Analytical approximations to predict performance measures of manufacturing systems with job failures and parallel processing

Parallel processing is prevalent in many manufacturing and service systems. Many manufactured products are built and assembled from several components fabricated in parallel lines. An example of this manufacturing system configuration is observed at a manufacturing facility equipped to assemble and test web servers. Characteristics of a typical web server assembly line are: multiple products, job circulation, and paralleling processing. The primary objective of this research was to develop analytical approximations to predict performance measures of manufacturing systems with job failures and parallel processing. The analytical formulations extend previous queueing models used in assembly manufacturing systems in that they can handle serial and different configurations of paralleling processing with multiple product classes, and job circulation due to random part failures. In addition, appropriate correction terms via regression analysis were added to the approximations in order to minimize the gap in the error between the analytical approximation and the simulation models. Markovian and general type manufacturing systems, with multiple product classes, job circulation due to failures, and fork and join systems to model parallel processing were studied. In the Markovian and general case, the approximations without correction terms performed quite well for one and two product problem instances. However, it was observed that the flow time error increased as the number of products and net traffic intensity increased. Therefore, correction terms for single and fork-join stations were developed via regression analysis to deal with more than two products. The numerical comparisons showed that the approximations perform remarkably well when the corrections factors were used in the approximations. In general, the average flow time error was reduced from 38.19% to 5.59% in the Markovian case, and from 26.39% to 7.23% in the general case. All the equations stated in the analytical formulations were implemented as a set of Matlab scripts. By using this set, operations managers of web server assembly lines, manufacturing or other service systems with similar characteristics can estimate different system performance measures, and make judicious decisions - especially setting delivery due dates, capacity planning, and bottleneck mitigation, among others.

Hydrogeophysical characterization of anisotropy in the Biscayne Aquifer using geophysical methods

The anisotropy of the Biscayne Aquifer which serves as the source of potable water for Miami-Dade County was investigated by applying geophysical methods. Electrical resistivity imaging, self potential and ground penetration radar techniques were employed in both regional and site specific studies. In the regional study, electrical anisotropy and resistivity variation with depth were investigated with azimuthal square array measurements at 13 sites. The observed coefficient of electrical anisotropy ranged from 1.01 to 1.36. The general direction of measured anisotropy is uniform for most sites and trends W-E or SE-NW irrespective of depth. Measured electrical properties were used to estimate anisotropic component of the secondary porosity and hydraulic anisotropy which ranged from 1 to 11% and 1.18 to 2.83 respectively. 1-D sounding analysis was used to models the variation of formation resistivity with depth. Resistivities decreased from NW (close to the margins of the everglades) to SE on the shores of Biscayne Bay. Porosity calculated from Archie's law, ranged from 18 to 61% with higher values found along the ridge. Higher anisotropy, porosities and hydraulic conductivities were on the Atlantic Coastal Ridge and lower values at low lying areas west of the ridge. The cause of higher anisotropy and porosity is attributed to higher dissolution rates of the oolitic facies of the Miami Formation composing the ridge. The direction of minimum resistivity from this study is similar to the predevelopment groundwater flow direction indicated in published modeling studies. Detailed investigations were carried out to evaluate higher anisotropy at West Perrine Park located on the ridge and Snapper Creek Municipal well field where the anisotropy trend changes with depth. The higher anisotropy is attributed to the presence of solution cavities oriented in the E-SE direction on the ridge. Similarly, the change in hydraulic anisotropy at the well field might be related to solution cavities, the surface canal and groundwater extraction wells.^

Analytical Approximations to Predict Performance Measures of Manufacturing Systems with Job Failures and Parallel Processing

Parallel processing is prevalent in many manufacturing and service systems. Many manufactured products are built and assembled from several components fabricated in parallel lines. An example of this manufacturing system configuration is observed at a manufacturing facility equipped to assemble and test web servers. Characteristics of a typical web server assembly line are: multiple products, job circulation, and paralleling processing. The primary objective of this research was to develop analytical approximations to predict performance measures of manufacturing systems with job failures and parallel processing. The analytical formulations extend previous queueing models used in assembly manufacturing systems in that they can handle serial and different configurations of paralleling processing with multiple product classes, and job circulation due to random part failures. In addition, appropriate correction terms via regression analysis were added to the approximations in order to minimize the gap in the error between the analytical approximation and the simulation models. Markovian and general type manufacturing systems, with multiple product classes, job circulation due to failures, and fork and join systems to model parallel processing were studied. In the Markovian and general case, the approximations without correction terms performed quite well for one and two product problem instances. However, it was observed that the flow time error increased as the number of products and net traffic intensity increased. Therefore, correction terms for single and fork-join stations were developed via regression analysis to deal with more than two products. The numerical comparisons showed that the approximations perform remarkably well when the corrections factors were used in the approximations. In general, the average flow time error was reduced from 38.19% to 5.59% in the Markovian case, and from 26.39% to 7.23% in the general case. All the equations stated in the analytical formulations were implemented as a set of Matlab scripts. By using this set, operations managers of web server assembly lines, manufacturing or other service systems with similar characteristics can estimate different system performance measures, and make judicious decisions - especially setting delivery due dates, capacity planning, and bottleneck mitigation, among others.

Hydrogeophysical Characterization of Anisotropy in the Biscayne Aquifer Using Geophysical Methods

The anisotropy of the Biscayne Aquifer which serves as the source of potable water for Miami-Dade County was investigated by applying geophysical methods. Electrical resistivity imaging, self potential and ground penetration radar techniques were employed in both regional and site specific studies. In the regional study, electrical anisotropy and resistivity variation with depth were investigated with azimuthal square array measurements at 13 sites. The observed coefficient of electrical anisotropy ranged from 1.01 to 1.36. The general direction of measured anisotropy is uniform for most sites and trends W-E or SE-NW irrespective of depth. Measured electrical properties were used to estimate anisotropic component of the secondary porosity and hydraulic anisotropy which ranged from 1 to 11% and 1.18 to 2.83 respectively. 1-D sounding analysis was used to models the variation of formation resistivity with depth. Resistivities decreased from NW (close to the margins of the everglades) to SE on the shores of Biscayne Bay. Porosity calculated from Archie's law, ranged from 18 to 61% with higher values found along the ridge. Higher anisotropy, porosities and hydraulic conductivities were on the Atlantic Coastal Ridge and lower values at low lying areas west of the ridge. The cause of higher anisotropy and porosity is attributed to higher dissolution rates of the oolitic facies of the Miami Formation composing the ridge. The direction of minimum resistivity from this study is similar to the predevelopment groundwater flow direction indicated in published modeling studies. Detailed investigations were carried out to evaluate higher anisotropy at West Perrine Park located on the ridge and Snapper Creek Municipal well field where the anisotropy trend changes with depth. The higher anisotropy is attributed to the presence of solution cavities oriented in the E-SE direction on the ridge. Similarly, the change in hydraulic anisotropy at the well field might be related to solution cavities, the surface canal and groundwater extraction wells.

Verification of a mixed high-order accurate DNS code for laminar turbulent transition by the method of manufactured solutions

This paper presents results on a verification test of a Direct Numerical Simulation code of mixed high-order of accuracy using the method of manufactured solutions (MMS). This test is based on the formulation of an analytical solution for the Navier-Stokes equations modified by the addition of a source term. The present numerical code was aimed at simulating the temporal evolution of instability waves in a plane Poiseuille flow. The governing equations were solved in a vorticity-velocity formulation for a two-dimensional incompressible flow. The code employed two different numerical schemes. One used mixed high-order compact and non-compact finite-differences from fourth-order to sixth-order of accuracy. The other scheme used spectral methods instead of finite-difference methods for the streamwise direction, which was periodic. In the present test, particular attention was paid to the boundary conditions of the physical problem of interest. Indeed, the verification procedure using MMS can be more demanding than the often used comparison with Linear Stability Theory. That is particularly because in the latter test no attention is paid to the nonlinear terms. For the present verification test, it was possible to manufacture an analytical solution that reproduced some aspects of an instability wave in a nonlinear stage. Although the results of the verification by MMS for this mixed-order numerical scheme had to be interpreted with care, the test was very useful as it gave confidence that the code was free of programming errors. Copyright (C) 2009 John Wiley & Sons, Ltd.

Root Water Extraction under Combined Water and Osmotic Stress

Using a numerical implicit model for root water extraction by a single root in a symmetric radial flow problem, based on the Richards equation and the combined convection-dispersion equation, we investigated some aspects of the response of root water uptake to combined water and osmotic stress. The model implicitly incorporates the effect of simultaneous pressure head and osmotic head on root water uptake, and does not require additional assumptions (additive or multiplicative) to derive the combined effect of water and salt stress. Simulation results showed that relative transpiration equals relative matric flux potential, which is defined as the matric flux potential calculated with an osmotic pressure head-dependent lower bound of integration, divided by the matric flux potential at the onset of limiting hydraulic conditions. In the falling rate phase, the osmotic head near the root surface was shown to increase in time due to decreasing root water extraction rates, causing a more gradual decline of relative transpiration than with water stress alone. Results furthermore show that osmotic stress effects on uptake depend on pressure head or water content, allowing a refinement of the approach in which fixed reduction factors based on the electrical conductivity of the saturated soil solution extract are used. One of the consequences is that osmotic stress is predicted to occur in situations not predicted by the saturation extract analysis approach. It is also shown that this way of combining salinity and water as stressors yields results that are different from a purely multiplicative approach. An analytical steady state solution is presented to calculate the solute content at the root surface, and compared with the outputs of the numerical model. Using the analytical solution, a method has been developed to estimate relative transpiration as a function of system parameters, which are often already used in vadose zone models: potential transpiration rate, root length density, minimum root surface pressure head, and soil theta-h and K-h functions.

Dissolution of a solid sphere in an unbounded, stagnant liquid

An exact analytical solution is obtained for the transient dissolution of solid spheres in a diffusion-controlled environment. This result provides a useful reference point for drug testing in humans. The dimensionless solution is expressed in terms of a single parameter, which accounts for solubility, bulk flow, and stagnant fluid composition. A simple, explicit and exact expression was found to predict time-to-complete dissolution (TCD). An approximate solution was also found which tracks the exact case for low solubility conditions.

Entropy generation for forced convection in a porous saturated circular tube with uniform wall temperature

A numerical study is reported to investigate both the First and the Second Law of Thermodynamics for thermally developing forced convection in a circular tube filled by a saturated porous medium, with uniform wall temperature, and with the effects of viscous dissipation included. A theoretical analysis is also presented to study the problem for the asymptotic region applying the perturbation solution of the Brinkman momentum equation reported by Hooman and Kani [1]. Expressions are reported for the temperature profile, the Nusselt number, the Bejan number, and the dimensionless entropy generation rate in the asymptotic region. Numerical results are found to be in good agreement with theoretical counterparts.

Turbulence in Hydraulic Jumps: Experimental Measurements

A hydraulic jump is the transition from a supercritical open channel flow to a subcritical regime. It is characterised by a highly turbulent flow with macro-scale vortices, some kinetic energy dissipation and a bubbly two-phase flow structure. New air-water flow measurements were performed in hydraulic jump flows for a range of inflow Froude numbers. The experiments were conducted in a large-size facility using two types of phase-detection intrusive probes: i.e., single-tip and double-tip conductivity probes. These were complemented by some measurements of free-surface fluctuations using ultrasonic displacement meters. The present study was focused on the turbulence characteristics of hydraulic jumps with partially-developed inflow conditions. The void fraction measurements showed the presence of an advective diffusion shear layer in which the void fractions profiles matched closely an analytical solution of the advective diffusion equation for air bubbles. The present results highlighted some influence of the inflow Froude number onto the air bubble entrainment process. At the largest Froude numbers, the advected air bubbles were more thoroughly dispersed vertically, and larger amount of air bubbles were detected in the turbulent shear layer. In the air-water mixing layer, the maximum void fraction and bubble count rate data showed some longitudinal decay function in the flow direction. Such trends were previously reported in the literature. The measurements of interfacial velocity and turbulence level distributions provided new information on the turbulent velocity field in the highly-aerated shear region. The present data suggested some longitudinal decay of the turbulence intensity. The velocity profiles tended to follow a wall jet flow pattern. The air–water turbulent time and length scales were deduced from some auto- and cross-correlation analyses based upon the method of CHANSON (2006,2007). The results provided the integral turbulent time and length scales of the eddy structures advecting the air bubbles in the developing shear layer. The experimental data showed that the auto-correlation time scale Txx was larger than the transverse cross-correlation time scale Txz. The integral turbulence length scale Lxz was a function of the inflow conditions, of the streamwise position (x-x1)/d1 and vertical elevation y/d1. Herein the dimensionless integral turbulent length scale Lxz/d1 was closely related to the inflow depth: i.e., Lxz/d1 = 0.2 to 0.8, with Lxz increasing towards the free-surface. The free-surface fluctuations measurements showed large turbulent fluctuations that reflected the dynamic, unsteady structure of the hydraulic jumps. A linear relationship was found between the normalized maximum free-surface fluctuation and the inflow Froude number.

Theoretical and numerical analyses of convective instability in porous media with upward throughflow

Exact analytical solutions have been obtained for a hydrothermal system consisting of a horizontal porous layer with upward throughflow. The boundary conditions considered are constant temperature, constant pressure at the top, and constant vertical temperature gradient, constant Darcy velocity at the bottom of the layer. After deriving the exact analytical solutions, we examine the stability of the solutions using linear stability theory and the Galerkin method. It has been found that the exact solutions for such a hydrothermal system become unstable when the Rayleigh number of the system is equal to or greater than the corresponding critical Rayleigh number. For small and moderate Peclet numbers (Pe less than or equal to 6), an increase in upward throughflow destabilizes the convective flow in the horizontal layer. To confirm these findings, the finite element method with the progressive asymptotic approach procedure is used to compute the convective cells in such a hydrothermal system. Copyright (C) 1999 John Wiley & Sons, Ltd.

Finite element modelling of heat transfer through permeable cracks in hydrothermal systems with upward throughflow

We use the finite element method to model the heat transfer phenomenon through permeable cracks in hydrothermal systems with upward throughflow. Since the finite element method is an approximate numerical method, the method must be validated before it is used to soh,e any new, kind of problem. However, the analytical solution, which can be used to validate the finite element method and other numerical methods, is rather limited in the literature, especially, for the problem considered here. Keeping this in mind, we have derived analytical solutions for the temperature distribution along the vertical axis of a crack in a fluid-saturated porous layer. After the finite element method is validated by comparing the numerical solution with the analytical solution for the same benchmark problem, it is used to investigate the pore-fluid flow and heat transfer in layered hydrothermal systems with vertical permeable cracks. The related analytical and numerical results have demonstrated that vertical cracks are effective and efficient members to transfer heat energy from the bottom section to the top section in hydrothermal systems with upward throughflow.

BeachWin: modelling groundwater effects on swash sediment transport and beach profile changes

Field and laboratory observations have shown that a relatively low beach groundwater table enhances beach accretion. These observations have led to the beach dewatering technique (artificially lowering the beach water table) for combating beach erosion. Here we present a process-based numerical model that simulates the interacting wave motion on the beach. coastal groundwater flow, swash sediment transport and beach profile changes. Results of model simulations demonstrate that the model replicates accretionary effects of a low beach water table on beach profile changes and has the potential to become a tool for assessing the effectiveness of beach dewatering systems. (C) 2002 Elsevier Science Ltd. All rights reserved.

Tidal fluctuations in a leaky confined aquifer: localised effects of an overlying phreatic aquifer

Damping of tidal head fluctuations in a leaky confined coastal aquifer is enhanced by leakage into an overlying phreatic aquifer. We show that the phreatic aquifer is, however, resistant to the leakage flow and in particular, a deep phreatic aquifer can reduce the leakage effects significantly. An analytical solution, based on a vertical flow model for the phreatic aquifer, is derived for quantifying the role of this upper free water body in tidal propagation in the lower semi-confined aquifer. (C) 2002 Elsevier Science B.V. All rights reserved.

Analysis of steady-state heat transfer through mid-crustal vertical cracks with upward throughflow in hydrothermal systems

We conduct a theoretical analysis of steady-state heat transfer problems through mid-crustal vertical cracks with upward throughflow in hydrothermal systems. In particular, we derive analytical solutions for both the far field and near field of the system. In order to investigate the contribution of the forced advection to the total temperature of the system, two concepts, namely the critical Peclet number and the critical permeability of the system, have been presented and discussed in this paper. The analytical solution for the far field of the system indicates that if the pore-fluid pressure gradient in the crust is lithostatic, the critical permeability of the system can be used to determine whether or not the contribution of the forced advection to the total temperature of the system is negligible. Otherwise, the critical Peclet number should be used. For a crust of moderate thickness, the critical permeability is of the order of magnitude of 10(-20) m(2), under which heat conduction is the overwhelming mechanism to transfer heat energy, even though the pore-fluid pressure gradient in the crust is lithostatic. Furthermore, the lower bound analytical solution for the near field of the system demonstrates that the permeable vertical cracks in the middle crust can efficiently transfer heat energy from the lower crust to the upper crust of the Earth. Copyright (C) 2002 John Wiley Sons, Ltd.

Convective instability of 3-D fluid-saturated geological fault zones heated from below

We conduct a theoretical analysis to investigate the convective instability of 3-D fluid-saturated geological fault zones when they are heated uniformly from below. In particular, we have derived exact analytical solutions for the critical Rayleigh numbers of different convective flow structures. Using these critical Rayleigh numbers, three interesting convective flow structures have been identified in a geological fault zone system. It has been recognized that the critical Rayleigh numbers of the system have a minimum value only for the fault zone of infinite length, in which the corresponding convective flow structure is a 2-D slender-circle flow. However, if the length of the fault zone is finite, the convective flow in the system must be 3-D. Even if the length of the fault zone is infinite, since the minimum critical Rayleigh number for the 2-D slender-circle flow structure is so close to that for the 3-D convective flow structure, the system may have almost the same chance to pick up the 3-D convective flow structures. Also, because the convection modes are so close for the 3-D convective flow structures, the convective flow may evolve into the 3-D finger-like structures, especially for the case of the fault thickness to height ratio approaching zero. This understanding demonstrates the beautiful aspects of the present analytical solution for the convective instability of 3-D geological fault zones, because the present analytical solution is valid for any value of the ratio of the fault height to thickness. Using the present analytical solution, the conditions, under which different convective flow structures may take place, can be easily determined.