Steady-state Hydraulics Research Articles

River hydraulic modeling with ICESat-2 land and water surface elevation

Abstract. Advances in geodetic altimetry instruments are providing more accurate measurements, thus enabling satellite missions to produce useful data for narrow rivers and streams. Altimetry missions produce spatially dense land and water surface elevation (WSE) measurements in remote areas where in situ data are scarce that can be combined with hydraulic and/or hydrodynamic models to simulate WSE and estimate discharge. In this study, we combine ICESat-2 (Ice, Cloud and land Elevation Satellite) land and water surface elevation measurements with a low-parameterized hydraulic calibration to simulate WSE and discharge without the need for surveyed cross-sectional geometry and a rainfall–runoff model. ICESat-2 provides an opportunity to map river cross-sectional geometry very accurately, with an along-track resolution of 0.7 m, using the ATL03 product. These measurements are combined with the inland water product ATL13 to calibrate a steady-state hydraulic model to retrieve unobserved hydraulic parameters such as river depth or the roughness coefficient. The low-parameterized model, together with the assumption of steady-state hydraulics, enables the application of a global search algorithm for a spatially uniform parameter calibration at a manageable computational cost. The model performance is similar to that reported for highly parameterized models, with a root mean square error (RMSE) of around 0.41 m. With the calibrated model, we can calculate the WSE time series at any chainage point at any time for an available satellite pass within the river reach and estimate discharge from WSE. The discharge estimates are validated with in situ measurements at two available gauging stations. In addition, we use the calibrated parameters in a full hydrodynamic model simulation, resulting in a RMSE of 0.59 m for the entire observation period.

Coordinated Control Strategy of Electro-Hydraulic Composite Braking Torque for the Distributed Electric Vehicles

The difference in response to electric and hydraulic braking causes sudden changes in braking torque during braking mode switching. An electro-hydraulic composite braking system’s dynamic torque coordination control strategy is proposed under braking mode switching conditions. By establishing the dynamic response model of the electro-hydraulic braking system (EHB), the key factors affecting the response speed of the EHB are analyzed, and the dynamic fuzzy controller for the pressure regulation of the brake wheel cylinder is designed. At the same time, the nonlinearity and hysteresis in the hydraulic braking process are considered, as well as electrical brake response overshoots. The electric brake response model is established, and the PID controller with feedforward feedback is designed to control the motor to adjust the inertia overpressure or lag pressure deficiency in the hydraulic braking process. Finally, the simulation verification is carried out; the results show that the proposed strategy can increase the hydraulic brake response speed by 25.4%, the impact degree of the vehicle is not more than 6.25 GB, and the hydraulic steady state error does not exceed 2.3%, which improves the vehicle ride comfort under braking mode switching.

Numerical modeling of an abiotic hyporheic mixing-dependent reaction: Chemical evolution of mixing and reactant production zones

Mixing-dependent reactions occur where groundwater and surface water mix in shallow sediments (hyporheic zone) and can attenuate contaminants along upwelling flowpaths, thus reducing transport to surface water. Here we used MODFLOW/SEAM3D to numerically simulate prior laboratory observations of a mixing-dependent reaction between sodium sulfite (Na2SO3) and dissolved oxygen (DO) to produce sodium sulfate (Na2SO4). This reaction is not common in nature but is used as a surrogate for mixing-dependent DO consuming reactions of environmental significance. We evaluated how location and thickness of mixing zones and reaction product production zones dynamically respond to variations in hydraulic and chemical boundary conditions and reaction kinetic rate. Sensitivity analysis showed that location and thickness of mixing zones and reactant production zones were most sensitive to changes in the balance of hydrologic inflow from groundwater and surface water (inflow ratio). Mixing zone thickness for reactive DO calibrated to experimental data was thinner than that for the “DO tracer” (identical source location and concentration as DO but conservative tracer), indicating that as DO is consumed its mixing zone narrows. The SO4 production zone was consistently thicker than the DO mixing zone. Small changes in mixing/production zone thicknesses were linked to large changes in mass consumed and produced, indicating the potential for simpler field metrics like thickness to act as surrogates for more challenging measurements such as contaminant flux or consumption in monitoring natural attenuation. This study improves understanding of the evolution of hyporheic mixing-dependent reaction zones that occur even under steady state hydraulics, emphasizing their complex controls.

The stability enigma of hydraulic vulnerability curves: addressing the link between hydraulic conductivity and drought-induced embolism.

Maintaining xylem water transport under drought is vital for plants, but xylem failure does occur when drought-induced embolisms form and progressively spread through the xylem. The hydraulic method is widely considered the gold standard to quantify drought-induced xylem embolism. The method determines hydraulic conductivity (Kh) in cut branch samples, dehydrated to specific drought levels, by pushing water through them. The technique is widely considered for its reliable Kh measurements, but there is some uncertainty in the literature over how to define stable Kh and how that relates to the degree of xylem embolism formation. Therefore, the most common setup for this method was extended to measure four parameters: (i) inlet Kh, (ii) outlet Kh, (iii) radial flow from xylem to surrounding living tissue and (iv) the pressure difference across the sample. From a strictly theoretical viewpoint, hydraulic steady state, where inflow equals outflow and radial flow is zero, will result in stable Kh. Application of the setup to Malus domestica Borkh. branches showed that achieving hydraulic steady state takes considerable time (up to 300min) and that time to reach steady state increased with declining xylem water potentials. During each experimental run, Kh and xylem water potentials dynamically increased, which was supported by X-ray computed microtomography visualizations of embolism refilling under both high- (8kPa) and low-pressure (2kPa) heads. Supplying pressurized water can hence cause artificial refilling of vessels, which makes it difficult to achieve a truly stable Kh in partially embolized xylem.

Improved Loop-Flow Method for Hydraulic Analysis of Water Distribution Systems

AbstractDifferent methods have been developed in the past to formulate and solve steady-state hydraulics of a water distribution system (WDS). The most widely used method nowadays is probably the g...

Performance of a microalgal photobioreactor treating toilet wastewater: Pharmaceutically active compound removal and biomass harvesting

In this study, a 1200L outdoor pilot scale microalgal photobioreactor (PBR) was used for toilet wastewater (WW) treatment and evaluate its ability to remove pharmaceutically active compounds (PhACs). The PBR was operated at two different hydraulic retention times (HRTs), which were 8 and 12days, during Period I (September–October) and Period II (October–December), respectively. Algal biomass concentrations varied by operating period because of seasonal changes. Nutrients (ammonia, nitrogen and total phosphorous) and chemical oxygen demand (COD) were monitored and efficiently removed in both periods (>80%), attaining the legislation limits. At the theoretical hydraulic steady state in both periods, pharmaceutical removal reached high levels (>48%). Two harvesting techniques were applied to the PBR microalgae effluent. Gravity sedimentation was efficient for biomass removal (>99% in 7min) in Period I when large particles, flocs and aggregates were present. In contrast, a longer sedimentation time was required when biomass was mainly composed of single cells (88% clarification in a 24h in Period II). The second harvesting technique investigated was the co-pelletization of algal biomass with the ligninolytic fungus Trametes versicolor, attaining >98% clarification for Period II biomass once pellets were formed. The novel technology of co-pelletization enabled the complete harvesting of single algae cells from the liquid medium in a sustainable way, which benefits the subsequent use of both biomass and the clarified effluent.

Fast Graph Matrix Partitioning Algorithm for Solving the Water Distribution System Equations

AbstractIn this paper a method that determines the steady-state hydraulics of a water distribution system, the graph matrix partitioning algorithm (GMPA), is presented. This method extends the technique of separating the linear and nonlinear parts of the problem and using the more time-consuming nonlinear solver only on the nonlinear parts of the problem and faster linear techniques on the linear parts of the problem. The previously developed forest-core partitioning algorithm (FCPA) used this approach to separate the network graph’s external forest from its looped core but did not address the fact that within the core of a network graph there may be many internal trees—nodes in series—for which a more economical linear process can be used. This extension of the separation process can significantly reduce the dimension of the nonlinear problem that must be solved: GMPA applied to eight case study networks with between 900 and 20,000 pipes show reductions to between 5 and 55% of the core dimension (after F...

Unified Framework for Deriving Simultaneous Equation Algorithms for Water Distribution Networks

AbstractThe known formulations for steady-state hydraulics within looped water distribution networks are rederived in terms of linear and nonlinear transformations of the original set of partly linear and partly nonlinear equations that express conservation of mass and energy. All of these formulations lead to a system of nonlinear equations that can be linearized as a function of the chosen unknowns using either the Newton-Raphson (NR) or the linear theory (LT) approaches. This produces a number of different algorithms, some of which are already known in the literature, whereas others have been originally developed within this work. For the sake of clarity, all the different algorithms were rederived using the same analytical approach and a unified notation. They were all applied to the same test case network with randomly perturbed demands to compare their convergence characteristics. The results show that all of the linearly transformed formulations have exactly the same convergence rate, whose value d...

A Concise Numerical Model of Gas-Liquid Stratified Wavy Flow

On the basis of the conservation law of the flow field and the two-fluid model, a one-dimensional steady state hydraulics model of the gas-liquid stratified wavy flow is established. The method accounts for the effects of the turbulence through the use of the standard K-ε two-equation model of turbulence with the wall function method employed near the wall. The gas phase and the liquid phase in the wavy region are considered respectively as two points for simplification. The model permits the prediction of flow parameters such as liquid holdup,pressure drop, velocity profile and so on. It is easy to calculate and the result is compared with the experiments and other models and agrees well with them.

Flow path and hydraulic analysis for on-farm pressurized irrigation systems

A model was developed to analyze the steady-state hydraulics of branching pipe networks as found in on-farm pressurized irrigation systems with multiple outlets at sprinklers or emitters. The model uses a new methodology to identify all flow paths based on a shortest-path algorithm. It also uses elevation and hydraulic parameters to determine which outlets are flowing and which (if any) are not. An iterative solution approach results in the calculated flow rates and pressures at all nodes in the network with a single source node, which can have a fixed head (reservoir) or a pump. The methodology provides a guaranteed steady-state hydraulic solution for the network, regardless of the available pressure, pipe layout and characteristics, or field topography.

The ecological complexity of the Thai-Laos Mekong River: I. Geology, seasonal variation and human impact assessment on river quality

The objective of this study is to assess the variation of pollution in the Thai–Laos Mekong associated with seasonal dynamics concomitant with the natural geological features and human activities that impact on the adverse quality of the river. The complex ecology of the 1500 km stretch of the Thai-Laos Mekong River has been studied in this paper to understand the relationship with the geomorphology, with the sub-tropical monsoonal climate and the impact of human activity. Sub-surface geology controls the nature and extent of the drainage basin and of the river channel. The volume flow of the river varies naturally and dynamically in phase with the rainfall; traditional models based on steady state hydraulics are inappropriate. Continuous erosion of the river banks and bed generates a sediment load of impure silt, mica, quartz and clay minerals that inhibits light penetration and limits the primary productivity of the river. The river separates two countries at different stages of development; it flows through or close to eight non-industrial conurbations (Populations 350,000–2,000,000) but is otherwise sparsely populated. The river is used for subsistence agriculture, village transport, fishing including aquaculture and as a source of domestic water. Hydroelectricity is generated from the Laos tributaries. The river is a depository for partially treated urban waste and untreated village waste, hence populations of E.coli bacteria sometimes render the water unsuitable for drinking unless treated with the highest value of 240/100ml found at station 7 during the summer season of 2003. Furthermore the river is polluted by trace metals, notably cadmium and mercury, and by Polycyclic Aromatic Hydrocarbons (PAHs), which are particularly concentrated in the sediments. Previous work has shown that cadmium and mercury exceed the Probable Effect Level (PEL) values of Canadian Environmental Quality Guidelines and that the PAH concentrations were also greater than the Interim Sediment Quality Guidelines (ISQG). Consequently the fish stock, a vital source of protein for the local human population maybe seriously affected. As conflict between the demands of human activities will be exacerbated by the continuing development of the basin; monitoring must be continued and a better model of the river's ecology is needed to predict the impact of development.

Tracer experiments within composite soil column investigated by MRI

The magnetic resonance imaging (MRI) technique was used for the visualisation and interpretation of flow paths. A set of tracer-infiltration experiments was performed on soil columns filled with packed homogeneous sand and with a composite sand-soil system. The flow paths were visualised using a tracer-solution containing Ni(NO<sub>3</sub>)<sub>2</sub> which is characterised by relaxation times different from that of the infiltrating water. The tracer pulse was added under hydraulic steady state conditions. Small disturbances in the tracer front were observed during the breakthrough in the case of a homogeneous sample. More pronounced effects were seen with the composite sample. The vertical components of the velocity fields were evaluated for the experiments presented. The irregularities in the tracer front and in the velocity fields were in this case attributed to the preferential flow phenomena in combination with air bubble entrapment. Beside that, two consecutive tracer pulses were performed with the aim of testing the potential influence of the different solute concentrations on the adsorption power. Both concentrations had negligible impacts on the acquired image. The presented results are constrained by the limits of the described technology; further investigations are being carried out using more advanced equipment. I

Efficient numerical method for district heating system hydraulics

An efficient method for numerical simulation and analyses of the steady state hydraulics of complex pipeline networks is presented. It is based on the loop model of the network and the method of square roots for solving the system of linear equations. The procedure is presented in the comprehensive mathematical form that could be straightforwardly programmed into a computer code. An application of the method to energy efficiency analyses of a real complex district heating system is demonstrated. The obtained results show a potential for electricity savings in pumps operation. It is shown that the method is considerably more effective than the standard Hardy Cross method still widely used in engineering practice. Because of the ease of implementation and high efficiency, the method presented in this paper is recommended for hydraulic steady state calculations of complex networks.

Minimizing residence times by rerouting flows to improve water quality in distribution networks

Management of water quality is a major issue for water companies, especially as many systems are old and have excess capacity. A methodology which uses an evolutionary algorithm to minimize water age, and hence improve water quality, is presented in this article. A steady-state model is used to find the water age at various nodes of a network. Three parameters are derived from these nodal age values to represent quality for the entire network. The evolutionary algorithm reconfigures the network by selecting a set of pipes for closure. The optimal network configuration is achieved when the chosen water age parameter is minimized subject to maintaining connectivity and hydraulic feasibility in the network. The methodology is applied to an example network to identify the age parameter that best represents quality over the entire network. The evolutionary model is then applied to re-route flows in a real water distribution network and the results are compared with those from the unmodified network. The validity of the use of steady-state hydraulics is tested by conducting an extended period simulation (EPS) on these results.

Mathematical modeling of open-channel velocity profiles for float method calibration

A computational method based on mathematical modeling of steady-state hydraulics is described for improving the accuracy of the float method for estimating open-channel discharge. Both two-dimensional (2-D) and three-dimensional (3-D) velocity distribution model versions were developed for steady-state uniform flow in open channels with rectangular cross-sections. The normal depth of flow was obtained by solving the Chézy equation for uniform flow conditions. Cross-sectional velocity distributions were calculated by solving the Reynolds-averaged Navier-Stokes (RANS) equations and an algebraic model for turbulent stresses, without the use of wall proximity corrections to the pressure strain term. The calculated 3-D velocity coefficients were found to be in the same range as previously published United States Bureau of Reclamation (USBR) coefficients, but the results also indicate that the USBR coefficients, which are based solely on average water depth, can be improved by taking into account other hydraulic parameters such as longitudinal bed slope, channel base width, and wall roughness. The mathematical model exhibited considerable sensitivity to initial conditions, boundary condition parameters, and numerical convergence criteria, also manifesting spikes in the calculated surface velocity coefficients for discrete changes in hydraulic parameters. Finally, it was found that the 2-D version of the model is not appropriate for calculating surface velocity coefficients because it does not account for secondary flow in the channel cross-section, and the calculated surface velocity in the center of the cross-section is overestimated.

Numerical modelling of hydraulic decompression due to the excavation of tunnel and drifts at the Tournemire underground laboratory

The Tournemire underground laboratory is situated in a clay formation and consists of a disaffected railway tunnel and two perpendicular drifts. The paper presents modelling and 3D simulations of the hydraulic behaviour of the argillaceous formation around the works. Experimental measurements of porosity, permeability and specific storage coefficients allowed us to model the hydraulic properties of the shale. Numerical simulations are performed with the code CASTEM. Numerical results of hydraulic heads are compared to experimental measurements. Calculations show that the excavation of the tunnel and drifts has induced an hydraulic decompression of the indurated argillaceous formations. The zones of decompression are centred around the structures and extend depending on the values of hydraulic parameters such as permeability and specific storage selected in the model. Six years after the excavation of the drifts, the hydraulic steady state in the fractured zone is not yet reached.

Modeling transient substrate loads in completely mixed aeration basins at hydraulic steady state

Abstract A numerical technique for predicting the response of a completely mixed activated sludge system (with recycle) to transient substrate inputs is presented. Substrate utilization and biomass growth are modeled by Monod kinetics. Computational efficiency is achieved by a) “locally linearizing”; the Monod expression, and b) decoupling the two mass balances by assuming biomass to be constant locally over a time step. The subsequent solutions are simple and ideally suited for PCs. Comparisons with numerical solutions of the complete equations show a high degree of accuracy and robustness for the proposed technique.

Diffusion coefficients in gravel under unsaturated conditions

Diffusion coefficients were experimentally determined in unsaturated gravel to evaluate the effectiveness of gravel as a diffusion barrier to ionic transport in the vadose zone. Water contents were fixed by use of an ultracentrifuge with an ultralow constant rate flow pump supplying solution to the sample via a rotating seal. Once the gravel was at hydraulic steady state, the electrical conductivity was measured, and the diffusion coefficient calculated using the Nernst‐Einstein equation. Diffusion coefficient values for potassium ion (De) in four types of angular gravel ranged from 1.7 × 10−11 m2/s (1.7 × 10−7 cm2/s) for a 6.3–9.5 mm angular granitic gravel at a volumetric water content of 5.5% to 2.2 × 10−14 m2/s (2.2 × 10×10 cm2/s) in a 4.0–6.3 mm quartzite gravel at a volumetric water content of 0.47%. Variations in De values resulted primarily from differences in water content which depends on gravel type and particle size.