Analysis of Transient Pressures in Bubbly, Homogeneous, Gas-Liquid Mixtures

1990 ◽  
Vol 112 (2) ◽  
pp. 225-231 ◽  
Author(s):  
M. Hanif Chaudhry ◽  
S. Murty Bhallamudi ◽  
C. Samuel Martin ◽  
M. Naghash
Keyword(s):  
Fluid Flow ◽  
Finite Difference ◽  
Liquid Mixture ◽  
Nonlinear Partial Differential Equations ◽  
Transient State ◽  
Liquid Mixtures ◽  
Finite Difference Schemes ◽  
Piping System ◽  
Governing Equations ◽  
Explicit Finite Difference

Flow of a gas-liquid mixture in a piping system may be treated as a pseudo-fluid flow if the mixture is homogeneous and the void fraction is small. The governing equations for such flows are a set of nonlinear partial differential equations with pressure dependent coefficients. Shocks may be produced during transient state conditions. For numerical integration of these equations, two second-order explicit finite-difference schemes are introduced. To verify validity of the computed results, they are compared with the experimental results.

Second-Order Accurate Explicit Finite-Difference Schemes for Waterhammer Analysis

1985 ◽  
Vol 107 (4) ◽  
pp. 523-529 ◽  
Author(s):  
M. H. Chaudhry ◽  
M. Y. Hussaini
Keyword(s):  
Finite Difference ◽  
Computer Time ◽  
Second Order ◽  
Difference Schemes ◽  
Hyperbolic Partial Differential Equations ◽  
Finite Difference Schemes ◽  
Piping System ◽  
Characteristic Method ◽  
First Order ◽  
Explicit Finite Difference

Three second-order accurate explicit finite-difference schemes—MacCormack’s method, Lambda scheme and Gabutti scheme—are introduced to solve the quasilinear, hyperbolic partial differential equations describing waterhammer phenomenon in closed conduits. The details of these schemes and the treatment of boundary conditions are presented. The results computed by using these schemes for a simple frictionless piping system are compared with the exact solution. It is shown that for the same accuracy, second-order schemes require fewer computational nodes and less computer time as compared to those required by the first-order characteristic method.

Thermal Modeling of Unlooped and Looped Pulsating Heat Pipes

2001 ◽  
Vol 123 (6) ◽  
pp. 1159-1172 ◽  
Author(s):  
Mohammad B. Shafii ◽  
Amir Faghri ◽  
Yuwen Zhang
Keyword(s):  
Heat Transfer ◽  
Finite Difference ◽  
Heat Pipes ◽  
Analytical Models ◽  
Charge Ratio ◽  
Sensible Heat ◽  
Governing Equations ◽  
Heating Wall ◽  
Heat Mode ◽  
Explicit Finite Difference

Analytical models for both unlooped and looped Pulsating Heat Pipes (PHPs) with multiple liquid slugs and vapor plugs are presented in this study. The governing equations are solved using an explicit finite difference scheme to predict the behavior of vapor plugs and liquid slugs. The results show that the effect of gravity on the performance of top heat mode unlooped PHP is insignificant. The effects of diameter, charge ratio, and heating wall temperature on the performance of looped and unlooped PHPs are also investigated. The results also show that heat transfer in both looped and unlooped PHPs is due mainly to the exchange of sensible heat.

scholarly journals Analysis and optimization of higher order explicit finite-difference schemes for the advection stage implementation in the lattice Boltzmann method

2017 ◽  
pp. 227-246
Author(s):  
Г.В. Кривовичев ◽  
Е.С. Марнопольская
Keyword(s):  
Finite Difference ◽  
Lattice Boltzmann ◽  
Kinetic Equations ◽  
Difference Schemes ◽  
Numerical Dispersion ◽  
Finite Difference Schemes ◽  
Maximum Function ◽  
Driven Cavity ◽  
Explicit Finite Difference ◽  
The Stability

Статья посвящена анализу и оптимизации явных разностных схем для решения уравнений переноса, возникающих на этапе адвекции метода расщепления по физическим процессам. Метод может применяться как для решеточных уравнений Больцмана, так и при решении кинетических уравнений общего вида. Рассматриваются схемы второго-четвертого порядков аппроксимации. Для уменьшения эффектов численных диссипации и дисперсии используются схемы с параметром. С использованием метода фон Неймана и полиномиальной аппроксимации границ областей устойчивости получены условия устойчивости схем в виде неравенств на значения параметра Куранта. Оптимальные значения параметра для регулирования диссипативных и дисперсионных эффектов предлагается находить посредством решения задач минимизации функций максимума. Схемы с оптимальными значениями параметра применяются при решении тестовых задач - для одномерного и двумерного уравнений переноса, а также при применении метода расщепления к решению задачи о течении в каверне с подвижной крышкой. This paper is devoted to the analysis and optimization of explicit finite-difference schemes for solving the transport equations arising at the advection stage in the method of splitting into physical processes. The method can be applied to the lattice Boltzmann equations and to the kinetic equations of general type. The second-to-fourth order schemes are considered. In order to minimize the effect of numerical dispersion and dissipation, the parametric schemes are used. The Neumann method and the polynomial approximation of the boundaries of stability domains are employed to obtain the stability conditions in the form of inequalities imposed on the Courant parameter. The optimal values of the parameter used to control the dissipation and dispersion effects are found by minimizing the maximum function. The schemes with optimal parameters are applied for the numerical solution of 1D and 2D advection equations and for the problem of lid-driven cavity flow.

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