Analytical Solution for Well Design with Respect to Discharge Ratio

For a well in the vicinity of a surface water body, a formula is developed that relates the share of bank filtrate on total pumpage, that is, the discharge ratio, on one side, to basic well and aquifer characteristics on the other. The application of the formula is demonstrated for solving the inverse problem: for an aimed discharge ratio, well characteristics (pumping rate, distance to shore) can be determined. Other useful applications of the formula are outlined

Mathematical modeling of channel-porous layer interfaces in PEM fuel cells

In proton exchange membrane (PEM) fuel cells, the transport of the fuel to the active zones, and the removal of the reaction products are realized using a combination of channels and porous diffusion layers. In order to improve existing mathematical and numerical models of PEM fuel cells, a deeper understanding of the coupling of the flow processes in the channels and diffusion layers is necessary. After discussing different mathematical models for PEM fuel cells, the work will focus on the description of the coupling of the free flow in the channel region with the filtration velocity in the porous diffusion layer as well as interface conditions between them. The difficulty in finding effective coupling conditions at the interface between the channel flow and the membrane lies in the fact that often the orders of the corresponding differential operators are different, e.g., when using stationary (Navier-)Stokes and Darcy's equation. Alternatively, using the Brinkman model for the porous media this difficulty does not occur. We will review different interface conditions, including the well-known Beavers-Joseph-Saffman boundary condition and its recent improvement by Le Bars and Worster

Experimental and numerical model study of the limiting current in a channel flow cell with a circular electrode

We describe first measurement in a novel thin-layer channel flow cell designed for the investigation of heterogeneous electrocatalysis on porous catalysts. For the interpretation of the measurements, a macroscopic model for coupled species transport and reaction, which can be solved numerically, is feasible. In this paper, we focus on the limiting current. We compare numerical solutions of a macroscopic model to a generalization of a Leveque-type asymptotic estimate for circular electrodes, and to measurements obtained in the aforementioned flow cell. We establish, that on properly aligned meshes, the numerical method reproduces the asymptotic estimate. Furthermore, we demonstrate, that the measurements are partially performed in the sub-asymptotic regime, in which the boundary layer thickness exceeds the cell height. Using the inlet concentration and the diffusion coefficient from literature, we overestimate the limiting current. On the other hand, the use of fitted parameters leads to perfect agreement between model and experiment

Documentation of atmospheric constants over Niamey, Niger: a theoretical aid for measuring instruments

The frequent failures of ground measuring devices, e.g. radiosondes, weather stations, in developing regions is worrisome. From the literature, established projects such as the Aerosol Robotic Network (AERONET) and the African Monsoon Multidisciplinary Analyses (AMMA) are burdened by the same challenge. At the moment, the AERONET and AMMA databases show a large volume of data loss. With only about 47% of data available to scientists, it is evident that accurate nowcasts or forecasts cannot be guaranteed. It is proposed that the challenge is not measuring device design error but systemic, i.e. the configuration of accurate calibration constants in the compact flash card of the devices. The calibration constants of most radiosonde or weather stations are not compatible with the atmospheric conditions of the West African climate. A dispersion model was developed to incorporate salient mathematical representations such as the unified number. The unified number was derived to describe the turbulence of aerosol transport in the frictional layer of the lower atmosphere. A 14 year dataset from the Multi-angle Imaging SpectroRadiometer was tested using the dispersion model. A yearly estimation of the atmospheric constants over Niamey using the model was obtained with about 87.5% accuracy. This further revealed that the average atmospheric constants for Niamey, Niger, are a1 = 0.77975 and a2 = 0.693021 and the tuning constants are n1 = 0.140187 and n2 = 0.759236. Also, the yearly atmospheric constants confirmed that the lower atmosphere of Niamey is very dynamic. Hence, it is recommended that radiosonde and weather station manufacturers should constantly review the atmospheric constants over a geographical location to enable about 80% data retrieva

Systematic chemical variations in large 3AB iron meteorites: Clues to core crystallization

Analysis of numerous individual iron meteorites have shown that fractional crystallization of iron cores result in variations in chemical concentration of the solid core which span several orders of magnitude. The magnitude and direction of the resulting spatial gradients in the core can provide clues to the physical nature of the core crystallization process. We have analyzed suites of samples from three large 3AB irons (Cape York, 58t; Chupaderos, 24t; Morito, 10t) in order to estimate local chemical gradients. Initial results for the concentrations of Ge, Pd, Pt (Massey group), Ir, Au, As, Co, Os, and Rh (Dalhouse group), and P (Arizona group) show significant ranges among the Cape York and Chupaderos samples and marginally significant ranges among the Morito samples. Measurements of Au, Ir, Co, Ni, Cu, Ga, As, W, Re (from UCLA) and Ni and Co (Arizona group) are in progress. We find a spatial Ir gradient in Chupaderos with a magnitude similar to the one reported for Agpalilik (Cape York iron) by Esbensen et al

Numerical error in groundwater flow and solute transport simulation

Models of groundwater flow and solute transport may be affected by numerical error, leading to quantitative and qualitative changes in behavior. In this paper we compare and combine three methods of assessing the extent of numerical error: grid refinement, mathematical analysis, and benchmark test problems. In particular, we assess the popular solute transport code SUTRA [ Voss, 1984 ] as being a typical finite element code. Our numerical analysis suggests that SUTRA incorporates a numerical dispersion error and that its mass-lumped numerical scheme increases the numerical error. This is confirmed using a Gaussian test problem. A modified SUTRA code, in which the numerical dispersion is calculated and subtracted, produces better results. The much more challenging Elder problem [ Elder, 1967 ; Voss and Souza, 1987 ] is then considered. Calculation of its numerical dispersion coefficients and numerical stability show that the Elder problem is prone to error. We confirm that Elder problem results are extremely sensitive to the simulation method used.Juliette A. Woods, Michael D. Teubner, Craig T. Simmons and Kumar A. Naraya