, the flow field turbulence is simulated using the standard \(k-\varepsilon \) and RNG \(k-\varepsilon \) turbulence models. According to the numerical modeling results, the standard \(k-\varepsilon \) turbulence model estimates the flow characteristics with more accuracy. A comparison between the laboratory and numerical results shows that the numerical model simulates the flow field characteristics with good accuracy. For example, in the hydraulic jump model with a relative discharge \(({q=Q/{\sqrt{( {gD^{5}})}}})\) equal to 0.321 and a Froude number \(({{F}_1})\) equal to 4.85, the values of MAPE, RMSE and \({R}^{2}\) are calculated 7.617, 0.022 and 0.989, respectively. Next, 45 numerical models are simulated in different hydraulic conditions and some relationships are provided for calculating the sequent depth \(({{h_2 }/{h_1 }})\), hydraulic length \(({{L_\mathrm{j}}/{h_1}})\) and roller length \(({{L_\mathrm{r} }/{h_1}})\) ratios by analyzing their results.

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Abbreviations

\(A_{x}, A_{y}, A_{z}\) :

Fractional areas open to flow (−)

CDIS1:

Coefficient of production (−)

CDIS2:

Coefficient of decay (−)

CDIS3:

is coefficient of buoyancy (−)

D :

U-shaped channel diameter (L)

\(\mathrm{Diff}_\mathrm{T} \) :

Diffusion term (−)

\(\mathrm{Diff}_\varepsilon \) :

Diffusion of dissipation (−)

F :

Fluid volume fraction in a cell (−)

\(F_{1}\) :

Froude number at upstream of hydraulic jump (−)

\(f_{x},f_{y},f_{z}\) :

Viscous accelerations (−)

\(G_{x},G_{y},G_{z}\) :

Body accelerations (−)

\({G}_\mathrm{T}\) :

Turbulence production due to buoyancy effects (−)

g :

Acceleration gravity (L T\(^{-2}\))

\(k_\mathrm{T}\) :

Turbulence kinetic energy (L\(^{2}\) T\(^{-2}\))

\(L_\mathrm{j}\) :

Length of hydraulic jump (L)

\(L_\mathrm{r}\) :

Roller length (L)

p :

Pressure (M L\(^{-1}\) T\(^{-2}\))

\(P_\mathrm{T}\) :

Turbulent kinetic energy production (−)

Q :

Discharge in U-shaped channel (L\(^{3}\) T\(^{-1}\))

q :

Relative discharge (−)

R :

Mass source (−)

t :

Time (T)

u, v, w :

Velocity components (L T\(^{-1}\))

\(u_*\) :

Wall shear velocity (L T\(^{-1}\))

\(V_\mathrm{F}\) :

Fractional volume open to flow (−)

x, y, z :

Cartesian coordinate directions (L)

\(y_1 \) :

Distance of the cell center from the solid wall (L)

\(y^{+}\) :

Non-dimensional parameter (−)

\(h_{1}\) :

Depth of flow at upstream of hydraulic jump (L)

\(h_{2}\) :

Depth of the flow at downstream of hydraulic jump (L)

\(\mu \) :

Water viscosity (M L\(^{-1}\) T\(^{-1}\))

\(\varepsilon _\mathrm{T} \) :

Turbulence dissipation rate (L\(^{2}\) T\(^{-3}\))

\(\nu \) :

Kinematic viscosity (L\(^{2}\) T\(^{-1}\))

\(\rho \) :

Fluid density (M L\(^{-3}\))

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Authors and Affiliations

  1. Department of Civil Engineering, Razi University, Kermanshah, Iran

    Hamed Azimi

  2. Water and Wastewater Research Center, Razi University, Kermanshah, Iran

    Hamed Azimi

  3. Department of Water Engineering, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran

    Saeid Shabanlou

  4. Department of Environmental Engineering, College of Environment and Energy, Science and Research Branch, Islamic Azad University, Tehran, Iran

    Saeid Kardar

Authors
  1. Hamed Azimi
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  2. Saeid Shabanlou
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  3. Saeid Kardar
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Correspondence to Saeid Shabanlou.

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Azimi, H., Shabanlou, S. & Kardar, S. Characteristics of Hydraulic Jump in U-Shaped Channels. Arab J Sci Eng 42, 3751–3760 (2017). https://doi.org/10.1007/s13369-017-2503-5

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