On a New Passive Scalar Equation With Variable Mass Diffusivity: Flow Between Parallel Plates

2010 ◽  
Vol 132 (11) ◽  
Author(s):  
Fabio Gori ◽  
Andrea Boghi
Keyword(s):  
Variable Mass ◽  
Species Conservation ◽  
Mass Conservation ◽  
Passive Scalar ◽  
Conservation Equation ◽  
Average Concentration ◽  
Parallel Plates ◽  
Conservation Equations ◽  
Concentration Variance ◽  
Mass Diffusivity

The present work investigates mass conservation equations in turbulent flow between parallel plates with variable mass diffusivity. Species conservation equations are relative to the average concentration, as well as to the concentration variance. The product of fluctuating mass diffusivity and space gradient of concentration fluctuation is appearing in the equation of mean and concentration variance. A physical interpretation is given to the different terms. The assumption of a relation between mass diffusivity and concentration allows writing expressions for average and fluctuating mass diffusivity, which can be simplified on the basis of theoretical considerations. The new mass flux is expressed as a function of mass diffusivity and a gradient of concentration variance. Further considerations make it possible to model the new terms appearing in the concentration variance equation. The mass conservation equation can be solved when coupled to the equation of concentration variance. The equations are solved numerically for flow between parallel plates in order to evaluate the influence of the new terms.

On a New Passive Scalar Equation With Variable Mass Diffusivity

2008 ◽  
Author(s):  
Fabio Gori ◽  
Andrea Boghi
Keyword(s):  
Mass Flux ◽  
Variable Mass ◽  
Mass Conservation ◽  
Passive Scalar ◽  
Conservation Equation ◽  
Average Concentration ◽  
Concentration Fluctuation ◽  
Mass Diffusivity ◽  
Coupled Solution ◽  
Mass Conservation Equation

The present work investigates the mass conservation equation of a Newtonian and non-Newtonian fluid in turbulent flow with variable mass diffusivity. The mass conservation equation is considered with the fluctuating terms in the concentration as well as in the mass diffusivity and is written for the average concentration, for the fluctuating concentration one as well as for the square of the fluctuating concentration. A new term appears in the form of product of the fluctuating mass diffusivity to the space gradient of the concentration fluctuation. This new term is interpreted and introduced in the mass conservation equation of the square of the fluctuating concentration where other new terms are also appearing. A possible physical interpretation is given to the different terms. Assuming several relations between mass diffusivity and concentration it is then possible to write expressions for the average and the fluctuating mass concentration which can be simplified on the basis of physical and mathematical considerations. Specifically, the mass flux is then expressed as the product of the derivative of the mass diffusivity to the gradient of the square of the mass fluctuation. Further considerations make possible to write a new mass conservation equation of the average concentration which include a new term which takes into account the space gradient of the mass flux. The mass conservation equation can be solved with the coupled solution of the equation of the square of the concentration fluctuation.

Establishment and Solution of the RNC Flow Network Model

2014 ◽  
Vol 548-549 ◽  
pp. 1783-1789
Author(s):  
Li Ying Sun ◽  
Lu Jie Zhen ◽  
Yi Tong Li
Keyword(s):  
Network Model ◽  
Mass Conservation ◽  
Momentum Conservation ◽  
Conservation Equation ◽  
Two Phase ◽  
Conservation Equations ◽  
Flow Network ◽  
Cycle System ◽  
Variable Step ◽  
The Mathematical Model

The mathematical model based on graph theory and the refrigerant natural cycle system of gas-liquid two-phase flow network is established. Incidence matrix was used to describe the relationships between the various components. The node conservation equations, branch equations, momentum conservation equation in return circuit and mass conservation equations of system are established. The model was solved by using variable step gird iterative method. Then refrigerant state of each node and refrigerant flow of each branch in network model are obtained. Establishment and solution of the RNC network model provides an effective way for the further performance analysis of system.

scholarly journals Reconstructing spatially variable mass balances from past ice extents by inverse modeling

2018 ◽  
Vol 64 (248) ◽  
pp. 957-968 ◽  
Author(s):  
VJERAN VIŠNJEVIĆ ◽  
FRÉDÉRIC HERMAN ◽  
YURY PODLADCHIKOV
Keyword(s):  
Variable Mass ◽  
Mass Conservation ◽  
Conservation Equation ◽  
Inversion Method ◽  
Last Glacial ◽  
Ice Caps ◽  
Inverse Approach ◽  
Temperature And Precipitation ◽  
Geomorphic Features ◽  
Graphical Processing

ABSTRACTWith the conclusion of the Last Glacial Maximum (LGM), about 20 000 years ago, ended the most recent long-lasting cold phase in Earth history. This last glacial advance left a strong observable imprint on the landscape, such as moraines, trimlines and other glacial geomorphic features. These features reflect the extent of former glaciers and ice caps, which in turn provides information on past temperature and precipitation conditions. Here we present an inverse approach to reconstruct the equilibrium line altitudes (E) from observed ice extents. The ice-flow model is developed solving the mass conservation equation using the shallow ice approximation and implemented using Graphical Processing Units (GPUs). We present the theoretical basis of the inversion method, which relies on a Tikhonov regularization, and demonstrate its ability to constrain spatial variations in mass balance with idealized and real glaciers.

Numerical Simulation of Low-Current Vacuum Arc Plasma

2011 ◽  
Vol 383-390 ◽  
pp. 4843-4847
Author(s):  
Peng Sun ◽  
Rong Ni Yan
Keyword(s):  
Fluid Model ◽  
Mass Conservation ◽  
Momentum Conservation ◽  
Conservation Equation ◽  
Vacuum Arc ◽  
Symmetric Model ◽  
Ion Temperature ◽  
Plasma Parameters ◽  
Conservation Equations ◽  
Mhd Model

Three-dimensional magnetohydrodynamic(MHD) model of vacuum arc was built based on two-fluid model of ion and electron and Maxwell equation. In the MHD model mass conservation equation, momentum conservation equations, energy conservation equations of ion and electron, electric potential equations and magnetic equations were considered. With the aid of Computational Fluid Dynamics(CFD) software FLUENT and Re-development by visual C++, the important plasma parameters of low current vacuum arc , such as axial current density , ion temperature, electron temperature, mach number, were analyzed. The simulation results shown that the distribution of plasma parameters is consistent with that of the 2D axis-symmetric model.

Segregated Parallel Computing for Isoelectric Focusing of Proteins

2013 ◽  
Author(s):  
Kisoo Yoo ◽  
Jin Liu ◽  
Prashanta Dutta
Keyword(s):  
Isoelectric Focusing ◽  
Troponin I ◽  
Hot Spot ◽  
Computing Time ◽  
Mass Conservation ◽  
Conservation Equation ◽  
Numerical Code ◽  
Time Step ◽  
Conservation Equations ◽  
Amphoteric Molecules

A parallel algorithm is introduced to simulate isoelectric focusing (IEF) in a microfluidic device. This new algorithm is based on segregated method for solving a large number of mass conservation equations in the system. An in house numerical code is developed to simulate the transient focusing behavior of cardiac troponin I (cTnI) protein in a pH field formed by ampholytes in presence of an applied electric field. The effectiveness of the parallel scheme is assessed by analyzing the CPU times for each process. Numerical results show that the electric potential distribution is nearly independent of time or concentration of amphoteric molecules. Thus, the charge conservation equation is not solved after the first time step to reduce the computational expenses. As expected, the solution of mass conservation equations for ampholytes is the computational hot spot, and solving them in parallel reduces the overall computing time. The proposed algorithm is very suitable for solving mass conservation equations of 100∼1000 components used to form continuous pH in IEF.

Transport of Microorganisms in the Underground – Processes, Experiments and Simulation Models

1991 ◽  
Vol 24 (2) ◽  
pp. 309-314 ◽  
Author(s):  
G. Teutsch ◽  
K. Herbold-Paschke ◽  
D. Tougianidou ◽  
T. Hahn ◽  
K. Botzenhart
Keyword(s):  
Simulation Models ◽  
Mass Conservation ◽  
Breakthrough Curves ◽  
Conservation Equation ◽  
Retardation Factor ◽  
Natural Systems ◽  
Laboratory Setup ◽  
Preliminary Model ◽  
Sand And Gravel ◽  
Mass Conservation Equation

In this paper the major processes governing the persistence and underground transport of viruses and bacteria are reviewed in respect to their importance under naturally occurring conditions. In general, the simulation of the governing processes is based on the macroscopic mass-conservation equation with the addition of some filter and/or retardation factor and a decay coefficient, representing the natural “die-off” of the microorganisms. More advanced concepts try to incorporate growth and decay coefficients together with deposition and declogging factors. At present, none of the reported concepts has been seriously validated. Due to the complexity of natural systems and the pathogenic properties of some of the microorganisms, experiments under controlled laboratory conditions are required. A laboratory setup is presented in which a great variety of natural conditions can be simulated. This comprises a set of 1 metre columns and an 8 metre stainless-steel flume with 24 sampling ports. The columns are easily filled and conditioned and therefore used to study the effects of different soil-microorganism combinations under various environmental conditions. In the artificial flume natural underground conditions are simulated using sand and gravel aquifer material from the river Neckar alluvium. A first set of results from the laboratory experiments is presented together with preliminary model simulations. The large variety of observed breakthrough curves and recovery for the bacteria and viruses under investigation demonstrates the great uncertainty encountered in microbiological risk assessment.

A New Model for the Simulation of CO2 Absorption in an Industrial-Scale Packed Column

2012 ◽  
Vol 557-559 ◽  
pp. 2208-2216 ◽  
Author(s):  
Wen Bin Li ◽  
Guo Cong Yu ◽  
Bo Tan Liu ◽  
Xi Gang Yuan
Keyword(s):  
Mass Transfer ◽  
Packed Column ◽  
Mass Conservation ◽  
Conservation Equation ◽  
Industrial Scale ◽  
Transfer Model ◽  
Turbulent Heat ◽  
Proposed Model ◽  
Heat Conservation ◽  
Phase Temperature

A new computational mass transfer model is proposed for simulating the chemical absorption process with heat effect by solving the average fluctuating mass flux in turbulent mass conservation equation and the average fluctuating heat flux in turbulent heat conservation equation, so that the concentration profile and the temperature profile of column can be obtained. The feather of the proposed model is to abandon the conventional way of introducing the unknown turbulent mass transfer diffusivity Dtand the turbulent thermal diffusivity αtin the mass and heat conservation equations. By using the proposed model, the simulated results of CO2absorption by aqueous monoethanolamine (MEA) solution in an industrial scale column is presented, including MEA concentration, CO2loading and liquid phase temperature. The simulations are in agreement with the published experiment data.

Mathematical Modelling of Thermo-Hydro-Mechanical Behaviour for Concrete under Elevated Temperature

2014 ◽  
Vol 670-671 ◽  
pp. 355-364
Author(s):  
Shao Bo Zhang ◽  
Xiao Chun Wang ◽  
Xin Pu Shen
Keyword(s):  
Elevated Temperature ◽  
Stokes Equations ◽  
Constitutive Relations ◽  
Gaseous Mixture ◽  
Mass Conservation ◽  
Momentum Conservation ◽  
Conservation Equation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Energy Conservation Equation

A hydro-thermo-mechanical model was presented for concrete at elevated temperature. Three phases of continuum were adopted in this model: gaseous mixture of water vapor and dry air, liquid water, and solid skeleton of concrete. Mass conservation equations, linear momentum conservation equation, and energy conservation equation were derived on the basis of the macroscopic Navier-Stokes equations for a general continuum, along with assumptions made for the purpose of simplification. Mathematical relationships between selected primary variables and secondary variables were given with existing data from references. Specifications of the constitutive relations were made for the kinetic variables and their conjugate forces.

An Unstructured Reacting Flow Solver With Coupled Implicit Solution of the Species Conservation Equations

2008 ◽  
Author(s):  
Ankan Kumar ◽  
Sandip Mazumder
Keyword(s):  
Species Conservation ◽  
Domain Size ◽  
Reacting Flow ◽  
Computational Domain ◽  
Conservation Equations ◽  
Flow Solver ◽  
As Species ◽  
Minimum Residual ◽  
Volume Method ◽  
Coupled Solution

Many reacting flow applications mandate coupled solution of the species conservation equations. A low-memory coupled solver was developed to solve the species transport equations on an unstructured mesh with implicit spatial as well as species-to-species coupling. First, the computational domain was decomposed into sub-domains comprised of geometrically contiguous cells—a process termed internal domain decomposition (IDD). This was done using the binary spatial partitioning (BSP) algorithm. Following this step, for each sub-domain, the discretized equations were developed using the finite-volume method, written in block implicit form, and solved using an iterative solver based on Krylov sub-space iterations, i.e., the Generalized Minimum Residual (GMRES) solver. Overall (outer) iterations were then performed to treat explicitness at sub-domain interfaces and non-linearities in the governing equations. The solver is demonstrated for a laminar ethane-air flame calculation with five species and a single reaction step, and for a catalytic methane-air combustion case with 19 species and 22 reaction steps. It was found that the best performance is manifested for sub-domain size of about 1000 cells, the exact number depending on the problem at hand. The overall gain in computational efficiency was found to be a factor of 2–5 over the block Gauss-Seidel procedure.

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