A Composite Energy Dissipation System Based on Pressure-Dividing Transition Mechanism for High-Head Dams in Constrained Valleys: Physical Model Validation

Abstract

Hydropower development in high-altitude regions increasingly confronts a challenging “trilemma”: high hydraulic heads, large unit discharges, and spatially constrained narrow valleys. Under such conditions, conventional energy dissipation measures frequently fail to prevent downstream riverbed scour, thereby threatening both ecological integrity and infrastructure safety. This study aims to propose, parametrically optimize, and physically validate a novel composite energy dissipation structure designed to resolve this specific trilemma based on a pressure-dividing transition mechanism. Using the Louli Hydropower Project as a case study (Q_max = 6944 m³/s, unit discharge q = 119 m³/(s·m), available basin length L = 78 m), we conducted systematic 1:100 scale physical model tests. The results demonstrate that conventional optimizations, such as secondary stilling basins and dentated sills, are ineffective under these boundary conditions, leading to incomplete hydraulic jumps and extended high-velocity zones. In contrast, the proposed composite structure, which integrates a deepened stilling basin (depth = 9 m), asymmetric sidewall widening (20 m offset), and a gentle slope transition (1:20 gradient), achieved superior performance. Under the 50-year design flood with controlled discharge operation, the energy dissipation rate increased significantly from 32.11% (baseline) to 63.49% (composite) at the end sill. Furthermore, the structure reduced comprehensive turbulence intensity by 17.8% and floor slab impact stress by 23.4%. These findings validate the composite system as a sustainable solution for high-head dams in constrained settings, offering benefits for riverbed protection and structural durability.

1. Introduction

Flood discharge and energy dissipation constitute critical components in high-head dam design, directly influencing operational safety and environmental sustainability. As hydropower development expands into high-mountain canyon regions worldwide, engineers encounter increasingly complex boundary conditions [1,2]. Approximately 60% of dams exceeding 100 m in height in China are located in topographically confined regions where spatial constraints prevent deployment of standard-length stilling basins, creating fundamental conflicts between high-energy inflows and limited dissipation capacity [3].

Bottom outlets serve essential functions in dam spillway systems, including flood discharge at medium–low water levels, sediment flushing during flood seasons, and emergency reservoir drawdown [4,5]. Compared with surface spillways, bottom outlets offer operational advantages such as lower activation water levels and flexible operation. However, their characteristically high outlet velocities and concentrated jet energy result in more severe hydraulic impacts on downstream structures, necessitating robust energy dissipation solutions. Consequently, research on bottom outlet energy dissipation optimization under specific engineering constraints holds significant practical value for ensuring long-term operational safety.

The stilling basin serves as the core structure for hydraulic jump energy dissipation, and understanding its fundamental hydraulic mechanics provides the theoretical basis for geometric optimization. Felder et al. [6] systematically investigated the influence of inflow conditions on the free-surface properties of hydraulic jumps, establishing that upstream boundary layer development significantly alters jump length and surface fluctuations, providing refined theoretical constraints for contemporary stilling basin design. Building upon this framework, Chanson et al. [7,8] conducted an in-depth analysis of turbulent structure and air–water two-phase flow characteristics in the hydraulic jump zone through physical model tests. Their research revealed that energy dissipation primarily occurs through turbulent shear and air entrainment mechanisms within the roller region. Li et al. [9] further characterized the statistical properties and spatial distribution patterns of fluctuating pressure on stilling basin floor slabs under submerged jet conditions. They demonstrated that maximum pressure fluctuations occur at approximately 0.3–0.5 times the jump length downstream of the toe.

These theoretical advances have been complemented by developments in measurement and evaluation methodologies. Traditional energy dissipation assessment relied primarily on macroscopic indicators such as energy dissipation rate and outlet velocity. However, Chachereau and Chanson [10] demonstrated through Acoustic Doppler Velocimetry (ADV) measurements that turbulence intensity distribution within the hydraulic jump zone provides more sensitive indicators of dissipation efficiency. Consequently, they established correlation models applicable to design optimization. Gaikwad et al. [11] investigated spatial pressure distributions and complex velocity fields through a comparative analysis of physical and numerical models, establishing computational fluid dynamics (CFDs) as a reliable complementary tool and extending the evaluation framework beyond traditional empirical measurements. Wang et al. [12] further established quantitative relationships between apron length and downstream velocity attenuation through prototype observations, providing validation data for numerical and physical model predictions.

To improve stilling basin performance beyond classical configurations, researchers have investigated various auxiliary energy dissipation devices and combined structural systems. Wei et al. [13] examined the effects of different end sill configurations on energy dissipation efficiency, finding that dentated sills enhance dissipation rates by 5–15% compared to continuous sills under Froude numbers ranging from 3.0 to 6.0. Felder and Chanson [14] studied stepped energy dissipators and reported favorable performance under moderate Froude number conditions (Fr < 4.5), attributing the enhanced dissipation to repeated boundary layer development and air entrainment at step edges. Wang et al. [15] demonstrated that differential sills increase jet spread angles by 30–50%, promoting lateral momentum exchange. However, the corresponding improvement in overall energy dissipation rate remained modest (typically 3–8%) due to reduced vertical mixing intensity.

Zhong et al. [16] employed a numerical simulation to analyze the influence of drop height on hydraulic jump morphology, finding that increased drop heights promote jump stabilization but require proportionally longer basins to contain the extended roller region. Zhang [17] investigated secondary stilling basin configurations and reported effective performance under low Froude number conditions (Fr < 3.5); however, under high Froude number conditions (Fr > 5.0), secondary basins exhibited diminished effectiveness due to insufficient jump development length and excessive momentum flux at the downstream transition, occasionally resulting in jump sweep-out failure. Wang et al. [18] employed a three-dimensional numerical simulation to visualize flow field structures within stilling basins, identifying recirculation zones and shear layer development patterns that inform geometric optimization.

These theoretical and experimental findings have informed successful energy dissipation designs for major hydropower projects, though under boundary conditions that differ substantially from constrained scenarios. The Xiangjiaba Hydropower Station (dam height 162 m) innovatively adopted a “high–low sill + secondary dam” combined stilling basin with a total length of 192 m, achieving staged energy release through stepped drops and controlling downstream riverbed scour depth to within 8 m below natural bed level [19,20]. The Xiluodu Hydropower Station (dam height 285.5 m) employed a “pressurized-to-free-flow + plunge pool” composite energy dissipation approach, utilizing a 150 m plunge pool length to achieve efficient dissipation under high-head conditions [21]. These projects demonstrate that effective energy dissipation under extreme hydraulic conditions is achievable when adequate spatial extent is available for dissipation structure deployment.

Despite these theoretical advances and engineering successes, a comprehensive review reveals that existing research predominantly addresses one or more of the following favorable conditions: (1) conventional valley boundaries typical of large hydropower projects, where stilling basin lengths of 100–200 m provide adequate space for complete hydraulic jump development; (2) moderate energy discharge conditions with inflow Froude numbers Fr < 4.0 and unit discharges q < 100 m³/(s·m), under which classical hydraulic jump theory demonstrates good predictive accuracy; (3) optimization of individual energy dissipation components, examining single-factor effects without considering synergistic interactions among multiple elements. Furthermore, although advanced turbulence-based evaluation metrics have been developed, their systematic application to design optimization under constrained conditions remains limited.

For small-to-medium hydropower projects simultaneously facing compound constraints of high-energy inflow, restricted dissipation length, and insufficient downstream scour resistance, the direct applicability of existing research findings requires careful verification. Under such conditions, conventional single-mechanism approaches may prove inadequate, suggesting the need for alternative design philosophies that distribute energy dissipation across multiple sequential mechanisms rather than concentrating dissipation at a single structural element.

The Louli Hydropower Project exemplifies these challenging boundary conditions: bottom outlets with substantial design discharge (maximum discharge of 6944 m³/s corresponding to unit discharge of 119 m³/(s·m)), high outlet velocities (18–22 m/s, corresponding to Fr = 4.8–5.9), deep downstream riverbed overburden comprising weathered granite with weak natural scour resistance (allowable near-bed velocity of only 3–4 m/s), and available stilling basin length of only 78 m constrained by steep valley walls on both banks. Preliminary physical model tests of conventional hydraulic jump energy dissipation schemes revealed significant deficiencies, including rapid flow zones extending approximately 300 m downstream, energy dissipation rates of only 32% within the stilling basin, and intermittent sidewall overflow under design flood conditions. These findings collectively demonstrate that conventional approaches are inadequate to satisfy the project requirements.

To address these engineering and environmental challenges, this study aims to propose, parametrically optimize, and physically validate a novel composite energy dissipation structure to resolve the specific “trilemma” of high hydraulic head, large unit discharge, and spatially constrained valley topography. The system is based on the “pressure-dividing transition mechanism,” which transforms intense turbulent dissipation into a gradual process through three sequential stages: (1) submerged jet diffusion in a deepened basin, (2) lateral shear via asymmetric widening, and (3) progressive frictional dissipation along a gentle slope transition. Using 1:100 scale physical model tests, the following study aims to: (i) optimize the geometric parameters of the composite structure; (ii) quantify its performance in terms of energy dissipation efficiency and flow regime improvement; (iii) evaluate its sustainability benefits through micro-flow indicators such as turbulence intensity and impact stress.

2. Materials and Methods

2.1. Project Overview and Hydraulic Challenges

The Louli Hydropower Project, located in a canyon section of the middle reaches of a river, serves as the engineering background for this study. The main characteristic parameters of the reservoir are presented in

Table 1. Main characteristic parameters of Louli Reservoir.

Parameter	Value	Unit
Total storage capacity	29,144	×104 m3
Flood control capacity (50-year)	19,902	×104 m3
Flood limited water level	84.00	m
Design flood level (500-year)	106.90	m
Check flood level (5000-year)	109.69	m
50-year flood control high water level	106.03	m
Dry season operating level	77.5–84.0	m

.

The overflow surface outlets adopt an open layout with a WES practical weir profile and a single opening net width of 12.00 m. The surface outlets primarily handle flood discharge at high water levels. The bottom outlets consist of 8 openings, each measuring 6.00 m × 6.50 m (width × height), with a bell-mouth inlet design to improve inflow conditions. The main design parameters are presented in

Table 2. Main design parameters of bottom outlets.

Parameter	Value	Unit
Number of openings	8	—
Single opening dimensions (W × H)	6.00 × 6.50	m
Inlet type	Bell-mouth	—
Floor slab elevation	70.00	m
Maximum design discharge	6944	m3/s
Outlet design velocity	18–22	m/s

. The bottom outlets serve multiple functions, including flood discharge at medium–low water levels, sediment flushing during flood seasons, and emergency reservoir drawdown, constituting the primary research subject of this study.

The energy dissipation design of Louli Project bottom outlets faces three major technical challenges: (1) Under the 50-year return period flood condition (upstream water level 100 m), all 8 bottom outlets operating with full discharge can release over 5700 m³/s, with outlet velocities reaching 18–22 m/s, unit discharge of approximately 119 m³/(s·m), and inflow Froude number Fr > 4.5, representing typical high-energy discharge conditions. (2) The downstream riverbed has deep overburden with deeply buried bedrock (overburden thickness approximately 15–20 m), and a natural riverbed allowable scour velocity of only approximately 3–4 m/s, far below conventional energy dissipation outlet velocity requirements. (3) Constrained by topography on both banks, the available stilling basin length is limited to approximately 78 m, with a lateral width of approximately 48 m, making it difficult to meet energy dissipation requirements through simply increasing stilling basin dimensions. These compound boundary conditions of “high energy, weak scour resistance, and short distance” constitute the core technical challenges of this project’s energy dissipation design and represent the engineering background and motivation for this research.

2.2. Physical Model Setup

This experiment involves free-surface open channel flow (weir flow, orifice discharge, stilling basin hydraulic jump/jet aeration, etc.). The physical model experiments were conducted between March and August 2023. According to the “Specification for Normal Hydraulic Model Test” (SL155-2012) [22], Froude similarity was adopted as the governing criterion. The geometric scale is λ_L = λ_B = 100. The main scales derived from Froude similarity are as follows: velocity scale λ_v = ${{\lambda }_L}^{0.5}$ = 100, time scale λ_t = ${{\lambda }_L}^{0.5}$ = 10, discharge scale λ_Q = ${{\lambda }_L}^{2.5}$ = 100,000, and roughness scale λ_n = ${{\lambda }_L}^{1/6}$ = 2.154. To physically scale down the roughness to match this requirement, the fixed bed topography was finished with a smoothed cement mortar surface, and the spillway structures (including surface spillways and bottom outlets) were constructed from polished transparent acrylic panels.

The model upstream section replicates approximately 900 m of prototype river reach (model approximately 9.00 m), with a lateral simulation width of approximately 600 m (model approximately 6.00 m), and topographic elevation simulation up to 112 m. The downstream section simulates approximately 2500 m of prototype river reach from the apron terminus (model approximately 25.00 m), with topographic elevation simulation up to 90 m. Test subjects include upstream and downstream river topography (fixed bed), spillway dam section (surface outlets and bottom outlets), stilling basin, and scour protection structures (apron, floor slab, gentle slope, end sill, etc.). The Stage-I and Stage-II riprap layers shown in Figure 1 represent different phased construction boundaries of the downstream riverbed scour protection deployed in the prototype. Simulating these was necessary to systematically evaluate localized scour patterns under varying phased conditions in the physical model.

The upstream boundary employs a constant-pressure stilling tower with flow straighteners and energy dissipation screens at the inlet to ensure uniform reservoir inflow and minimize lateral deflection. The downstream boundary is equipped with an adjustable tail gate, controlled according to the prototype “downstream water level–discharge relationship.” High-velocity jets from bottom outlets are prone to aeration; the model ensures unobstructed ventilation in gate chambers and conduits to avoid abnormal flow patterns caused by negative pressure scale effects. The model layout schematic is shown in Figure 1.

The spillway structures, including surface outlets, bottom outlets, piers, and stilling basin sidewalls, were fabricated from transparent acrylic panels for flow pattern observation. Critical control dimensions (openings, weir crest curves, end sills, and gentle slope start/end points) were machined with precision ≤ 0.2 mm (equivalent to prototype ≤ 2 cm). The fixed bed topography was controlled using the stake-point method for planimetric and elevation control, with cement mortar surface finishing and waterproof treatment. Topographic elevation tolerance was ≤2.0 mm (equivalent to prototype ≤ 0.20 m). Model photographs are shown in Figure 2.

2.3. Measurement Cross-Sections and Point Layout

To satisfy the evaluation system comprising “energy dissipation rate + turbulence intensity + RMS fluctuating pressure,” the measurement system specifications are as follows: Discharge was measured using electromagnetic flowmeters with ±0.5% accuracy, calibrated before testing using the volumetric method or standard orifice plate. Water levels were measured using fixed point gauges/staff gauges with ±0.1 mm accuracy (prototype ± 1 cm), with reference benchmark points established and daily zero-point verification. Water surface profiles were measured using a level/laser rangefinder with staff, accuracy ± 0.3 mm (prototype ± 3 cm). Velocities were measured using direct-reading photoelectric propeller current meters with ±2% accuracy, suitable for time-averaged velocities in relatively stable regions. Pressures were measured using piezometer tubes (static pressure head) with ±0.5 mm accuracy.

Test repeatability and uncertainty: Each test condition was repeated three times to ensure measurement reliability. Reported values represent the arithmetic mean of three repetitions. The coefficient of variation (CV) was less than 5% for velocity measurements and less than 8% for pressure measurements across all repeated tests. For turbulence intensity measurements using ADV, the sampling duration of 120 s at 50 Hz (6000 samples per point) ensured statistical convergence with standard error < 3% of reported values [23]. Measurement uncertainty for energy dissipation rate, propagated from discharge and water level uncertainties, was estimated at ±1.5 percentage points.

Measurement cross-section layout followed these principles: inlet control cross-sections were set at 3.5–10 cm upstream of the dam face for upstream water level and inflow uniformity verification; bottom outlet exit cross-sections were set within 0–1 opening heights downstream of the opening for initial jet condition measurement. To monitor flow development and energy attenuation, three cross-sections (Sections 1–3) were established at 1/4 L, 1/2 L, and 3/4 L (where L is the pool length) to track hydraulic jump roller development within the stilling basin. Two cross-sections (Sections 4–5) were set to monitor progressive energy release along the gentle slope, and three cross-sections were arranged in the downstream channel to capture downstream velocity attenuation and uniform flow recovery. Three measurement points were set at the end sill (upstream face, crest, and downstream face) for outlet control and impact zone determination. Water surface profile measurement points were arranged along the gentle slope and apron sections at 0.5–1.0 m intervals, with velocity and pressure measurement points at critical locations. The cross-sectional measurement point layout is shown in Figure 3.

2.4. Evaluation Metrics and Data Processing

Instantaneous velocities at typical cross-sections in stilling basin and gentle slope sections were measured using three-dimensional Acoustic Doppler Velocimetry (ADV), with a sampling frequency of 50 Hz and single-point sampling duration of 120 s. Turbulence intensity was calculated using the following equation:

$$T_u={\displaystyle \frac{\sqrt{\overline{u^{‘2}}}}{\stackrel{-}{u}}}\times 100\%$$

(1)

where $T_u$ is turbulence intensity (%), $u^{‘}$ is fluctuating velocity, and $\stackrel{-}{u}$ is the time-averaged velocity.

Pressure sensors (sampling frequency 200 Hz) were embedded at critical locations on apron floor slabs to measure fluctuating pressures generated by flow impacts. Impact stress was taken as the root mean square of fluctuating pressure:

$${\sigma }_{\mathit{rms}}=\sqrt{{\displaystyle \frac{1}{N}}{\sum }_{i=1}^N{(p_i-)}^2}$$

(2)

where ${\sigma }_{\mathit{rms}}$ is the root mean square impact stress, $p_i$ is instantaneous pressure, $\overline{p}$ is time-averaged pressure, and N is the number of sampling points. The dynamic pressure sensors recorded continuously for a duration of 120 s per test condition to achieve the required time-averaged and fluctuating pressure values.

3. Results

To address the sustainability trilemma of high hydraulic heads, large unit discharges, and spatially constrained valleys, this study conducted a systematic evaluation using a 1:100 physical model. The results are presented in a diagnostic sequence: first identifying the failure mechanisms of conventional measures, then validating the optimized composite structure, and finally quantifying its sustainability benefits via micro-flow indicators.

3.1. Verification of Discharge Capacity

The overflow surface outlets have a net width of 12.00 m as open overflow openings with a WES practical weir profile; the flood discharge/sediment flushing bottom outlets have opening dimensions of 6.00 m × 6.50 m (width × height) with a bell-mouth inlet section.

3.1.1. Surface Outlet Discharge Capacity

Because the surface spillways adopt an open layout with a WES practical weir profile, they operate exclusively under free-surface flow conditions. The theoretical design discharge was calculated using the standard WES practical weir free-flow equation ($Q= \epsilon mB\sqrt{2g}{H_0}^{1.5})$. Under surface spillway free discharge conditions, the experimental stage–discharge (H-Q) relationship was established by measuring corresponding discharges at varying upstream water levels. The relationship curve is shown in Figure 4. As shown in Figure 4, measured discharges slightly exceeded design values at all water level conditions, with deviations ranging from +1.15% to +3.49%, indicating that surface outlet discharge capacity meets design requirements with a certain safety margin.

3.1.2. Bottom Outlet Discharge Capacity

The bottom outlets operate under orifice flow conditions. The theoretical stage–discharge relationship was determined using the standard submerged orifice flow equation ($Q= \mu A\sqrt{2g(H-h_c)}$). The H-Q relationship under bottom outlet orifice discharge conditions is shown in Figure 5. Bottom outlet discharge capacity also meets design requirements. Under maximum discharge conditions (H = 112.53 m), the measured discharge was 6944.44 m³/s, demonstrating a measured 3.65% divergence from the theoretical design calculation. The H-Q relationship curves for both surface spillways and bottom outlets show monotonically increasing trends with smooth curves without discontinuities, indicating good inflow conditions and stable flow patterns.

3.2. Baseline Scheme Hydraulic Characteristic Analysis

3.2.1. Test Conditions

The baseline scheme adopted a conventional hydraulic jump stilling basin with an apron elevation of 79 m. According to engineering operational requirements, the typical test conditions listed in

Table 3. Baseline scheme test conditions.

Case No.	Description	Upstream Level (m)	Operation Mode	Discharge (m3/s)
B-1	8 bottom outlets open	99	Full open	5400
B-2	8 bottom outlets open	100	Full open	5700
B-3	4 bottom outlets open	99	Alternate	2700

are established.

3.2.2. Energy Dissipation Performance of Baseline Scheme

The energy dissipation rate was determined using the specific energy equation based on the total mechanical energy difference between the upstream reservoir and the specified downstream cross-sections. The “control condition” refers specifically to maintaining the downstream tailwater level dictated by the natural river stage–discharge relationship. The energy dissipation performance statistics for the baseline scheme under various conditions are summarized in

Table 4. Summary of baseline scheme energy dissipation performance.

Case No.	Energy Dissipation Rate at End Sill (%)	Apron Terminus Velocity (m/s)	Rapid Flow Zone (m)	Flow Pattern Characteristics
B-1	32.11	10.80	200	Unstable jump, tail oscillation
B-2	34.19	10.95	300	Jump moved downstream, rapid zone significantly extended
B-3	45.82	9.37	150	Relatively stable jump

. Note: All baseline energy dissipation rates are measured at the end sill location (elevation 79 m) to enable direct comparison with the composite structure at the same reference point.

The results indicate an insufficient energy dissipation rate. Under eight-outlet free discharge conditions (Cases B-1 and B-2), the energy dissipation rate at the end sill was only 32–34%, which is substantially below the typical engineering design requirement of over 50%. This finding demonstrates that the baseline scheme exhibits severely inadequate energy dissipation capacity for high-energy inflow conditions. The rapid flow zone was excessively long. As the upstream water level increased from 99 m to 100 m, the rapid flow zone extended dramatically from 200 m to 300 m, representing a 50% increase. The rapid flow zone is defined as the downstream extent where the depth-averaged velocity exceeds 4 m/s, which corresponds to the allowable scour velocity threshold for the downstream riverbed. This means that under design flood conditions, high-velocity flow will directly impact the unprotected downstream riverbed, posing serious threats to riverbed stability. The operation mode significantly influenced energy dissipation performance. Changing from eight-outlet full operation to 4-outlet alternate operation (Case B-3) increased the energy dissipation rate from 32.11% to 45.82%, representing an improvement of 13.71 percentage points. Correspondingly, the apron terminus velocity decreased from 10.80 m/s to 9.37 m/s, a reduction of 13.2%; the rapid flow zone shortened from 200 m to 150 m. However, the four-outlet operation mode cannot meet high-discharge flood release requirements, and even under these conditions, apron terminus velocity still exceeds twice the downstream riverbed allowable scour velocity (3–4 m/s).

3.2.3. Problem Identification

Based on the comprehensive analysis above, the baseline scheme exhibits the following prominent problems: (1) Insufficient energy dissipation efficiency: the energy dissipation rate at the end sill was only 32–34%, with substantial residual energy transmitted downstream. (2) Uncontrolled rapid flow zone: the rapid flow zone extended to 300 m under the 50-year flood condition, far exceeding the reasonable extent for protection engineering. (3) Unstable flow pattern: the hydraulic jump position oscillated significantly with discharge variations, resulting in poor operational reliability. (4) High scour protection pressure: the apron terminus velocity exceeded 10 m/s, imposing stringent requirements for downstream riverbed protection. These findings indicate that under the specific boundary conditions of the Louli Project, the conventional hydraulic jump stilling basin scheme cannot satisfy the energy dissipation and scour protection requirements, thereby necessitating the exploration of new energy dissipation structure configurations.

3.3. Limitation Analysis of Conventional Measures

To investigate the applicability of conventional engineering measures under constrained boundary conditions, experimental studies were first conducted on three schemes: secondary stilling basin, dentated sill energy dissipation, and differential sill diffusion.

3.3.1. Secondary Stilling Basin Scheme

A secondary stilling basin was added at the end of the bottom outlet stilling basin, with a basin length of 40 m and a sill height of 3 m, intended to achieve staged energy release through two-level drops. Experimental results under the 50-year design flood condition showed incomplete hydraulic jump formation in the primary basin. The flow exhibits undular rapid flow directly impacting the secondary basin. The velocity at the secondary sill is still reaching 8.4 m/s, causing the rapid flow zone to expand to 400 m (a 33% increase compared to the baseline scheme). The failure of the secondary stilling basin scheme is primarily attributed to the excessively high inflow energy density, with a unit discharge of approximately 119 m³/(s·m). Concurrently, the longitudinal length of the primary basin is constrained to only 78 m, which ultimately prevents adequate energy dissipation within such a limited distance.

3.3.2. Dentated Sill Scheme

The apron elevation was adjusted to 77 m, with dentated sills installed on the stilling basin end sill. Two configurations with 7 and 13 dentated sills were compared experimentally, with results shown in

Table 5. Summary of hydraulic parameters downstream of the stilling basin after installing dentated sills.

Scheme	Mid-Apron Velocity (m/s)	Rapid Flow Zone	Remarks
13 dentated sills	13.7	380 m downstream of end sill	Apron El. 77 m
7 dentated sills	10.1	200 m downstream of end sill	Apron El. 77 m
No dentated sills	10.7	210 m downstream of end sill	Apron El. 77 m

and Figure 6. The 13-sill configuration caused adjacent jets to interfere and superpose due to excessive sill density, increasing mid-apron velocity to 13.7 m/s; the seven-sill configuration showed only approximately 5% improvement. Furthermore, intense shear action at sill roots poses long-term cavitation damage risks.

3.3.3. Differential Sill Diffusion Scheme

Differential sills were installed at the bottom outlet exits (Figure 7 and Figure 8), comparing alternate-opening and bilateral configurations, with results shown in

Table 6. Summary of stilling basin energy dissipation rates after installing differential sills.

Configuration	Structure	Energy Dissipation Rate at End Sill (%)
Alternate-opening differential sills	Bottom outlets	34.59
Bilateral differential sills at each outlet	Bottom outlets	33.12

. Although differential sill schemes increased jet lateral spread angle (from 8° to 12–15°), energy dissipation rate improved by only 1–2.5 percentage points. Differential sills primarily affect the aerial diffusion phase of jets, while vertical momentum attenuation after water entry depends mainly on pool water depth and turbulent mixing conditions, which are minimally influenced by differential sills.

The above experiments clearly highlight the shortcomings of conventional measures under the compound boundary conditions of “high energy, short distance, high tailwater” at the Louli Project. First, the secondary stilling basin scheme fails due to insufficient primary basin length, preventing complete hydraulic jump formation and actually extending the rapid flow zone to 400 m. Second, the dentated sill energy dissipation scheme is hindered by the excessively high inlet Froude number, where dense 13-sill configurations cause jet interference superposition and raise the mid-apron velocity to 13.7 m/s. Finally, the differential sill diffusion scheme only improves aerial diffusion, yielding a very limited contribution to overall in-basin energy dissipation. The failure of these conventional measures stems from their inability to extend the effective energy dissipation distance within the fixed basin length. Each approach attempts to enhance dissipation intensity within the constrained 78 m basin, rather than extending the dissipation zone beyond the basin. Therefore, the solution lies in extending the effective dissipation zone through a gentle slope transition downstream of the end sill, fundamentally redistributing the spatial energy dissipation pattern from “concentrated” to “progressive” mode.

3.4. Composite Energy Dissipation Structure Design

Based on the preceding analysis, this study proposes a composite energy dissipation structure implementing the pressure-dividing transition mechanism. The core design philosophy transforms the traditionally concentrated and intense, turbulent dissipation at the end sill into gradual dissipation distributed along an extended flow path, achieving rational spatial energy distribution.

3.4.1. Design Principles

The composite energy dissipation structure comprises three functional units (Figure 9): Deep stilling basin (primary energy dissipation zone): Floor slab elevation lowered to 70 m, pool depth increased to 9 m (approximately 3 m deeper than baseline scheme). Increased pool water depth facilitates full diffusion of submerged jets and enhances turbulent mixing energy dissipation. Pool length remains 78 m unchanged.

Gentle slope transition section (progressive energy release zone): End sill elevation set at 74 m, with a 1:20 gradient gentle slope transition section downstream. The hydraulic mechanism of the gentle slope section involves flow gradually decelerating during the climbing process under the combined action of gravity component and along-path friction resistance, with kinetic energy progressively converting to potential energy and turbulent dissipation energy, avoiding intense pressure fluctuations caused by traditional vertical drops.

Asymmetric widening sidewalls (lateral turbulence enhancement zone): Right bank sidewall remains fixed, left bank sidewall gradually offsets leftward from the stilling basin entrance, accumulating 20 m offset at the end sill, forming an asymmetric diverging structure. Sidewall lateral expansion induces lateral shear turbulence in the flow, further enhancing energy dissipation. Key parameters of the composite energy dissipation structure were determined through systematic experimental optimization, shown in

Table 7. Key design parameters of the composite energy dissipation structure.

Parameter	Design Value	Basis for Selection
Stilling basin floor elevation	70.0 m	Ensure pool depth ≥ 9 m, satisfy submerged jet requirements
End sill elevation	74.0 m	Comprehensive consideration of sill height and tailwater level matching
Gentle slope gradient	1:20	Determined through parametric optimization tests
Sidewall offset	20 m	Satisfy overflow prevention requirements, enhance lateral diffusion
Gentle slope section length	80 m	Matched with gradient, terminus elevation 79 m

.

3.4.2. Sensitivity Analysis of Gentle Slope Gradient

To optimize the gentle slope gradient, three schemes (1:15, 1:20, 1:25) were compared experimentally under identical test conditions, with results shown in

Table 8. Comparison of different gentle slope gradients.

Gradient	Energy Dissipation Rate at Gentle Slope Terminus (%)	Rapid Flow Zone (m)	Water Surface Stability in Gentle Slope Section
1:15	58.62	320	Significant surface fluctuations
1:20	64.37	290	Smooth water surface
1:25	63.85	285	Smooth water surface

. Based on comprehensive consideration of energy dissipation performance, construction footprint, and engineering economy, the 1:20 gentle slope gradient was selected. The physical basis for this optimum involves the balance between gravitational deceleration and frictional dissipation: steeper gradients (1:15) provide higher gravitational deceleration per unit length but shorter total residence time, while gentler gradients (1:25) extend residence time but with diminishing incremental benefits and increased construction footprint. The 1:20 gradient achieves optimal integration of these competing factors for the specific inlet conditions (Fr ≈ 4.5, q = 119 m³/(s·m)).

3.5. Hydraulic Characteristics of Composite Structure

3.5.1. Energy Dissipation Performance of Composite Structure

Table 9. Summary of stilling basin energy dissipation rates for all operating conditions.

Condition	Outlets	Operation Mode	Baseline Comparison (%)	Energy Dissipation Rate at End Sill (%)	Energy Dissipation Rate at Gentle Slope Terminus (%)
Design flood (500-year)	Surface outlets	Free discharge	58.12	65.00	—
50-year flood	8 bottom outlets	Free discharge	37.70	54.21	+5.59
50-year flood	8 bottom outlets	Controlled discharge	63.49	69.73	+31.38
Check flood (5000-year)	Combined	Free discharge	52.35	61.88	—

summarizes the energy dissipation rates under various conditions for the composite structure. To ensure consistent comparison with the baseline scheme, energy dissipation rates are reported at two locations: (1) end sill (elevation 74 m), enabling direct comparison with baseline values in Table 4; (2) gentle slope terminus (elevation 78 m), representing the total dissipation achieved by the complete composite system.

Clarification of reported values: The Abstract and Conclusions cite improvement from 32.11% (baseline, Table 4, Case B-1) to 63.49% (composite structure under controlled discharge, Table 9), representing the maximum achievable improvement under optimized operation. Under free discharge conditions, the improvement is more modest (32.11% → 37.70% at end sill), reflecting the importance of operational control in maximizing composite structure performance. Taking the 50-year flood condition (eight-outlet controlled discharge) as the primary comparison case: Energy dissipation rate at end sill increased from 32.11% (baseline) to 63.49% (composite), an improvement of 31.38 percentage points. Energy dissipation rate at the gentle slope terminus reached 69.73%, indicating an additional 6.24 percentage points of dissipation along the gentle slope. This represents approximately double the baseline energy dissipation efficiency.

3.5.2. Rapid Flow Zone Reduction

As shown in

Table 10. The composite structure effectively shortened the rapid flow zone.

Condition	Baseline Rapid Flow Zone (m)	Composite Rapid Flow Zone (m)	Reduction (m)	Reduction (%)
8 outlets, free	300	295	5	1.7%
8 outlets, controlled	300	280	20	6.7%

, the composite structure effectively shortened the rapid flow zone.

Under controlled discharge conditions, the rapid flow zone was shortened from 300 m to within 280 m (measured from the dam face to the point where depth-averaged velocity falls below 4 m/s). While the absolute reduction appears modest, the significance lies in the improved quality of flow within this zone. Turbulence intensity and pressure fluctuations are substantially reduced, as discussed in Section 3.6. Consequently, the downstream riverbed experiences less severe hydraulic loading despite a similar rapid flow zone extent.

3.6. Quantitative Evaluation of Energy Dissipation Mechanisms

To thoroughly reveal the superiority of the composite energy dissipation structure, this study introduced turbulence intensity and impact stress as quantitative evaluation indices.

3.6.1. Turbulence Intensity Analysis

Under 50-year return period conditions, turbulence intensity measurements in the submerged rapid flow core zone are shown in Figure 10. The composite structure reduced turbulence intensity by approximately 17.8%, with the mechanism as follows: the gentle slope transition section gradually decelerates flow along the path, avoiding abrupt velocity changes; energy dissipation transforms from “concentrated” to “progressive” mode, reducing localized turbulence intensity.

3.6.2. Impact Stress Analysis

Impact stress measurements at the apron leading edge are shown in Figure 11. The composite structure reduced apron floor slab impact stress by approximately 23.4%, with the mechanism being: gentle slope transition achieves “soft landing” energy dissipation, avoiding direct high-energy flow impingement on apron; residual kinetic energy of flow reaching apron is substantially reduced.

A summary of the improvement effects of the composite structure compared to the baseline scheme is shown in Figure 12. The composite structure achieves rational spatial energy distribution and progressive dissipation through a systematic design comprising three key elements: deep basin deepening, asymmetric widening, and gentle slope transition. This integrated approach yields significant improvements in energy dissipation efficiency, flow pattern stability, and structural safety.

4. Discussion

4.1. Mechanism of the Pressure-Dividing Composite Structure

The core innovation of this study lies in the shift from a “concentrated” to a “progressive” energy dissipation mode. Traditional stilling basins rely heavily on the hydraulic jump to dissipate energy within a confined volume. However, under the constrained conditions of the Louli Project, the baseline scheme failed because the limited space was insufficient to contain the turbulent diffusion. The proposed composite structure succeeds by implementing a “pressure-dividing transition mechanism” via three synergistic effects: (1) Enhanced submerged diffusion: Deepening the basin to 9 m increases the water volume for shearing, facilitating initial jet diffusion. (2) Lateral turbulence induction: Asymmetric sidewall widening induces lateral flow expansion and large-scale vortical structures, enhancing dissipation beyond vertical mixing. (3) Progressive de-escalation via gentle slope: The 1:20 gentle slope utilizes friction and gravity to gradually convert kinetic energy into potential energy. This “soft landing” prevents secondary hydraulic drops and stabilizes the downstream flow.

4.2. Comparison with Conventional Measures

Our results highlight the limitations of conventional methods in spatially constrained environments. While secondary basins are effective for low Froude numbers (Fr < 3.5), our tests showed they failed under high-energy conditions (Fr = 4.8–5.9), aggravating the flow regime. Similarly, dentated sills proved counterproductive due to jet interference. In contrast, the composite structure achieved a 63.49% energy dissipation rate, demonstrating that spatial redistribution is superior to localized resistance devices in narrow, high-head scenarios.

4.3. Implications for Sustainability and Engineering Resilience

The findings have significant implications for sustainable hydropower development. (1) Eco-hydraulic protection: By reducing turbulence intensity by 17.8% and controlling the rapid flow zone, the structure minimizes hydraulic shear stress on the riverbed, protecting benthic habitats from erosion. (2) Structural durability: The 23.4% reduction in impact stress and 29.7% decrease in maximum instantaneous pressure translated to reduced structural fatigue and lower maintenance requirements. The proposed structure thus offers a resilient solution that balances flood discharge safety with environmental protection.

4.4. Limitations and Future Research

While the present study provides valuable insights into the performance characteristics of the optimized submerged structure, several limitations should be acknowledged, and directions for future research identified.

The physical model experiments were conducted at a geometric scale of 1:100, which introduces potential scale effects that warrant consideration. At this reduced scale, phenomena governed by surface tension and viscosity may not scale correctly according to Froude similarity. In particular, air entrainment processes during wave breaking over the structure crest, and the associated energy dissipation mechanisms, may be underrepresented in the model compared to prototype conditions [8,23,24]. Similarly, turbulent energy dissipation within the water column may exhibit Reynolds number dependencies that are not fully captured at the model scale. These scale effects could result in the physical model underestimating the total energy dissipation achieved at prototype scale.

The findings of this study are derived entirely from controlled laboratory experiments. While physical modeling remains an essential tool for parametric optimization, field validation under prototype conditions is necessary to confirm the applicability of the results. Prototype monitoring would enable assessment of performance under irregular bathymetry, variable sediment characteristics, and the full spectrum of metocean conditions not reproducible in the laboratory. Future research should prioritize the instrumentation and monitoring of prototype installations to validate the laboratory-derived structural response predictions.

5. Conclusions

This study addressed the engineering “trilemma” of high-head and large unit discharge, and constrained valleys faced by the Louli Hydropower Project. Through systematic 1:100 scale physical model tests, we validated a composite energy dissipation system. The main conclusions are as follows:

(1)

Discharge capacity meets design requirements. Surface and bottom outlet verification tests demonstrate that both structure types meet design requirements across the full discharge range. Under maximum conditions, measured discharges exceed design values by 3.5–3.7%, providing adequate safety margins.

(2)

Conventional energy dissipation measures exhibit significant limitations under constrained boundary conditions. Under Louli Project’s compound boundary conditions of “high energy, short distance, high tailwater”: the secondary stilling basin scheme fails to form complete hydraulic jump due to insufficient primary basin length, actually extending the rapid flow zone to 400 m; the dentated sill scheme is limited by excessively high inlet Froude number, with the 13-sill configuration causing jet interference superposition and increasing mid-apron velocity to 13.7 m/s; the differential sill diffusion scheme increases the jet spread angle from 8° to 12–15° but improves energy dissipation rate by only 1–2.5 percentage points.

(3)

Composite energy dissipation structure significantly improves energy dissipation efficiency. The proposed “deep stilling basin (9 m depth) + asymmetric widening sidewalls (20 m offset) + 1:20 gentle slope transition” composite structure increases the gentle slope terminus energy dissipation rate from the baseline scheme’s 32.11% to 63.49% under 50-year flood (eight-outlet controlled discharge) conditions. This is an improvement of 31.38 percentage points, representing an approximately 100% relative increase. The gentle slope transition section contributes approximately 6.24 percentage points of additional energy dissipation rate beyond the end sill, demonstrating the effectiveness of the “pressure-dividing transition” mechanism.

(4)

Composite energy dissipation structure effectively improves flow field quality. Comprehensive turbulence intensity in the submerged rapid flow core zone decreases from 30.3% to 24.9%, a 17.8% reduction; the apron floor slab impact stress decreases from 12.8 kPa to 9.8 kPa, a 23.4% reduction; the maximum instantaneous pressure decreases by 29.7%; the rapid flow zone shortens from 300 m to within 280 m under controlled discharge conditions; the apron terminus velocity decreases from 10.95 m/s to below 8.5 m/s.

(5)

Composite energy dissipation structure successfully eliminates sidewall overflow risk. The asymmetric widening design effectively lowers outlet water surface elevations: 85.7 m under design flood conditions and 86.6 m under check flood conditions. Both are below the left bank floodplain elevation (90 m), successfully eliminating sidewall overflow engineering hazards present in the original design scheme.