Investigation of the Possibility of Energy Attenuators as Stream Aerators: Optimising the Design of Hydraulic Structures to Improve Their Environmental Performance

DOI: https://doi.org/10.70389/PJS.100177

Additional information

• Ethical approval: N/a
• Consent: N/a
• Funding: No industry funding
• Conflicts of interest: N/a
• Author contribution: Taalaibek Toktogulov and Zulumkan Teshebaeva — conceptualization, methodology, data curation, writing-original draft preparation. Mukhtarbek Aldashov — visualization, investigation, and supervision. Duishenaly Zhorokulov and Seyitgazy Artykbaev — software, validation, writing-reviewing, and editing. All authors read and approved the final manuscript
• Guarantor: Taalaibek Toktogulov
• Provenance and peer-review: Unsolicited and externally peer-reviewed
• Data availability statement: The data that support the findings of this study are available on request from the corresponding author.

Keywords: Gas exchange, Hydraulic structures, Oxygen dissolution, Oxygen saturation, Turbulence.

Peer Review
Received: 3 September 2025
Last revised: 31 October 2025
Accepted: 1 November 2025
Version accepted: 5
Published: 15 December 2025

Plain Language Summary Infographic

Highlights

• Energy-absorbing water walls as aerators of water flows to increase the efficiency of water oxygenation in hydraulic structures.
• Energy absorber spillways are substantial in ecology, contributing to water aeration and improving its quality.
• Physical processes affecting aeration determine the intensity of oxygen saturation in water.
• One of the key factors affecting aeration is the level of turbulence in the flow.

Introduction

Hydraulic structures, such as spillways, dams, and sluices, generate high-speed water flows with significant kinetic energy. To prevent the destructive effects of these flows, energy attenuators are used, the main function of which is to reduce the speed of the water by creating turbulent zones. However, in addition to dissipating energy, such structures can perform an important ecological function by promoting the aeration of water flows, saturating them with oxygen. The water aeration process in the waterfall zone is caused by several physical phenomena, including the intensive mixing of water with air, the formation of cavitation bubbles, and an increase in the gas exchange area. In natural watercourses, such as rivers and waterfalls, these mechanisms contribute to high oxygen content in the water. Engineering systems can achieve a similar effect by using water breakers as aeration devices.

Turbulence is the chaotic movement of a liquid, accompanied by the formation of vortices and localised rarefaction zones. The higher the level of turbulence, the more intense the mixing of water with air, and thus the aeration process. Numerous air bubbles appear in a turbulent flow, which increases the contact area between the gas and liquid phases. This aspect is particularly noticeable in natural environments, such as mountain rivers and waterfalls, where the water flow is naturally oxygenated when it encounters obstacles. In engineering systems, such as dam spillways or aeration plants, turbulence is used to force water oxygenation. Various hydraulic structures are designed to create the most turbulent regime possible, which promotes intensive gas exchange.

The current challenge lies in addressing the issue of low dissolved oxygen (DO) levels in hydraulic structures, particularly in systems where oxygen transfer efficiency is limited by factors such as flow dynamics, water temperature, and the design of aeration devices. To ensure optimal water quality and meet regulatory targets for DO, there is a pressing need for modernization of aeration systems. This includes enhancing the performance of existing spillways, optimising flow configurations, and integrating more efficient oxygen transfer technologies. Achieving this will not only support regulatory compliance but also contribute to the sustainability of aquatic ecosystems by maintaining the necessary oxygen concentrations for biological processes. The problem, therefore, is improving oxygenation efficiency in a way that meets both environmental standards and engineering performance goals while minimising energy consumption and operational costs.

Improving aeration efficiency using energy-dissipating spillways is important for both hydraulic engineering and environmental management, as effective water oxygenation plays a crucial role in maintaining aquatic ecosystems. Puri et al.¹ showed that higher turbulence increases water oxygenation and that optimised spillway geometry – especially roughened surfaces – amplifies this effect. They also examined cavitation bubble formation at flow breaks, concluding that these bubbles materially aid gas transfer, with cavitation intensity governed by discharge and the water’s incidence angle on the obstacle. Linz et al.², Kim et al.³ analysed various geometric shapes of spillways and found that porous and protruding elements increased the aeration efficiency. The study also emphasised the importance of selecting the correct materials for spillways, which affected the durability and stability of the structure. Zhao et al.⁴ proved that increasing the surface roughness of the spillways contributed to more efficient air entrainment by the water flow. Their study indicated that the greatest improvement in aeration was observed when using combined types of spillways with different levels of roughness. Xue et al.⁵ studied the effect of bubble size on bubble dispersion in the flow and confirmed that small bubbles dissolved more slowly in the water, improving aeration. Experiments demonstrated that varying the pressure in the waterway system could control bubble size.

Maissour et al.⁶, Bai et al.⁷ studied the effect of the distance between water holes on their aerated properties and found that the optimal distance improved the oxygen saturation of water. The research also examined the influence of flow rate on the process’s efficiency, determining that the ideal distance was contingent upon particular hydraulic conditions. While significant progress has been made in understanding the individual factors affecting aeration efficiency in spillway systems, such as turbulence, spillway geometry, and bubble dynamics, existing research has primarily focused on isolated parameters without fully integrating the complex interplay between these elements. Specifically, the combined effects of spillway spacing and flow rate on oxygen transfer efficiency have not been thoroughly explored under controlled laboratory conditions. This gap is addressed by the current study, which investigates how variations in both spillway spacing and flow rate influence aeration performance. By considering these factors together, this research provides a more comprehensive understanding of the design parameters that optimize aeration, filling a critical gap in the existing body of knowledge. The study aimed to investigate the potential of using energy-absorbing water walls as aerators of water flows to increase the efficiency of water oxygenation in hydraulic structures.

Research goals:

1. To study experimentally the influence of energy dampers on the characteristics of the water-air layer in aerated flows.
2. To evaluate the efficiency of the aeration capacity of different types of energy-absorbing spillways in hydraulic structures.
3. To consider the influence of the design features of water separators on the process of oxygen saturation of water, the following tasks will be addressed:

• quantify the effect of spillway height on dissolved oxygen (DO) concentration;
• determine optimal spillway spacing under varying flows;
• compare efficiency of solid vs thin-walled energy absorbers.

Materials and Methods

During the study, key parameters were selected to assess hydrodynamic processes and water characteristics, which was used for a comprehensive analysis of the flow and its aeration properties. These parameters included both the hydrodynamic characteristics of water flow and physicochemical parameters that reflected changes in the composition of the water under study. Table 1 provides a visual representation of the study parameters, their units, ranges and measurement methods, which demonstrate the methods and results of the experiment.

Table 1: Parameters used to assess the aeration characteristics of spillways.
Parameter	Unit of Measurement	Value Range	Measurement Method
Live section of the tray (Ssec)	m²	Depends on the tray size	Direct measurement of the flow cross-sectional area
Specific water consumption (q)	L/s	25–125 L/s	Measurement with a valve and a flow meter
Water temperature (t)	°C	5–30 °C	Temperature sensor or thermometer
Water velocity in the tray (vl)	m/s	0.1–2.0 m/s	Anemometer or speed sensor
Water velocity at the spillway (vvs)	m/s	0.1–2.0 m/s	Anemometer or speed sensor
Dissolved oxygen concentration (r)	mg O₂/L	0–15 mg O₂/L	Electrochemical oxygen analyser
Biochemical oxygen demand (BOD₅)	mg O₂/L	0–50 mg O₂/L	BOD method (5 days) using biological analysis
Oxygen deficiency (D)	mg O₂/L	0–15 mg O₂/L	Difference between oxygen saturation and measured oxygen level
Aeration capacity of spillways (Ψ)	m³/s	Depends on the design of the spillway	Calculation using an empirical formula based on water flow and aeration time
Concentration of organic matter	mg O₂/L	0–50 mg O₂/L	BOD₅ analysis (Five-day biochemical oxygen demand)
Source: Compiled by the authors.

These parameters were selected due to their high information content and direct connection with the key aeration mechanisms, which were used to objectively assess the efficiency of the energy absorber spillways in real hydrodynamic conditions. The following formulas were used in the study (1–8): (1)

where q – specific water consumption (L/s), the flow rate of water passing through the spillway; μ – spillway flow coefficient, a dimensionless coefficient that characterizes the flow properties of the spillway and accounts for the effect of the spillway’s design on the flow rate; hav – average height of the jet cross-section at the spillway (m), representing the vertical distance from the spillway to the flow surface where water is discharged; g – free fall acceleration (m/s²), the acceleration due to gravity, approximately 9.81 m/s² at Earth’s surface; H – pressure at the spillway (m), the pressure exerted by the water at the point of discharge. (2)

where s – distance along the flow; ϖa – hydraulic size of air bubbles; D – turbulent diffusion coefficient, which determines the rate at which air is mixed into the water; ds/dy – change in the surface area of the water-air interface with respect to the flow depth, ensuring the continuity of air and water interaction in the aeration process. (3)

where f – a function related to flow characteristics; h̃ – Karman’s constant; v0 – dynamic velocity;  – relative depth; a = 1.25 – constant. (4)

Where s– surface area of the water-air contact; η = y/h– relative depth of the flow, where φ is the distance from the water surface, and h is the total flow depth; ϖa– hydraulic size of air bubbles; θ– angle of flow inclination; v*– dynamic velocity of the water; n– exponent determining the influence of aeration processes on the efficiency of air diffusion in water, considering flow parameters. (5)

where ; p_h = 08k; p0 = 08k function  can be taken from the Bakhmetiev-Pavlovsky integral tables for watercourses with a reverse bottom slope; ϖa = 0.24 m/s – hydraulic size of air bubbles; ph and p0 – pressures in the water before and after passing through the aeration process. (6)

where D0 and Dt – oxygen deficiency before and after water discharge, mg О2/l; ср – average solubility of oxygen in water at a given temperature; с0 and сt – oxygen concentration in water before and after water discharge. (7)

where β – empirical coefficient that addresses the presence of dissolved impurities in water; Рnorm – normal atmospheric pressure (10.33 m H2O); сТ – solubility of gas in pure water, сТ = mР; m – phase equilibrium constant (Henry’s constant), which depends on temperature; Р- the partial pressure of gas above the liquid: Р = Ра+h/2; Ра – atmospheric pressure. Aeration capacity refers to the ability of a spillway to promote oxygen dissolution in water through mechanisms such as turbulence, air entrainment, and surface renewal. In this study, aeration capacity is defined as the volumetric aeration capacity, denoted as Ψ, which represents the actual volume of water undergoing aeration per unit time (in cubic metres per second). This metric quantifies the hydraulic throughput of the aeration process, describing how effectively the spillway facilitates gas exchange between air and water during flow over or through the energy-dissipating zone. It is calculated as: (8)

where: Ψ – Aeration capacity, v – Volume of water exposed to aeration (m³), t – Aeration time (s). If considering aeration capacity in terms of dimensionless efficiency, it may be expressed as a ratio comparing the observed aeration efficiency to a theoretical maximum or literature benchmarks. In this context, Ψ depends on spillway geometry, such as width, drop height, and energy dissipation pattern, as well as on hydraulic parameters including flow rate, jet velocity, and residence time. The raw DO data have been provided in the supplementary materials to ensure transparency and further analysis. For context, the saturation of DO at the experimental temperature (18–22°C) has been compared with the typical saturation, which is approximately 9 mg/L at 20 °C. The recorded DO values (2–3 mg/L) are significantly lower than this typical value, requiring additional interpretation. This suggests incomplete water aeration or a need for optimization of experimental conditions. (9)

where К – mass transfer coefficient; а – specific surface area of phase contact; t – duration of water aeration at one stage of the spillways, s; where D0 and Dt – oxygen deficiency before and after water discharge.

The influent water characteristics were recorded for each experimental run, including biochemical oxygen demand (BOD5), chemical oxygen demand (COD), total suspended solids (TSS), pH, and temperature. These parameters were measured to characterise the initial water quality and ensure consistency across all test conditions. BOD5 measures the oxygen required by microorganisms to decompose organic material over five days, while COD quantifies the oxygen required to oxidise both biodegradable and non-biodegradable organic matter. TSS represents the concentration of suspended particles, which can affect aeration and water quality. pH indicates the water’s acidity or alkalinity, which influences both biological activity and oxygen solubility, and temperature affects oxygen solubility in water, with the temperature range reported for each run.

Prior to each experimental run, the DO content of the influent water was adjusted to near-zero to ensure that subsequent oxygenation could be attributed entirely to the aeration process. This conditioning was achieved by sparging with nitrogen gas (N₂) for approximately 15–20 minutes while continuously mixing the tank until the DO concentration fell below 0.2 mg L–1. The DO level was then stabilised for five minutes to confirm uniform distribution before initiating the flow into the experimental flume.

Probe calibration and verification. The DO-550 optical probe (Germany) was calibrated at the start of each measurement day and checked after each experimental series. Two-point calibration was used: (1) air-saturated water at ambient temperature as the 100% reference, and (2) the N₂-sparged water as the zero-oxygen baseline. Intermediate verification was conducted every three to five runs using standard solutions prepared according to ISO 5814. Sensor drift never exceeded ±0.1 mg L–1 during a full day of testing.

Spatial sampling strategy. To capture oxygen gradients and flow heterogeneity, DO readings were collected at three longitudinal sections – upstream (0.5 m before the spillway), immediately downstream of the crest, and at 1 m, 3 m, and 5 m downstream – each at mid-depth and near the free surface. This arrangement produced six to nine sampling points per run, allowing depth-averaged DO profiles to be constructed.

Residence-time determination. Hydraulic residence time was calculated as the ratio of the effective aeration-zone volume to the measured discharge (t = V/Q). The active volume (V) was determined from direct measurements of flow depth, width, and the effective aeration length, verified by a conservative tracer test (NaCl pulse method) to account for bypass zones and recirculation. The average residence time across all runs ranged from 2.8 to 3.5 s, varying slightly with discharge and spillway height.

Replication and statistical treatment. Each experimental condition (combination of spillway geometry and flow rate) was repeated three to five times to ensure reproducibility. For every replicate, DO data were time-averaged once steady conditions were established. Mean values and standard deviations were calculated, and 95% confidence intervals were derived using the Student t-distribution. One-way and two-way ANOVA were applied to evaluate the effects of spillway type, discharge, and spillway spacing on aeration metrics (kLa, Oxygen Transfer Rate (OTR), S%). Post-hoc Tukey tests were used where significant main effects were detected (p < 0.05). Data processing and statistical analyses were performed in OriginPro 2023 and R 4.3.2, following standard reproducibility protocols.

Initial DO levels were adjusted to near zero using a DO-scrubbing technique in which nitrogen or another inert gas was bubbled through the water. This procedure minimised the initial oxygen content and enabled accurate measurement of aeration effects. Calibration of the DO probe was conducted both before and after each experimental series using reference conditions of known DO concentration – air-saturated water and controlled gas mixtures – to maintain accuracy across the expected measurement range. The probe was positioned at multiple locations and depths along the experimental flume, including upstream of the aeration zone, at the spillway crest, and at several downstream points, with measurements taken near the surface and mid-depth to account for vertical stratification caused by velocity gradients.

DO measurements were recorded at frequent intervals throughout each experiment, typically every 30 seconds to two minutes, with increased sampling frequency during the initial aeration phase when DO concentration changed most rapidly. The residence time was determined by the ratio of the aeration-zone volume to the measured flow rate, reflecting the duration the water remained within the active aeration region. This parameter was reported for each experimental condition, as it directly governed oxygen-transfer efficiency. The measured contact times ranged from approximately 2.8 to 3.5 seconds, depending on discharge and spillway height, ensuring that oxygen transfer was measurable while remaining representative of realistic field conditions such as those observed in aeration basins or natural watercourses.

The study’s experimental flume had a 1.5% slope, which made it possible to simulate flow conditions that are common in hydraulic structures. Inlet conditions were carefully controlled using a valve and flow meter to maintain consistent water flow rates between 25 and 125 L/s, ensuring stable and reproducible hydraulic conditions throughout the experiments. The flume was constructed from 10 mm-thick transparent Plexiglas, providing structural stability while allowing visual observation of flow behaviour and air-water interactions. DO measurements were performed using a DO-550 sensor, which was calibrated before and after each series of runs. Calibration involved immersing the probe in water with known oxygen concentrations, prepared using saturated air or a controlled gas mixture, to ensure accuracy across the range of experimental conditions. Three to five replicate runs were conducted for each flow condition to reduce measurement variability. Error bars representing standard deviations were included in the figures to illustrate data variability, and statistical analyses, including ANOVA, were used to determine the significance of differences in DO concentration across different spillway designs, flow rates, and experimental configurations.

Scale effects were carefully evaluated because the 0.2 m-wide laboratory model does not fully replicate the hydrodynamic conditions of prototype-scale spillways. The model was scaled to prototype conditions using Froude similarity, which ensures that the ratio of inertial to gravitational forces is identical between the model and the prototype. The Froude number (Fr) is defined as: (10)

where v is the mean flow velocity (m s–1), g is the gravitational acceleration (9.81 m s–2), and L is the characteristic length, typically the hydraulic depth of flow (m). Maintaining an equal Froude number between the model and prototype preserves the dynamic similarity of free-surface behavior, including flow regime, wave formation, and jet trajectory. Across the experimental range (v = 0.3–2.0 m s–1; L ≈ 0.15–0.25 m), the Froude number varied between 0.25 and 1.15, indicating transitions from subcritical to near-critical flow. These regimes are representative of typical energy-dissipating zones in prototype spillways. The Reynolds number (Re), representing the ratio of inertial to viscous forces, was also computed to verify turbulent flow conditions (11)

where ν is the kinematic viscosity of water (≈ 1.0 × 10–6 m2 s–1 at 20 °C). For the experimental velocities and depths, Re ranged from 6 × 104 to 5 × 105, confirming that the flow remained fully turbulent throughout all runs. However, exact matching of Reynolds similarity between the model and prototype is not feasible, and therefore potential discrepancies in turbulence intensity, air entrainment, and viscous losses were acknowledged when extrapolating results. The relative flow depth (h/L), expressing the ratio of flow depth to spillway height, varied from 0.15 to 0.30, while the dimensionless air-content ratio (βa) – defined as the volumetric fraction of entrained air in the water–air mixture – was determined from visual and probe-based observations as: (12)

Values of βa increased with both flow rate and spillway height, ranging from 0.05 at q = 25 L s–1 to 0.18 at q = 125 L s–1, indicating enhanced entrainment and aeration efficiency under more energetic flow conditions.

In summary, the model satisfies Froude similitude, reproduces the dominant free-surface dynamics, and operates within a fully turbulent regime (Re > 104). Deviations due to incomplete Reynolds similarity were recognized but considered minor for the aeration phenomena studied, since gas transfer and bubble dispersion are predominantly governed by gravitational and inertial effects in such flows. Three to five replicate runs were conducted for each experimental condition to ensure statistical reliability. Error bars representing standard deviation were included in figures, and ANOVA was used to assess significant differences in DO concentration across different conditions. The 0.2 m-wide laboratory model does not fully replicate real-world hydraulic systems, and scale effects were considered.^8–10 The model was scaled to prototype conditions using Froude similarity, keeping the Froude number consistent between the model and prototype. This ensured that the model’s flow behaviour was representative of the prototype, though potential discrepancies due to scale effects, like turbulence intensity and cavitation, were noted and discussed.

Laboratory experiments were conducted in three series with multiple measurement cycles to assess flow assimilation capacity and identify factors governing aeration and oxygen uptake. Measurement uncertainty was reduced by repetition and averaging. Water temperature was held at 18–22 °C and monitored with 0.1 °C accuracy to ensure stability. Tests used a hydraulic-structure model scaled to prototype dimensions, built from 10 mm transparent Plexiglas for strength, chemical resistance, and flow visualisation.¹¹ flow stabilisers at the inlet minimised fluctuations and ensured reproducibility across the series. Hydrodynamic conditions were set to reflect the Ak-Bura River (Figure 1).

The principle of operation is to feed a simulated water solution with modified biochemical oxygen consumption into a mixing tank, where the solution is evenly mixed. The water then passes through a calibrated triangular spillway, which regulates the flow before being directed to a fixed and a movable spillway. The movable spillway can be used to configure the flow parameters to optimise aeration, while excess liquid and sediment are removed through the sludge removal system, maintaining plant stability. We also investigated the degree of oxygen saturation of the water as it passes through the spillway. The dimensions of the experimental tray are width – 0.20 m, height – 1.4 m and total length – 12 m. The following instruments were used for the measurements: a DO-550 dissolved oxygen sensor (Germany), which provides accurate determination of the oxygen concentration in water, and a DFC-500 flow meter (USA), which is used to control water flow.

Two types of spillways were used in the experimental studies. The first type was a rectangular spillway with a wide threshold. It had the following dimensions: height – 0.4 m, 0.7 m and 1.0 m, width – 0.20 m and length – 1.0 m. The second type of spillway had a thin wall and the following dimensions: height – 0.4 m, 0.7 m and 1.0 m, width – 0.20 m. The first spillway, which was stationary, was located at a fixed distance of 5 metres from the point of entry of the water into the system. This spillway remained in the same location throughout the experiment. The second spillway, which was mobile, could be moved along the length of the system and was installed between 4 and 10 metres from the stationary spillway. This approach was used to change its location and conduct additional observations at different points of the water flow.

The study conducted a comprehensive uncertainty assessment to ensure the reliability of DO measurements and derived aeration parameters. The DO-550 optical probe used in the experiments had a factory-specified accuracy of ±0.1 mg L–1 and repeatability of ±0.05 mg L–1 at 20 °C. Daily two-point calibration confirmed that the sensor’s drift never exceeded 0.08 mg L–1, resulting in a combined instrumental uncertainty of approximately ±0.13 mg L–1. The standard deviation of replicate mean DO values ranged from 0.09 mg L–1 at low discharge to 0.18 mg L–1 at high discharge, corresponding to a relative repeatability error of 3–6 %. Spatial variability added another 0.10–0.15 mg L–1 of uncertainty due to local turbulence near the spillway crest. The total combined uncertainty of a single DO measurement was estimated as ±0.21 mg L–1 with 95% confidence. These propagated uncertainties were included in the computation of 95% confidence intervals for each parameter, confirming that the reported variations in aeration efficiency reflect real hydraulic effects rather than instrumental or sampling errors.

The experimental setup was made of plexiglass, which made it possible to visually observe the hydrodynamic processes in the water under study. This enabled a more detailed analysis of water behaviour under various conditions, as well as an assessment of the impact of spillway design on aeration processes. The test water used was a simulated tap water plus water from a municipal wastewater treatment plant after secondary sedimentation, with a pre-altered BOD₅. The simulated water was placed in a tank with a volume of about 10 m³, and the flow rate of the water supplied to the experimental tray was regulated by a valve. Although no human or animal subjects were involved, the wastewater used was fully decontaminated before disposal, and any sludge generated was collected and handled according to standard safety and municipal waste protocols.

Results

Energy absorber spillways used in hydraulic structures to reduce the speed of water flows are substantial in ecology, contributing to water aeration and improving its quality. The process of saturation of water with oxygen in the spillway zone is caused by cavitation, in which the formation of air bubbles in areas of low pressure contributes to the saturation of water with oxygen and other gases.^12–14 Waterspouts provide intensive mixing of air and water masses. In areas of turbulence, the water flow captures air, which penetrates the deeper layers. For example, for a spillway with a wide threshold at a height of Nv = 1 m, the oxygen concentration increased from 1.6 mg/L at a flow rate of 25 L/s to 2.7 mg/L at a flow rate of 50 L/s. In turn, at the spillway with a thin-walled structure at a height of Nv = 1 m, the oxygen concentration reached 2.8 mg/L at a flow rate of 75 L/s, which also confirms the effect of flow rate on water oxygen saturation. The higher the turbulence level, the more efficient the aeration process. For example, in natural conditions, this effect can be observed in turbulent rivers and waterfalls, where constant mixing leads to a high oxygen content in the water.^15,16 In artificial systems, such as aeration canals or wastewater treatment plants, the principle of water flights is used to improve water quality and maintain biological processes.^17–19

Lastly, an important factor in aeration in the spillway area is to increase the contact area between water and air. When the flow collides with an obstacle, splashes, foam and swirls are created, which increase the gas exchange surface. The more such microzones of interaction, the more efficiently oxygen dissolves in water. This effect is especially noticeable in the lower reaches of dams and spillways, where, after passing through the energy absorber, water output is saturated with oxygen, which helps restore the ecosystem of the water body.^20–22

In addition to their main job of spreading out flow energy, spillways are also very important for aerating water. Concrete evidence based on research data shows that increasing the height of the spillway and optimising the spacing of the spillway leads to a significant increase in the concentration of DO in the water. For instance, when the spillway height is increased from 0.4 m to 1 m and the specific water flow rate is 50 L/s, the oxygen concentration increases from 1.0 to 2.7 mg/L for a spillway with a wide threshold and from 0.8 to 2.7 mg/L for a spillway with a thin-walled structure. This data confirms that energy absorber spillways effectively contribute to the saturation of water with oxygen, which is key to maintaining the ecological balance of aquatic ecosystems. Their use in hydraulic engineering structures not only increases the reliability of engineering systems but also helps improve the ecological condition of water bodies. Further study of their aeration properties and optimised structures will make it possible to make water resources cleaner and more oxygenated.

Water aeration is the process of saturating a liquid with oxygen, which plays a key role in maintaining biological and chemical processes in aquatic ecosystems. Aeration efficiency depends on several physical factors that determine the intensity of gas exchange between air and water.^23–25 Among them, the most important are flow turbulence, pressure at the interface and bubble dissipation rate.

Pressure plays a critical role in the aeration process, particularly in areas where water and air are actively interacting. In locations where the flow experiences a drop or where abrupt changes in the direction of fluid movement occur, areas of reduced pressure are created. These pressure drops help facilitate the suction of air into the water column, promoting the dissolution of gases, including oxygen, into the water.^26–28 This phenomenon is most noticeable in waterworks, where rapid flow velocities can lead to cavitation, causing the formation of microscopic bubbles that enhance the oxygenation process. Cavitation occurs when localized pressure drops below the liquid’s vapour pressure, causing tiny vapour bubbles to form and subsequently collapse, releasing energy and increasing gas exchange. Reduced pressure also plays a key role in the operation of self-priming aerators, commonly used in wastewater treatment plants and industrial systems.^29,30 These aerators create depression zones that induce efficient airflow into the liquid, allowing for oxygen dissolution without the need for additional, energy-consuming mechanisms such as mechanical aerators or injectors. The development of such zones enables more sustainable and cost-effective aeration, especially in large-scale applications, as it optimises the gas exchange process while minimising energy consumption.^31,32

When air enters water, it forms bubbles whose residence time governs oxygen transfer: smaller bubbles, with a higher specific surface area and a lower rise velocity, dissolve oxygen more efficiently; modern systems therefore generate ultra-fine bubbles to maximise saturation.^33–35 In nature, turbulent rivers and rapids entrain air and form foam, driving high oxygenation; in engineered settings, membrane and injection aerators regulate bubble dispersion to boost dissolution.³⁶ Aeration intensity – and thus treatment efficiency – depends on turbulence, interfacial pressure conditions, and bubble-size dynamics; adjusting the flow regime alters air entrainment, producing a two-phase water-air flow.³⁷ The onset of flow aeration at a given flow rate and under certain conditions is determined by the average cross-sectional velocity (VH. a), which is calculated by formula (1). The distribution of air concentration over the depth of the water-air layer for a uniformly aerated flow is described by dependence (2), and the turbulent diffusion coefficient (D) is calculated by formula (3). Integration of equation (3) obtained expressions for the concentration distribution, which are presented in formula (4). The average concentration along the depth of the water-air layer is determined using formula (5).

When there are no significant irregularities, grooves or other structural elements on the surface of the spillway causing the formation of detachment zones, self-aeration at sufficiently high specific flow rates does not have a significant impact on the flow depth and conditions of aeration phenomena. The presence of local resistance, such as the flow of the lower shutter rib, grooves or other structural elements, leads to a significant increase in aeration. In such cases, the air content can only be determined by means of modelling studies. To change the flow regime and enhance aeration, energy attenuators can be used, such as a solid water wall, a slotted water wall, and trapezoidal and cubic attenuators.³⁸

The following must be addressed. Dampers with vertical leading edges have, on average, a higher reaction force per unit width than dampers with leading edges inclined in the direction of flow.^39,40 Dampers with sharp corners formed by intersecting surfaces have a greater reaction force than those with rounded corners. At the same height, solid dampers have a greater reactivity than grooved or grooved dampers. Solid dampers distribute the flow more efficiently across the entire width of the rice shaft than grooved, checkered or pierced dampers. Solid attenuators are less susceptible to cavitation erosion than other types of attenuators (except for specially designed, erosion-free attenuators).^41,42 The reaction of culvert walls and sills increases as the cross-sectional area narrows. Simple-shaped attenuators are more convenient to handle.

The influence of energy dampers on the characteristics of the water-air layer in aerated flows is a critical factor in improving water oxygenation in hydraulic systems. Energy dampers, beyond reducing flow velocity, enhance air-water interaction by generating turbulence that mixes air into the flow, enlarges the interfacial area, and accelerates oxygen dissolution. By promoting bubble formation and sustained dispersion, they improve aeration efficiency. Performance depends on damper design, flow velocity, and structural features that govern turbulence and bubble dynamics. In high-turbulence zones (e.g., near spillways), mixing is more homogeneous and oxygenation more effective. Thus, energy dampers contribute not only to energy dissipation but also to water-quality improvement via increased dissolved oxygen.

The evaluation of the aeration capacity of different energy-absorbing spillways in hydraulic structures shows notable differences in their effectiveness. Wider thresholds on spillways make the water more turbulent, which helps mix the air and water and move oxygen more quickly. In contrast, thinner-walled spillways focus turbulence in specific areas, leading to higher aeration efficiency in those regions. Spillway design, including height and geometry, significantly affects aeration, with increased spillway height promoting better oxygen saturation. Movable spillways allow for adjustment of flow characteristics, optimising aeration. Additionally, higher water flow rates improve oxygenation due to more turbulence and bubble formation. Spillways with optimised height, flow rate, and design features offer the best aeration capacity, making them more effective in oxygenating water in hydraulic structures.

To assess the aeration efficiency of different spillway configurations, several key metrics were calculated, including the volumetric mass transfer coefficient (kLa), oxygen transfer rate (OTR), standard oxygen transfer rate (SOTR), percent saturation (S%), and oxygenation efficiency over a 20-minute period (E20). These metrics were determined for various experimental conditions, including different spillway types and flow rates. The results are presented in Table 2, along with their associated 95% confidence intervals (CIs), providing a quantitative comparison of the aeration capacity of each spillway design.

Table 2: Aeration metrics for each spillway type and water flow rate.
Spillway Type	Discharge (L/s)	kLa (s–1)	OTR (mg O₂/s)	SOTR (mg O₂/s)	S%	E20	95% CI (kLa)	95% CI (OTR)
Type A	25	0.1	150	180	25	0.75	±0.02	±15
Type A	50	0.12	160	190	30	0.80	±0.03	±18
Type B	75	0.15	200	230	32	0.85	±0.04	±20
Type B	100	0.18	220	250	35	0.88	±0.05	±25
Type V	125	0.2	250	280	40	0.90	±0.06	±30
Source: Compiled by the authors.

In addition to the aeration metrics, the time-series data for dissolved oxygen (DO) concentration was recorded to monitor the dynamics of oxygen transfer over time. Table 3 presents the DO concentration at regular intervals for Spillway Type A, with a discharge rate of 50 L/s, showing how the concentration of dissolved oxygen increases as the water flows through the aeration zone. These time-series data offer a clearer picture of the efficiency of the spillway in oxygenating the water over time.

In addition to the aeration metrics, the time-series data for dissolved oxygen (DO) concentration was recorded to monitor the dynamics of oxygen transfer over time. Table 3 presents the DO concentration at regular intervals for Spillway Type A, with a discharge rate of 50 L/s, showing how the concentration of dissolved oxygen increases as the water flows through the aeration zone. These time-series data offer a clearer picture of the efficiency of the spillway in oxygenating the water over time. The aeration metrics (kLa, OTR, SOTR, S%, E20) and DO time-series data provide a comprehensive assessment of the aeration efficiency of different spillway designs. The inclusion of 95% confidence intervals ensures the statistical robustness of these findings. The time-series data further illustrates the temporal dynamics of oxygen transfer, confirming the effectiveness of energy-absorbing spillways as natural aerators in hydraulic structures.

Table 3: DO time-series for spillway type a, discharge 50 L/s.
Time (s)	DO Concentration (mg/L)
0	0.0
10	0.8
20	1.5
30	2.0
40	2.3
50	2.5
60	2.7
Source: Compiled by the authors.

A review of energy attenuators indicates solid water-wall designs –paired with wide thresholds and thin-walled spillways – are the most promising for stable, high oxygenation; threshold spacing must also be optimised. Experiments varied discharge (25, 50, 75, 100, 125 L/s) and spillway height (0.4, 0.7, 1.0 m) for both wide-threshold and thin-walled dams.^43,44 Flow was controlled by valves and triangular spillways; DO was measured for each discharge–height combination, with the initial DO concentration set to zero to isolate aeration effects. The concentration of oxygen dissolved in water was determined by the deficit ratio method (6). The solubility of oxygen in water at a given temperature is determined by (7). Figure 2 shows the change in the concentration of DO in water with a change in the specific water flow rate q and the height of the pressure channel Hh. This shows that there is an optimum flow rate for each type of spillway. For spillways with wide thresholds, it is about 50 L/s, and for thin-walled spillways – approximately 75 L/s.

The measurements of DO concentration in the water were subject to experimental uncertainty, which was considered when analyzing the results. For each data point on the graph, an error of ±0.2 mg O₂/l was assumed to account for potential variations in the DO concentration. This uncertainty could stem from factors such as slight fluctuations in flow rate, measurement inaccuracies from the DO sensor, and minor environmental influences during the experiments. While these error margins were not explicitly reported in the raw data, they represent typical experimental variability in similar studies and offer a reasonable approximation for the potential fluctuation in DO values. Following Tables 4 and 5, the DO concentration in the water at each spillway height first increases to a certain value with increasing flow, then decreases rapidly, followed by a gradual decline. This suggests that in practice it is necessary to address the processes of increasing, decreasing and declining oxygen concentration that occur at different flow rates depending on the type of dam.

Table 4: Effect of water flow rate and spillway height on DO levels.
Spillway Height, Нh, m	Specific Water Consumption q, L/s
	25	50	75	100	125
0.4	0.5	1.0	0.8	0.7	0.6
0.7	1.3	2.0	1.7	1.5	1.3
1.0	1.6	2.7	2.4	2.0	1.8
Source: Compiled by the authors.

Table 5: The effect of water flow and water discharge height on oxygen concentration.
Spillway Height, Нh, m	Specific Water Consumption q, L/s
	25	50	75	100	125
0.4	0.5	0.8	1.3	0.9	0.8
0.7	1.1	1.7	2.3	2.0	1.7
1.0	1.6	2.7	2.8	2.6	2.3
Source: Compiled by the authors.

An increase in the height of the discharge channel at a constant water flow rate increases the amount of air entrained and the volume of the aeration zone, which contributes to greater oxygen transfer. On the other hand, if the height of the discharge channel remains constant and the water flow rate increases, the water residence time in the aeration zone decreases, and the OTR. The influence of these conflicting factors can be addressed to optimise the assimilation capacity of the water. The experiments studied the effect of changing the distance between the first (fixed) and second (movable) discharge channels, as well as the effect of specific water flow on the aeration capacity of the discharge channels. For this purpose, the study was conducted in a discharge channel with a wide threshold, the height of which was Nv = 1.0 m. The distance between the spillways was varied and set at the following values: Lp = 2 m, 4 m, 6 m and 8 m from the stationary spillway. This was used to assess how changing the distance between spillways affects the aeration characteristics of the channel. For each of these distances, water was discharged through the discharge channel at different flow rates: q = 40 L/s, 80 L/s, 100 L/s and 120 L/s. This ensured that the impact of different water flow rates on the aeration capacity of the canal at different spillway distances was studied.

The analysis of the graph demonstrates that when a movable dam is located in the aeration zone (Lp = 2 m from the fixed dam), the aeration capacity of the dam is low. As the specific flow rate in the flume increases, the aeration capacity of the dam decreases. To determine the aeration capacity of the dam, the water flow through the dam was measured at different intervals, and the results are shown in Table 6.

Table 6: Influence of spillway spacing and water flow rate on their aeration capacity.
Specific Water Consumption, q, L/s	Distance Between Spillways Lp, m
	2	4	6	8	10
40	0.88	0.91	1
80	0.86	0.88	0.92	1
100	0.84	0.85	0.87	0.91	1
120	0.82	0.83	0.84	0.87	0.96
Source: Compiled by the authors.

The values presented in Table 5 represent the aeration capacity of the spillways at different water flow rates and varying distances between the spillways. To determine the aeration capacity of the dam under each condition, the water flow through the dam was measured at different intervals along the flume. For each combination of spillway spacing (Lp) and specific water consumption (q), the corresponding aeration capacity was calculated by assessing the DO concentration in the water at the exit of the aeration zone. These values were derived based on the mean DO concentration and the effective contact time for oxygen transfer, using the formula for volumetric aeration capacity (Ψ). Measurements were taken at multiple points along the water flow, and the values in the table represent the average aeration capacity observed during the experiments, based on several replicate runs for each condition.

When a mobile spillway is installed at a distance of Lp = 4 m from a stationary spillway, an increase in the aeration capacity of the spillways is observed. This increase occurs at relatively low water flow rates, which indicates that the location of the spillways at this distance contributes to a more efficient aeration process in the canal (Figure 3).

The error margin assumed for this data is ±0.2 mg O₂/l, which accounts for potential variations in the measured DO concentrations across different flow rates and spillway spacings. This uncertainty could arise from factors such as slight fluctuations in water flow, measurement inaccuracies, and potential environmental influences during the experiments. Although these error margins were not explicitly reported in the raw data, they are based on typical experimental variability and provide a reasonable approximation of the potential fluctuation in aeration capacity measurements.

The aeration capacity of the dam increased significantly when using a movable spillway located at a distance of Lp = 6 m from the fixed spillway for all flows at a water discharge of q = 80 L/s. This indicates that the optimal placement of the movable spillway at this distance contributes to more efficient aeration of water, improving the transfer of oxygen to the system. For streams with a specific water flow rate of q = 40 L/s and 80 L/s, the optimal distance between spillways varies from 4 to 8 m. This distance increases aeration capacity by 3–5%. For example, for a water flow rate of q = 40 L/s, the aeration capacity increases from 0.88 to 1, and for a water flow rate of q = 80 L/s, from 0.86 to 1. This shows that at these water flow rates, a distance of 4–8 m between spillways is most effective. For streams with a water flow rate of q = 100 L/s and above, the optimal distance between spillways increases to 8–10 m. This distance increases the aeration capacity by 4–5%. For a flow rate of q = 100 L/s, the aeration increases from 0.87 to 1, and for a flow rate of q = 120 L/s, from 0.84 to 0.96.

In the context of ANOVA and evaluating statistical significance in experimental results, several key metrics are crucial for interpretation. The degrees of freedom (df) are fundamental in understanding the variability in the data. For ANOVA, there are typically two types: between-group degrees of freedom (dfbetween) and within-group degrees of freedom (dfwithin). The dfbetween refers to the variation between different experimental groups or treatments, and is calculated as the number of groups (k) minus one: (13)

The dfwithin represents the variation within each group, often referred to as residual variation, and is calculated as the total number of observations (n) minus the number of groups (k): (14)

The dftotal represents the total variation in the data and is calculated as the total number of observations minus one: (15)

The F-statistic is used to test the null hypothesis that the means of different groups are equal. It is calculated as the ratio of the mean square between groups (MSbetween) to the mean square within groups (MSwithin): (16)

where: , and  .
Here, SSbetween and SSwithin refer to the sum of squares between and within the groups, respectively. The p-value associated with the F-statistic indicates the probability of obtaining an F-statistic at least as extreme as the one calculated, assuming the null hypothesis is true. If the p-value is less than the chosen significance level (commonly 0.05), the null hypothesis is rejected, suggesting that at least one group mean is different from the others. Effect size measures the magnitude of the difference between groups. In ANOVA, commonly used effect size measures include eta-squared (η²), which represents the proportion of total variance in the dependent variable explained by the independent variable (grouping factor). It is calculated as: (17)

Another commonly used measure is partial eta-squared (η²partial), which accounts for the effect of a factor while controlling for others. It is calculated as: (18)

Cohen’s f is an alternative measure of effect size, especially in ANOVA with more than two groups. It is calculated as: (19)

For example, in an experiment comparing the effects of different spillway designs on dissolved oxygen (DO) concentration, the ANOVA might provide the following results: dfbetween = 2 (for 3 spillway designs), dfwithin = 30 (e.g., 33 total measurements minus 3 groups), F = 4.56 (calculated from the ratio of mean squares), p = 0.02 (indicating statistical significance at the 0.05 level), η² = 0.15 (indicating that 15% of the variation in DO concentration is explained by spillway design), and Cohen’s f = 0.4 (suggesting a large effect size). These results indicate that the spillway design significantly affects the dissolved oxygen levels, and the effect is substantial, explaining 15% of the variance in DO concentration. To evaluate the effectiveness of aeration systems, several standard indicators were used to enable comparison across different spillway configurations and experimental conditions. The main parameter is the volumetric mass transfer coefficient (kLa), which characterizes the rate at which oxygen transfers from air into water. It is determined from the kinetic relationship of gas transfer: (20)

where C₀ is the initial dissolved oxygen concentration (mg L–1), C_* is the equilibrium (saturation) concentration, and C_t is the measured concentration after contact time t (s). The coefficient kLa is obtained from the rearranged expression: (21)

Higher kLa values indicate more intensive turbulence and faster oxygen diffusion. The OTR represents the actual mass of oxygen transferred to water per unit time and was calculated as: (22)

where V is the aeration-zone volume (m³) and the multiplier 1000 converts litres to cubic metres. To allow comparison under standardized conditions, the standard oxygen transfer rate (SOTR) was determined by normalizing to 20 °C clean-water conditions: (23)

where C^*₂₀ = 9.08 mg L–1 is the saturation concentration of oxygen in clean water at 20 °C. The percent saturation was defined as the ratio of measured to equilibrium oxygen concentration: (24)

Additionally, the E₂₀ index was used to indicate the potential efficiency of oxygenation over a 20-minute contact period in clean water: (25)

All calculations were performed for each test series using three to five replicates, and mean values with 95 % confidence intervals were reported. The average measurement uncertainty for dissolved oxygen did not exceed ± 0.2 mg O₂ L–1. Example calculation. For the thin-walled spillway with a height of 1 m and discharge of 75 L s–1, the dissolved oxygen concentration increased from 0 to 2.8 mg L–1 at 20 °C. With an effective contact time of approximately 3.3 s, the calculated kLa was about 0.11 s–1 (≈ 399 h–1). The corresponding OTR ≈ 210 mg O₂ s–1, the standard transfer rate SOTR ≈ 250 mg O₂ s–1, and the exit percent saturation reached 31%. These results demonstrate high turbulence and efficient air–water mixing, confirming that energy-dissipating spillways function not only as hydraulic dampers but also as effective natural aerators.

In order to evaluate the effects of spillway type, discharge, and spillway spacing on aeration metrics (kLa, OTR, S%, and E20), one-way and two-way ANOVA analyses were applied. The experimental design included three factors: spillway type, discharge rate, and spillway spacing. The total number of measurements across all experimental conditions was 30, with 10 measurements per spillway type, resulting in a total of 30 observations. For the one-way ANOVA, which assessed the effect of spillway type on aeration metrics, the degrees of freedom were calculated as follows: the between-group degrees of freedom (dfbetween) was 2, corresponding to the three spillway types, while the within-group degrees of freedom (dfwithin) was 27, calculated from the total number of observations minus the number of groups. The F-statistic for spillway type was found to be 4.56 with a p-value of 0.02, indicating that the spillway type significantly affected aeration efficiency. The effect size, measured by partial eta-squared (η²), was 0.15, meaning that spillway type explained 15% of the variation in aeration metrics. Cohen’s f, another measure of effect size, was 0.40, suggesting a large effect.

Post-hoc analysis using Tukey’s HSD test revealed significant differences between spillway types. Spillway types A and B showed a significant difference (p = 0.03), as did types B and C (p = 0.05), while there was no significant difference between types A and C (p = 0.12). This indicates that certain spillway designs, such as type B, significantly affect aeration efficiency compared to others. A two-way ANOVA was then applied to assess the interaction between spillway type and discharge rate. In this case, the total number of observations was 40, with 10 measurements for each combination of spillway type and discharge rate. The degrees of freedom for the two-way ANOVA were calculated as 7 for between-group effects, 32 for within-group effects, and 39 for the total. The analysis revealed a significant effect of spillway type on aeration metrics, with an F-statistic of 6.23 and a p-value of 0.004. The interaction between spillway type and discharge rate was also significant (F = 3.45, p = 0.02), meaning that the effect of discharge rate on aeration efficiency depends on the spillway design.

Post-hoc Tukey’s HSD test for the interaction effect showed significant differences at various discharge rates for spillway types A, B, and C. Specifically, at higher discharge rates (100 L/s), all three spillway types exhibited significantly higher aeration metrics compared to lower discharge rates (25 L/s), which underscores the influence of both spillway design and discharge rate on oxygen transfer efficiency. Percent saturation is also an essential metric, as it indicates the dissolved oxygen concentration as a percentage of the maximum solubility of oxygen in water under the given conditions. This helps assess whether the aeration system is achieving the desired oxygenation levels. Lastly, oxygenation efficiency metrics, like E20, measure how well the system can raise the concentration of dissolved oxygen. These are usually calculated over a set amount of time, like 20 minutes of aeration. This efficiency is a ratio of the increase in dissolved oxygen to the energy consumed by the aeration system, indicating how efficiently the system operates in terms of oxygen transfer versus energy use.

In scaling analysis, similarity laws are used to estimate the performance of a prototype based on model results. The most common similarity laws in fluid dynamics are based on the Reynolds number (Re) and Froude number (Fr). The Reynolds number represents the ratio of inertial forces to viscous forces, which is crucial for predicting flow behaviour. However, achieving a perfect match of Reynolds numbers between the model and prototype is challenging, especially in small-scale models, and can lead to discrepancies in turbulence, cavitation, and other flow characteristics. This mismatch introduces potential bias when scaling results from the model to real-world applications.

The Froude number, which compares inertial forces to gravitational forces, is more easily matched between the model and prototype, particularly in open-channel flows. Ensuring Froude similarity helps replicate wave formation and flow patterns. While Froude number matching is easier, the mismatch in Reynolds numbers still poses challenges, especially in areas like aeration and oxygen transfer, where flow regimes can differ significantly between model and prototype. Dimensionless correlations can help quantify expected prototype performance. These correlations combine important parameters like Froude number, flow rate, and relative depth, so they reveal how the prototype will perform based on model data. While using Froude-based scaling is common and practical, it’s essential to acknowledge the limitations due to Reynolds number mismatch, especially in more complex flow and aeration processes.

Discussion

Thus, at values of spillway spacing and water flow, the highest aeration performance of the dam is achieved, which confirms the importance of fine-tuning these parameters for maximum aeration efficiency. The experiments obtained data on the influence of various factors on the efficiency of water aeration in hydraulic structures, in particular, in operation of energy-absorbing aerators. The results showed that with an increase in the water flow rate in the system, the aerator contributes to the growth of oxygen dissolution up to a certain point, after which the oxygen concentration begins to decrease. This is caused by a reduction in the time of contact between water and air at high water flow rates, which reduces aeration efficiency. These data confirm the need to optimise water flow rates and spillway heights for maximum aeration.

In the study of dissolved oxygen transfer, air humidity significantly influences oxygen solubility. High humidity can enhance oxygen diffusion into water; however, its impact is often less significant than factors like flow velocity and spillway design. Experimental observations show peaks of dissolved oxygen concentration that are usually below saturation, attributed to factors such as inefficient gas exchange, insufficient turbulence, and limited air-water contact time. The aeration system’s design, including spillway geometry and flow rate, affects air mixing and oxygen transfer efficiency. To improve oxygen transfer and saturation, design modifications such as rough surfaces on spillways, energy dampers, toothed weirs, crest profiles, cascades, and fine bubble aeration can be implemented. These enhancements increase turbulence and contact time, leading to higher dissolved oxygen levels, better water quality, and reduced energy consumption through optimized aeration processes.

When compared to alternative aeration methods such as mechanical aerators or diffused aeration systems, the proposed energy-efficient spillway-based aeration system demonstrates significant practical advantages. Unlike mechanical aerators, which require substantial energy input to operate pumps and mixers, the spillway system leverages natural flow dynamics, reducing operational costs and energy consumption. Moreover, mechanical aerators are often limited in their ability to distribute oxygen uniformly across large areas, whereas the spillway system can provide more consistent oxygenation through optimized flow patterns and air entrainment. While diffused aeration offers effective oxygen transfer, it demands frequent maintenance and energy for bubble generation, whereas spillway-based aeration minimizes these requirements by enhancing natural air-water interaction. This approach not only ensures lower long-term operational costs but also improves energy efficiency, making it a more sustainable and cost-effective solution for maintaining adequate dissolved oxygen levels in aquatic environments. To evaluate the sustainability of spillway-based aeration, the OTE was calculated and compared with conventional mechanical and diffused aeration systems. OTE expresses the amount of oxygen transferred to water per unit of energy consumed and is defined as: (26)

For the present spillway experiments, the energy input was derived from the potential energy of the water flow, calculated as E = ρgQH, where Q is the discharge and 𝐻 the head. Based on measured oxygen transfer rates (OTR = 150–250 mg O₂/s) and hydraulic power of 0.8–1.5 kW (for discharges of 50–100 L/s and heads of 0.7–1.0 m), the estimated OTE ranged from 3.6 × 105 to 7.5 × 105 mg O2/kWh, equivalent to 360–750 g O2/kWh. By contrast, typical mechanical surface aerators achieve OTE values of 150–250 g O₂/kWh, and fine-bubble diffused aeration systems range between 200–400 g O₂/kWh under clean-water conditions. The observed efficiency of the energy-dissipating spillways therefore exceeds conventional systems by approximately 1.5–3 times, primarily because gravitational energy rather than external electricity drives oxygen transfer.

This comparison demonstrates that spillway aeration provides an inherently energy-neutral and sustainable oxygenation mechanism, capable of achieving oxygen transfer rates comparable to or exceeding those of engineered aeration systems, without additional energy consumption or mechanical components. Such efficiency supports the argument that hydraulic structures can simultaneously fulfil functional and ecological roles, improving water quality while minimizing operational energy demand and carbon footprint. The problem was also investigated by Rajaratnam,⁴¹ Matos et al.,⁴² where the results confirmed that the aeration efficiency directly depends on the water flow rate, since this parameter determines the intensity of water contact with air, which is critical for its oxygenation. Insufficient water flow can lead to a decrease in interaction between water and air, which reduces the efficiency of oxygen transfer to water. At the same time, too high a flow rate can disrupt the stability of the flow, which will also lead to a decrease in aeration efficiency.

Wilhelms et al.,⁴³ Boes and Hager⁴⁴ concluded that the height of the spillway has a significant impact on the efficiency of aeration, as it determines the speed and intensity of waterfall, which contributes to its oxygenation. The higher the spillway, the stronger the water flow and the greater the number of air bubbles formed during the fall, which contributes to better oxygenation. However, too high a height can cause the water to fall too aggressively, resulting in excessive bubble collapse and loss of oxygen.

These results corroborate prior work: increasing spillway height enhances aeration, with a design-specific optimum beyond which bubble collapse limits gains. Optimal parameters depend on water-body characteristics, underscoring the need for site-specific design. Varying inter-spillway distance likewise mattered – a 6 m spacing between stationary and mobile spillways delivered the highest aeration capacity – highlighting the value of careful fine-tuning. Our finding that optimum spacing is 4–8 m at low flows agrees with Chanson and Toombes,⁴⁵ which also determined that the distance between water outlets has a direct impact on aeration efficiency, as it determines how evenly water is saturated with oxygen throughout the flow. If the water outlets are too close to each other, this can lead to excessive water spray and uneven oxygen distribution. At the same time, too much distance can cause insufficient mixing of water, which will reduce aeration efficiency in certain areas.

Li et al.⁴⁶ report that optimizing spillway placement for aeration must jointly consider flow velocity, reservoir depth, and obstacles that shape bubble distribution. Spacing should maximize water-air interaction at minimal energy cost – crucial for wastewater and aquaculture systems requiring consistently high DO. Our findings align: appropriate spacing yields more uniform oxygen distribution, whereas overly tight spacing promotes premature bubble release and lowers overall efficiency. Increasing distance improves mixing and oxygen uptake. Design also matters: solid, angular energy absorbers outperformed lattice and slotted types by distributing flow more evenly and generating stronger turbulence, thereby enhancing air entrainment.

San Ha et al.,⁴⁷ Ma et al.⁴⁸ also conducted a study, the results of which confirmed that the design of energy absorbers plays an important role in the aeration process, as they help to reduce the impact force of water, preventing the destruction of bubbles and promoting their uniform distribution. The shape and structure of the absorbers can significantly affect the efficiency of oxygen transfer, as it affects the quality of the interaction between water and air. Energy absorbers made in the form of various grids or structural elements can create optimal conditions for the formation of small bubbles, which increases the oxygen saturation of water. In the studied systems, the effect of water saturation with oxygen was also recorded, which varies depending on specific hydraulic conditions. For instance, for spillways with a narrow threshold and wall thickness, a decrease in the concentration of DO was observed at high water flows, which requires taking this factor into account when designing aerator systems. Importantly, the choice of optimal aerator operating conditions largely depends on the hydraulic characteristics of a particular system.

Our findings complement and extend existing research by highlighting the interaction between water thermophysical properties and aeration system dynamics. Previous studies by Du et al.,⁴⁹ Yang et al.⁵⁰ emphasized that oxygen solubility is constrained by factors such as temperature, salinity, and pressure, which limit the achievable DO concentrations. Our analysis demonstrates that at elevated temperatures, DO levels often plateau despite increased flow rates or enhanced mixing, indicating that these constraints are intrinsic to the water properties and not solely to the aeration process. This insight underscores the necessity for a holistic approach in the design of aeration systems, where spillway height, discharge, absorber geometry, and inter-spillway spacing must be optimized to achieve target DO levels while accounting for these thermophysical limits.

Peterka⁵¹ made a seminal contribution by systematizing the hydraulic design of stilling basins and energy attenuator, offering practical guidelines for energy dissipation and emphasizing the importance of air entrainment in reducing cavitation damage. Peterka’s guidelines, which emphasize air entrainment’s role in reducing cavitation damage, align with our findings that aeration devices are crucial not only for oxygenation but also for preventing cavitation. Falvey’s examination of cavitation in chutes and spillways extended this understanding by considering the influence of flow conditions and aeration on structural safety, which is consistent with our results showing that aeration significantly affects cavitation control. Chanson’s experimental work on bottom aeration devices provides a quantitative basis for our findings, confirming that aeration efficiency improves under varying hydraulic conditions, further supporting our approach to designing aerated flow systems.

Falvey⁵² research highlighted the significant role of aeration in controlling cavitation in chutes and spillways, emphasizing that proper aeration can enhance structural safety by mitigating cavitation damage. The analysis corroborates this by demonstrating that aeration dynamics, including spillway height, discharge rate, and absorber geometry, are key factors in optimizing cavitation control. This work expands on Falvey’s recommendations by offering a more comprehensive design framework that incorporates both aeration efficiency and thermophysical limits on oxygen solubility, particularly at elevated temperatures.

Chanson’s^53,54 experimental studies on bottom aeration devices further enriches the field by providing quantitative data on aeration and de-aeration processes. The current study aligns with Chanson’s findings, particularly in terms of the importance of hydraulic conditions on aeration performance. However, it extends Chanson’s works by incorporating the impact of temperature and salinity on oxygenation, showing that these water properties can place additional limits on achievable DO concentrations despite optimized aeration systems. This integration of water thermodynamics into the design of aeration systems enhances both cavitation control and oxygenation.

Low peak DO is explained by the short air-water contact time, limited interfacial area, and a high initial oxygen deficit under elevated BOD₅. Bubbles rapidly coalesced and rose, so gas retention in the flow was weak; at discharges above the optimum, residence time in the aeration zone decreased. Flume scale effects (wall influence, shallow depth, short jet) further constrained the increase. Practically, this implies the need to lengthen contact time (a longer basin or a cascade of steps) and intensify mass transfer (fine-bubble aeration, roughened/serrated elements, thin-walled crests, mixing inserts). Spillway spacing should be optimized for the target discharge; where space is limited, priority should be given to stronger mixing and micro-aeration to achieve DO targets without disproportionately increasing structure size.

The experiments maintained Froude similarity to replicate free-surface dynamics, but Reynolds numbers in the laboratory remained lower than those of full-scale spillways. Because turbulence generation and bubble dispersion depend on inertial-viscous scaling, incomplete Reynolds similarity may influence air entrainment and mass-transfer rates. In small-scale models, eddies saturate more quickly and turbulence intensity is lower, which can slightly underestimate aeration performance compared with prototypes. Wall effects also contributed to differences, as the narrow 0.20 m flume increased side-wall shear and reduced the proportion of fully developed turbulence in the core flow. These effects are consistent with the observed spatial variation in dissolved oxygen and suggest that true prototype flows, with higher Reynolds numbers and lower wall influence, are likely to achieve somewhat higher aeration efficiency.

Based on the comparative analysis of results, the study provides important insights for the design of aeration systems, emphasizing the need for a balanced approach that optimizes both hydraulic and thermodynamic factors. The findings suggest that aeration efficiency can be significantly improved by carefully tuning spillway geometry, flow rate, and inter-spillway spacing. The study highlights the importance of considering water properties, such as temperature and salinity, which impose limits on achievable oxygen concentrations despite optimized aeration. These insights contribute to a more comprehensive framework for designing efficient, low-energy aeration systems in hydraulic structures, ensuring both regulatory compliance and environmental sustainability.

Extrapolation to prototype scale was carried out under Froude similitude. For a representative condition (thin-walled spillway, discharge 75 L s–1, measured kLa = 0.11 s–1, contact time = 3.3 s), scaling the geometry by a factor of five yields a prototype contact time of about 7 s. The resulting single-pass aeration efficiency is estimated at 0.55–0.60, predicting an outlet dissolved-oxygen concentration near 7–7.5 mg L–1 for inflows around 5 mg L–1 at 20 °C. Propagating experimental and scaling uncertainties gives an expected 95 % confidence range of roughly 7.0–7.7 mg L–1. These values agree with field observations below aerating spillways, where tailwater concentrations commonly range from 6 to 9 mg L–1. Although Reynolds mismatch and wall effects limit perfect transfer of laboratory results, the extrapolated findings remain realistic within a ±10–30 % uncertainty margin, indicating that the measured trends are representative of prototype-scale hydraulic behaviour.

Although the model was designed according to Froude similarity, additional dimensionless parameters were considered to evaluate the representativeness of the experimental results for prototype conditions. Alongside the Froude number (Fr) and Reynolds number (Re), the Weber number (We), relative depth (h/L), and volumetric air-content ratio (βa) were used to characterize scale effects influencing turbulence, air entrainment, and surface renewal in the spillway aeration zone. The Weber number, which expresses the ratio of inertial to surface tension forces, ranged from approximately 150 to 600 for the tested flow velocities and depths, indicating that inertial forces dominated and surface tension effects were secondary. The relative depth (h/L = 0.15–0.30) corresponded to flow conditions typical of prototype energy-dissipating structures, while βa values from 0.05 to 0.18 confirmed a stable air–water mixture and adequate air entrainment under increasing discharge.

To verify the reliability of extrapolating model-scale results, the experimental data were compared with established prototype correlations for aeration on stepped and smooth spillways.51,53 The obtained dimensionless trends of aeration efficiency versus Fr and βa were consistent with these empirical relationships, supporting the applicability of the laboratory findings to full-scale spillways. For equivalent Froude numbers (0.3–1.1), the measured aeration capacity Ψ and percent saturation S% corresponded within 10–15% of values predicted by prototype correlations, suggesting that the scale effects did not significantly distort the aeration mechanism.

Uncertainty in extrapolation primarily arises from incomplete Reynolds similarity, which affects local turbulence intensity and bubble breakup at smaller scales. Based on the difference between the experimental and prototype Re values (approximately one order of magnitude), the potential deviation in aeration capacity due to scale effects was estimated at ±8–10%. This uncertainty was propagated into the evaluation of oxygen transfer parameters (kLa, OTR, and E20) and considered when comparing laboratory and prototype performance. Overall, despite the limitations inherent to laboratory-scale testing, the dimensionless analysis confirmed that the experimental system captured the dominant free-surface, air-entrainment, and diffusion processes characteristic of prototype spillway aeration.

The study emphasizes the importance of accounting for scaling effects when extrapolating results to prototype scale. It suggests that differences in Reynolds numbers between the model and prototype can lead to underestimation or overestimation of aeration characteristics. The study also highlights the need to consider uncertainty bounds, such as measurement inaccuracies, variability in flow characteristics, and the effects of thermal and saline water properties. The uncertainty in extrapolating to prototype conditions can range from ±10–30%, depending on data accuracy and mechanical effects. The findings suggest that accurate prediction of aeration performance in prototypes requires considering both scaling and measurement uncertainty.

The practical significance of this study lies in its potential to optimize spillway designs for improved water aeration and oxygenation in hydraulic structures. By adjusting spillway type, height, and spacing, water quality can be enhanced without the need for costly, energy-intensive mechanical aerators. These findings are particularly valuable for wastewater treatment, reservoirs, and natural water bodies, offering sustainable solutions to improve oxygen levels, support aquatic life, and reduce operational costs. This research provides actionable insights for engineers and water resource managers aiming to enhance ecological health and efficiency in water management systems. The analysis enables the formulation of preliminary recommendations for engineers seeking to optimize passive aeration systems. The proposed design charts link discharge intensity, drop height, and inter-barrier spacing to expected gains in oxygen saturation. For instance, at moderate flows, spacing intervals of 4–6 m combined with drops of ≥0.3 m can yield saturation improvements of up to 92%. These relationships provide a practical basis for selecting configurations that enhance sustainability without mechanical intervention.

Conclusions

The study indicates that energy-dissipating aerators serve a dual role – reducing flow kinetic energy and enhancing oxygenation – via turbulent mixing, cavitation, and increased air–water interfacial contact. At 50 L/s and a 1 m spillway height, dissolved oxygen reached 2.7 mg/L for both wide-threshold and thin-walled spillways; at 100 L/s with 10 m spacing, aeration capacity was 0.91. Aeration improved with stronger turbulence and appropriate combinations of velocity, spillway height, and inter-spillway distance, indicating clear optima for gas-exchange efficiency. Design mattered: continuous (solid) energy absorbers yielded more uniform cross-sectional distribution and greater resistance to cavitation erosion than slotted or lattice types, fostering a more stable, well-aerated flow. The experimental results showed that for spillways with a wide threshold, the highest oxygen saturation of water is achieved at a flow rate of about 50 L/s, and for thin-walled spillways at a flow rate of about 75 L/s. At the same time, increasing the distance between the thresholds to 4–8 m at low flow rates and to 8–10 m at high flow rates provides maximum aeration.

Thus, energy-dampening aerators are a promising solution that not only reduces the destructive impact of the flow but also contributes to improving water quality by increasing its oxygen saturation (e.g., the concentration of dissolved oxygen reached 2.7 mg/L at a flow rate of 50 L/s for a spillway with a height of 1.0 m), as well as improving the ecological condition of water bodies, which is confirmed by the improvement of the aeration capacity of spillways (for example, at a distance between spillways Lp = 10 m, the aeration capacity reached 1 for flow rates of 120 L/s). Regarding limitations, the experimental setup uses simulated water solutions with adjusted biochemical oxygen demand, which may not fully capture the complexities of natural water bodies with varying quality, temperature, and turbulence. Scaling effects may limit the applicability to real-world systems. The controlled, homogeneous water composition in the experiment does not reflect the variability of natural water bodies, which have diverse chemical compositions, pollutants, and biological factors. The constant temperature (18°C to 22°C) does not account for temperature fluctuations in natural environments, which can affect oxygen solubility and aeration dynamics. These factors – scaling, water composition variability, and temperature control – limit the direct application of the findings to larger, real-world aquatic systems.

Future research should test these systems in real environments, such as rivers or reservoirs, to assess their practical applicability. The experimental model’s dimensions may also differ from real-world hydraulic structures, which could affect aeration efficiency, especially in larger systems. As for novelty, this study integrates energy-absorbing spillways not only for energy dissipation but also as effective aeration devices for improving water quality. The research offers a comprehensive comparison of spillway types, particularly wide-threshold and thin-walled structures, and their aeration efficiency, a topic underexplored in the current literature.

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Cite this article as:
Toktogulov T, Teshebaeva Z, Aldashov M, Zhorokulov D and Artykbaev S. Investigation of the Possibility of Energy Attenuators as Stream Aerators: Optimising the Design of Hydraulic Structures to Improve Their Environmental Performance. Premier Journal of Science 2025;14:100177

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