Numerical simulation of the viscous incompressible fluid flow and heat transfer in a plane channel with backward-facing step

Фомин, А. А.; Fomina, L.N.

doi:10.20537/vm150212

Vestn. Udmurt. Univ. Mat. Mekh. Komp’yut. Nauki

2015

DOI: 10.20537/vm150212

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Numerical simulation of the viscous incompressible fluid flow and heat transfer in a plane channel with backward-facing step

А. А. Фомин¹,

L.N. Fomina²

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“…But in this case the open outlet border of the channel will approach close to zone of the stream perturbation. And, as is well known, the problem of formulation of conditions at open boundaries is still far from a complete solution.The correction algorithm for solving the incompressible fluid dynamics problems in areas with open borders is proposed in [6]. This algorithm makes it possible to position the open border almost anywhere in the fluid flow with minimal distortions of the problem solution in a narrow border zone.…”

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confidence: 99%

“…The correction algorithm for solving the incompressible fluid dynamics problems in areas with open borders is proposed in [6]. This algorithm makes it possible to position the open border almost anywhere in the fluid flow with minimal distortions of the problem solution in a narrow border zone.…”

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confidence: 99%

“…Herewith two modifications of the technique are used: 1) on the first step of splitting the pressure is taken into account from the previous time layer and implicit difference schemes for the movement equations are used; 2) on the second step of splitting the Neumann problem is formulated for the increment of pressure p , which is equal to a difference of pressure on the current and previous time layers. Details of the technology which allows to construct solution of the problem are presented in [6].…”

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confidence: 99%

“…As a result, all the solutions of the problem were received for this grid step. Also, the increasing of the step length up to l c = 1 has not led to significant differences in the solution [6], so all subsequent calculations have been carried out at the fixed l c = 0.5.…”

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On the solution of fluid flow and heat transfer problem in a 2D channel with backward-facing step

Alexander

Liubov

2017

Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki

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Use of the all-Russian mathematical portal Math-Net.Ru implies that you have read and agreed to these terms of use http://www.mathnet.ru/eng/agreement Download details: IP: 52.36.4.81 May 12, 2018, 09:52:56 Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2017, vol. 21, no. 2, pp. 362-375 ISSN: 2310-7081 (online), 1991 http://doi. AbstractThe stable stationary solutions of the test problem of hydrodynamics and heat transfer in a plane channel with the backward-facing step have been considered in the work for extremely high Reynolds numbers and expansion ratio of the stream ER. The problem has been solved by numerical integration of the 2D Navier-Stokes equations in 'velocity-pressure' formulation and the heat equation in the range of Reynolds number 500Re 3000 and expansion ratio Introduction. Permanent improvement of numerical techniques for modeling fluid dynamics and heat transfer requires adequate methods to assess their effectiveness. For these purposes, consideration of well-known test problems which solutions have all main features of real fluid flows is the best approach. On the one hand, for these problems the huge volume of experimental and theoretical results is saved up that provides their maximum reliability. On the other hand the critical parameters are unambiguously determined for them. The 'intensification' of these parameters increases the complexity of the problems. The efficiency evaluation of a new computing technology follows from this: the more critical parameters of the problem are 'intense', the more the technology is effective. The well-known example of such problem of hydrodynamics of incompressible viscous liquids is the classical lid-driven cavity problem. Reynolds number is the critical parameter for this problem.The problem of separated flow in a 2D channel with backward-facing step is one more such a problem [1]. The problem is characterized by a simple geometry. Its solution, in general, depends on two parameters: Reynolds number Re and expansion ratio ER, where ER is defined as the ratio of the full height of the channel to the height of its inlet segment. Prandtl number Pr is added when heat transfer is taken into account. Change of these few input parameters allows to receive radically various solutions of the problem-namely, separated flow patterns, which are characterized by the quantity, form, size, and position of the vortices. Furthermore, they can have a very complex structure. The maximum value of Reynolds number (Re = 3000 at ER = 2) was reached in the article [2], and expansion ratio (ER = 4 at Re 300) was reached in the works [3,4].Further increase in these parameters causes computational instability which, in particular, is discussed in [2]. E. Erturk recommends to reduce a mesh step for overcoming this instability (see, for example, [5]). But in this case, the systems of the linear algebraic equations (SLAE) with huge number of unknowns are generated, and more effective methods are needed to solve the...

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confidence: 99%

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confidence: 99%

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confidence: 99%

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On the solution of fluid flow and heat transfer problem in a 2D channel with backward-facing step

Alexander

Liubov

2017

Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki

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Numerical Solution of the Problem of Incompressible Fluid Flow in a Plane Channel with a Backward-Facing Step at High Reynolds Numbers

Фомин

Fomina

2018

J Appl Mech Tech Phy

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Numerical solutions of 2D steady incompressible backward-facing step flow at high Reynolds numbers

Фомин¹,

Fomina²

2017

Comp. Contin. Mech.

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Исследуются высокочастотные упругие колебания слоистых волноводов, состоящих из повторяющихся ячеек, каждая из которых представляет собой пакет из упругих слоев. Колебания в подобных структурах (фононных кристаллах) характеризуются тем, что в определенных частотных диапазонах, называемых запрещенными зонами или полосами запирания волновода, наблюдается эффект полного отражения плоских гармонических волн, падающих из внешнего полупространства на фононный кристалл. Для описания упругих колебаний в слоистых фононных кристаллах, расположенных между двумя полупространствами, на основе метода матриц переноса разработаны математическая модель и численно устойчивый алгоритм вычисления проходящего через ячеистую структуру волнового поля. При этом амплитудные коэффициенты перед собственными формами продольных и поперечных волн в полупространствах (коэффициенты прохождения и отражения) находятся в форме разложения по собственным значениям матрицы переноса ячейки. Предложена классификация запрещенных и разрешенных зон в слоистых анизотропных фононных кристаллах, основанная на анализе волновых чисел Блоха, соответствующих собственным значениям матрицы переноса ячейки, и асимптотики полученных полуаналитических соотношений. В запрещенных зонах первого типа все волны Блоха являются затухающими, в то время как в зонах второго типа незатухающие волны Блоха не возбуждаются. Происходит это за счет особенностей их поляризации и граничных условий на интерфейсе периодической структуры и внешнего полупространства. При изменении параметров падающего поля, например, направления распространения плоской волны, зоны второго типа непрерывно трансформируются в разрешенные зоны, в которых амплитудные и энергетические коэффициенты прохождения оказываются достаточно малыми. Поэтому с инженерной точки зрения зоны с малым коэффициентом прохождения подобны классическим запрещенным зонам. Приведены результаты численного исследования коэффициентов прохождения и волновых чисел распространяющихся волн, демонстрирующие особенности формирования запрещенных и разрешенных зон в анизотропных слоистых фононных кристаллах.

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Numerical simulation of the viscous incompressible fluid flow and heat transfer in a plane channel with backward-facing step

Cited by 3 publications

References 0 publications

On the solution of fluid flow and heat transfer problem in a 2D channel with backward-facing step

On the solution of fluid flow and heat transfer problem in a 2D channel with backward-facing step

Numerical Solution of the Problem of Incompressible Fluid Flow in a Plane Channel with a Backward-Facing Step at High Reynolds Numbers

Numerical solutions of 2D steady incompressible backward-facing step flow at high Reynolds numbers

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