Abstract
The paper is devoted to construction of a numerical model and computations of continuously stratified fluid flows in field of external mass forces accounting for dissipative factors, viscosity and diffusion. Mathematical model is based on the fundamental set of differential equations of inhomogeneous multicomponent fluid mechanics. Solution of the problem is constructed numerically in the completenon-linear formulation using finite volume method in frame of the open source package OpenFOAM. To take in to account the stratification and diffusion effects a new own solver, stratifiedFoam, was developed and tested using the standard and extended libraries of the package. A particular attention is focused at construction of a high quality computational grid which satisfies basic requirements for resolution of all the microscales of the problem in high-gradient regions of the flow. The calculations performed in parallel regime on computational facilities of the web-laboratory UniHUB demonstrated a pretty high efficiency of the proposed numerical model and a good agreement with the experimental data.
Highlights
The paper is devoted to construction of a numerical model and computations of continuously stratified fluid flows in field of external mass forces accounting for dissipative factors, viscosity and diffusion
Mathematical model is based on the fundamental set of differential equations of inhomogeneous multicomponent fluid mechanics
The calculations performed in parallel regime on computational facilities of the web-laboratory UniHUB demonstrated a pretty high efficiency of the proposed numerical model and a good agreement with the experimental data
Summary
В качестве базовой математической модели для изучаемых физических процессов выбрана система дифференциальных балансных уравнений механики неоднородных многокомпонентных жидкостей в приближении Буссинеска и пренебрежении эффектами сжимаемости, поскольку скорости изучаемых течений малы по сравнению со скоростью звука [1, 10]. Она включает в себяуравнение состояния S y , неразрывности Даламбера, баланса вещества Фикаи импульса Навье-Стокса: divv 0, 00 exp y s ,. Где s – возмущение солености (стратифицирующей примеси), включающее коэффициент солевого сжатия, v vx ,vy – скорость жидкости, где ось 0y направлена вертикально вверх, P – давление за вычетом гидростатического,. – коэффициент кинематической вязкости, ks – коэффициент диффузии соли, t – время, g– ускорение свободного падения, и – операторы Гамильтона и. Лапласа, d ln 0 dy 1 – длина, N g – частота и Tb 2 N – период плавучести
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