4.1 Energy dissipation analysis
Figure 2 demonstrates that relative energy dissipation increases with increasing side jet angles. The largest ∆E/E1 values occur at θ = 150° for a constant Froude number and inclination of angle. Increasing the side jet angle results in more force and resistance against the incoming supercritical flow. Therefore, the use of side jets arrangement can dissipate higher energy for hydraulic jump as compared to the case of without jets and this is consistent with the observations of El Sayed [45]. Figure 2 also displays that ΔE/E1 increases with increasing Fr1 at a constant angle.
4.2 Side jet angles analysis
Figure 3a displays the component value of Ds/H decreases with increasing Fr1 for all test configurations, as maximum scour depth Ds value was less than the value of flow depth upstream the sluice gate H in the term Ds/H during the tests. Therefore, the maximum scour depth parameter Ds increases only with Fr1, since a higher energy of Fr1 results in an increase in scour hole parameters. In addition, increasing θ reduces the Ds/H value for all arrangements indicating that the maximum scour depth reduces as the jet angles increase. For average Froude numbers, using a jet with θ = 90°, 120°, and 150° decreases the scour depth Ds by approximately 11, 16, and 25%, respectively, compared to without a jet. The presence of side jets can dissipate more energy [45], and hence, the reduction in scour depth occurs. In particular, the flow of side jet against the incoming supercritical flow increases with the jet angle, and hence the energy dissipation increases, which results in reducing the scour hole parameters. In contrast, θ affects the maximum scour depth.
Given the same flow conditions, larger θ results in smaller Ls/H values (Fig. 3b). Hence, the scour length Ls decreases with increasing jet angles. Specifically, the average scour length reductions are approximately 9, 13, and 15% for jet angles of θ = 90°, 120°, and 150°, respectively, compared to without jet case. Increasing jet angles θ, against the incoming flow under gate, results in more energy dissipation, thus reducing hydraulic jump length, leading to a smaller scour length.
The results show that increasing θ can minimize the relative term Vs/H3 at all tested flow conditions (Fig. 3c). Specifically, the volume of a scour hole Vs decreases by 19, 31, and 40% compared to the case of no side jet for θ = 90°, 120°, and 150°, respectively. Furthermore, the minimum value of Fr1 produces the maximum term Vs/H3 value, as Vs value was less than H3 value in the term Vs/H3, and the maximum volume of scour Vs only occurs with larger Fr1 for each angle. As previously demonstrated, increasing θ dissipates more flow energy, and hence Vs decreases because the depth and length of scour become smaller downstream of the apron. In summary, it should be noted that the side flow jets can significantly be considered as a scour countermeasure especially with angles against the incoming flow. Furthermore, side jets may have more utility in eliminating the clog of jets that result from suspended solids and sediments, and are also simpler in design compared to floor flow jets.
4.2.1 Design equation for scour hole dimensions
Experimental data with dimensionless terms were employed to propose three equations to predict local scour parameters (Ds, Ls, and Vs) with the presence of side flow jets. With regard to regression analysis, the effective variables on local scour were used and the following equations were deduced:
$$\frac{{D_{{\text{s}}} }}{H} = 0.026 \cos \theta + 0.047 F_{r1} + 0.945\frac{G}{H} - 0.232F_{r2} - 0.061$$
(3)
$$\frac{{L_{{\text{s}}} }}{H} = 0.252 \cos \theta + 2.519 F_{r2} + 14.740\frac{G}{H} + 1.107F_{r1} + 1.042\frac{{V_{j} }}{{V_{1} }} - 5.289$$
(4)
$$\frac{{V_{{\text{s}}} }}{{H^{3} }} = 0.353 \cos \theta + 1.038 F_{r2} + 4.094\frac{G}{H} + 0.531\frac{{V_{j} }}{{V_{1} }} - 0.711$$
(5)
where G = sluice gate opening; H = flow depth upstream the sluice gate; and Fr2 = Froude number downstream of the jump.
Parameters that affect the scour hole in Eqs. 3–5 have p- values ˂ 0.0001 indicating a significant impacts on the local scour. Theses equations are valid for 90° ≤ θ ≤ 150°, 0.49 ≤ Vj/V1 ≤ 0.71, 0.16 ≤ G/H ≤ 0.26, 2.31 ≤ Fr1 ≤ 3.71, and 0.31 ≤ Fr2 ≤ 0.41. Figure 4 shows the comparison between the values of the measured relative local scour dimensions (Ds/H, Ls/H, Vs/H3) and the predicted values by Eqs. 3–5, respectively. These figures illustrate that the predicted values of Ds/H, Ls/H, and Vs/H3 are consistent with the measured values with R2 = 0.92, 0.89, and 0.98, respectively.
