A Mathematical Model for Transient Subchannel Analysis of Rod-Bundle Nuclear Fuel Elements

1973 ◽  
Vol 95 (2) ◽  
pp. 211-217 ◽  
Author(s):  
D. S. Rowe
Keyword(s):  
Mathematical Model ◽  
Nuclear Fuel ◽  
Flow Rate ◽  
Transient Flow ◽  
Momentum Equation ◽  
Flow Area ◽  
Inlet Flow ◽  
Rod Bundle ◽  
Inlet Flow Rate ◽  
Fuel Elements

This paper presents a mathematical method for analyzing transient flow and enthalpy transport in rod-bundle nuclear fuel elements during both boiling and nonboiling conditions. A mathematical model is formulated by dividing the bundle flow area into flow subchannels that are assumed to contain one-dimensional flow and are coupled to each other by turbulent and diversion crossflow mixing. The mathematical model neglects sonic velocity propagation and neglects temporal and spatial acceleration in the transverse momentum equation. A semiexplicit finite-difference scheme is used to perform a boundary-value solution where the boundary conditions are the inlet enthalpy, inlet flow rate, and exit pressure. Calculations are presented to show the effect of rapid changes in heat flux, inlet enthalpy, and inlet flow rate on the subchannel flow and enthalpy distribution in rod bundles.

scholarly journals Mathematical Model of Air Pocket Evolution during Water Filling a Long-Slope Pipeline and Its Application to Air Removal Prediction

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Yuanyuan Chen ◽  
Yanyu Cui ◽  
Wenhui Chen ◽  
Tao Deng ◽  
Jing Gong
Keyword(s):  
Mathematical Model ◽  
Flow Rate ◽  
Great Role ◽  
Inlet Flow ◽  
Air Pocket ◽  
Peak Point ◽  
Inlet Flow Rate ◽  
Water Filling ◽  
Air Removal ◽  
Terrain Category

During water filling a long-slope pipeline, air pocket is very likely to be entrapped at peak point. In order to track air movement and predict air removal conditions, a mathematical model of air pocket evolution, including its formation, compression, and entrainment, is proposed in this paper. The simulation results were compared with the engineering field data and the two are basically consistent. Furthermore, the two most important factors which play a great role in the removal of air pocket, i.e., the terrain category and the inlet flow rate, are analyzed in detail. It is concluded that the removal conditions reach three outcomes: air pocket compressed and partly removed, compressed and completely removed, and compressed without any removal. In this paper, the terrain which leads to the last outcome is called the “Dangerous Terrain.” And for the “Dangerous Terrain,” it is of great importance that the inlet flow rate should be strictly confined within a certain level. While for the other two categories of terrains, an increased flow rate is in any respect beneficial to the removal of air pocket.

scholarly journals A Systematically Reduced Mathematical Model for Organoid Expansion

2021 ◽  
Vol 9 ◽  
Author(s):  
Meredith A. Ellis ◽  
Mohit P. Dalwadi ◽  
Marianne J. Ellis ◽  
Helen M. Byrne ◽  
Sarah L. Waters
Keyword(s):  
Mathematical Model ◽  
Mass Transport ◽  
Flow Rate ◽  
Operating Conditions ◽  
Seeding Density ◽  
Cell Seeding ◽  
Inlet Flow ◽  
Cell Seeding Density ◽  
Inlet Flow Rate ◽  
Reproducible Manner

Organoids are three-dimensional multicellular tissue constructs. When cultured in vitro, they recapitulate the structure, heterogeneity, and function of their in vivo counterparts. As awareness of the multiple uses of organoids has grown, e.g. in drug discovery and personalised medicine, demand has increased for low-cost and efficient methods of producing them in a reproducible manner and at scale. Here we focus on a bioreactor technology for organoid production, which exploits fluid flow to enhance mass transport to and from the organoids. To ensure large numbers of organoids can be grown within the bioreactor in a reproducible manner, nutrient delivery to, and waste product removal from, the organoids must be carefully controlled. We develop a continuum mathematical model to investigate how mass transport within the bioreactor depends on the inlet flow rate and cell seeding density, focusing on the transport of two key metabolites: glucose and lactate. We exploit the thin geometry of the bioreactor to systematically simplify our model. This significantly reduces the computational cost of generating model solutions, and provides insight into the dominant mass transport mechanisms. We test the validity of the reduced models by comparison with simulations of the full model. We then exploit our reduced mathematical model to determine, for a given inlet flow rate and cell seeding density, the evolution of the spatial metabolite distributions throughout the bioreactor. To assess the bioreactor transport characteristics, we introduce metrics quantifying glucose conversion (the ratio between the total amounts of consumed and supplied glucose), the maximum lactate concentration, the proportion of the bioreactor with intolerable lactate concentrations, and the time when intolerable lactate concentrations are first experienced within the bioreactor. We determine the dependence of these metrics on organoid-line characteristics such as proliferation rate and rate of glucose consumption per cell. Finally, for a given organoid line, we determine how the distribution of metabolites and the associated metrics depend on the inlet flow rate. Insights from this study can be used to inform bioreactor operating conditions, ultimately improving the quality and number of bioreactor-expanded organoids.

scholarly journals Investigation of the transport characteristics of Pb(II) in sand-bone char columns

2021 ◽  
Vol 104 (2) ◽  
pp. 003685042110236
Author(s):  
Gang Li ◽  
Jinli Zhang ◽  
Jia Liu ◽  
Tao Luo ◽  
Yu Xi
Keyword(s):  
Adsorption Capacity ◽  
Flow Rate ◽  
Dose Response ◽  
Construction Materials ◽  
Column Height ◽  
Maximum Adsorption Capacity ◽  
Complexation Reaction ◽  
Bone Char ◽  
Inlet Flow ◽  
Inlet Flow Rate

Pb(II) leakage from batteries, dyes, construction materials, and gasoline threaten human health and environmental safety, and suitable adsorption materials are vitally important for Pb(II) removal. Bone char is an outstanding adsorbent material for water treatment, and the effectiveness in Pb(II) removing need to be verified. In this paper, the transport characteristics of Pb(II) in columns filled with a sand and bone char mixture were studied at the laboratory scale, and the influences of the initial concentration, column height, inlet flow rate, and competing ion Cu(II) on Pb(II) adsorption and transport were analyzed. The Thomas and Dose-Response models were used to predict the test results, and the mechanisms of Pb(II) adsorption on bone char were investigated. The results showed that the adsorption capacity of the bone char increased with increasing column height and decreased with increasing initial Pb(II) concentration, flow rate, and Cu(II) concentration. The maximum adsorption capacity reached 38.466 mg/g and the saturation rate was 95.8% at an initial Pb(II) concentration of 200 mg/L, inlet flow rate of 4 mL/min, and column height of 30 cm. In the competitive binary system, the higher the Cu(II) concentration was, the greater the decreases in the breakthrough and termination times, and the faster the decrease in the Pb(II) adsorption capacity of the bone char. The predicted results of the Dose-Response model agreed well with the experimental results and were significantly better than those of the Thomas model. The main mechanisms of Pb(II) adsorption on bone char include a surface complexation reaction and the decomposition-replacement-precipitation of calcium hydroxyapatite (CaHA). Based on selectivity, sensitivity, and cost analyses, it can be concluded that bone char is a potential adsorbent for Pb(II)-containing wastewater treatment.

Research on the Removal Results of Hydrogen Sulfide of the Treatment of Coal Gasification Wastewater Biogas in the Anaerobic Biotrickling Filter

2012 ◽  
Vol 610-613 ◽  
pp. 2000-2005
Author(s):  
Chun Yan Xu ◽  
Hong Jun Han
Keyword(s):  
Hydrogen Sulfide ◽  
Removal Efficiency ◽  
Flow Rate ◽  
Retention Time ◽  
Operating Parameters ◽  
Inlet Flow ◽  
H2s Removal ◽  
Outlet Concentration ◽  
Volume Load ◽  
Inlet Flow Rate

The uncertainty of operating parameters hinders the practical application of the biological desulfurization. To solve this problem, this study which was conducted in room temperature, pH around seven conditions, investigated the effects of the operating parameters on the hydrogen sulfide (H2S) removal performance in the biotrickling filter, including inlet H2S concentration, inlet flow rate or gas retention time, inlet volume load and circulating liquid spraying flux. The results showed that, the inlet H2S concentration should be controlled within 800mg/m3, 650mg/m3, 400mg/m3, 300mg/m3 respectively while the inlet flow rate was 150L/h, 200L/h, 250L/h, 300L/h, at those conditions, the outlet H2S concentrations were lower than 8mg/m3 and the H2S removal efficiencies were more than 98%. The optimum gas retention time was 12.37s, corresponding to the inlet flow rate of 200L/h, at this time, even if the inlet H2S concentration as high as 700mg/m3, the removal efficiency could be still more than 98%, the outlet concentration of H2S was only 13.1mg/m3. The maximum inlet volume load was 130g/(m3•h), in this condition, the outlet concentration of H2S could be controlled below 12mg/m3, the removal efficiency could above 98.4%.

A new method for prediction of the acoustic performance and design parameter sensitivity analysis of multi-chamber perforated resonators with an irregular cross-section

2021 ◽  
pp. 1-24
Author(s):  
Rong Guo ◽  
Zanzan Sun ◽  
Zhen Huang ◽  
Rui Luo
Keyword(s):  
Theoretical Prediction ◽  
Cross Section ◽  
Flow Rate ◽  
New Method ◽  
Frequency Noise ◽  
Acoustic Characteristics ◽  
Inlet Flow ◽  
Acoustic Performance ◽  
Inlet Flow Rate ◽  
Prediction Approach

Abstract Aiming at reducing the high-amplitude and wide-frequency noise in charged air intake system of the powertrain, this paper proposes a new method for predicting the acoustic characteristics of an irregular cross-section multi-chamber perforated resonator under flow conditions. By this method, the presence of three-dimensional sound waves and the effects of higher-order modes are considered, and the acoustic performance of the resonator can be evaluated through the computation of transmission loss. Moreover, by discretizing the cross-section of perforated resonator and extracting node information, this method can solve the acoustic characteristics of the perforated resonator with any cross-section. Based on the transfer matrix method, the quadrupole parameters of each chamber are obtained. Then the acoustic characteristics of the multi-chamber perforated resonator could be calculated. The theoretical prediction data and the experimental data have been compared and the results show good agreement within the entire frequency range, which verifies the accuracy of the theoretical prediction approach. Based on this prediction approach, the influence of section ratio, structure parameters and inlet flow rate on the acoustic characteristics of the resonator is explored. The results show that when the structural parameters change, the peak resonance frequency of the resonator will have a regular shift. With the increase of the inlet flow rate, the main frequency band of sound attenuation will decrease significantly. The theoretical method developed in this work can be used for the calculation and optimization of multi-chamber resonators in various applications.

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