Steady Water Flow Research Articles

Numerical modeling of surge wave in downstreams of the waterworks

Basic requirements for water measuring and water accounting devices developed to fulfil static control of water distribution have not changed virtually in recent decades. It is due primarily to the use of water accounting and measuring instruments developed and used in conditions of steady uniform water flow when unique dependence on depth and water discharge on the rise and decline of the waterline levels is observed. Under operation of watercourses in the unsteady water flow regimen, the existing means of water measurement are not applicable. Simultaneous direct measurement of hydraulic parameters in controlled cross sections of waterways is complicated even under steady water flow regimen. Nowadays there is the lack of data to predict extreme values of discharges and water depth in downstreams of the waterworks due to the absence of tested and feasible methods of water depth and discharge measurement in calculated cross sections of waterways. With the application of the complete integral theory, a hydraulic calculation of the changes in the flow rate and the depth of flow in fixed sections of the downstream of the waterworks was performed. It is based on the analytical method of linearized system solution of one-dimensional differential equations in partial derivatives of Saint-Venant hyperbolic type.

Estimation of Conservative Contaminant Travel Time through Vadose Zone Based on Transient and Steady Flow Approaches

Estimation of contaminant travel time through the vadose zone is needed for assessing groundwater vulnerability to pollution, planning monitoring and remediation activities or predicting the effect of land use change or climate change on groundwater quality. The travel time can be obtained from numerical simulations of transient flow and transport in the unsaturated soil profile, which typically require a large amount of data and considerable computational effort. Alternatively, one can use simpler analytical methods based on the assumptions of steady water flow and purely advective transport. In this study, we compared travel times obtained with transient and steady-state approaches for several scenarios. Transient simulations were carried out using the HYDRUS-1D computer program for two types of homogeneous soil profiles (sand and clay loam), two types of land cover (bare soil and grass) and two values of dispersion constant. It was shown that the presence of root zone and the dispersion constant significantly affect the results. We also computed the travel times using six simplified methods proposed in the literature. None of these methods was in good agreement with transient simulations for all scenarios and the discrepancies were particularly large for the case of clay loam with grass cover.

Velocity mapping of steady water flow through methane hydrate bearing samples

The productivity of methane from natural gas hydrate reservoirs is predominantly controlled by the fluid migration mechanisms in hydrate-bearing sediments. Thus, the characterization of the effects of hydrate distribution on fluid migration is significant in the exploitation of natural gas hydrates. In this work, a phase contrast method was used to visualize water flow velocity fields at three cross-sections under different injecting flow rates by using magnetic resonance imaging (MRI). Four experimental cases were performed to directly measure the cross-sectional velocity fields in a sand packed hydrate-bearing sample with hydrate saturations varying from 22.5% to 32.7%. The effect of hydrate distribution on the water velocity fields was discussed. It was found that hydrate formed nonuniformly in the sand packed sample in all four cases, and the hydrate distribution predominantly affected the water effective permeability and cross-sectional velocity fields when steady water flow was injected. When hydrate saturation was higher than 22.5%, a two-region flow pattern was observed with a clear boundary between the fast-flowing region and the slow-flowing region. The cross-sectional flow rates calculated according to the velocity field images fitted well with the injecting flow rates.

Experimental validation of an ultrasonic flowmeter for unsteady flows

An ultrasonic flowmeter was developed for further applications in cryogenic conditions and for measuring flow rate fluctuations in the range of 0 to 70 Hz. The prototype was installed in a flow test rig, and was validated experimentally both in steady and unsteady water flow conditions. A Coriolis flowmeter was used for the calibration under steady state conditions, whereas in the unsteady case the validation was done simultaneously against two methods: particle image velocimetry (PIV), and with pressure transducers installed flush on the wall of the pipe. The results show that the developed flowmeter and the proposed methodology can accurately measure the frequency and amplitude of unsteady fluctuations in the experimental range of 0–9 l s−1 of the mean main flow rate and 0–70 Hz of the imposed disturbances.

Application of the DIDAS program for the design and scheduling of drip irrigation

The DIDAS software package assists in drip-irrigation system design and irrigation scheduling. It is based on analytical solutions of the linearized water flow equation. The problem of water flow and uptake is described by superposing solutions for positive sources (on-surface or subsurface emitters) and negative sinks (root systems). Steady water flow is assumed in the design module and unsteady flow in the irrigation-scheduling module. The design tool, based on the relative water-uptake rate (RWUR) criterion, assesses the effects on water-use efficiency of geometrical attributes: distances between emitters along drip lines, separation between drip lines, depth of subsurface emitters, and size and depth of root systems. For design purposes, it is assumed that there is no plant-atmosphere resistance to water uptake, i.e., roots are assumed to apply maximum suction and water-uptake rate depends only on the soil's ability to conduct water from sources to sinks. The RWUR computations require only three parameters describing soil texture, root-zone size, and potential evaporation. The optimizing tool for irrigation scheduling is based on a relative water-uptake volume (RWUV) criterion. The RWUV computations for a given drip-irrigation design require additional information on the diurnal pattern of plant resistance to water uptake and soil hydraulic conductivity. DIDAS also contains a diurnal pattern module to evaluate diurnal water-uptake patterns; it assumes quasi-steady flow, accounts for diurnal variations in plant-atmosphere resistance and evaporation, and serves for fine-tuning the design and in preliminary evaluation of scheduling scenarios. DIDAS was programmed in Delphi, runs on a PC under the Windows operating system, and requires no further software. The drip-irrigation scenario is constructed via a few GUI windows, which also contain a library of the required soil input parameters, and a best-fitting procedure to determine them. The computed RWURs and RWUVs are displayed graphically and the tabulated output results can be exported to, e.g., Microsoft Excel for further processing. An updated DIDAS version can be downloaded freely from http://app.agri.gov.il/didas. From March 2014 through July 2016, 877 people from 94 countries downloaded the first or second DIDAS versions (1.0.1 and 1.1.1, respectively). We briefly introduce drip irrigation and other available programs for its design and scheduling, outline the major DIDAS concepts, and illustrate the operation of the main software modules.

Heat Development and Comparison Between the Steady and Pulsating Flows Through Aluminum Foam Heat Sink

Continuous improvements in electronic devices for high-performance computers have led to a need for new and more effective methods of chip cooling. The first purpose of this study was to investigate the heat transfer development and characteristics of aluminum foam heat sink subjected to steady water flow for electronics cooling (Intel core i7 processor). The second purpose was to implement a new type of water flow through the aluminum foam, which is pulsating or oscillating flow in order to achieve more uniform temperature distribution over the electronic surfaces. The aluminum foam heat sink was subjected to a water flow covering the non-Darcy laminar flow regime (297–1353 Reynolds numbers). The bottom side of the heat sink was heated with a heat flux between 8.5 and 13.8 W/cm2. The pulsating flow frequency was ranged from 0.04 to 0.1 Hz. In addition, in order to complement the experimental studies, a numerical model was developed using finite element method and compared with the experimental data. The results revealed that the thermal entry length of the fluid flow through metal foam (porous media) is much smaller than that for laminar internal flow through empty channel. The result also showed that the local surface temperature increases along with increasing the axial flow direction for steady water flow case. On the other hand, for pulsating flow, the local temperature distributions act as a convex profile with the maximum surface temperature at the center of the test section. In addition, it was observed that the pulsating water flow through the aluminum foam heat sink achieves enhancement by 14% in the average Nusselt number and by 73% in temperature uniformity over the surface compared with steady water flow case.

Capturing Excess Nutrients from Waterways

Capturing Excess Nutrients from Waterways

Erosion patterns on a granular bed around a vertical cylinder

We report on two different patterns that can be observed at the bed surface close to a vertical cylinder when submitted to a strong enough steady water flow. The classical scour pattern observed at the cylinder foot and due to the “horseshoe” vortex around occurs at a critical velocity U c 1 below the critical velocity U c 0 for erosion without any cylinder, thus under clear-water conditions. But we observe also another pattern downstream the cylinder which consists of two symmetrical ovoid holes that look like “bunny ears”. This new scour pattern referred as BES can be observed at lower velocities that the horseshoe scour (HSS), above a critical velocity U c 2 c 1 , with a timescale formation much higher that the one of HSS.

Variations of hydraulic properties of granular sandstones during water inrush: Effect of small particle migration

The evaluation of the hydraulic properties evolution of granular sandstones in relation with groundwater inrush within faults is an important issue for mining engineering applications. This paper presents the results of an experimental investigation of small particle migration from granular sandstone samples under different original porosities, particle size compositions and water flow pressures. A new rock testing system has been setup to carry out the tests. Based on the results, it is observed that the overall permeability evolution during the tests can be divided into four different phases, including i) re-arrangement of large rock fragments, ii) water inrush with substantial particle migration, iii) continued moderate particles seepage, and iv) steady state water flow. The crushing of edges and corners of large rock fragments, and the evolution of the fracture network has mainly been observed in the first two phases of the tests. The results indicate that the migration of small particles has an essential effect on permeability and porosity increase during water inrush through fractured sandstone. The samples with higher original porosity, higher percentage of fine particles in their formation and under higher water flow pressures, achieve higher permeability and porosity values when the test is complete. Furthermore, using the measured data, the performances of a number of empirical models, for permeability evolution in fractured porous media, have been studied. The prediction results indicate that not all of the fractures in a sample domain contribute in small particle migration. There are parts of the fracture network that are not effective in particle flow, a sample with less original porosity, more fine particles and under lower water pressure shows less ineffective fractures. Therefore, using the concept of the effective porosity (fracture) is sufficient enough for the flow calculation.

An exponential boundary-layer solution to the convection-dispersion equation of solute transport in soils

The dispersion coefficient (D) and retardation factor (R) are key parameters in convection–dispersion equation (CDE). The boundary-layer theory provides a simple and convenient method to solve the CDE for a third-type boundary condition under steady water flow. However, the present boundary-layer solutions cannot accurately describe the solute concentration at higher average pore-water velocities for a long-period solute transport process. In this study, an improved exponential solution to the CDE was developed using boundary-layer theory with the assumption that the resident solute concentration in soil was an exponential function related to the position under steady water flow. The accuracies of three boundary-layer solutions (parabolic polynomial, cubic polynomial, and exponential) were evaluated by comparing with the exact solution in concentration predictions for a third-type boundary condition under steady water flow. The solute concentration distributions calculated from the three boundary-layer solutions were close to those from the exact solution. At higher average pore-water velocities, the exponential solution was better than the polynomial solutions in D and R estimations. Moreover, the feasibility of the three boundary-layer solutions was verified using a column experiment. This study provides an effective way for estimating D and R in laboratory or field studies.

Irrotational two-dimensional free-surface steady water flows over a flat bed with underlying currents

We investigate the free boundary non-linear problem for large amplitude smooth Stokes waves in flows of finite depth with underlying currents. The qualitative nature of the flow and pressure fields is investigated using maximum principles. Bounds on the surface profile have been derived. Influence of the relative magnitude of wave and current speed on the flow and pressure fields has been shown. The possible co-existence of propagating surface waves and an underlying uniform current at the wave speed is settled—this can only happen if the surface is flat.

Simulation of violent water flows over a movable bed using smoothed particle hydrodynamics

The interaction between bed-load sediment and water flow is an important topic of great concern which should be modeled for a wide range of hydrodynamic systems such as sea, rivers and estuaries. In this paper, smoothed particle hydrodynamics (SPH) is utilized for the simulation of dam-break propagation over an erodible bed and sediment distribution beneath the steady water flow. The proposed model describes both fluid and sediment particles as weakly compressible flow where the sediment is treated as a non-Newtonian fluid using Bingham–Cross model coupled with Newtonian treat (Owen’s relation) at interface. To cope with the difficulties arisen from different densities, the continuity and momentum equations are rather modified so that the interactions between the sediment and water are accurately modeled. First, the model is used to simulate the five dam-break models with PVC and sand bed materials and then the bed-load sediment transportation is considered for both Meyer-Peter and Einstein formulations. Comparisons are then made with the available experimental data indicating that the defined SPH model provides sensible predications for all given test cases.

Electronic cooling using water flow in aluminum metal foam heat sink: Experimental and numerical approach

Rapid developments in the design of chips and electronic devices for high-performance computers have led to a need for new and more effective methods of chip cooling. The purpose of this study was to investigate the heat transfer development and characteristics of the aluminum foam heat sink for Intel core i7 processor. The aluminum foam heat sink was subjected to a steady flow of water covering the non-Darcy flow regime (297–1353 Reynolds numbers). The bottom side of the heat sink was heated with a heat flux between 8.5 and 13.8 W/cm2. The heat development and thermal entry length of the aluminum foam heat sink were examined and presented. The distributions of the local surface temperature and the local Nusselt number were measured and compared with the numerical data obtained using finite element method. The average Nusselt number was obtained for the range of Reynolds numbers and an empirical correlation of the average Nusselt number as a function of the Reynolds number was derived. A comparison of previous studies using water as a coolant through aluminum foam was conducted in order to calibrate the empirical correlation of the average Nusselt number. The pressure drop across the foam was measured. The thermal performance of aluminum foam heat sink was evaluated based on the average Nusselt number and the required pumping power. The experimental results revealed that the thermal entry length increases along with increases in the Reynolds number. The results also revealed that local surface temperature increases as the heat flux increases, decreasing the Reynolds number and increasing the flow direction axis. In the fully developed region, the local Nusselt number is strongly dependent on the Reynolds number. The thermal efficiency index was defined in the study in order to evaluate the thermal performance for the aluminum foam heat sink. The results were also compared with those of previous experimental studies that used air as a coolant. The results indicated that, as a coolant, water provides lower average surface temperatures and a more uniform temperature profile. The numerical results were in good agreement with the local Nusselt number and the local experimental temperature with a maximum relative error of 0.83% and 0.43%, respectively.

A Lattice Boltzmann model for simulating water flow at pore scale in unsaturated soils

The Lattice Boltzmann (LB) method is an established prominent model for simulating water flow at pore scale in saturated porous media. However, its application in unsaturated soil is less satisfactory because of the difficulties associated with most two-phase LB models in simulating immiscible fluids, such as water and air, which have contrasting densities and viscosities. While progress has been made in developing LB models for fluids with high density ratio, they are still prone to numerical instability and cannot accurately describe the interfacial friction on water–air interface in unsaturated media. Considering that one important application of the LB model in porous materials is to calculate their hydraulic properties when flow is at steady state, we develop a simple LB model to simulate steady water flow at pore scale in unsaturated soils. The method consists of two steps. The first one is to determine water distribution within the soil structure using a morphological model; once the water distribution is known, its interfaces with air are fixed. The second step is to use a single-phase LB model to simulate water flow by treating the water–air interfaces as free-flow boundaries where the shear resistance of air to water flow is assumed to be negligible. We propose a method to solve such free-flow boundaries, and validate the model against analytical solutions of flows of water film over non-slip walls in both two and three dimensions. We then apply the model to calculate water retention and hydraulic properties of a medium acquired using X-ray computed tomography at resolution of 6 μm. The model is quasi-static, similar to the porous network model, but is an improvement as it directly simulates water flow in the pore geometries acquired by tomography without making any further simplifications.

Heat transfer characteristics of aluminum metal foam subjected to a pulsating/steady water flow: Experimental and numerical approach

The microminiaturization of electronic components has led to an increase in the heat dissipation rate (per unit area) of electronic chips. This paper presents the results of an experimental and numerical study of the use of aluminum foam as a heat sink for the Intel core i7 processor. The aluminum foam was subjected to a pulsating water flow with a frequency range between 0.04 and 0.1Hz, an amplitude range between 297 and 1353, and a heat flux range between 8.5 and 13.8W/cm2. The distributions of the cycle average local surface temperature over the heater representing the electronic surface and cycle average local Nusselt number were measured and compared with the numerical data obtained using the finite element method. The numerical results were in good agreement with the experimental data for different flow amplitudes and heat flux within a maximum relative error of 0.75% for the local temperature and 1.8% for the local Nusselt number. The pressure drop across the aluminum foam heat sink was measured and the effects of the dimensionless flow frequency and the flow amplitude on the heat transfer characteristics of the pulsating flow through the aluminum foam were analyzed. An empirical correlation of the average Nusselt number as a function of the dimensionless flow frequency and flow amplitude was developed. A comparison between the heat transfer characteristics of the steady and pulsating water flows was also conducted. The experimental results revealed that the cycle average local temperature decreases along with decreasing heat flux, increasing the pulsating flow frequency and amplitude. The local temperature distribution shows a convex profile due to the reversing flow and development of a boundary layer. Results also revealed a 14% increase in the average Nusselt number for pulsating flow when compared to the steady flow. Lastly, the thermal performance of the aluminum foam heat sink was evaluated. The experimental result revealed a 73% decrease in the uniformity index for pulsating flow when compared to the steady flow, indicating that the pulsating water flow leads to a more uniform temperature distribution. This finding is very important to the field of electronic cooling since the reliability of transistors and the operating speed are dependent upon temperature uniformity along the surface.

DIDAS – User-friendly software package for assisting drip irrigation design and scheduling

The DIDAS software package, based on analytical solutions of linearized water flow and uptake problems, assists in drip-irrigation system design and irrigation scheduling. Water flow is described by superposition of solutions for positive sources (on-surface or subsurface emitters) and negative sinks (root systems). Steady water flow is assumed in the design module and unsteady flow in the irrigation scheduling module. The design tool, based on relative water uptake rate (RWUR) criterion, assesses the effects on water use efficiency of geometrical attributes: distances between emitters along drip lines; separation between drip lines; depth of subsurface emitters; and size and depth of root systems. Evaluation of the maximum possible RWUR assumes no plant–atmosphere resistance to water uptake, i.e., the roots are assumed to apply maximum suction and the water uptake rate depends only on the soil capability to conduct water from sources to sinks. The RWUR computations require only three parameters describing the soil texture, the root zone size, and the potential evaporation, in accounting also for evaporation from the soil surface. The optimizing tool for irrigation scheduling is based on a relative water uptake volume (RWUV) criterion. The computations of diurnal variations of water uptake rates and RWUV for a given irrigation scenario require additional information on the diurnal pattern of plant resistance to water uptake and on the soil hydraulic conductivity. DIDAS also contains a diurnal pattern module for evaluating diurnal water-uptake patterns; it assumes quasi-steady flow and accounts for the diurnal variations of plant–atmosphere resistance and evaporation in fine-tuning the design and in preliminary evaluation of scheduling scenarios. DIDAS was programmed in Delphi, runs on a PC under the Windows operating system, and requires no further software. The drip irrigation scenario is constructed via a few GUI windows, which contain also a library of the required soil input parameters, and a best-fitting procedure for determining them. The computed RWURs and RWUVs are displayed graphically and the tabulated output results can be exported to, e.g., Microsoft Excel for further processing. An updated DIDAS version can be downloaded freely from http://app.agri.gov.il/didas.

Assessment of Equivalence of Small and Large Orifice Computational Models

Abstract The aim of this paper was to analyze theoretical aspects of calculating steady water flow through unsubmerged circular orifices. Theoretical analysis shows that the values of discharge obtained by using formulas intended for small orifices are greater than those calculated using formulas for large orifices. These differences attain a maximum value when the water level reaches the upper edge of the orifice, and decrease when water head increases. It has been proven that the volumetric flow rate for circular unsubmerged orifices can be calculated by formulas for small orifices when the water level above the center of gravity is at least four times as high as the diameter of the orifice.

Morphological signatures of normal faulting in low‐gradient alluvial rivers in south‐eastern Louisiana, USA

AbstractWe explore the fluvial response to faulting in three low‐gradient, sand‐bed rivers in south‐eastern Louisiana, USA, that flow across active normal faults from footwall (upstream) to hangingwall (downstream). We calculate sinuosity, migration rate and migration direction in order to identify anomalies spatially associated with fault scarps. In two of the rivers we model one‐dimensional steady water flow to identify anomalies in surface water slope, width‐to‐depth ratio, and shear stress. In each of these rivers there is one location where flow modeling suggests potential channel incision through the footwall, as indicated by relatively high surface water slopes and shear stress values. In one of these footwall locations, the river straightens and width‐to‐depth ratios decrease, likely contributing to higher surface water slopes and shear stress. This is in contrast to previous studies that have proposed increased sinuosity across fault footwalls and decreased sinuosity across hangingwalls. However, in two hangingwall locations we also observe relatively less sinuous channels. Other planform changes on the hangingwall include topographic steering of channels along and towards the fault and one example of an avulsion. The most notable anomaly in migration rate occurs on the hangingwall of a fault where a river has cut off a meander loop. Although fluvial response to faulting varies here, comparatively large and small channels exhibit similar responses. Further, Pleistocene fault slip rates are orders of magnitude lower than the channel migration rates, suggesting that faulting should not be a major influence on the fluvial evolution. Nonetheless, notable channel anomalies exist near faults, suggesting that recent fault slip rates are higher than Pleistocene rates, and/or that low‐gradient alluvial channels are more sensitive to faulting than previous studies have suggested. Rivers appear to be influenced by faulting in this setting, however background rates of meander loop cutoff may be just as influential as faulting. Copyright © 2015 John Wiley & Sons, Ltd.

Partition of unity methods for approximation of point water sources in porous media

Several partition of unity methods (PUM) are compared on the problem of steady water flow in an aquifer-well system. In order to improve the approximation of a singular behavior of the pressure near the wells, the standard finite element space is enriched with a cut-off fundamental solution to a Laplace problem with a point source on the whole R2 space. The optimal order of convergence of PUM in terms of L2 norm of the error is demonstrated. The error of adaptive integration is analysed and a new adaptive strategy is proposed. The influence of the choice of the enriched domain is investigated and its impact on the error is demonstrated numerically.

Visualization of fluid flow pathways in wood by low-field 1H and 3He contrast MRI

A low-field Magnetic Resonance Imaging (MRI) technique was used for noninvasive studies of the internal structure of three types of wood, using water and 3He gas as contrast agents. In the conditions of steady state water flow through the sample, the fluid flow pathways were found to be mainly located in the late wood. A substantial increase in sensitivity, or equivalently, a decrease in experiment time was demonstrated, when the hyperpolarized 3He gas was used. The method opens new opportunities of studying a wide range of similar biologically permeable materials in a nondestructive way.