We present direct numerical simulation results of turbulent open channel flow at bulk Reynolds numbers up to 12 000, coupled with (passive) scalar transport at Schmidt numbers up to 200. Care is taken to capture the very large-scale motions which appear already for relatively modest Reynolds numbers. The transfer velocity at the flat, free surface is found to scale with the Schmidt number to the power ‘
’, in accordance with previous studies and theoretical predictions for uncontaminated surfaces. The scaling of the transfer velocity with Reynolds number is found to vary, depending on the Reynolds number definition used. To compare the present results with those obtained in other systems, we define a turbulent Reynolds number at the edge of the surface-influenced layer. This allows us to probe the two-regime model of Theofanous et al. (Intl J. Heat Mass Transfer, vol. 19, 1976, pp. 613–624), which is found to correctly predict that small-scale vortices significantly affect the mass transfer for turbulent Reynolds numbers larger than 500. It is further established that the root mean square of the surface divergence is, on average, proportional to the mean transfer velocity. However, the spatial correlation between instantaneous surface divergence and transfer velocity tends to decrease with increasing Schmidt number and increase with increasing Reynolds number. The latter is shown to be caused by an enhancement of the correlation in high-speed regions, which in turn is linked to the spatial distribution of surface-parallel vortices.
Woodchip bioreactors are capable of removing nitrate from agricultural runoff and subsurface tile drain water, alleviating human health hazards and harmful discharge to the environment. Water pumped from agricultural tile drain sumps to nearby ditches or channels could be cost effectively diverted through a woodchip bioreactor to remove nitrate prior to discharge into local waterways. Sizing the bioreactor to achieve targeted outlet concentrations within a minimum footprint is important to minimizing cost. Determining the necessary bioreactor size should involve a hydrological component as well as reaction type and rates. We measured inflow and outflow nitrate concentrations in a pumped open-channel woodchip bioreactor over a 13-month period and used a tanks-in-series approach to model hydrology and estimate parameter values for reaction kinetics. Both zero-order and first-order reaction kinetics incorporating the Arrhenius equation for temperature dependence were modeled. The zero-order model fit the data better. The rate coefficients (k = 17.5 g N m−3 day−1 and theta = 1.12 against Tref = 20 °C) can be used for estimating the size of a woodchip bioreactor to treat nitrate in agricultural runoff from farm blocks on California's central coast. We present an Excel model for our tanks-in-series hydrology to aid in estimating bioreactor size.
The critical depth and normal depth computation are essential for hydraulic engineers to understanding the characteristics of varied flow in open channels. These depths are fundamental to analyze the flow for irrigation, drainage, and sewer pipes. Several explicit solutions to calculate critical and normal depths in different shape open channels were discovered over time. Regardless of the complexity of using these explicit solutions, these formulas have a significant error percentage compared to the exact solution. Therefore, this research explicitly calculates the normal and critical depth in circular channels and finds simple, fast, and accurate equations. First, the dimensional analysis was used to propose an analytical equation for measuring the circular channels' critical and normal depths. Then, regression analysis has been carried for 2160 sets of discharge versus critical and normal depths data in a circular open channel. The results show that this study's proposed equation for measuring the circular channels' critical and normal depths overcomes the error percentage in previous studies. Furthermore, the proposed equation offers efficiency and precision compared with other previous solutions.