Diffusive contaminant transport in a multi-layered aquifer-aquitard system

2021 ◽  
Author(s):  
Seonggan Jang ◽  
Minjune Yang
Keyword(s):  
Analytical Solutions ◽  
Experimental Validation ◽  
Finite Thickness ◽  
Unconfined Aquifer ◽  
Flow Chamber ◽  
Measured Data ◽  
Solute Diffusion ◽  
Confined Aquifer ◽  
State Diffusion ◽  
Two Dimensional Flow

<p>A flow chamber experiment was conducted to investigate solute diffusion in a multi-layered aquifer-aquitard system. The two-dimensional flow chamber consisted of a finite thickness aquitard (kaolinite, 2 cm) bounded by two parallel aquifers at the top (unconfined aquifer, 2 cm) and bottom (confined aquifer, 4 cm). New Coccine (red dye) of 500 mg/L in the top aquifer and distilled water in the bottom aquifer were injected with 0.02 mL/min for 13 days. One-dimensional analytical solutions were developed for advection and diffusion through a finite aquitard and compared with the measured data to evaluate experimental validation. The simulated aquitard concentration profiles (E > 0.97) and breakthrough curve (E = 0.95) showed good agreement with the measured data. During the experiment, the penetration distance in the aquitard increased over time and the vertical concentration distribution showed a linear profile through the aquitard after 7 days of loading in the top aquifer, indicating steady-state diffusion. The New Coccine diffused across the aquitard to the bottom aquifer after 1 day of loading. The bottom aquifer concentration increased at early times and was maintained after 7 days of loading (11 ~ 12 mg/L). This study provides experimental validation of the developed analytical solutions and quantitatively evaluates contaminant occurrences of the confined aquifer through the aquitard.</p>

Modeling the Microwave Transmissivity of Row Crops

2021 ◽  
Vol 36 (6) ◽  
pp. 816-823
Author(s):  
Jeil Park ◽  
Praveen Gurrala ◽  
Brian Hornbuckle ◽  
Jiming Song
Keyword(s):  
Soil Moisture ◽  
Analytical Solutions ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Measured Data ◽  
Row Crops ◽  
Satellite Retrieval ◽  
Unit Cells ◽  
Simulation Results ◽  
Agricultural Regions

We develop a method to model the microwave transmissivity of row crops that explicitly accounts for their periodic nature as well as multiple scattering. We hypothesize that this method could eventually be used to improve satellite retrieval of soil moisture and vegetation optical depth in agricultural regions. The method is characterized by unit cells terminated by periodic boundary conditions and Floquet port excitations solved using commercial software. Individual plants are represented by vertically oriented dielectric cylinders. We calculate canopy transmissivity, reflectivity, and loss in terms of S-parameters. We validate the model with analytical solutions and illustrate the effect of canopy scattering. Our simulation results are consistent with both simulated and measured data published in the literature.

Verification Benchmarks to Assess the Implementation of Computational Fluid Dynamics Based Hemolysis Prediction Models

2015 ◽  
Vol 137 (9) ◽  
Author(s):  
Prasanna Hariharan ◽  
Gavin D’Souza ◽  
Marc Horner ◽  
Richard A. Malinauskas ◽  
Matthew R. Myers
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Power Law ◽  
Analytical Solutions ◽  
Experimental Validation ◽  
Cfd Simulations ◽  
Flow Models ◽  
Flow Acceleration ◽  
Blood Damage ◽  
Eulerian Models

As part of an ongoing effort to develop verification and validation (V&V) standards for using computational fluid dynamics (CFD) in the evaluation of medical devices, we have developed idealized flow-based verification benchmarks to assess the implementation of commonly cited power-law based hemolysis models in CFD. The verification process ensures that all governing equations are solved correctly and the model is free of user and numerical errors. To perform verification for power-law based hemolysis modeling, analytical solutions for the Eulerian power-law blood damage model (which estimates hemolysis index (HI) as a function of shear stress and exposure time) were obtained for Couette and inclined Couette flow models, and for Newtonian and non-Newtonian pipe flow models. Subsequently, CFD simulations of fluid flow and HI were performed using Eulerian and three different Lagrangian-based hemolysis models and compared with the analytical solutions. For all the geometries, the blood damage results from the Eulerian-based CFD simulations matched the Eulerian analytical solutions within ∼1%, which indicates successful implementation of the Eulerian hemolysis model. Agreement between the Lagrangian and Eulerian models depended upon the choice of the hemolysis power-law constants. For the commonly used values of power-law constants (α  = 1.9–2.42 and β  = 0.65–0.80), in the absence of flow acceleration, most of the Lagrangian models matched the Eulerian results within 5%. In the presence of flow acceleration (inclined Couette flow), moderate differences (∼10%) were observed between the Lagrangian and Eulerian models. This difference increased to greater than 100% as the beta exponent decreased. These simplified flow problems can be used as standard benchmarks for verifying the implementation of blood damage predictive models in commercial and open-source CFD codes. The current study used only a power-law model as an illustrative example to emphasize the need for model verification. Similar verification problems could be developed for other types of hemolysis models (such as strain-based and energy dissipation-based methods). And since the current study did not include experimental validation, the results from the verified models do not guarantee accurate hemolysis predictions. This verification step must be followed by experimental validation before the hemolysis models can be used for actual device safety evaluations.

Some Exact Analytical Solutions for Two-Dimensional Flow of an Incompressible Second Grade Fluid

2015 ◽  
Vol 137 (10) ◽  
Author(s):  
Saif Ullah
Keyword(s):  
Analytical Solutions ◽  
Separation Of Variables ◽  
Point Of View ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Exact Analytical Solutions ◽  
Contour Plots ◽  
Two Dimensional Flow ◽  
Grade Fluid ◽  
Physical Features

This investigation deals with some exact analytical solutions of the incompressible second grade fluid by using the method based on the separation of variables. In many cases, this method can derive exact analytical solutions easier than other methods. A family of solutions is derived in this paper, which governs scientific and engineering experimentations. The derived solutions represent the flows having streamlines as a family of ellipses, parabolas, concentric circles, and rectangular hyperbolas. From practical point of view, these flows have applications in many manufacturing processes in industry. Some physical features of the derived solutions are also illustrated by their contour plots.

Thin-film and curtain flows on the outside of a rotating horizontal cylinder

1999 ◽  
Vol 394 ◽  
pp. 29-49 ◽  
Author(s):  
B. R. DUFFY ◽  
S. K. WILSON
Keyword(s):  
Thin Film ◽  
Finite Thickness ◽  
Surface Profile ◽  
Rotating Cylinder ◽  
Horizontal Cylinder ◽  
Lubrication Approximation ◽  
Coating Flows ◽  
Stagnation Points ◽  
Free Surface Profile ◽  
Two Dimensional Flow

We use the lubrication approximation to investigate the steady two-dimensional flow of a thin film of viscous fluid on the outside of a rigid circular cylinder that is rotating about its (horizontal) axis. Primarily we are concerned with the flow that ensues when fluid is supplied continuously as a ‘curtain’ from above the cylinder, so that it flows round the cylinder and eventually falls off near the bottom. This problem may be thought of as a ‘hybrid’ of the two classical problems studied by Nusselt (1916a, b) and Moffatt (1977), concerning, respectively, flow on a stationary cylinder with a prescribed supply flux, and flow on a rotating cylinder when the supply flux is zero. For all these problems there are indeterminacies in the steady lubrication solution; we present a variety of possible solutions, including both ‘full-film’ and ‘partial-film’ solutions, and solutions that involve smooth ‘jumps’ in the free-surface profile. We show, for example, that stagnation points can occur in the flow, that solutions exist that do not have top-to-bottom symmetry, that in curtain flows the curtain generally takes a characteristic ‘buckled’ shape, and that in full-film curtain flows there is always some fluid that is ‘trapped’ near the rotating cylinder, never escaping as part of the curtain that detaches at the bottom of the cylinder. Also we show that finite-thickness films involving jumps cannot occur in these coating flows (though they are known to occur in rimming flows).

Effects of monitoring and pumping well pipe capacities during pumping tests in confined aquifers

2003 ◽  
Vol 40 (6) ◽  
pp. 1093-1103 ◽  
Author(s):  
Robert P Chapuis ◽  
Djaouida Chenaf
Keyword(s):  
Water Storage ◽  
Pumping Test ◽  
Unconfined Aquifer ◽  
Confined Aquifer ◽  
Pumping Tests ◽  
Constant Flow Rate ◽  
Pumping Wells ◽  
Confined Aquifers ◽  
Large Tank ◽  
Definition Of

This paper establishes how the water stored in the pipes of monitoring and pumping wells influences the drawdown curves of pumping tests in confined aquifers. Experimental and numerical results obtained with a physical model are first studied and then confirmed by field-test data. A large tank was used for fully controlled pumping tests. It contains a lower confined aquifer, an aquitard, and an upper unconfined aquifer. Pumping tests at a constant flow rate in the confined aquifer provided drawdowns that were analyzed for unsteady-state, steady-state, and recovery conditions. For a single monitoring well, the different interpretation methods provided similar values of transmissivity, T, and storativity, S. Drawdown curves gave much too high S values. These S values were equal to those resulting from water storage in the pipes of monitoring and pumping wells, according to the physical definition of storativity. The experimental T and S values were confirmed by two numerical analyses (finite elements) of the pumping test, one considering no water was stored in the pipes and the other considering stored water. Data of real pumping tests in confined aquifers confirmed that the S value calculated from drawdown curves can be influenced by water storage in monitoring and pumping wells for usual pipe diameters.Key words: pumping test, transmissivity, storativity, sandbox, in situ test, pipe capacity.

Experimental Validation of Analytical Solutions for Vertical Flat Plate of Finite Thickness Under Natural-Convection Cooling

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Vipin Yadav ◽  
Keshav Kant
Keyword(s):  
Natural Convection ◽  
Analytical Solutions ◽  
Heated Surface ◽  
Finite Thickness ◽  
Uniform Heat Flux ◽  
Heated Plate ◽  
Thin Wall ◽  
Uniform Wall Temperature ◽  
Uniform Wall ◽  
Convection Cooling

The analytical solution for a vertical heated plate subjected to conjugate heat transfer due to natural convection at the surface and conduction below is presented. The heated surface is split into two regions; the uniform heat flux region toward upstream and remaining fraction as the uniform wall temperature region. The fractional areas under the two regions are considered variable. Adopting thermally thin wall regime approximation, the possible solutions were investigated and found to satisfactorily deal with longitudinal conduction and temperature variation in the transverse direction. A test setup was developed and the experiments were conducted to obtain relevant data for comparison with the analytical solutions. The ranges for Rayleigh number and heat conduction parameter (α) during various test conditions were 2×108–6×108, and 0.001–1, respectively. The limiting solutions for stipulated conditions are analyzed and compared with experimental data. Reasonable agreement is observed between the experimental and analytical results.

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