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Article

Chao Wang, Jinju Sun and Yan Ba

The purpose of this paper is to develop a Vortex-In-Cell (VIC) method with the semi-Lagrangian scheme and apply it to the high-Re lid-driven cavity flow.

Abstract

Purpose

The purpose of this paper is to develop a Vortex-In-Cell (VIC) method with the semi-Lagrangian scheme and apply it to the high-Re lid-driven cavity flow.

Design/methodology/approach

The VIC method is developed for simulating high Reynolds number incompressible flow. A semi-Lagrangian scheme is incorporated in the convection term to produce unconditional stability, which gets rid of the constraint of the convection Courant-Friedrichs-Lewy (CFL) condition; the adaptive time step is used to maintain the numerical stability of the diffusion term; and the velocity boundary condition is readily converted to the vorticity formulation to suit discontinuous boundary treatment. The VIC simulation results are compared with those produced by other gird methods reported in open literature studies.

Findings

The lid-driven cavity flow is simulated from Re = 100 to 100,000. Similar vortex birth mechanisms are exhibited though, but distinct flow characteristics are revealed. At Re = 100 to 7,500, the cavity flow is confirmed steady. At Re = 10,000, 15,000 and 20,000, the cavity flow is periodical with a primary vortex held spatially at the center. In particular, at Re = 100,000 highly turbulent characteristics is first revealed and an analogous primary vortex is formed but in motion rather than stationary, which is caused by the considerable flow separation at all the boundaries.

Originality/value

In the lid-driven cavity, the flow becomes extremely complex and highly turbulent at Re = 100,000, and the analogous primary vortex structure is observed. Boundary layer separation is observed at all walls, producing small vortices and causing the displacement of the analogous primary vortex. Such a finding original and has not yet been reported by other investigators. It may provide a basis for conducting in-depth studies of the lid-driven cavity flow.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 27 no. 6
Type: Research Article
ISSN: 0961-5539

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Article

Sintu Singha and K.P. Sinhamahapatra

The purpose of this paper is to simulate the flow of a conducting fluid past a circular cylinder placed centrally in a channel subjected to an imposed transverse magnetic…

Abstract

Purpose

The purpose of this paper is to simulate the flow of a conducting fluid past a circular cylinder placed centrally in a channel subjected to an imposed transverse magnetic field to study the effect of a magnetic field on vortex shedding at different Reynolds numbers varying from 50 to 250.

Design/methodology/approach

The two‐dimensional incompressible laminar viscous flow equations are solved using a second‐order implicit unstructured collocated grid finite volume method.

Findings

An imposed transverse magnetic field markedly reduces the unsteady lift amplitude indicating a reduction in the strength of the shed vortices. It is observed that the periodic vortex shedding at the higher Reynolds numbers can be completely suppressed if a sufficiently strong magnetic field is imposed. The required magnetic field strength to suppress shedding increases with Reynolds number. The simulation shows that the separated zone behind the cylinder in a steady flow is reduced as the magnetic field strength is increased.

Originality/value

In this paper, due attention is given to resolve and study the unsteady cylinder wake and its interaction with the shear‐layer on the channel wall in the presence of a magnetic field. A critical value of the Hartmann number for complete suppression of the shedding at a given Reynolds number is found.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 21 no. 1
Type: Research Article
ISSN: 0961-5539

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Article

Haibo Huang, T.S. Lee and C. Shu

The aim of the present study is to evaluate the accuracy and efficiency of Lattice‐BGK (LBGK) method application in simulation of the 3D flow through complex geometry. On…

Abstract

Purpose

The aim of the present study is to evaluate the accuracy and efficiency of Lattice‐BGK (LBGK) method application in simulation of the 3D flow through complex geometry. On the other hand, the steady flows through vascular tube with Reynolds number 10‐150 and different constriction spacing ratios are simulated.

Design/methodology/approach

The numerical method is based on the LGBK method with an incompressible D3Q19 model. To treat the curved boundary, the “bounce back” scheme combined with spatial interpolation of second order is applied.

Findings

The highly axisymmetric property in the direct 3D tube flow simulation is observed. Solutions obtained from LBGK method are quite consistent with that of finite volume method (FVM). The overall order of accuracy of these LBGK solutions is about 1.89. The LBGK incompressible D3Q19 model with the curved boundary treatment can handle the problems of 3D steady flow through complex geometry.

Research limitations/implications

Investigating the flow in constricted vascular tubes with different stenose shape and higher Reynolds number is left for future work.

Practical implications

Lattice BGK method is the very useful tool to investigate the steady vascular flow.

Originality/value

Applying LBGK method with incompressible D3Q19 model to simulate the steady flow through complex geometry. The accuracy and efficiency of the present LBGK solver are examined.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 16 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

Eslam Ezzatneshan

Numerical simulations are performed for studying the vorticity dynamics of a dipole colliding with the wall in a bounded flow and the wake structure and separated flow

Abstract

Purpose

Numerical simulations are performed for studying the vorticity dynamics of a dipole colliding with the wall in a bounded flow and the wake structure and separated flow properties past a circular cylinder at the values of Reynolds numbers.

Design/methodology/approach

The near wake statistics of separated fluid flows are investigated by using the lattice Boltzmann method (LBM) in a two-dimensional framework. A multi-block technique is applied to accurately resolve the flow characteristics by the grid refinement near the wall and preserve the stability of the numerical solution at relatively high Reynolds numbers.

Findings

The results show that the rolling-up of the boundary layer occurs due to the shear-layer instabilities near the surface which causes a boundary layer detachment from the wall and consequently leads to the formation of small-scale vortices. These shear-layer vortices shed at higher frequencies than the large-scale Strouhal vortices which result in small-scale high-frequency fluctuations in the velocity field in the very near wake. The present study also demonstrates that the efficiency of the multi-block LBM used for predicting the statistical features of flow problems is comparable with the solvers based on the Navier-Stokes equations.

Practical implications

Studying the separated flow characteristics in aerospace applications.

Originality/value

Applying a multi-block lattice Boltzmann method (LBM) for simulation of separated fluid flows at high-Reynolds numbers. Studying of the near wake statistics of unsteady separated fluid flows using the multi-block LBM. Comparison of flow characteristics obtained based on the LBM with those of reported based on the Navier-Stokes equations.

Details

Aircraft Engineering and Aerospace Technology, vol. 93 no. 1
Type: Research Article
ISSN: 1748-8842

Keywords

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Article

Mingyang Liu, Huifen Zhu, Guangjun Gao, Chen Jiang and G.R Liu

The purpose of this paper is to investigate a novel stabilization scheme to handle convection and pressure oscillation in the process of solving incompressible laminar…

Abstract

Purpose

The purpose of this paper is to investigate a novel stabilization scheme to handle convection and pressure oscillation in the process of solving incompressible laminar flows by finite element method (FEM).

Design/methodology/approach

The semi-implicit stabilization scheme, characteristic-based polynomial pressure projection (CBP3) consists of the Characteristic-Galerkin method and polynomial pressure projection. Theoretically, the proposed scheme works for any type of element using equal-order approximation for velocity and pressure. In this work, linear 3-node triangular and 4-node tetrahedral elements are the focus, which are the simplest but most difficult elements for pressure stabilizations.

Findings

The present paper proposes a new scheme, which can stabilize FEM solution for flows of both low and relatively high Reynolds numbers. And the influence of stabilization parameters of the CBP3 scheme has also been investigated.

Research limitations/implications

The research in this work is limited to the laminar incompressible flow.

Practical implications

The verification and validation of the CBP3 scheme are conducted by several 2 D and 3 D numerical examples. The scheme could be used to deal with more practical fluid problems.

Social implications

The application of scheme to study complex hemodynamics of patient-specific abdominal aortic aneurysm is also presented, which demonstrates its potential to solve bio-flows.

Originality/value

The paper simulated 2 D and 3 D numerical examples with superior results compared to existing results and experiments. The novel CBP3 scheme is verified to be very effective in handling convection and pressure oscillation.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 31 no. 5
Type: Research Article
ISSN: 0961-5539

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Article

Santanu De, K. Nagendra and K.N. Lakshmisha

The purpose of this paper is to apply lattice Boltzmann equation method (LBM) with multiple relaxation time (MRT) model, to investigate lid‐driven flow in a…

Abstract

Purpose

The purpose of this paper is to apply lattice Boltzmann equation method (LBM) with multiple relaxation time (MRT) model, to investigate lid‐driven flow in a three‐dimensional (3D), rectangular cavity, and compare the results with flow in an equivalent two‐dimensional (2D) cavity.

Design/methodology/approach

The second‐order MRT model is implemented in a 3D LBM code. The flow structure in cavities of different aspect ratios (0.25‐4) and Reynolds numbers (0.01‐1000) is investigated. The LBM simulation results are compared with those from numerical solution of Navier‐Stokes (NS) equations and with available experimental data.

Findings

The 3D simulations demonstrate that 2D models may predict the flow structure reasonably well at low Reynolds numbers, but significant differences with experimental data appear at high Reynolds numbers. Such discrepancy between 2D and 3D results are attributed to the effect of boundary layers near the side‐walls in transverse direction (in 3D), due to which the vorticity in the core‐region is weakened in general. Secondly, owing to the vortex stretching effect present in 3D flow, the vorticity in the transverse plane intensifies whereas that in the lateral plane decays, with increase in Reynolds number. However, on the symmetry‐plane, the flow structure variation with respect to cavity aspect ratio is found to be qualitatively consistent with results of 2D simulations. Secondary flow vortices whose axis is in the direction of the lid‐motion are observed; these are weak at low Reynolds numbers, but become quite strong at high Reynolds numbers.

Originality/value

The findings will be useful in the study of variety of enclosed fluid flows.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 19 no. 6
Type: Research Article
ISSN: 0961-5539

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Article

Younes Menni, A. Chamkha, Chafika Zidani and Boumédiène Benyoucef

A computational fluid dynamics (CFD) analysis has been carried out on the aerodynamic and thermal behavior of an incompressible Newtonian fluid having a constant property…

Abstract

Purpose

A computational fluid dynamics (CFD) analysis has been carried out on the aerodynamic and thermal behavior of an incompressible Newtonian fluid having a constant property and flowing turbulently through a two-dimensional horizontal high-performance heat transfer channel with a rectangular cross section. The top surface of the channel was kept at a constant temperature, while it was made sure to maintain the adiabatic condition of the bottom surface. Two obstacles, with different shapes, i.e. flat rectangular and V-shaped, were inserted into the channel; they were fixed to the top and bottom surfaces of the channel in a periodically staggered manner to force vortices to improve the mixing and consequently the heat transfer. The first fin-type obstacle is placed on the heated top channel surface, and the second baffle-type one is placed on the insulated bottom surface. Five different obstacle situations were considered in this study, which are referred as cases FF (flat fin and flat baffle), FVD (flat fin and V-downstream baffle), FVU (flat fin and V-upstream baffle), VVD (V-downstream fin and V-downstream baffle) and VVU (V-Upstream fin and V-upstream baffle).

Design/methodology/approach

The flow model is governed by Reynolds-averaged Navier–Stokes equations with the k-epsilon turbulence model and the energy equation. These governing equations are discretized by the finite volume method, in two dimensions, using the commercial CFD software FLUENT software with the Semi Implicit Method for Pressure Linked Equations (SIMPLE) algorithm for handling the pressure-velocity coupling. Air is the test fluid with the flow rate in terms of Reynolds numbers ranging from 12,000 to 32,000.

Findings

Important deformations and large recirculation regions were observed in the flow field. A vortex causes a rotary motion inside the flow field, which enhances the mixing by bringing the packets of fluid from the near-wall region of the channel to the bulk and the other way around. The largest value of the axial variations of the Nusselt number and skin friction coefficient is found in the region facing the baffle, while the smallest value is in the region near the fin, for all cases. The thermal enhancement factor (TEF) was also introduced and discussed to assess the performance of the channel for various obstacle situations. It is found that the TEF values are 1.273-1.368, 1.377-1.573, 1.444-1.833, 1.398-1.565 and 1.348-1.592 for FF, FVD, FVU, VVD and VVU respectively, depending on the Re values. In all cases, the TEF was found to be much larger than unity; its maximum value was around 1.833 for FVU at the highest Reynolds number. Therefore, the FVU may be considered as the best geometrical configuration when using the obstacles to improve the heat transfer efficiency inside the channel.

Originality/value

This study can be a real application in the field of shell-and-tube heat exchangers and flat plate solar air collectors.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 6
Type: Research Article
ISSN: 0961-5539

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Article

M.F. Webster, I.J. Keshtiban and F. Belblidia

We introduce a second‐order accurate time‐marching pressure‐correction algorithm to accommodate weakly‐compressible highly‐viscous liquid flows at low Mach number. As the…

Abstract

We introduce a second‐order accurate time‐marching pressure‐correction algorithm to accommodate weakly‐compressible highly‐viscous liquid flows at low Mach number. As the incompressible limit is approached (Ma ≈ 0), the consistency of the compressible scheme is highlighted in recovering equivalent incompressible solutions. In the viscous‐dominated regime of low Reynolds number (zone of interest), the algorithm treats the viscous part of the equations in a semi‐implicit form. Two discrete representations are proposed to interpolate density: a piecewise‐constant form with gradient recovery and a linear interpolation form, akin to that on pressure. Numerical performance is considered on a number of classical benchmark problems for highly viscous liquid flows to highlight consistency, accuracy and stability properties. Validation bears out the high quality of performance of both compressible flow implementations, at low to vanishing Mach number. Neither linear nor constant density interpolations schemes degrade the second‐order accuracy of the original incompressible fractional‐staged pressure‐correction scheme. The piecewise‐constant interpolation scheme is advocated as a viable method of choice, with its advantages of order retention, yet efficiency in implementation.

Details

Engineering Computations, vol. 21 no. 7
Type: Research Article
ISSN: 0264-4401

Keywords

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Article

D. Xu, B.C. Khoo and M.A. Leschziner

The flow inside an axisymmetric diffuser with a curved surface centre body is numerically simulated using different turbulence models, namely a high‐Reynolds number k‐ε in…

Abstract

The flow inside an axisymmetric diffuser with a curved surface centre body is numerically simulated using different turbulence models, namely a high‐Reynolds number k‐ε in conjunction with wall function turbulence model, a high‐Reynolds number k‐ε with one‐equation turbulence model, a low‐Reynolds number k‐ε turbulence model, a RNG turbulence model and an anisotropic turbulence model. For the separation and reattachment positions, the comparisons made between the various numerical predictions and experimental measurements show that the high‐Reynolds number k‐ε with one‐equation turbulence model is superior to other models in the present study.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 8 no. 2
Type: Research Article
ISSN: 0961-5539

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Article

V. Üstoğlu Ünal

The purpose of this paper is to develop and test an implicit scheme, accurate to the second order, for solving full Navier‐Stokes equations for three dimensional problems…

Abstract

Purpose

The purpose of this paper is to develop and test an implicit scheme, accurate to the second order, for solving full Navier‐Stokes equations for three dimensional problems, using parallel algorithm.

Design/methodology/approach

Parallel solution to the 3‐D incompressible full Navier‐Stokes equations is presented, based on two fractional steps in time and finite element in space. The accuracy of the scheme is second order in both time and space domains. Large time‐step sizes, with Courant‐Friedrichs‐Lewy (CFL) numbers much larger than unity, are taken since the momentum equation is solved implicitly. A fourth order artificial viscosity term is added. In order to stabilize the numerical solution, fourth order artificial viscosity term is used for high Reynolds number flows. The domain decomposition technique is implemented for parallel solution to the problem with matching and non‐overlapping sub‐domains. It is aimed to study both a 3D free and mixed convection problems using the developed scheme. The segregate solution for temperature field is calibrated by a 3‐D free convection problem. Then the flow case where the forced convection is one order of magnitude higher than the free convection is studied.

Findings

It is observed that the long time solution to the flow field shows oscillatory behaviour as the Reynolds number of the flow doubled while keeping the ratio of the forced to free convection fixed. The solution using a parallel algorithm gives satisfactory results, in terms of computation time and accuracy, for the natural convection problem in cubic cavity, and, the forced cooling of a room with chilled ceiling having a parabolic geometry as presented at the end. It is observed that doubling the Reynolds number, while keeping all the parameters unchanged, varies the flow behaviour completely.

Originality/value

A code previously developed and published by the author only solved momentum equation and studied the velocity field. In this study, full Navier Stokes equation is solved and the code is calibrated with a well‐known 3D free‐convection for two different Rayleigh number cases and then 3D mixed convection problem is studied for two cases. Re=2000 case results, solved both by the scheme in this study and by commercial code, presented an interesting physics of the problem. For Re=2000 case, continuous cooling of the room is not possible. Doubling the Reynolds number, raising it from 1000 to 2000, while keeping all the parameters unchanged, varies the flow behaviour completely.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 23 no. 4
Type: Research Article
ISSN: 0961-5539

Keywords

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