Mathematical modelling of salt purification by recrystallization. A cross-current flow model and its comparison with the countercurrent arrangement

1986 ◽  
Vol 51 (11) ◽  
pp. 2489-2501
Author(s):  
Benitto Mayrhofer ◽  
Jana Mayrhoferová ◽  
Lubomír Neužil ◽  
Jaroslav Nývlt
Keyword(s):  
Flow Model ◽  
Current Flow ◽  
Countercurrent Flow ◽  
Flow Models ◽  
Multi Stage ◽  
Stage Crystallization ◽  
The Cross ◽  
Current Flows ◽  
Set Up ◽  
Cross Current

A model is derived for a multi-stage crystallization with cross-current flows of the solution and the crystals being purified. The purity of the product is compared with that achieved in the countercurrent arrangement. A suitable function has been set up which allows the cross-current and countercurrent flow models to be compared and reduces substantially the labour of computation for the countercurrent arrangement. Using the recrystallization of KAl(SO4)2.12 H2O as an example, it is shown that, when the cross-current and countercurrent processes are operated at the same output, the countercurrent arrangement is more advantageous because its solvent consumption is lower.

A Study of Steam-Water Countercurrent Flow Model in TRACE Code

2009 ◽  
Author(s):  
Yi-Hsiang Cheng ◽  
Chunkuan Shih ◽  
Jong-Rong Wang ◽  
Hao-Tzu Lin
Keyword(s):  
Flow Model ◽  
Plate Thickness ◽  
Perforated Plate ◽  
Calculation Model ◽  
Hydraulic Diameter ◽  
Pipe Diameter ◽  
Countercurrent Flow ◽  
Flow Models ◽  
Pipe Model ◽  
Single Pipe

This paper studied the countercurrent flow model in the TRACE code version 5.0. Steam and water are chosen as the working fluids that flow counter-currently in a circular pipe. Three types of the countercurrent flow models, the Wallis, the Kutateladze and the Bankoff correlations, are investigated. A single pipe model was built for the studies of the Wallis and the Kutateladze correlations, and the variable in the calculation model is the pipe diameter. A perforated plate model was built to study the Bankoff correlation, and the variables include the pipe diameter, the hole diameter, the number of holes and the plate thickness. The hydraulic diameter of the pipe varies from 2.5–200 mm for validating both the Wallis and the Kutateladze correlations. While validating the Bankoff correlation, the hydraulic diameter of the pipe is of 50 and 200 mm, and the plate thickness changes as 10 and 40 mm. Through this study, we validate the countercurrent flow model in the TRACE code, and provides comments on the application ranges of these three correlations.

Study of the Response of PW Traffic Flow Model to a Bottleneck on a Circular Road and its Suitability for Heterogeneous Traffic Conditions

2021 ◽  
Vol 9 (4) ◽  
pp. 460-463
Keyword(s):  
Fluid Flow ◽  
Traffic Flow ◽  
Flow Model ◽  
Equation Model ◽  
Heterogeneous Traffic ◽  
Flow Conditions ◽  
Flow Models ◽  
Traffic Conditions ◽  
Model Response ◽  
Traffic Flow Models

The traffic flow conditions in developing countries are predominantly heterogeneous. The early developed traffic flow models have been derived from fluid flow to capture the behavior of the traffic. The very first two-equation model derived from fluid flow is known as the Payne-Whitham or PW Model. Along with the traffic flow, this model also captures the traffic acceleration. However, the PW model adopts a constant driver behavior which cannot be ignored, especially in the situation of heterogeneous traffic.This research focuses on testing the PW model and its suitability for heterogeneous traffic conditions by observing the model response to a bottleneck on a circular road. The PW model is mathematically approximated using the Roe Decomposition and then the performance of the model is observed using simulations.

Multi-phase information aggregation and dynamic synthetic evaluation based on grey inspiriting control lines

2014 ◽  
Vol 4 (2) ◽  
pp. 154-163 ◽  
Author(s):  
San-dang Guo ◽  
Sifeng Liu ◽  
Zhigeng Fang ◽  
Lingling Wang
Keyword(s):  
Future Development ◽  
Information Aggregation ◽  
Development Trend ◽  
Future Application ◽  
Phase Information ◽  
Content Type ◽  
Multi Stage ◽  
Comprehensive Evaluations ◽  
Set Up ◽  
Multi Phase

Purpose – The purpose of this paper is to put forward a multi-stage information aggregation method based on grey inspiriting control lines to evaluate the objects dynamically and comprehensively. Design/methodology/approach – According to the evaluation value of the objects, the positive and negative incentive lines were set up and the predicted values were solved based on the grey GM(1, 1) model, so the value with expected information could be evaluated. In the evaluation, the part above the positive incentive line should be “rewarded” and that below the negative incentive line should be “punished” appropriately. Thereby the double incentive effects of “the current development situation and future development trend” to objects could be implemented on the basis of control. Findings – This method can primarily describe the decision maker's expectancy of the development of evaluation objects and make the evaluation results have better practical application value. Research limitations/implications – Many comprehensive evaluations were always based on the past information. However, the future development trend of the evaluated object is also very important. This study can be used in the evaluation for future application and development. Originality/value – The paper succeeds in providing not only a method of multi-phase information aggregation with expectancy information, but also a simple and convenient method solving nonlinear inspiring lines objectively.

scholarly journals tDCS changes in motor excitability are specific to orientation of current flow

2017 ◽  
Author(s):  
Vishal Rawji ◽  
Matteo Ciocca ◽  
Andre Zacharia ◽  
David Soares ◽  
Dennis Truong ◽  
...  
Keyword(s):  
Animal Studies ◽  
Current Flow ◽  
Motor Evoked Potentials ◽  
Flow Direction ◽  
Brain Regions ◽  
Afferent Pathways ◽  
Flow Models ◽  
Cortical Columns ◽  
Local Fluctuations ◽  
Hand Region

Measurements and models of current flow in the brain during transcranial Direct Current Stimulation (tDCS) indicate stimulation of regions in-between electrodes. Moreover, the cephalic cortex result in local fluctuations in current flow intensity and direction, and animal studies suggest current flow direction relative to cortical columns determines response to tDCS. Here we test this idea by measuring changes in cortico-spinal excitability by Transcranial Magnetic Stimulation Motor Evoked Potentials (TMS-MEP), following tDCS applied with electrodes aligned orthogonal (across) or parallel to M1 in the central sulcus. Current flow models predicted that the orthogonal electrode montage produces consistently oriented current across the hand region of M1 that flows along cortical columns, while the parallel electrode montage produces none-uniform current directions across the M1 cortical surface. We find that orthogonal, but not parallel, orientated tDCS modulates TMS-MEPs. We also show modulation is sensitive to the orientation of the TMS coil (PA or AP), which is through to select different afferent pathways to M1. Our results are consistent with tDCS producing directionally specific neuromodulation in brain regions in-between electrodes, but shows nuanced changes in excitability that are presumably current direction relative to column and axon pathway specific. We suggest that the direction of current flow through cortical target regions should be considered for targeting and dose-control of tDCS.

scholarly journals A system of conservative regridding for ice/atmosphere coupling in a GCM

2013 ◽  
Vol 6 (4) ◽  
pp. 6493-6568 ◽  
Author(s):  
R. Fischer ◽  
S. Nowicki ◽  
M. Kelley ◽  
G. A. Schmidt
Keyword(s):  
Finite Element ◽  
General Circulation ◽  
Flow Model ◽  
Source Code ◽  
Circulation Model ◽  
Surface Mass Balance ◽  
Ice Flow ◽  
Surface Mass ◽  
Flow Models ◽  
Ice Model

Abstract. The method of elevation classes has proven to be a useful way for a low-resolution general circulation model (GCM) to produce high-resolution downscaled surface mass balance fields, for use in one-way studies coupling GCMs and ice flow models. Past uses of elevation classes have been a cause of non-conservation of mass and energy, caused by inconsistency in regridding schemes chosen to regrid to the atmosphere vs. downscaling to the ice model. This causes problems for two-way coupling. A strategy that resolves this conservation issue has been designed and is presented here. The approach identifies three grids between which data must be regridded, and five transformations between those grids required by a typical coupled GCM–ice flow model. This paper shows how each of those transformations may be achieved in a consistent, conservative manner. These transformations are implemented in GLINT2, a library used to couple GCMs with ice models. Source code and documentation are available for download. Confounding real-world issues are discussed, including the use of projections for ice modeling, how to handle dynamically changing ice geometry, and modifications required for finite element ice models.

scholarly journals EAST RIVER BATTLE FOR SHEEN: SKIMMING AN OIL SHEEN IN A 3- TO 5-KNOT CURRENT

2001 ◽  
Vol 2001 (2) ◽  
pp. 1431-1434
Author(s):  
Dennis E. Connelly ◽  
Dennis J. McCarthy ◽  
John E. Westerlind
Keyword(s):  
New York ◽  
Current Flow ◽  
Discharge Rate ◽  
Water Discharge ◽  
Cooling Water ◽  
High Discharge ◽  
East River ◽  
Discharge Canal ◽  
High Discharge Rate ◽  
Set Up

ABSTRACT This paper explores the challenges involved with the recovery of oil from a discharge canal with limited access and high relative currents. In March 1999, a sheen was observed in the cooling water discharge canal of Consolidated Edison's 2.5-million kilowatt generating station in Queens (New York City), New York At the time the sheen was discovered, the entire station had been shut down for several months for a maintenance outage. As the tide rose and fell in the East River, into which the discharge canal emptied, the oil sheen moved in and out of a 1,000-foot long tunnel connecting the generating station to the canal. The major challenges to the recovery and removal of the oil sheen were: (1) the low over head of the discharge tunnel and canal support girders, which prevented getting a skimmer into the tunnel and canal; (2) the high discharge rate of the station's cooling water pump; and (3) skimming the sheen in a 3-to 5-knot current. Consolidated Edison is a member of Clean Harbors Cooperative, L.L.C, which was brought in to remove the sheen. This was accomplished utilizing two JBF Scientific DIP Belt Skimmers, which were set up parallel to the current flow, and deflection booming.

Abstract TP458: High Accuracy of Predictive Models for SAH Using Different Machine Learning Approaches

Stroke ◽  
2020 ◽  
Vol 51 (Suppl_1) ◽  
Author(s):  
Paul Litvak ◽  
Jeevan Medikonda ◽  
Girish Menon ◽  
Pitchaiah Mandava
Keyword(s):  
Machine Learning ◽  
Predictive Models ◽  
Prediction Accuracy ◽  
Support Vector ◽  
World Federation ◽  
Learning Approaches ◽  
Flow Models ◽  
Multi Stage ◽  
Stage 1 ◽  
Categorical Scale

Background: Patients suffering from subarachnoid hemorrhage (SAH) have poor long-term outcomes. There are predictive models for ischemic and hemorrhagic stroke. However, there is paucity of models for SAH. Machine learning concepts were applied to build multi-stage Neural Networks (NN), Support Vector Machines (SVM) and Keras/Tensor Flow models to predict SAH outcomes. Methods: A database of ~800 aneurysmal SAH patients from Kasturba Medical College was utilized. Baseline variables of World Federation of Neurosurgeons 5-point scale (WFNS 1-5), age, gender, and presence/absence of hypertension and diabetes were considered in Stage 1. Stage 2 included all Stage 1 variables along with presence/absence of radiologic signs vasospasm and ischemia. Stage 3 includes earlier 2 stages and discharge Glasgow Outcome Scale (GOS 1-5). GOS at 3 months was predicted using 2-layer NN/SVM/Keras-TensorFlow models on the five point categorical scale as well as dichotomized to dead/alive and favorable (GOS 4-5) or unfavorable (GOS 1-3). Prediction accuracy of models was compared to the recorded GOS. Results: Prediction accuracy shown as percentages (See Table) for all three stages was similar for SVM, NN and Keras/TensorFlow models. Accuracy was remarkably higher with dichotomization compared to the complete five point GOS categorical scale. Conclusions: SVM, NN, and Keras-TensorFlow based machine learning models can be used to predict SAH outcomes to a high degree of accuracy. These powerful predictive models can be used to prognosticate and select patients into trials.

Discounted Cash Flow Method for Valuing International Chemical Distributors

2018 ◽  
Keyword(s):  
Cash Flow ◽  
Discounted Cash Flow ◽  
Case Scenario ◽  
Flow Models ◽  
Flow Method ◽  
Study Approach ◽  
Equity Value ◽  
Multiple Case ◽  
Set Up ◽  
Discounted Cash Flow Method

Do special considerations apply to valuation in the case of large global chemical distributors? This study seeks to identify whether Income-based Discounted Cash Flow method based on projected future income would be suitable to value international chemical distributors. Two- and Three-stage Discounted Cash Flow models will be used. The expected companies’ enterprise and equity value are compared with the existing companies’ valuations. A base, bear and bull case scenario will be set up to establish the range of the company’s value for comparison with the existing valuation. This study adopts a single multiple-case study approach where actual financial data from three of the world’s largest chemical distributors were used to establish the existing companies’ valuation to demonstrate the validity and applicability of the Discounted Cash Flow method for sensitivity analysis.

Non-Equilibrium Phenomena in Liquids and Solutions

2004 ◽  
Author(s):  
W. Ronald Fawcett
Keyword(s):  
Cold Water ◽  
Metallic Copper ◽  
Hot Water ◽  
Uniform Density ◽  
Local Concentration ◽  
Hot Plate ◽  
Copper Electrodes ◽  
Current Flows ◽  
Set Up ◽  
Isothermal Water

The topics considered up to this point have involved liquids and solutions at equilibrium. Attention is now turned to systems which are not at equilibrium, and the processes which occur spontaneously in such systems. The physical phenomena involved can be quite complex, so that the task faced in early experiments was to separate the various processes and understand the physical properties of the system which govern them. Consider what happens when a beaker of pure isothermal water is placed on a hot plate. The water near the bottom rises in temperature and a temperature gradient is set up. As a result heat flows from the bottom of the beaker, producing a gradual increase in temperature in the water at a given height above the bottom. In addition, the temperature varies with distance, being highest at the bottom and lowest at the top. Eventually, the temperature of the water in the beaker is uniform and equal to that of the hot plate, assuming that the water does not boil. However, the flow of heat is not the only process resulting from the heat source. The density of the hot water is less than that of the cold water, so that a convection process is set up in order to achieve uniform density. Convection results in cold water moving down into the hot region so that the flow of water molecules assists the flow of heat. The changes which occur in this system cannot be understood without considering both processes. A system undergoing an irreversible change involving an electrolyte is electrolysis in an electrochemical cell. When current flows between two copper electrodes in an aqueous solution of CuSO4 the charge in solution is carried by migration of Cu2+ ions moving in one direction and SO42− ions moving in the opposite. At the cathode, the incoming Cu2+ ions are reduced to metallic copper, thereby lowering the concentration of these ions in the electrode’s vicinity. At the anode, Cu metal is oxidized to produce Cu2+ ions in the solution, so that the local concentration of cations is increased.

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