Effect of Triangular Zigzag Blocks on Hydraulic Jump Characteristics and Energy Dissipation in a Rectangular Stilling Basin

Abstract
Background and Objectives
Hydraulic jumps are fundamental phenomena in hydraulic engineering, serving as critical mechanisms for dissipating excess kinetic energy in supercritical flows. These abrupt transitions from high-velocity, shallow-depth regimes to slower, deeper states are critical for protecting downstream structures such as spillways, dams, and irrigation channels from erosion and structural damage. The efficiency of energy dissipation during a hydraulic jump directly influences the design, durability, and cost-effectiveness of hydraulic systems. Stilling basins, which are engineered structures designed to stabilize hydraulic jumps, often incorporate roughness elements like baffle blocks to enhance turbulence and energy dissipation. However, traditional designs with smooth beds or uniform block arrangements may fail to optimize performance, leading to oversized basins, higher construction costs, or insufficient energy dissipation under variable flow conditions. This study addresses these limitations by investigating the effects of non-uniform, zigzag-arranged triangular blocks on hydraulic jump characteristics. The primary objectives of this study are threefold:
Quantify Performance Metrics: Evaluate the effects of triangular blocks with varying lengths (4.5 cm, 5.5 cm, and 6 cm), installation angles (30°, 45°, and 60°), and roughness densities (10%, 12.2%, and 13.3%) on key hydraulic jump characteristics, including sequent ratio, jump length, and energy dissipation efficiency.
Identify Optimal Configuration: Determine the block geometry and arrangement that maximize energy dissipation while minimizing basin dimensions.
Economic and Practical Implications: Develop actionable design guidelines for cost-effective stilling basins that achieve high hydraulic performance with adhering to material and construction constraints.

Methodology
The experimental setup consisted of a 6 m long, 0.5 m wide, and 0.6 m high rectangular flume, with a steel bed and transparent Plexiglas sidewalls to facilitate flow visualization. A closed-loop recirculating system provided steady water supply, while discharge was continuously monitored using an ultrasonic flowmeter with ±1% accuracy. Supercritical inflow was generated by a sharp-edged sluice gate fixed at a 1.5 cm opening, yielding initial Froude numbers (Fr1) ranging from 6.8 and 9.5. Downstream polypropylene tubes (2–12 cm diameter) were strategically placed perpendicular to the flow to control hydraulic jump location and ensure flow regime stability.
Triangular blocks were fabricated from 1 cm thick Plexiglas sheets, featuring right-angled triangular profiles with a uniform height of 2 cm and base lengths of 4.5 cm, 5.5 cm, and 6 cm. The blocks were arranged in three rows spaced 10 cm apart, with each row oriented at 30°, 45°, or 60° relative to the channel centerline. Roughness density, defined as the ratio of total projected block area to stilling basin floor area, was 10%, 12.2%, and 13.3% for the respective base lengths. Each row comprised 15 blocks, yielding a total of 45 units per configuration. A smooth-bed control case was tested to establish baseline hydraulic jump characteristics. Dimensional analysis using the Buckingham π-theorem was employed to reduce governing parameters (block geometry, incoming Froude number Fr1, and Reynolds number) to dimensionless groups, facilitating systematic performance evaluation of block performance across the tested flow regimes. The effectiveness of each configuration was assessed by measuring sequent depth ratio (y₂/y₁), relative jump length (Lj/y₁), and relative energy dissipation (ΔE/E₁), with all results compared against the smooth-bed reference condition.

Findings
Sequent Depth Reduction
- The 12.2% roughness density configuration (5.5 cm base blocks at 45°) produced the greatest sequent depth reduction of 13 %–24 % relative to the smooth-bed case, with maximum effectiveness at higher incoming Froude numbers (Fr1 > 7). This marked reduction in sequent depth ratio (y₂/y₁) lowers tailwater elevation, enabling shorter and more cost-effective stilling basin sidewalls.
- The 13.3% density arrangement (6 cm blocks at 30°) exhibited minimal influence at Fr1 < 6.8, but performance improved progressively with increasing Fr1, achieving 12%–15% reduction at Fr₁ = 9.5.
- The 10% density configuration (4.5 cm blocks at 60°) displayed the lowest efficacy, yielding only 3%–10% sequent depth reduction and underscoring the critical role of intermediate block dimensions and optimal alignment angles in hydraulic jump control.
Jump Length Optimization
- The 12.2% roughness density configuration (5.5 cm blocks at 45°) shortened jump length by 16%–24% across the tested Froude number range (Fr₁ = 5.6–6.8), consistently outperforming both the lower-density (10%) and higher-density (13.3%) arrangements.
- At Fr1 = 5.6, jump length decreased from 0.62 m (smooth bed) to 0.47 m (12.2% density), corresponding to a 24% reduction in required stilling basin length.
- Paradoxically, the 13.3% configuration (6 cm blocks at 30°) increased jump length by 10%–15% at lower Froude numbers values (Fr₁ = 6.8–7.5), likely due to excessive turbulence disrupting jump cohesion and delaying transition to subcritical flow.
Energy Dissipation Efficiency
- The 12.2% roughness density configuration achieved an average increase in relative energy dissipation (ΔE/E₁) of 13.4% compared with the smooth-bed case, demonstrating the superior ability of optimally arranged zigzag triangular blocks to generate turbulent vortices that effectively break down residual kinetic energy.
- The 13.3% density arrangement attained an average increase of 11.9% at higher Froude numbers (Fr₁ > 7.5) but proved less effective at lower inflows, reflecting the sensitivity of excessive roughness to flow regime.
- The 10% density configuration lagged considerably, registering only 10.7% average increase and thereby emphasizing the necessity of balanced roughness density for maximizing energy dissipation efficiency within stilling basins.
Mechanisms of Performance Enhancement
Angled Block Arrangement
The 45° installation angle proved optimal for lateral flow redirection, generating strong cross-channel secondary currents and coherent roller vortices that significantly intensified turbulence intensity without compromising hydraulic jump stability or cohesion.
Zigzag Pattern
The staggered row spacing of 10 cm effectively disrupted coherent longitudinal flow structures, suppressing the formation of large-scale spanwise eddies that would elongate the hydraulic jump.
Block Geometry
The right-angled triangular profiles significantly minimized flow separation and form drag compared to rectangular or cylindrical baffle elements, thereby reducing undesirable head loss upstream of the hydraulic jump.

Conclusion
Triangular zigzag blocks with a 12.2% roughness density (5.5 cm base length, 45° orientation) emerged as the optimal design for rectangular stilling basins. This configuration reduced sequent depth ratio (y₂/y₁) by up to 24%, shortened relative jump length (Lj/y₁) by 24%, and increased relative energy dissipation (ΔE/E₁) by an average of 13.4% compared with the smooth-bed reference, significantly outperforming traditional smooth-bed and alternative block arrangements. These findings provide practical, actionable design for hydraulic engineers, enabling the development of significantly more compact, cost-effective stilling basins without compromising hydraulic performance. By substantially reducing basin length, sequent depth, and required sidewall height, the proposed zigzag triangular block system minimizes concrete volume, excavation, and long-term maintenance costs while enhancing structural resilience against high-energy supercritical flows. Future research should investigate hybrid stilling basin configurations combining zigzag blocks with complementary dissipative elements, such as end sills, or chute blocks, to further optimize energy dissipation across extended Froude number regimes and variable approach flow conditions.