scholarly journals Mathematical Model of Fluids Motion in Poroelastic Snow-ice Cover

2021 ◽  
pp. 47-56
Author(s):  
Margarita A. Tokareva ◽  
Alexander A. Papin
Keyword(s):  
Mass Conservation ◽  
Ice Cover ◽  
Governing Equations ◽  
Rheological Equation ◽  
Model Case ◽  
Three Phase ◽  
Nonstationary Filtration ◽  
Phase Medium ◽  
Conservation Of Momentum ◽  
Phase Momentum

The dynamics of a snow-ice cover is considered within the theory of poroelasticity. The snow-ice cover is modeled by a three-phase medium consisting of water, air and ice. The governing equations are the equations of mass conservation for each phase with phase transitions, the equations of conservation of phase momentum in the form of Darcy’s law, the equation of conservation of momentum of the whole system, the rheological equation for porosity and the equation of heat balance of snow. In the full formulation the liquid and air pressures are functions of the temperature and the corresponding densities, and the viscosity and compressibility coefficients of ice are functions of the temperature. The problem of two-dimensional nonstationary filtration of water in a thin poroelastic ice plate is considered in the model case. The solution is obtained in quadratures

scholarly journals Thermochemical Nonequilibrium in Rapidly Expanding Flows of High-Temperature Air

1997 ◽  
Vol 52 (4) ◽  
pp. 358-368 ◽  
Author(s):  
Michio Nishida ◽  
Masashi Matsumotob
Keyword(s):  
High Temperature ◽  
Vibrational Energy ◽  
Stokes Equations ◽  
Computational Study ◽  
Mass Conservation ◽  
Navier Stokes ◽  
Tvd Scheme ◽  
Governing Equations ◽  
Navier Stokes Equations ◽  
Free Jet

Abstract • This paper describes a computational study of the thermal and chemical nonequilibrium occuring in a rapidly expanding flow of high-temperature air transported as a free jet from an orifice into low-density stationary air. Translational, rotational, vibrational and electron temperatures are treated separately, and in particular the vibrational temperatures are individually treated; a multi-vibrational temperature model is adopted. The governing equations are axisymmetric Navier-Stokes equations coupled with species vibrational energy, electron energy and species mass conservation equations. These equations are numerically solved, using the second order upwind TVD scheme of the Harten-Yee type. The calculations were carried out for two different orifice temperatures and also two different orifice diameters to investigate the effects of such parameters on the structure of a nonequilibrium free jet.

Viscoelectric Effect on the Electroosmotic Flow in Nanochannels With Heterogeneous Zeta Potentials

2018 ◽  
Author(s):  
Edson M. Jimenez ◽  
Federico Méndez ◽  
Juan P. Escandón
Keyword(s):  
Electroosmotic Flow ◽  
Fluid Velocity ◽  
Volumetric Flow Rate ◽  
Mass Conservation ◽  
Double Layers ◽  
Fluid Viscosity ◽  
Governing Equations ◽  
Flat Plates ◽  
Zeta Potentials ◽  
Poisson Boltzmann

In the present work, we realize a study about the influence of viscoelectric effect on the electroosmotic flow of Newtonian fluids in nanochannels formed by two parallel flat plates. In the problem, the channel walls have heterogeneous zeta potentials which follow a sinusoidal distribution; moreover, viscoelectric effects appear into the electric double layers when high zeta potentials are considered at the channel walls, modifying the fluid viscosity and the fluid velocity. To find the solution of flow field, the modified Poisson-Boltzmann, mass conservation and momentum governing equations, are solved numerically. In the results, combined effects from the zeta potential heterogeneities and viscosity changes yields different kind of flow recirculations controlled by the dephasing angle, amplitude and number of waves of the heterogeneities at the walls. The viscoelectric effect produces a decrease in the magnitude of velocity profiles and volumetric flow rate when the high zeta potentials are magnified. Additionally, the heterogeneous zeta potentials at the walls generate an induced pressure on the flow. This investigation extend the knowledge of electroosmotic flows under field effects for future mixing applications.

scholarly journals The Influence of Bioreactor Geometry and the Mechanical Environment on Engineered Tissues

2010 ◽  
Vol 132 (5) ◽  
Author(s):  
J. M. Osborne ◽  
R. D. O’Dea ◽  
J. P. Whiteley ◽  
H. M. Byrne ◽  
S. L. Waters
Keyword(s):  
Shear Stress ◽  
Culture Medium ◽  
Porous Scaffold ◽  
Two Dimensional ◽  
Governing Equations ◽  
Long Wavelength ◽  
Wavelength Limit ◽  
Aspect Ratios ◽  
Three Phase ◽  
Tissue Construct

A three phase model for the growth of a tissue construct within a perfusion bioreactor is examined. The cell population (and attendant extracellular matrix), culture medium, and porous scaffold are treated as distinct phases. The bioreactor system is represented by a two-dimensional channel containing a cell-seeded rigid porous scaffold (tissue construct), which is perfused with a culture medium. Through the prescription of appropriate functional forms for cell proliferation and extracellular matrix deposition rates, the model is used to compare the influence of cell density-, pressure-, and culture medium shear stress-regulated growth on the composition of the engineered tissue. The governing equations are derived in O’Dea et al. “A Three Phase Model for Tissue Construct Growth in a Perfusion Bioreactor,” Math. Med. Biol., in which the long-wavelength limit was exploited to aid analysis; here, finite element methods are used to construct two-dimensional solutions to the governing equations and to investigate thoroughly their behavior. Comparison of the total tissue yield and averaged pressures, velocities, and shear stress demonstrates that quantitative agreement between the two-dimensional and long-wavelength approximation solutions is obtained for channel aspect ratios of order 10−2 and that much of the qualitative behavior of the model is captured in the long-wavelength limit, even for relatively large channel aspect ratios. However, we demonstrate that in order to capture accurately the effect of mechanotransduction mechanisms on tissue construct growth, spatial effects in at least two dimensions must be included due to the inherent spatial variation of mechanical stimuli relevant to perfusion bioreactors, most notably, fluid shear stress, a feature not captured in the long-wavelength limit.

Study on the Mechanics State of Concrete under Penetration and the Deceleration of Projectile

2011 ◽  
Vol 413 ◽  
pp. 1-6
Author(s):  
Tao Deng ◽  
Tao Ge
Keyword(s):  
Differential Equation ◽  
Experimental Data ◽  
Velocity Field ◽  
Boundary Conditions ◽  
Wave Front ◽  
Mass Conservation ◽  
Conservation Of Mass ◽  
Conservation Of Momentum ◽  
Coulomb Criterion ◽  
The Continuum

The concrete under penetration has a restricted deform and is in intrinsic friction state. By used conservation of mass, conservation of momentum and velocity expression on wave front, the velocity field of the pulverized zone near penetration is obtained. The boundary conditions and the continuum conditions were also considered for the obtained velocity field. The pulverized concrete near the penetration is described by Mohr-Coulomb criterion. Based on the conclusions above, cavity expand theory and the expand equation of inconsistent deform, the resistance of projectile is gained in intrinsic friction state. In according to movement differential equation, the deceleration model is built which can describe different phases for penetration and perforation. The decelerations of different size projectiles with different velocity were calculated and were contrasted with experimental data.

Predictable Model for Characteristics of One-Dimensional Solid-Gas-Liquid Three-Phase Mixtures Flow Along a Vertical Pipeline With an Abrupt Enlargement in Diameter

1999 ◽  
Vol 121 (2) ◽  
pp. 330-342 ◽  
Author(s):  
Natsuo Hatta ◽  
Masaaki Omodaka ◽  
Fumitaka Nakajima ◽  
Takahiro Takatsu ◽  
Hitoshi Fujimoto ◽  
...  
Keyword(s):  
Gas Flow ◽  
Sudden Change ◽  
Flow Characteristics ◽  
Point Of View ◽  
Solid Particles ◽  
Governing Equations ◽  
One Dimensional ◽  
Three Phase ◽  
Experimental Values ◽  
The One

This paper treats the numerical analysis of the rising process of a solid-gas-liquid three-phase mixture along a vertical pipeline with an abrupt enlargement in diameter. The system of governing equations used is based upon the one-dimensional multifluid model and the transitions of gas flow pattern are taken into account in the system of governing equations. For the case of a sudden enlargement in diameter in a coaxial pipeline, the procedure of the numerical calculation to obtain the flow characteristics in the pipeline section after a sudden change in diameter has been established here. Furthermore, in order to confirm the validity of the present theoretical model by the comparison between the calculated and experimental values, the experiments have been made using four kinds of lifting pipes, including the straight one. Thereby, it has been found that the numerical model proposed here gives good fit to the prediction of the flow rates of lifted water and solid particles against that of air supplied for the case of a sudden change in diameter. In addition, the flowing process for each phase has been investigated from a photographic point of view. As a result, we found that the moving process of the solid particles depends strongly upon the volumetric flux of gas-phase as well as the submergence ratio.

scholarly journals Mathematical Simulation of the Behavior of a Cumulative Jet with Inert and Reactive Components

2019 ◽  
pp. 19-34
Author(s):  
A.V. Babkin ◽  
A.A. Medeltsev ◽  
F.S. Zagryadskiy ◽  
M.A. Krutskevich
Keyword(s):  
Extension Problem ◽  
Composite Liner ◽  
Three Phase ◽  
Phase Medium ◽  
Chemically Reacting Systems ◽  
Reactive Additives ◽  
Chemically Reacting ◽  
Characteristic Features ◽  
Reacting Systems ◽  
Multi Phase

The purpose of the research was to investigate the processes associated with the free flight of a cumulative jet formed from a composite liner of a cumulative charge. We mathematically simulated the process from the perspective of continuum mechanics using numerical methods for solving the corresponding equations. The cumulative jet was simulated in the quasi-two-dimensional nonstationary approximation as a high-gradient cylindrical compressible elastoplastic or liquid rod. The material of the jet was considered as a one-speed three-phase medium. The compressibility of each phase was described by its inherent barotropic dependence of pressure on density. The resulting pressure in a multiphase mixture of particles of the cumulative jet, considered as a composite material, was determined on the basis of the additivity condition of the volumes. When assessing the composition of the jet, we determined the initial concentrations of the components using a software package for thermo-dynamic simulation of chemically reacting systems. To find the numerical solution of the multi-phase, i.e., composite, jet extension problem, we used a finite-difference method based on Neumann --- Richtmyer scheme. The numerical analysis of the process under study was carried out on the example of a laboratory cumulative charge. Within the research, we found the characteristic features and possible variations in the behavior of the jet depending on the presence of the components of the composite liner, i.e., matrix, inert and reactive additives, and their properties. Finally, we estimated the change in the penetrating power of the jet compared to the reference variant of the cumulative liner of a homogeneous single-phase monolithic material.

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