A new predictive model can lead to a better prediction of gas transfer efficiency at low-head dams, which then allows the owners/operators of these structures to more reliably determine expected downstream dissolved oxygen levels.
By Adam M. Witt and John S. Gulliver
Dissolved oxygen concentrations in natural waters can vary greatly – from 0 mg/L to 15 mg/L – depending on water temperature, depth and use. Sufficient DO levels are vital to the aquatic biota, promoting diverse ecosystems and improving the assimilative capacity of rivers. For warm waters, typical mandates require DO of 4 mg/L minimum, with a daily average above 5 mg/L.1 At low-head structures, such as locks and dams on navigable rivers, dissolution of entrained air substantially increases DO levels. In areas with inherently low summertime DO levels, this is a benefit to fish and other aquatic animals.
The ability to predict DO levels downstream of low-head structures is a practical and economic tool for hydropower operators. Field testing is the only appropriate means of estimating gas transfer efficiency, or the transfer of atmospheric gases into the flow as water passes through or over a structure. However, field testing only applies to the structure being tested. Predictive models have been developed from field testing, and again many are only valid at the given location.
When facility owners increase their installed capacity or retrofit gates with turbines, the oxygen transfer efficiency potential of the structure changes and can impact design specifications. There is a need for predictive capabilities that, when used in union with field testing, can help optimize operational procedures for oxygen transfer at dams that also feature generating stations.
We propose an improved predictive model that leads to a better understanding of transfer efficiency at low-head gates. The model can be used as a surrogate for field measurements when they are deemed cost-prohibitive or when modifications to structures alter flow conditions. Using gate rating curves and elevation data, oxygen transfer efficiencies are predicted for a range of gate openings and head. Predictions developed from existing data, rather than field measurements, will result in greater economic savings for dam operators.
Two processes exist for oxygen transfer from the atmosphere into water. At a quiescent air-water interface, oxygen dissolves into water, approaching an equilibrium level, or saturation. At the same time, organisms in the water utilize DO, resulting in a steady state value that is typically below atmosphere-water equilibrium.
In turbulent flows, such as hydraulic jumps downstream of low-head gates, gas transfer primarily occurs from air entrainment. Pockets of air are captured when the upstream jet impacts the tailwater, and turbulent shear stress causes the air pockets to break apart and form bubbles. As the bubbles are sheared down in size, they are pushed deep into the tailwater by the mean flow. Increasing hydrostatic forces compress the bubbles, leading to a larger equilibrium concentration and further transferring oxygen across the bubble surface into the water. Because this occurs over a short distance, measurements taken simultaneously above and below low-head gates are representative of the structure’s gas transfer capabilities.
Field measurements are often the only available option to quantify the aeration capacity of a hydraulic jump downstream from a low-head gate. Froude-scaled physical models do not incorporate bubble physics and bubble dynamics as a critical role in oxygen transfer. And numerical modeling requires a number of unverified assumptions on the details of bubble breakup and coalescence and bubble-air transfer.
If DO measurements are obtained at a structure, its aeration capabilities are investigated using the computed transfer efficiency. Transfer efficiency relates downstream and upstream gas concentrations to the local saturation concentration2:
– E is transfer efficiency;
– Cd, Cu, and Cs refer to the downstream, upstream, and saturation concentrations, respectively;
– e is the exponential function;
– KL is a bulk liquid film coefficient;
– a is the interfacial area per air-water volume; and
– t is time the bubbles are in the flow.
A transfer efficiency of 1 indicates the gate has aerated flow to 100% of the saturation value, while a value of 0 means there has been no net transfer. When transfer efficiency is known, downstream concentration can be computed:
Cd = E (Cs – Cu) + Cs
Most hydropower operators are interested in predicting DO concentrations downstream, as this is the most-regulated water quality parameter. However, there are several challenges in measuring DO concentrations directly to determine transfer efficiency:
1. Often, upstream DO is not well-mixed, with vertical stratification or horizontal variations in concentration. This makes it difficult to know precisely from where in the water column the water downstream from the gate came. It is also difficult and expensive to place sufficient DO meters to determine the extent of mixing.
2. For many field measurement campaigns, the DO deficit upstream of a spillway is not sufficient to measure oxygen transfer within an acceptable uncertainty. A large margin of error results when the upstream concentration is near the saturation concentration.3
3. Field measurements do not apply across multiple structures. Testing at each site on a river is cost-prohibitive, leaving dam operators to rely on information from only one or two sites.
4. Bubbles in the tailwater experience increasing hydrostatic pressure with increasing depth. This pressure affects the saturation concentration in the plunge pool, known as the tailwater effect. An accurate measurement of saturation concentration at various depths in the plunge pool must account for the tailwater effect.
5. Regulators are generally interested in low DO events, which occur early in the morning during hot, calm weather. Field measurements planned in advance are not guaranteed to take place during these low DO events.
To mitigate these challenges, dissolved methane is used as a tracer gas for representing oxygen transfer through determination of KLa.4,5 Methane has a small atmospheric equilibrium concentration because there is little methane in the atmosphere. However, methane is abundant in sediments and is found in measurable concentrations in natural waters. Concentrations of methane downstream are diluted by oxygen-rich air entrained at the structure, and the rate of dilution is related to oxygen transfer efficiency.5 Thus, Equation 1 reduces to:
– m refers to methane.
Equation 3 is only dependent on the measured downstream and upstream concentrations. The second, fourth and fifth challenges above are solved for methane transfer, although the first and third challenges are not. If upstream mixing is sufficient, Equation 3 is assumed to be an accurate portrayal of methane transfer efficiency. The third challenge remains and will be investigated further.
Relating oxygen and methane transfer efficiencies
To relate the transfer efficiency of methane to that of oxygen, an indexing relationship is required. Under identical flow conditions, different gases exhibit different transfer efficiencies. With the majority of gas transfer occurring across the bubble interface, diffusivity of the gas is the limiting factor. There is an indexing parameter that relates the diffusion coefficients of methane and oxygen at different water temperatures, providing accurate estimates of oxygen transfer from measurements of dissolved methane:3
EO2CH4 = 1 – (1 – ECH4)f
– EO2CH4 is the transfer efficiency of oxygen, indexed from methane measurements;
– ECH4 is the transfer efficiency of methane; and
– f is an index given in Equation 5.
– DO2 and DCH4 are the diffusion coefficients of DO and methane, measured at the same temperature; and
– T is water temperature in Celsius.
The indexed transfer efficiency of oxygen relies on the assumption that its saturation concentration is consistent throughout the plunge pool. Due to the tailwater effect noted in the fourth challenge, this is not the case. There is a relationship between the saturation concentration and increased saturation concentration in the plunge pool, or effective saturation concentration:5
– Cse is the effective saturation concentration; and
– Cd and Cu are the measured oxygen concentrations downstream and upstream, respectively.
This ratio is directly related to the depth in the plunge pool where the hydrostatic force on the bubbles creates the increased saturation concentration. This effective bubble depth is:5
– deff is effective bubble depth;
– Patm is the local atmospheric pressure; and
– γ is the specific weight of water.
Often the uncertainty in deff is large due to the first challenge of unknown mixing at the gate. In this case, it is roughly estimated to be 0.286 times the tailwater depth.6 Effective bubble depth is a useful concept in comparing physical properties of a hydraulic structure to predicted gas transfer characteristics.
Methane, however, is not affected by the effective saturation and effective depth because there is close to no methane in the bubbles. Thus, if methane transfer measurements are obtained, they can be indexed to oxygen transfer efficiency at spillways. Those measurements must be corrected for the tailwater effect to get the best predicted concentration downstream of the structure. The second and third challenges above would be removed. Of course, the first challenge still remains, and the mixing of methane may be different than that of oxygen due to different sources and sinks.
The most prudent way of running a field measurement campaign is to measure dissolved methane and DO and quantify the uncertainty of each. These redundant measurements allow for a greater assurance that the expense of a field campaign will be met with high-quality results. Application of this technique will be illustrated below.
|This roller gate at a gated sill discharging downstream aerates the water, thereby increasing levels of dissolved oxygen.|
Measurements on the Ohio River
Intense industrialization in the Ohio River basin has led to poor water quality and low DO levels. The river is marked by a series of locks and dams with gated sills that assist in regulating flow over a spillway and have the potential to improve DO levels through aeration under certain flow conditions (see Figure 1).
Field experiments were conducted to quantify the gas transfer characteristics of gated sills operating under specific flow conditions in the Ohio River basin.7 Upstream and downstream measurements were obtained for methane and oxygen. Methane measurements were indexed to oxygen to determine transfer efficiency using Equations 4 and 5. Oxygen concentrations were used to determine the effective saturation concentration and effective bubble depth for a range of gate openings corresponding to different flow rates.
Their results showed a clear relationship between oxygen transfer and the operation of gated sills. Under specific gate openings, submerged and unsubmerged hydraulic jumps were observed. Significant air entrainment was observed at unsubmerged hydraulic jumps, translating to higher transfer efficiencies than with submerged jumps. For example, under gate submergence depths of 3 to 4 meters, no hydraulic jump was formed and transfer efficiencies were 0.03 to 0.09. Little air entrainment occurred, so the majority of gas transfer was from free-surface turbulence.
When unsubmerged hydraulic jumps were observed, transfer efficiencies were greater at 0.4 to 0.8. At certain locations, a spray of water, or rooster tail, formed as the hydraulic jump shifted from submerged to unsubmerged. Transfer efficiency increases when a rooster tail is present because the increased time of contact between the individual water droplets and air allows for greater gas transfer. Transfer efficiencies of 0.58 to 0.8 were observed under these conditions, inconsistent with efficiencies observed at other locations under similar sill submergence depths and flow conditions. This observation was important in characterizing behavior at that location because the rooster tail required specific gate parameters and a specific sill submergence.
The disparate transfer efficiencies and hydraulic phenomena observed at all gate locations suggest field measurements are the best way to quantify the gas transfer characteristics of a hydraulic structure. Unique behavior, i.e. rooster tail, is difficult to model. Uncertainty in transfer efficiency is inherent given the required measurement techniques, but it can be reduced through simultaneous quantification of oxygen and methane concentrations and an indexing technique. This research showed field measurements serve as a foundation for establishing operational procedures for water quality improvement using gated sills.4
Adjustment to estimate oxygen transfer efficiency
The significant limitation of field measurements is they are typically carried out at specific gate openings and discharges. Normal dam operation requires a variety of gate openings and discharges, thus any transfer efficiency obtained from oxygen and methane measurements must be adjusted accordingly. A new method is proposed to develop oxygen transfer efficiency predictions at all operational gate openings, which relies on gate opening, headwater, tailwater and sill elevation.
Small gate openings have been shown to produce submerged hydraulic jumps. When these jumps are present, the average oxygen transfer efficiency at the gate at 20 C, indexed from methane, is about 0.06 ± 0.03. Hydropower operators are generally not interested in these events because the low transfer efficiencies provide minimal aeration to the flow.
Once the hydraulic jump is unsubmerged, aeration becomes dependent on the height of the jump or the difference between the tailwater depth and the depth of the flow after it passes through the gate. Equation 1 becomes a function of KL, a and t, each of which can be estimated from the literature.6 Simplification of these relationships allows the transfer efficiency at gated sills to be estimated as a function of several dimensionless parameters related to inflow conditions. The parameters – Froude (Frh), Reynolds (Reh), Weber (Weh) and Schmidt (Sc) numbers and a dimensionless turbulence term Ψ – have been calculated with Δh as the length such that:
E20 = 1 – exp (-26.9 x Sc-½ Reh-¼ Frh Weh1/10 Ψ1/10)
– E20 is oxygen transfer efficiency at 20 C; and
– Ψ is a dimensionless turbulence term.
Equation 8 is dependent only on inflow conditions. Velocity at each gate opening is found from gated discharge rating curves, and elevation data – tailwater depth, headwater depth and sill height – is used to calculate the characteristic length scales. The leading constant, 26.9, can be adjusted for each structure if measurements are available. A full derivation of Equation 8 is available.6
Figure 2 shows the predictive relationship between transfer efficiency and gate opening for a range of static tailwater and headwater depths (above the sill) with constant sill depth of 5 meters. A deep static tailwater is typically associated with a submerged hydraulic jump and results in low transfer efficiency. This efficiency increases with gate opening and discharge, at a rate controlled by the static tailwater. When the gate rises, the height of the jump decreases, leading to greater turbulence and air entrainment. A shallow static tailwater with a small jump height provides less resistance to the flow, leading to higher transfer efficiency. Head has a noticeable effect on oxygen transfer efficiency, as evidenced by the rise in predicted E20 in Figure 2. However, the gains made in velocity and momentum through increasing head are not enough to overcome the effect of a large downstream static tailwater depth.
An example using data obtained at the Markland Lock and Dam on the Ohio River, with a head of 11 meters, validates this model. Predictions of E20 from Equation 8 are compared with measured data adjusted using Equations 6 and 7. Rating curves provide discharge values for each gate opening, and elevation data are obtained from a published source, which also includes oxygen transfer efficiency measurements for a variety of gate openings.8 The initial estimate of oxygen transfer efficiency from Equation 8 is much lower than the measured efficiencies for the highest discharges, which correlate with the highest transfer efficiencies. These measurements do not incorporate the effective saturation concentration the bubbles feel in the tailwater.
Equations 6 and 7 are used to adjust the measured transfer efficiency values. Because of the uncertainty in methane measurements, deff is estimated based on data obtained from a published source for similar dams as 0.286 * tailwater depth.4 Incorporating this value into Equation 7 gives an effective saturation concentration ratio of 1.13. Using this new value to replace Cs in Equation 1 gives improved values for E20. Unadjusted and adjusted values of E20 are compared with predicted values in Figure 3. Equation 8 can give an approximate prediction of oxygen transfer efficiency when compared with measurements adjusted to account for the effective saturation concentration.
Many low-head dams with gated sills have excellent flow duration for generating power and are good candidates for hydro facility development or expansion. One major impediment, however, is the additional oxygen transfer of flow through the gate. This is an important quantity to verify through field studies. An effective depth and effective saturation concentration are required to make sense of the field measurements, and accurate results necessitate simultaneous measurement of oxygen and methane transfer.
This article describes a model derived from Ohio River valley field data that predicts oxygen transfer efficiency from gated discharge rating curves and elevation data. When field studies are not feasible, the model estimates oxygen transfer efficiency for a range of gate openings, tailwater and headwater elevations.
This research was supported by funding from the U.S. Department of Energy and its Office of Energy Efficiency and Renewable Energy Water Power Program, through a graduate research fellowship awarded and managed by the Hydro Research Foundation. The authors acknowledge information provided by U.S. Army Corps of Engineers personnel: Steven Wilhelms, George Kincaid, Richard Pruitt, Thomas MacFarland, Leslie Rodgers and Daniel Egger.
1“D.O. and Temperature Monitoring,” Ohio River Valley Water Sanitation Commission, 2010, www.orsanco.org/index.php/dissolved-oxygen.
2Gameson, A.L.H., “Weirs and the Aeration of Rivers,” Journal of the Institute of Water Engineering, Volume 11, No. 5, 1957, pages 477-490.
3Gulliver, J.S., J.R. Thene, and A.J. Rindels, “Indexing Gas Transfer in Self-Aerated Flows,” Journal of Environmental Engineering, Volume 116, No. 3, 1990, pages 503-523.
4Urban, A.L., et al, “Field Experiments to Determine Gas Transfer at Gated Sills,” Journal of Hydraulic Engineering, Volume 127, No. 10, 2001, pages 848-859.
5Gulliver, J.S., D.E. Hibbs, and J.P. McDonald, “Measurement of Effective Saturation Concentration for Gas Transfer,” Journal of Hydraulic Engineering, Volume 123, No. 2, 1997, pages 86-97.
6Witt, A.M. and J.S. Gulliver, “Predicting Oxygen Transfer at Low-head Gated Sill Structures,” Journal of Hydraulic Research, submitted 2012.
7Urban, A.L., et al, Gas Transfer at Gated Sill Structures In the Ohio River Valley, Project Report No. 434, St. Anthony Falls Laboratory, Minneapolis, Mn., 1999.
8Hettiarachchi, S.L. et al., Gas Transfer Measurements at Hydraulic Structures on the Ohio River, Project Report No. 414, St. Anthony Falls Laboratory, Minneapolis, Mn., 1998.
Adam Witt is a Hydro Research Foundation Fellow and John Gulliver, PhD, is a professor at the University of Minnesota.
This article has been evaluated and edited in accordance with reviews conducted by two or more professionals who have relevant expertise. These peer reviewers judge manuscripts for technical accuracy, usefulness, and overall importance within the hydroelectric industry.
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