scholarly journals A computer simulation of solidification taking into account the movement of the liquid phase

2018 ◽  
Vol 157 ◽  
pp. 02008 ◽  
Author(s):  
Robert Dyja ◽  
Elżbieta Gawrońska ◽  
Andrzej Grosser
Keyword(s):  
Liquid Phase ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Solidification Process ◽  
Boussinesq Approximation ◽  
Navier Stokes ◽  
The Finite Element Method ◽  
Navier Stokes Equation ◽  
Solidification Simulation ◽  
Heat Released

In the paper, we present the results of solidification simulation taking into account the movement of the liquid phase. The results are obtained from an author software which is implemented on the base of a stabilized finite elements method (Petrov-Galerkin formulation). Using that formulation the Navier-Stokes equation is solved together with the convection term (Boussinesq approximation). The Finite Element Method (FEM) formulation is responsible for solidification, approximating the solution of the heat conduction equation (with the internal heat source term responsible for the heat released during the phase transition). The movement of the liquid phase in a solidifying cast that is caused by convection can significantly affect the process of heat transfer from the casting to the mold, which in turn has an influence on the temperature distribution in the cast and may cause a change in the location of the defects. The presented results allow to assess under what conditions the effect of convection on the solidification process is significant.

scholarly journals NUMERICAL CALCULATION OF VELOCITY FIELDS FOR VISCO-ELASTIC MATERIALS IN CYLINDRICAL CHANNELS

2019 ◽  
pp. 19-28
Author(s):  
Ekaterina Valer'evna Fomenko ◽  
Albert Hamed-Harisovich Nugmanov ◽  
Thi Sen Nguyen ◽  
Aleksanyan Igor Yuryevich Aleksanyan
Keyword(s):  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Stokes Equations ◽  
Radiation Power ◽  
Wheat Gluten ◽  
Internal Heat ◽  
Velocity Fields ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Suggested Approach

The article touches upon the application of the numerical finite difference method for solving Navier-Stokes equation in case of one-dimensional problem of passing a cooled viscoelastic material inside circular nozzles. There have been analyzed the specific features of using the method and presented the results of its application. The object of study was not chosen at random, because viscous properties of raw gluten are variable and depend on the temperature, chemical composition and properties of the feedstock. Working not properly with the object of research (phenomenon, process), but with its model helps to characterize its properties and behavior in various situations relatively quickly and without significant costs. The need to identify patterns of internal heat and mass transfer, which is based on studying the kinetics of the process, is obvious for physic-mathematical modeling of heat and mass transfer processes of wheat gluten granulation, in particular, analyzing the mechanism of moisture removal during its drying under radiation power supply. The results of the conducted research are consistent with the available data on the subject, and the suggested approach to solving the problem of choosing rational hydrodynamic regimes has been applied due to the difficulty of experimental determining the velocity fields and problematic analyzing the system of hydrodynamic differential Navier-Stokes equations with variable proportionality ratios.

scholarly journals Closed-Form Non-Stationary Solutionsfor Thermo and Chemovibrational Viscous Flows

Fluids ◽  
2019 ◽  
Vol 4 (3) ◽  
pp. 175 ◽  
Author(s):  
Dmitry Bratsun ◽  
Vladimir Vyatkin
Keyword(s):  
Viscous Flow ◽  
Closed Form ◽  
General Procedure ◽  
Fluid Velocity ◽  
Fluid Motion ◽  
Boussinesq Approximation ◽  
Navier Stokes ◽  
Chemical Transformations ◽  
Navier Stokes Equation ◽  
Harmonic Vibrations

A class of closed-form exact solutions for the Navier–Stokes equation written in the Boussinesq approximation is discussed. Solutions describe the motion of a non-homogeneous reacting fluid subjected to harmonic vibrations of low or finite frequency. Inhomogeneity of the medium arises due to the transversal density gradient which appears as a result of the exothermicity and chemical transformations due to a reaction. Ultimately, the physical mechanism of fluid motion is the unequal effect of a variable inertial field on laminar sublayers of different densities. We derive the solutions for several problems for thermo- and chemovibrational convections including the viscous flow of heat-generating fluid either in a plain layer or in a closed pipe and the viscous flow of fluid reacting according to a first-order chemical scheme under harmonic vibrations. Closed-form analytical expressions for fluid velocity, pressure, temperature, and reagent concentration are derived for each case. A general procedure to derive the exact solution is discussed.

scholarly journals Implementasi Metode Elemen Hingga Untuk Persoalan Aliran Air Pada Jaringan Pipa

2018 ◽  
Vol 1 (1) ◽  
Author(s):  
Cici Hayani ◽  
Tulus Tulus ◽  
Sawaluddin Sawaluddin
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Water Flow ◽  
Linear Interpolation ◽  
Navier Stokes ◽  
The Finite Element Method ◽  
Navier Stokes Equation ◽  
Water Flow Velocity ◽  
Boundary Field ◽  
Element Method

Pada zat cair yang mengalir di dalam bidang batas (contohnya pipa) akan terjadi tegangan geser dan gradien kecepatan pada seluruh medan aliran karena adanya kekentalan (viskositas). Penelitian ini bertujuan untuk melihat persoalan aliran air pada jaringan pipa yang diselesaikan dengan mengimplementasikan metode elemen hingga pada persamaan Navier-Stokes yang merupakan persamaan diferensial dasar yang menggambarkan aliran dari fluida Newtonian tak mampu-mampat. Dalam metode elemen hingga, medan aliran dipecah menjadi sekumpulan elemen-elemen fluida kecil (diskritisasi domain). Dalam penelitian ini peneliti menggambarkan aliran air pada bidang dua-dimensi (2D), kemudian dipilih fungsi interpolasi linier untuk elemen 2D, dan menurunkan elemen matriks dan vektor dengan metode Galerkin untuk mendapatkan persamaan Global. Hasil dari penelitian dengan bantuan komputer, memperlihatkan distribusi tekanan dan kecepatan aliran air untuk beberapa variasi bentuk pipa, yaitu pipa I dan pipa T, masing-masing juga dengan variasi posisi inlet/oulet. Hasil simulasi dengan COMSOL menunjukkan, bahwa terdapat hubungan antara tekanan dan kecepatan aliran air, kehilangan tekanan pada salah satu cabang pipa menyebabkan kecepatan aliran air menjadi tidak merata.   In liquid that flows inside the boundary field (e.g., pipe) there will be shear stress and velocity gradient in all flow fields due to viscosity. This study aimed to look at the problem of water flow in the pipe network solved by implementing the finite element method in the Navier-Stokes equation. This equation is a basic differential equation that describes the flow of incompressible Newtonian fluid. In the finite element method, the flow field is broken down into a set of small fluid elements (domain discretization). In this study the researcher described the flow of water in two-dimensional (2D) fields; then linear interpolation functions for 2D elements were selected and lowered the matrix and vector elements with the Galerkin method to obtain the Global equation. The results of the study with the help of computers showed the distribution of pressure and velocity of water flow for several variations in the shape of the pipe, namely pipe I and pipe T, each also with variations in position of inlet/outlet. The simulation with COMSOL showed that there was a relationship between the pressure and velocity of water flow, and the pressure loss on one of the pipe branches caused the water flow velocity to be uneven. 

INFLUENCE OF ELECTROLYTE COMPOSITION AND OVERHEATING ON THE SIDELEDGE IN THE ALUMINUM CELL

2018 ◽  
pp. 24-30 ◽  
Author(s):  
V. V. Stakhanov ◽  
A. A. Redkin ◽  
Yu. P. Zaikov ◽  
A. E. Galashev
Keyword(s):  
Boussinesq Approximation ◽  
Navier Stokes ◽  
Transfer Coefficients ◽  
Navier Stokes Equation ◽  
Cryolite Ratio ◽  
Heat Transfer Coefficients ◽  
Aluminum Smelting ◽  
Block Wall ◽  
The Difference ◽  
Aluminum Cell

The paper presents a theoretical study conducted to investigate the effect that the chemical composition of electrolyte and its overheating have on the size of sideledge formed in an aluminum smelting bath. Three electrolyte compositions were chosen: (1) sodium cryolite with the cryolite ratio CR = 2,7; (2) cryolite CR = 2,7 + 5 wt.% CaF2; (3) cryolite CR = 2,7 + 5 wt.% CaF2 + 5 wt.% Al2О3. The electrolyte liquidus overheating temperatures were 5, 10, 15 and 20 °C. Calculations were performed using the finite element method. A simplified design of an aluminum cell was used with a prebaked anode. The temperature field was calculated using a mathematical model based on the Boussinesq approximation, which contains the Navier–Stokes equation as well as thermal conductivity and incompressibility equations. The key role of electrolyte overheating in sideledge formation was established. The resulting sideledge profile depends on the heat transfer coefficients and thermophysical properties of materials. The smallest sideledge thickness with the same electrolyte overheating was observed in cryolite composition 3, and the profiles of the formed sideledge for samples 1 and 2 were nearly the same. The thickness of the sideledge formed with a 5 degree overheating exceeded 7 cm and the difference in temperature between the sideledge in contact with electrolyte and the side block wall was 20–25 degrees. It was found that the virtually total disappearance of the sideledge occurs at electrolyte liquidus overheating by 20 degrees.

scholarly journals Convective Instability of a Steady Flow in an Annulus Caused by Internal Heat Generation

2020 ◽  
Vol 74 (4) ◽  
pp. 293-298
Author(s):  
Andrei Kolyshkin ◽  
Valentina Koliskina ◽  
Inta Volodko ◽  
Ilmārs Iltins
Keyword(s):  
Linear Stability ◽  
Stokes Equations ◽  
Outer Boundary ◽  
Internal Heat ◽  
Convective Motion ◽  
Boussinesq Approximation ◽  
Base Flow ◽  
Navier Stokes ◽  
Heat Sources ◽  
Vertical Annulus

AbstractLinear stability of convective motion in a tall vertical annulus was analysed in the paper. The base flow was generated by a non-uniform distribution of heat sources in the radial direction. The base flow velocity and temperature were obtained analytically solving the system of Navier-Stokes equations under the Boussinesq approximation. The linear stability problem was solved for axi-symmetric and asymmetric perturbations by a collocation method based on the Chebyshev polynomials. Numerical results showed that there were three destabilising factors: (1) increase of the gap between the cylinders, (2) increase of the density of internal heat sources towards to the outer boundary of the annulus and (3) increase of the Prandtl number.

Double–diffusive convection in a porous medium with a concentration based internal heat source

2005 ◽  
Vol 461 (2054) ◽  
pp. 561-574 ◽  
Author(s):  
Antony A. Hill
Keyword(s):  
Heat Source ◽  
Linear Theory ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Boussinesq Approximation ◽  
Double Diffusive Convection ◽  
Diffusive Convection ◽  
Saturated Porous Layer ◽  
Linear And Nonlinear ◽  
Double Diffusive

Linear and nonlinear stability analyses of double–diffusive convection in a fluid–saturated porous layer with a concentration based internal heat source are studied. Darcy's law and the Boussinesq approximation are employed, with the equation of state taken to be linear with respect to temperature and concentration. Both the numerical and analytical analysis for the linear theory strongly suggest the presence of a critical value γ c , where γ is essentially a measure of the internal heat source, for which no oscillatory convection occurs when γ c ⩽ γ . This, in the present literature, appears to be an unobserved phenomenon. A nonlinear energy stability analysis demonstrates more comparable linear and nonlinear thresholds when the linear theory predicts the onset of fully stationary convection. However, irrespective of the γ value, the agreement of the thresholds does deteriorate as the solute Rayleigh number R c increases.

Wind turbine aerodynamics modeling by meshless method

2020 ◽  
pp. 0309524X2092117
Author(s):  
Asmae Mnebhi-Loudyi ◽  
El Mostapha Boudi ◽  
Driss Ouazar
Keyword(s):  
Finite Difference ◽  
Wind Turbine ◽  
Meshless Method ◽  
Finite Difference Methods ◽  
Navier Stokes ◽  
The Finite Element Method ◽  
Navier Stokes Equation ◽  
Wind Turbine Aerodynamics ◽  
Radial Basis ◽  
The One

This article presents wind turbine aerodynamics modeling by a meshless method. This method does not require meshing but it requires only a set of nodes. The radial basis function of finite difference method is a local meshless method, which is the coupling between the radial basis functions and the finite difference methods. When the number of nodes increases, the system might become ill-conditioned. Therefore, the local meshless method is adopted. It must be noted that Navier–Stokes equation is the one used for modeling purposes. Numerical results were compared to the meshless method and the finite element method results in terms of both velocity and pressure. Close agreements are observed.

Natural Convection in a Differentially Heated Cavity Using Splitting Method

2013 ◽  
Vol 388 ◽  
pp. 156-160
Author(s):  
Selamat Ubaidullah ◽  
Kahar Osman
Keyword(s):  
Natural Convection ◽  
Numerical Solutions ◽  
Splitting Method ◽  
Fluid Flows ◽  
Boussinesq Approximation ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Thermally Driven ◽  
Rayleigh Numbers ◽  
Good Agreement

The solution of thermally-driven flow of Navier-Stokes equation, in Boussinesq approximation, is presented. The results are obtained using splitting method and in good agreement with available benchmark numerical solutions. The convection terms are explicitly integrated using 3-step Range-Kutta scheme. Buoyancy-driven fluid flows data in a differentially heated cavity for low Rayleigh numbers (R=1000, R=10000 and R=100000) are presented.

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