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.

A PRIORI PRESSURE FIELD CONSTRUCTION ITERATIVE METHOD FOR THE SOLUTION OF THE STEADY-STATE NAVIER–STOKES EQUATIONS USING GENERAL FINITE-VOLUME CO-LOCATED GRIDS

2007 ◽  
Vol 04 (04) ◽  
pp. 567-601
Author(s):  
JOSE A. LAMAS
Keyword(s):  
Iterative Method ◽  
Pressure Field ◽  
Stokes Equations ◽  
A Priori ◽  
Mass Conservation ◽  
Momentum Conservation ◽  
Navier Stokes ◽  
Pressure Equation ◽  
Navier Stokes Equations ◽  
Correction Equations

An iterative method has been developed for the solution of the Navier–Stokes equations and implemented using finite volumes with co-located variable arrangement. A pressure equation is obtained combining algebraic momentum and mass conservation equations resulting in a self-consistent set of equations. An iterative procedure solves the pressure equation consistently with mass conservation and then updates velocities based on momentum equations without introducing velocity or pressure correction equations. The process is repeated until velocities satisfy both mass and momentum conservation. Tests demonstrate a priori pressure field solution consistent with mass conservation, and solution of hydrostatic problems in one iteration.

Modeling and Simulation of Resin Filling and Cure Processes in Molds Partially Filled with Porous Media

2007 ◽  
Vol 553 ◽  
pp. 33-38
Author(s):  
Vítor A.F. Costa
Keyword(s):  
Fluid Flow ◽  
Stokes Equations ◽  
Volume Fraction ◽  
Control Volume ◽  
Conservation Equation ◽  
Navier Stokes ◽  
Clear Fluid ◽  
Navier Stokes Equations ◽  
Energy Conservation Equation ◽  
Real Process

The complete and simultaneous simulation of the overall filling and curing processes is presented. Fluid flow in the porous medium is described by the Brinkman-Forchheimer flow model, and fluid flow in the clear fluid domain is described by the Navier-Stokes equations. The flow front is captured using the volume fraction concept and a compressive convective scheme. Energy conservation equation and resin conversion equation give the equations to obtain the temperature and degree of cure, respectively. The physical model is solved using a control volume based finite element method. A limited set of results is presented, showing the usefulness of the information obtained from the complete and simultaneous simulation of the overall real process.

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.

scholarly journals Experimental validation of wind energy estimation

2020 ◽  
Vol 24 (6 Part A) ◽  
pp. 3795-3806
Author(s):  
Predrag Zivkovic ◽  
Mladen Tomic ◽  
Vukman Bakic
Keyword(s):  
Wind Speed ◽  
Linear Model ◽  
Linear Models ◽  
Stokes Equations ◽  
Momentum Conservation ◽  
Electricity Production ◽  
Navier Stokes ◽  
Energy Estimation ◽  
Navier Stokes Equations ◽  
Non Linear

Wind power assessment in complex terrain is a very demanding task. Modeling wind conditions with standard linear models does not sufficiently reproduce wind conditions in complex terrains, especially on leeward sides of terrain slopes, primarily due to the vorticity. A more complex non-linear model, based on Reynolds averaged Navier-Stokes equations has been used. Turbulence was modeled by modified two-equations k-? model for neutral atmospheric boundary-layer conditions, written in general curvelinear non-orthogonal co-ordinate system. The full set of mass and momentum conservation equations as well as turbulence model equations are numerically solved, using the as CFD technique. A comparison of the application of linear model and non-linear model is presented. Considerable discrepancies of estimated wind speed have been obtained using linear and non-linear models. Statistics of annual electricity production vary up to 30% of the model site. Even anemometer measurements directly at a wind turbine?s site do not necessarily deliver the results needed for prediction calculations, as extrapolations of wind speed to hub height is tricky. The results of the simulation are compared by means of the turbine type, quality and quantity of the wind data and capacity factor. Finally, the comparison of the estimated results with the measured data at 10, 30, and 50 m is shown.

Influence of Vertical Vibration on Surface Velocity of a Liquid Bridge

2014 ◽  
Vol 580-583 ◽  
pp. 2890-2893
Author(s):  
Ru Quan Liang ◽  
Zhi Hui Zhang ◽  
Tai Yin Gao ◽  
Fu Sheng Yan
Keyword(s):  
Liquid Bridge ◽  
Stokes Equations ◽  
Silicone Oil ◽  
Conservation Equation ◽  
Vertical Vibration ◽  
Surface Velocity ◽  
Staggered Grid ◽  
Navier Stokes ◽  
Two Phase ◽  
Energy Conservation Equation

In this paper, the vertical vibration influence on the surface velocity of a 5cSt silicone oil liquid bridge has been investigated numerically. The Navier-Stokes equations coupled with the energy conservation equation are solved on a staggered grid, and the two-phase surface is captured by using the mass conserving level set method. The present results indicate that the axial and radial surface velocities of the liquid bridge are suppressed by the external vertical vibration.

Extension of the Curie principle and constitutive relations for fluids with antisymmetric stress

1972 ◽  
Vol 72 (2) ◽  
pp. 243-251
Author(s):  
Rosa M. Morris ◽  
W. G. Price
Keyword(s):  
Stokes Equations ◽  
Constitutive Relations ◽  
Navier Stokes ◽  
Spin Motion ◽  
Navier Stokes Equations ◽  
Curie Principle ◽  
Antisymmetric Stress ◽  
Material Points ◽  
Vector Sum ◽  
Micro Structures

In recent years several papers [Grad(9), Condiff and Dahler(5), Baronowski and Romatowski(2), Eringen(8), Allen and de Silva(i)] have been written dealing with the possibility of antisymmetric stress in a fluid and its relationship with the internal micro-structure of the fluid. In the classical fluid dynamics of the Navier–Stokes equations, the molecules of the fluid element are treated as material points devoid of any internal spin motion and the only type of angular motion that the macroscopic elements of the fluid possess is the usual vorticity ½ curl v, the velocity of the fluid being v. In the case of fluids whose molecules are not regarded as material points, but are treated as micro-structures having internal spin, the total angular velocity of a macroscopic volume element will be equal to the vector sum of spins of the micro-structures and the part due to the vorticity.

Numerical Simulation of Transient Three-Dimensional Temperature and Kerf Formation in Laser Fusion Cutting

2015 ◽  
Vol 137 (11) ◽  
Author(s):  
Karim Kheloufi ◽  
El Hachemi Amara ◽  
Ahmed Benzaoui
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Front Surface ◽  
Conservation Equation ◽  
Temperature Fields ◽  
Navier Stokes ◽  
Laser Fusion ◽  
Current Case ◽  
Energy Conservation Equation ◽  
Laser Fusion Cutting

In the present study, a three-dimensional transient numerical model was developed to study the temperature field and cutting kerf shape during laser fusion cutting. The finite volume model has been constructed, based on the Navier–Stokes equations and energy conservation equation for the description of momentum and heat transport phenomena, and the volume of fluid (VOF) method for free surface tracking. The Fresnel absorption model is used to handle the absorption of the incident wave by the surface of the liquid metal, and the enthalpy-porosity technique is employed to account for the latent heat during melting and solidification of the material. To model the physical phenomena occurring at the liquid film/gas interface, including momentum/heat transfer, a new approach is proposed which consists of treating friction force, pressure force applied by the gas jet, and the heat absorbed by the cutting front surface as source terms incorporated into the governing equations. All these physics are coupled and solved simultaneously in fluent CFD®. The main objective of using a transient phase change model in the current case is to simulate the dynamics and geometry of a growing laser-cutting generated kerf until it becomes fully developed. The model is used to investigate the effect of some process parameters on temperature fields and the formed kerf geometry.

Sign in / Sign up

Export Citation Format

Share Document