Three-dimensional transient flow in heterogeneous reservoirs: Integral transform solution of a generalized point-source problem

2021 ◽  
pp. 109976
Author(s):  
Leonardo O. Pelisoli ◽  
Renato M. Cotta ◽  
Carolina P. Naveira-Cotta ◽  
Paulo Couto
Keyword(s):  
Point Source ◽  
Transient Flow ◽  
Integral Transform ◽  
Three Dimensional ◽  
Heterogeneous Reservoirs

Incorporation of spatial variability in modeling non-point source groundwater nitrate pollution

1996 ◽  
Vol 33 (4-5) ◽  
pp. 233-240 ◽  
Author(s):  
F. S. Goderya ◽  
M. F. Dahab ◽  
W. E. Woldt ◽  
I. Bogardi
Keyword(s):  
Spatial Variability ◽  
Point Source ◽  
Three Dimensional ◽  
Nitrate Contamination ◽  
Geostatistical Simulation ◽  
Chemical Measurements ◽  
Spatially Distributed ◽  
Potential Benefits ◽  
Zone Modeling ◽  
Physical And Chemical

A methodology for incorporation of spatial variability in modeling non-point source groundwater nitrate contamination is presented. The methodology combines geostatistical simulation and unsaturated zone modeling for estimating the amount of nitrate loading to groundwater. Three dimensional soil nitrogen variability and 2-dimensional crop yield variability are used in quantifying potential benefits of spatially distributed nitrogen input. This technique, in combination with physical and chemical measurements, is utilized as a means of illustrating how the spatial statistical properties of nitrate leaching can be obtained for different scenarios of fixed and variable rate nitrogen applications.

Dynamics of a composite system in a point source-induced space–time

2021 ◽  
pp. 2150144
Author(s):  
Abdullah Guvendi
Keyword(s):  
Point Source ◽  
Composite System ◽  
Dimensional Space ◽  
Energy Levels ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Space Time ◽  
Spin Coupling ◽  
Quantum Oscillator ◽  
Dimensional Space Time

We investigate the dynamics of a composite system ([Formula: see text]) consisting of an interacting fermion–antifermion pair in the three-dimensional space–time background generated by a static point source. By considering the interaction between the particles as Dirac oscillator coupling, we analyze the effects of space–time topology on the energy of such a [Formula: see text]. To achieve this, we solve the corresponding form of a two-body Dirac equation (fully-covariant) by assuming the center-of-mass of the particles is at rest and locates at the origin of the spatial geometry. Under this assumption, we arrive at a nonperturbative energy spectrum for the system in question. This spectrum includes spin coupling and depends on the angular deficit parameter [Formula: see text] of the geometric background. This provides a suitable basis to determine the effects of the geometric background on the energy of the [Formula: see text] under consideration. Our results show that such a [Formula: see text] behaves like a single quantum oscillator. Then, we analyze the alterations in the energy levels and discuss the limits of the obtained results. We show that the effects of the geometric background on each energy level are not same and there can be degeneracy in the energy levels for small values of the [Formula: see text].

Calculation of Flow Induced Vibration Amplitudes of Radial Sewage Water Pumps

2003 ◽  
Author(s):  
Friedrich-Karl Benra ◽  
Hans Josef Dohmen ◽  
Oliver Schneider
Keyword(s):  
Transient Flow ◽  
Three Dimensional ◽  
Sewage Water ◽  
Flow Induced Vibration ◽  
Present Contribution ◽  
Unsteady Forces ◽  
Friction Forces ◽  
Pump Shaft ◽  
Water Pumps ◽  
Operating Points

The extreme vibrations of sewage water pumps with single-blade impellers are induced mainly by interaction of the flow in the impeller and the casing. The resulting periodically unsteady forces affect the impeller and produce radial deflections of the pump shaft. These oscillations of the rotor are transferred to the pump casing and attached pipes. They can be recognized as vibrations at the bearing blocks or at the pump casing. The present contribution describes the investigation of the transient flow in a sewage water pump. The three-dimensional, viscous, unsteady flow in a pump with a single blade impeller is determined by numerical simulation. After that the hydrodynamic stimulation forces are calculated from the so known transient flow field. The forces can be classified into pressure and friction forces. The pressure forces usually exceed the friction forces on several orders of magnitude. A separate view on the fluid-wetted impeller surfaces shows that the pressure forces acting on the blade are clearly larger than the forces at the hub and at the shroud. So they are decisive for the vibration amplitudes of single-blade sewage water pumps. By a following dynamic analysis of the pump rotor using a commercial Finite-Element-Method (FEM) the resulting vibration amplitudes are determined for several operating points. With the known pressure field and the calculated vibration amplitudes the vibration behavior of sewage water pumps can be influenced during the design by changing the relevant construction parameters.

Numerical Simulation of Start-Up Jets in a Mixing Chamber

2010 ◽  
Author(s):  
Chenzhou Lian ◽  
Dmytro M. Voytovych ◽  
Guoping Xia ◽  
Charles L. Merkle
Keyword(s):  
Transient Flow ◽  
Three Dimensional ◽  
Cost Effective ◽  
Grid Refinement ◽  
Mixing Process ◽  
Quantitative Estimates ◽  
Start Up ◽  
Mixing Chamber ◽  
Parametric Analyses ◽  
Transient Mixing

Numerical simulations of a transient flow of helium injected into an established background flow of nitrogen were carried out to identify the dominant features of the transient mixing process between these two dissimilar gases. The geometry of interest is composed of two helium slots on either side of a central nitrogen channel feeding into a ‘two-dimensional’ mixing chamber. Simulations were accomplished on both two- and three-dimensional grids using an unsteady DES approach. Results are compared with experimental measurements of species distributions. Unsteady 2-D solutions give a reasonable qualitative picture of the transient mixing process in the middle of the chamber and enable cost-effective parametric analyses and grid refinement studies. The 2-D solutions also provide quantitative estimates of representative characteristic times to guide the 3-D calculations. The 3-D solutions give a reasonable approximation to span-wise events.

scholarly journals Modeling of three-dimensional elastic strain fields by point-source method

2015 ◽  
Vol 15 (4) ◽  
pp. 13-23 ◽  
Author(s):  
Sergey Knyazev ◽  
Elena Shcherbakova ◽  
Viktor Pustovoyt ◽  
Anton- Shcherbakov-
Keyword(s):  
Point Source ◽  
Elastic Strain ◽  
Three Dimensional ◽  
Strain Fields ◽  
Source Method

scholarly journals Calibration Routine for Quantitative Three-Dimensional Flow Field Measurements in Drying Polymer Solutions Subject to Marangoni Convection

2019 ◽  
Vol 3 (1) ◽  
pp. 39
Author(s):  
Max Tönsmann ◽  
Fabian Kröhl ◽  
Philipp Cavadini ◽  
Philip Scharfer ◽  
Wilhelm Schabel
Keyword(s):  
Flow Field ◽  
Particle Tracking Velocimetry ◽  
Transient Flow ◽  
Marangoni Convection ◽  
Three Dimensional ◽  
Field Measurements ◽  
Calibration Procedure ◽  
Cover Glass ◽  
Spread Function ◽  
Multifocal Lens

Surface-tension induced flows may have a significant impact on the surface topography of thin films or small printed structures derived from polymer solution processing. Despite a century of research on Marangoni convection, the community lacks quantitative experimental flow field data, especially from within drying solutions. We utilize multifocal micro particle tracking velocimetry (µPTV) to obtain these data and show a calibration routine based on point spread function (PSF) simulations as well as experimental data. The results account for a varying sample refractive index, beneficial cover-glass correction collar settings as well as a multifocal lens system. Finally, the calibration procedure is utilized exemplarily to reconstruct a three-dimensional, transient flow field within a poly(vinyl acetate)-methanol solution dried with inhomogeneous boundary conditions.

scholarly journals Technical Note: Three-dimensional transient groundwater flow due to localized recharge with an arbitrary transient rate in unconfined aquifers

2016 ◽  
Vol 20 (3) ◽  
pp. 1225-1239 ◽  
Author(s):  
Chia-Hao Chang ◽  
Ching-Sheng Huang ◽  
Hund-Der Yeh
Keyword(s):  
Groundwater Flow ◽  
Integral Transform ◽  
Three Dimensional ◽  
Observation Point ◽  
Technical Note ◽  
Specific Yield ◽  
Vertical Flow ◽  
Dimensional Flow ◽  
Special Cases ◽  
Present Solution

Abstract. Most previous solutions for groundwater flow induced by localized recharge assumed either aquifer incompressibility or two-dimensional flow in the absence of the vertical flow. This paper develops a new three-dimensional flow model for hydraulic head variation due to localized recharge in a rectangular unconfined aquifer with four boundaries under the Robin condition. A governing equation describing spatiotemporal head distributions is employed. The first-order free-surface equation with a source term defining a constant recharge rate over a rectangular area is used to depict water table movement. The solution to the model for the head is developed with the methods of Laplace transform and double-integral transform. Based on Duhamel's theorem, the present solution is applicable to flow problems accounting for arbitrary time-dependent recharge rates. The solution to depth-average head can then be obtained by integrating the head solution to elevation and dividing the result by the aquifer thickness. The use of a rectangular aquifer domain has two merits. One is that the integration for estimating the depth-average head can be analytically achieved. The other is that existing solutions based on aquifers of infinite extent can be considered as special cases of the present solution before the time when the aquifer boundary had an effect on head predictions. With the help of the present solution, the assumption of neglecting the vertical flow effect on the temporal head distribution at an observation point outside a recharge region can be assessed by a dimensionless parameter related to the aquifer horizontal and vertical hydraulic conductivities, initial aquifer thickness, and the shortest distance between the observation point and the edge of the recharge region. The validity of assuming aquifer incompressibility is dominated by the ratio of the aquifer specific yield to its storage coefficient. In addition, a sensitivity analysis is performed to investigate the head response to the change in each of the aquifer parameters.

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