Steepened wave in two-phase Chaplygin flows comprising a source term

2022 ◽  
Vol 413 ◽  
pp. 126656
Author(s):  
Sarswati Shah ◽  
Randheer Singh ◽  
Jasobanta Jena
Keyword(s):  
Source Term ◽  
Two Phase

Flux Scheme: A Method for General Non-Conservative Two-Fluid Systems

2003 ◽  
Author(s):  
Anela Kumbaro
Keyword(s):  
Numerical Modeling ◽  
Source Term ◽  
Term Treatment ◽  
Two Phase ◽  
Advection Scheme ◽  
Fluid Systems ◽  
Boundary States ◽  
Upwind Discretization ◽  
Improved Accuracy ◽  
Two Fluid

This paper is concerned with numerical modeling issues arising when using a flux scheme for the approximation of two-phase flows. The paper puts emphasis on a general treatment of boundary conditions and reports on the interaction between an upwind discretization of the source terms and the boundary states. An upwind source term treatment consistent with the advection scheme results on an improved accuracy. Numerical results are provided to illustrate the method.

scholarly journals The space-time conservation element and solution element scheme for simulating two-phase flow in pipes

2019 ◽  
Vol 11 (12) ◽  
pp. 168781401989835 ◽  
Author(s):  
Rana Danish Aslam ◽  
Ashiq Ali ◽  
Asad Rehman ◽  
Shamsul Qamar
Keyword(s):  
Source Term ◽  
Two Phase Flow ◽  
Mass Conservation ◽  
Space Time ◽  
Upwind Scheme ◽  
Phase Flow ◽  
Two Phase ◽  
Conservation Equations ◽  
Element Scheme ◽  
Solution Element

In this article, the space-time conservation element and solution element scheme is extended to simulate the unsteady compressible two-phase flow in pipes. The model is non-conservative and the governing equations consist of three equations, namely, two mass conservation equations for each phase and one mixture-momentum equation. In the third equation, the non-conservative source term appears, which describes the sum of gravitational and frictional forces. The presence of source term and two mass conservation equations in considered model offers difficulties in developing the accurate and robust numerical techniques. The suggested space-time conservation element and solution element numerical scheme resolves the volume-contact discontinuities efficiently. Furthermore, the modified central upwind scheme is also extended to solve the same two-phase flow model. The number of test problems is considered, and the results obtained by space-time conservation element and solution element scheme are compared with the solutions of modified central upwind scheme. The numerical results show better performance of the space-time conservation element and solution element method as compare to the modified central upwind scheme.

Numerical Simulation of Heat Transfer outside the Tube of the Evaporative Air Cooler

2014 ◽  
Vol 672-674 ◽  
pp. 558-561
Author(s):  
Hong Jiao Liu ◽  
Liang Cai Chen ◽  
Jian Qi Zhang
Keyword(s):  
Heat Transfer ◽  
Wind Speed ◽  
Source Term ◽  
Environmental Temperature ◽  
Water Film ◽  
Phase Flow ◽  
Two Phase ◽  
Wall Distance ◽  
Spray Density ◽  
Air Cooler

By considering the momentum source term of surface tension and the source term of heat transfer in gas-liquid two phase flow, a computational model based on the VOF was established to discuss the rules of the temperature outside tube in the evaporative air cooler.The result shows that under a wind velocity and spray density, the temperature of water near the wall dropped sharply at first, with wall distance increasing, finally to environmental temperature, and with annular angle increase, the temperature of water film increases. And the higher the wind speed, the higher the water film temperature, but the changes of wind speed has little influence on the temperature within less than 60 º angle. The smaller the spray density, the higher water film temperature.

scholarly journals Improved ISPH method for natural convection from heated T-open pipe of Al2O3-water nanofluid in a cavity: Buongiorno’s two-phase model

2021 ◽  
pp. 148-148
Author(s):  
Abdelraheem Aly ◽  
Sameh Ahmed
Keyword(s):  
Natural Convection ◽  
Source Term ◽  
Volume Fraction ◽  
Lagrangian Description ◽  
Cool Temperature ◽  
Two Phase ◽  
Pressure Poisson Equation ◽  
Buongiorno’S Model ◽  
Relaxation Coefficient ◽  
Open Pipe

The unsteady natural convection of Al2O3-water nanofluid form heated open T-pipe inside a cavity has been investigated by ISPH method using non-homogenous two-phase Buongiorno's model. Different lengths and heights of T-pipe shape are considered. The side walls of the cavity are kept at cool temperature Tc and the horizontal walls are thermally insulated. The Lagrangian description of the controlling governing equations is discretized and solved using improved ISPH method. In this study, ISPH method is improved using kernel renormalization function for boundary treatment plus modification in the source term of pressure Poisson equation (PPE). The source term of PPE contains the velocity divergence plus density invariance multiply by relaxation coefficient. The calculations are performed for variable lengths of T-open pipe (0.2 ? Lb ? 0.6variable widths of T-open pipe (0.02 ?Wb?0.16), (0.02? Wt? 0.16) and variable concentration of nanoparticles volume fraction (1% ?.?avg ? 10). The obtained results showed that the maximum values of the stream function are reduced by 80.8% when ?avg is increased from 1% to 10%. Additionally, as lengths and widths of the T-pipe are raised, the average Nusselt numbers at the vertical walls are enhanced.

scholarly journals Existence and uniqueness of generalized solutions to hyperbolic systems with linear fluxes and stiff sources

2021 ◽  
Vol 18 (03) ◽  
pp. 653-700
Author(s):  
Teddy Pichard ◽  
Nina Aguillon ◽  
Bruno Després ◽  
Edwige Godlewski ◽  
Michael Ndjinga
Keyword(s):  
Initial Data ◽  
Existence And Uniqueness ◽  
Source Term ◽  
Hyperbolic Systems ◽  
Sufficient Conditions ◽  
Boiling Curve ◽  
Generalized Solutions ◽  
Two Phase ◽  
Numerical Illustration ◽  
Systems Of Balance Laws

Motivated by the modeling of boiling two-phase flows, we study systems of balance laws with a source term defined as a discontinuous function of the unknown. Due to this discontinuous source term, the classical theory of partial differential equations (PDEs) is not sufficient here. Restricting to a simpler system with linear fluxes, a notion of generalized solution is developed. An important point in the construction of a solution is that the curve along which the source jumps, which we call the boiling curve, must never be tangent to the characteristics. This leads to exhibit sufficient conditions which ensure the existence and uniqueness of a solution in two different situations: first when the initial data is smooth and such that the boiling curve is either overcharacteristic or subcharacteristic; then with discontinuous initial data in the case of Riemann problems. A numerical illustration is given in this last case.

Effect of Shock Loading on the Microstructure of Uniloy 326

1974 ◽  
Vol 32 ◽  
pp. 504-505
Author(s):  
K. P. Staudhammer ◽  
L. E. Murr
Keyword(s):  
Grain Size ◽  
Shock Loading ◽  
Current Investigation ◽  
Two Phase ◽  
05 C ◽  
Shock Deformation ◽  
Heat Treated

The effect of shock loading on a variety of steels has been reviewed recently by Leslie. It is generally observed that significant changes in microstructure and microhardness are produced by explosive shock deformation. While the effect of shock loading on austenitic, ferritic, martensitic, and pearlitic structures has been investigated, there have been no systematic studies of the shock-loading of microduplex structures.In the current investigation, the shock-loading response of millrolled and heat-treated Uniloy 326 (thickness 60 mil) having a residual grain size of 1 to 2μ before shock loading was studied. Uniloy 326 is a two phase (microduplex) alloy consisting of 30% austenite (γ) in a ferrite (α) matrix; with the composition.3% Ti, 1% Mn, .6% Si,.05% C, 6% Ni, 26% Cr, balance Fe.

Exsolution and inversion in pigeonite from the Whin Sill, Northern England

1978 ◽  
Vol 36 (1) ◽  
pp. 474-475
Author(s):  
P.P.K. Smith
Keyword(s):  
High Temperature ◽  
Low Temperature ◽  
Homogeneous Nucleation ◽  
Silicate Mineral ◽  
Antiphase Boundaries ◽  
Two Phase ◽  
Primitive Form ◽  
The Core ◽  
Nucleation Mechanisms ◽  
And Inversion

Grains of pigeonite, a calcium-poor silicate mineral of the pyroxene group, from the Whin Sill dolerite have been ion-thinned and examined by TEM. The pigeonite is strongly zoned chemically from the composition Wo8En64FS28 in the core to Wo13En34FS53 at the rim. Two phase transformations have occurred during the cooling of this pigeonite:- exsolution of augite, a more calcic pyroxene, and inversion of the pigeonite from the high- temperature C face-centred form to the low-temperature primitive form, with the formation of antiphase boundaries (APB's). Different sequences of these exsolution and inversion reactions, together with different nucleation mechanisms of the augite, have created three distinct microstructures depending on the position in the grain.In the core of the grains small platelets of augite about 0.02μm thick have farmed parallel to the (001) plane (Fig. 1). These are thought to have exsolved by homogeneous nucleation. Subsequently the inversion of the pigeonite has led to the creation of APB's.

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