scholarly journals Modeling and Experiments of Severe Slugging in a Riser System

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Lin Wang ◽  
Yuxing Li ◽  
Chang Liu ◽  
Qihui Hu ◽  
Yating Wang ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Numerical Solutions ◽  
Liquid Velocity ◽  
Momentum Equation ◽  
Gas Velocity ◽  
Experimental Conditions ◽  
Gas Phases ◽  
Continuity Equations ◽  
Backward Euler ◽  
Calculation Results

A transient mathematical model based on continuity equations for liquid and gas phases, with a momentum equation for the mixture, was developed, and numerical solutions and simulations corresponding to severe slugging in pipeline-riser system were presented, and the results were compared with the experimental data to verify the mathematical model. In numerical solutions, backward Euler schemes were adopted as predictors and trapezoidal methods were used as correctors. Variable time steps were employed for higher computational efficiency and accuracy in the integration. Experiments of severe slugging characteristics were performed, and the simulation results of the cycle periods and bottom pressure were compared with experimental values. Finally, the calculation results of detailed characteristics were analyzed thoroughly. The results show that the developed mathematical model can accurately predict the cycle time and the detailed characteristics of severe slugging. Under the experimental conditions, the liquid slug length can reach 1.6 times the height of the riser, and the maximum instantaneous gas velocity of outlet is 50 times the inlet gas velocity, and the maximum instantaneous liquid velocity of outlet is 28 times the inlet liquid velocity, having important implications for the hazard assessment of severe slugging.

Theoretical Analysis of CO2 Bubble Formation in Anode Flow Field of μDMFC

2014 ◽  
Vol 635-637 ◽  
pp. 346-353 ◽  
Author(s):  
Miao Miao Li ◽  
Jun Geng ◽  
Ru Peng Zhu
Keyword(s):  
Mathematical Model ◽  
Theoretical Analysis ◽  
Flow Field ◽  
Flow Velocity ◽  
Liquid Velocity ◽  
Bubble Formation ◽  
Cross Flow ◽  
Carbon Paper ◽  
Gas Velocity ◽  
Cross Flow Velocity

A mathematical model was established and validated to predict the microbubble diameter when it departing from the carbon paper and moving into the channel of μDMFC. Single bubble behaviors were studied using the model, which took the gas velocity, liquid cross-flow velocity, micro porous diameter and other parameters into account. Results indicate that the microbubble departure diameter decreases with the increasing liquid velocity, and increases with the increasing micro porous diameter and increasing gas velocity.

scholarly journals Mathematical modelling of far-infrared vacuum drying of apple slices

2019 ◽  
Vol 23 (1) ◽  
pp. 393-400 ◽  
Author(s):  
Vangelce Mitrevski ◽  
Aleksandar Dedinac ◽  
Cvetanka Mitrevska ◽  
Slobodan Bundalevski ◽  
Tale Geramitcioski ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Moisture Content ◽  
Numerical Solutions ◽  
Far Infrared ◽  
Vacuum Drying ◽  
Temperature Profiles ◽  
Experimental Conditions ◽  
Apple Slices ◽  
Plane Temperature ◽  
Good Agreement

In this study, a mathematical model of far-infrared vacuum drying of shrinkage body is presented. The system of two coupled PDE for heat and mass transfer with appropriate initial and boundary conditions are solved numerically with used of the finite difference method. On the basis of the numerical solutions a computer program for calculation of temperature profiles, transient moisture content, mid-plane temperature, and the volume averaged moisture content changes for different drying regime was developed. For verification of a mathematical model a series of numerical calculations were carried out with experimental conditions similar to those in the realized experiments of far-infrared vacuum drying of apple slices. Very good agreement between the experimental and numerical temperature and moisture content changes during the drying was obtained.

Atomic Imaging of Crystals using Large-Angle Electron Scattering in STEM

1990 ◽  
Vol 48 (1) ◽  
pp. 74-75
Author(s):  
D.E. Jesson ◽  
S. J. Pennycook
Keyword(s):  
Wave Function ◽  
Electron Scattering ◽  
Numerical Solutions ◽  
Large Angle ◽  
Real Space ◽  
High Angle ◽  
Analytical Treatment ◽  
Order Zero ◽  
Experimental Conditions ◽  
Ewald Sphere

It is well known that conventional atomic resolution electron microscopy is a coherent imaging process best interpreted in reciprocal space using contrast transfer function theory. This is because the equivalent real space interpretation involving a convolution between the exit face wave function and the instrumental response is difficult to visualize. Furthermore, the crystal wave function is not simply related to the projected crystal potential, except under a very restrictive set of experimental conditions, making image simulation an essential part of image interpretation. In this paper we present a different conceptual approach to the atomic imaging of crystals based on incoherent imaging theory. Using a real-space analysis of electron scattering to a high-angle annular detector, it is shown how the STEM imaging process can be partitioned into components parallel and perpendicular to the relevant low index zone-axis.It has become customary to describe STEM imaging using the analytical treatment developed by Cowley. However, the convenient assumption of a phase object (which neglects the curvature of the Ewald sphere) fails rapidly for large scattering angles, even in very thin crystals. Thus, to avoid unpredictive numerical solutions, it would seem more appropriate to apply pseudo-kinematic theory to the treatment of the weak high angle signal. Diffraction to medium order zero-layer reflections is most important compared with thermal diffuse scattering in very thin crystals (<5nm). The electron wave function ψ(R,z) at a depth z and transverse coordinate R due to a phase aberrated surface probe function P(R-RO) located at RO is then well described by the channeling approximation;

scholarly journals Mathematical model and calculation results of the kerosene aerosol combustion rate

2020 ◽  
Vol 1565 ◽  
pp. 012022
Author(s):  
V A Poryazov ◽  
K M Moiseeva ◽  
A Yu Krainov ◽  
D A Krainov
Keyword(s):  
Mathematical Model ◽  
Combustion Rate ◽  
Calculation Results

A Meshless Method for Solving the Mathematical Model Associated the Leakage Problem in Gas Pipeline

2014 ◽  
Vol 986-987 ◽  
pp. 1418-1421
Author(s):  
Jun Shan Li
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Partial Differential Equation ◽  
Inverse Problem ◽  
Basis Function ◽  
Meshless Method ◽  
Numerical Solutions ◽  
Basis Functions ◽  
Gas Pipeline ◽  
The Mathematical Model

In this paper, we propose a meshless method for solving the mathematical model concerning the leakage problem when the pressure is tested in the gas pipeline. The method of radial basis function (RBF) can be used for solving partial differential equation by writing the solution in the form of linear combination of radius basis functions, that is, when integrating the definite conditions, one can find the combination coefficients and then the numerical solution. The leak problem is a kind of inverse problem that is focused by many engineers or mathematical researchers. The strength of the leak can find easily by the additional conditions and the numerical solutions.

A NUMERICAL PROOF THAT CERTAIN CELLS FOLLOW THE TRAILS OF THE DIFFUSIONS OF SOME CHEMICALS IN THE EXTRACELLULAR MATRIX

2021 ◽  
pp. 2150027
Author(s):  
İREM ÇAY ◽  
SERDAL PAMUK
Keyword(s):  
Mathematical Model ◽  
Extracellular Matrix ◽  
Tumor Angiogenesis ◽  
Numerical Solutions ◽  
Extra Cellular Matrix ◽  
The Matrix ◽  
Good Agreement ◽  
Cellular Matrix

In this work, we obtain the numerical solutions of a 2D mathematical model of tumor angiogenesis originally presented in [Pamuk S, ÇAY İ, Sazci A, A 2D mathematical model for tumor angiogenesis: The roles of certain cells in the extra cellular matrix, Math Biosci 306:32–48, 2018] to numerically prove that the certain cells, the endothelials (EC), pericytes (PC) and macrophages (MC) follow the trails of the diffusions of some chemicals in the extracellular matrix (ECM) which is, in fact, inhomogeneous. This leads to branching, the sprouting of a new neovessel from an existing vessel. Therefore, anastomosis occurs between these sprouts. In our figures we do see these branching and anastomosis, which show the fact that the cells diffuse according to the structure of the ECM. As a result, one sees that our results are in good agreement with the biological facts about the movements of certain cells in the Matrix.

scholarly journals SIR Model for Dengue Disease with Effect of Dengue Vaccination

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Pratchaya Chanprasopchai ◽  
I. Ming Tang ◽  
Puntani Pongsumpun
Keyword(s):  
Mathematical Model ◽  
Mortality Rate ◽  
Dengue Virus ◽  
Numerical Solutions ◽  
Specific Treatment ◽  
Sir Model ◽  
Dengue Vaccine ◽  
Dengue Disease ◽  
Modelling Methods

The dengue disease is caused by dengue virus, and there is no specific treatment. The medical care by experienced physicians and nurses will save life and will lower the mortality rate. A dengue vaccine to control the disease is available in Thailand since late 2016. A mathematical model would be an important way to analyze the effects of the vaccination on the transmission of the disease. We have formulated an SIR (susceptible-infected-recovered) model of the transmission of the disease which includes the effect of vaccination and used standard dynamical modelling methods to analyze the effects. The equilibrium states and their stabilities are investigated. The trajectories of the numerical solutions plotted into the 2D planes and 3D spaces are presented. The main contribution is determining the role of dengue vaccination in the model. From the analysis, we find that there is a significant reduction in the total hospitalization time needed to treat the illness.

A sewer ventilation model applying conservation of momentum

2011 ◽  
Vol 64 (6) ◽  
pp. 1374-1382 ◽  
Author(s):  
M. Ward ◽  
G. Hamer ◽  
A. McDonald ◽  
J. Witherspoon ◽  
E. Loh ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Treatment Plant ◽  
Ambient Air ◽  
Momentum Equation ◽  
Ventilation Rate ◽  
Water Interface ◽  
Model Accuracy ◽  
Air Water Interface ◽  
Conservation Of Momentum ◽  
Gravity Sewer

The work presented herein was completed in an effort to characterize the forces influencing ventilation in gravity sewers and to develop a mathematical model, based on conservation of momentum, capable of accounting for friction at the headspace/pipe interface, drag at the air/water interface, and buoyancy caused by air density differences between a sewer headspace and ambient. Experiments were completed on two full scale sewer reaches in Australia. A carbon monoxide-based tracer technique was used to measure the ventilation rate within the sewer headspaces. Additionally, measurements of pressure, relative humidity, and temperature were measured in the ambient air and sewer headspace. The first location was a five kilometre long sewer outfall beginning at a wastewater treatment plant and terminating at the ocean. The second location was a large gravity sewer reach fitted with ventilation fans. At the first location the headspace was entirely sealed except for openings that were controlled during the experiments. In this situation forces acting on the headspace air manifested mostly as a pressure distribution within the reach, effectively eliminating friction at the pipe wall. At the second location, air was forced to move near the same velocity as the wastewater, effectively eliminating drag at the air/water interface. These experiments allowed individual terms of the momentum equation to be evaluated. Experimental results were compared to the proposed mathematical model. Conclusions regarding model accuracy are provided along with model application guidance and assumptions.

scholarly journals ПОБУДОВА МАТЕМАТИЧНОЇ МОДЕЛІ СКЛАДНОГО РУХУ ФЛАКОНІВ НА ЛІНІЯХ РОЗЛИВУ ЛІКІВ ФАРМАЦЕВТИЧНОЇ ПРОМИСЛОВОСТІ

2012 ◽  
Author(s):  
N. О. Kravets
Keyword(s):  
Mathematical Model ◽  
Experimental Evaluation ◽  
Theoretical Dependence ◽  
Complex Product ◽  
Lateral Lines ◽  
Calculation Results ◽  
The Mathematical Model

The  mathematical model of the complex product motion along the lateral lines at the plate conveyers of the bottle lines is presented in the artcle. The experimental evaluation of the gained theoretical dependence is suggested.   The calculation results coordinate well with the modelling and experiment resuls.

scholarly journals Memory effects on the proliferative function in the cycle-specific of chemotherapy

2021 ◽  
Author(s):  
Najma Ahmed ◽  
Dumitru Vieru ◽  
Fiazud Din Zaman
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Numerical Solutions ◽  
Classical Model ◽  
Cell Mass ◽  
Time Derivative ◽  
Fractional Model ◽  
Fractional Differential ◽  
Mathcad Software

A generalized mathematical model of the breast and ovarian cancer is developed by considering the fractional differential equations with Caputo time-fractional derivatives. The use of the fractional model shows that the time-evolution of the proliferating cell mass, the quiescent cell mass, and the proliferative function are significantly influenced by their history. Even if the classical model, based on the derivative of integer order has been studied in many papers, its analytical solutions are presented in order to make the comparison between the classical model and the fractional model. Using the finite difference method, numerical schemes to the Caputo derivative operator and Riemann-Liouville fractional integral operator are obtained. Numerical solutions to the fractional differential equations of the generalized mathematical model are determined for the chemotherapy scheme based on the function of "on-off" type. Numerical results, obtained with the Mathcad software, are discussed and presented in graphical illustrations. The presence of the fractional order of the time-derivative as a parameter of solutions gives important information regarding the proliferative function, therefore, could give the possible rules for more efficient chemotherapy.

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