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Article
Publication date: 26 September 2019

Van Luc Nguyen, Tomohiro Degawa, Tomomi Uchiyama and Kotaro Takamure

The purpose of this study is to design numerical simulations of bubbly flow around a cylinder to better understand the characteristics of flow around a rigid obstacle.

Abstract

Purpose

The purpose of this study is to design numerical simulations of bubbly flow around a cylinder to better understand the characteristics of flow around a rigid obstacle.

Design/methodology/approach

The bubbly flow around a circular cylinder was numerically simulated using a semi-Lagrangian–Lagrangian method composed of a vortex-in-cell method for the liquid phase and a Lagrangian description of the gas phase. Additionally, a penalization method was applied to account for the cylinder inside the flow. The slip condition of the bubbles on the cylinder’s surface was enforced, and the outflow conditions were applied to the liquid flow at the far field.

Findings

The simulation clarified the characteristics of a bubbly flow around a circular cylinder. The bubbles were shown to move around and separate from both sides of the cylinder, because of entrainment by the liquid shear layers. Once the bubbly flow fully developed, the bubbles distributed into groups and were dispersed downstream of the cylinder. A three-dimensional vortex structure of various scales was also shown to form downstream, whereas a quasi-stable two-dimensional vortex structure was observed upstream. Overall, the proposed method captured the characteristics of a bubbly flow around a cylinder well.

Originality/value

A semi-Lagrangian–Lagrangian approach was applied to simulate a bubbly flow around a circular cylinder. The simulations provided the detail features of these flow phenomena.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 12
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 5 June 2017

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.

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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
Publication date: 11 February 2019

Van Luc Nguyen, Tomohiro Degawa and Tomomi Uchiyama

This study aims to provide discussions of the numerical method and the bubbly flow characteristics of an annular bubble plume.

Abstract

Purpose

This study aims to provide discussions of the numerical method and the bubbly flow characteristics of an annular bubble plume.

Design/methodology/approach

The bubbles, released from the annulus located at the bottom of the domain, rise owing to buoyant force. These released bubbles have diameters of 0.15–0.25 mm and satisfy the bubble flow rate of 4.1 mm3/s. The evolution of the three-dimensional annular bubble plume is numerically simulated using the semi-Lagrangian–Lagrangian (semi-LL) approach. The approach is composed of a vortex-in-cell method for the liquid phase and a Lagrangian description of the gas phase.

Findings

First, a new phenomenon of fluid dynamics was discovered. The bubbly flow enters a transition state with the meandering motion of the bubble plume after the early stable stage. A vortex structure in the form of vortex rings is formed because of the inhomogeneous bubble distribution and the fluid-surface effects. The vortex structure of the flow deforms as three-dimensionality appears in the flow before the flow fully develops. Second, the superior abilities of the semi-LL approach to analyze the vortex structure of the flow and supply physical details of bubble dynamics were demonstrated in this investigation.

Originality/value

The semi-LL approach is applied to the simulation of the gas–liquid two-phase flows.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 3
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 11 July 2019

Van Luc Nguyen, Tomohiro Degawa and Tomomi Uchiyama

This paper aims to provide discussions of a numerical method for bubbly flows and the interaction between a vortex ring and a bubble plume.

Abstract

Purpose

This paper aims to provide discussions of a numerical method for bubbly flows and the interaction between a vortex ring and a bubble plume.

Design/methodology/approach

Small bubbles are released into quiescent water from a cylinder tip. They rise under the buoyant force, forming a plume. A vortex ring is launched vertically upward into the bubble plume. The interactions between the vortex ring and the bubble plume are numerically simulated using a semi-Lagrangian–Lagrangian approach composed of a vortex-in-cell method for the fluid phase and a Lagrangian description of the gas phase.

Findings

A vortex ring can transport the bubbles surrounding it over a distance significantly depending on the correlative initial position between the bubbles and the core center. The motion of some bubbles is nearly periodic and gradually extinguishes with time. These bubble trajectories are similar to two-dimensional-helix shapes. The vortex is fragmented into multiple regions with high values of Q, the second invariant of velocity gradient tensor, settling at these regional centers. The entrained bubbles excite a growth rate of the vortex ring's azimuthal instability with a formation of the second- and third-harmonic oscillations of modes of 16 and 24, respectively.

Originality/value

A semi-Lagrangian–Lagrangian approach is applied to simulate the interactions between a vortex ring and a bubble plume. The simulations provide the detail features of the interactions.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 9
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 1 January 2014

Tomomi Uchiyama, Yutaro Yoshii and Hirotaka Hamada

This study is concerned with the direct numerical simulation (DNS) of a turbulent channel flow by an improved vortex in cell (VIC) method. The paper aims to discuss these…

Abstract

Purpose

This study is concerned with the direct numerical simulation (DNS) of a turbulent channel flow by an improved vortex in cell (VIC) method. The paper aims to discuss these issues.

Design/methodology/approach

First, two improvements for VIC method are proposed to heighten the numerical accuracy and efficiency. A discretization method employing a staggered grid is presented to ensure the consistency among the discretized equations as well as to prevent the numerical oscillation of the solution. A correction method for vorticity is also proposed to compute the vorticity field satisfying the solenoidal condition. Second, the DNS for a turbulent channel flow is conducted by the improved VIC method. The Reynolds number based on the friction velocity and the channel half width is 180.

Findings

It is highlighted that the simulated turbulence statistics, such as the mean velocity, the Reynolds shear stress and the budget of the mean enstrophy, agree well with the existing DNS results. It is also shown that the organized flow structures in the near-wall region, such as the streaks and the streamwise vortices, are favourably captured. These demonstrate the high applicability of the improved VIC method to the DNS for wall turbulent flows.

Originality/value

This study enables the VIC method to perform the DNS for wall turbulent flows.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 24 no. 1
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 14 September 2018

Chao Wang, Jinju Sun and Zihao Cheng

The present study aims to develop a vortex method capable for solving the complex vortical flows past the moving/deforming bodies.

Abstract

Purpose

The present study aims to develop a vortex method capable for solving the complex vortical flows past the moving/deforming bodies.

Design/methodology/approach

To achieve such a goal, some innovative work is conducted on the basis of vortex-in-cell (VIC) method that uses the improved semi-Lagrangian scheme. The penalization technique is incorporated with the VIC, which makes the complex boundaries of moving/deforming bodies readily treated. Iterative algorithm is further proposed for the penalization and used to solve the Poisson equation, which enhances the vorticity solution accuracy at the body boundary.

Findings

The developed method is used to simulate some distinct flows of different boundaries and features: the impulsively started circular cylinder flow represents the one-way coupling; the falling circular cylinder flow and ellipse leaf flow both represent the two-way coupling of moving boundary; the fish-like body flow represents the two-way fluid-structure interaction of deforming boundary. The vortical physics of the above flows are well revealed, and the developed method is proven capable in dealing with the complex fluid-structure interaction problems.

Originality/value

The penalization technique is incorporated with the semi-Lagrangian VIC method, which makes the complex boundaries of moving/deforming bodies readily treated. An iterative algorithm is further proposed for the penalization and used to solve the Poisson equation, which enhances the vorticity solution accuracy at the body boundary. The complex vortical physics of the moving/deforming body flows are well revealed, and the propulsive mechanism of fish-like swimmer is well illustrated with the present method.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 28 no. 8
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 5 March 2018

Jun-Hyeok Lee, Seung-Jae Lee and Jung-chun Suh

As the penalized vortex-in-cell (pVIC) method is based on the vorticity-velocity form of the Navier–Stokes equation, the pressure variable is not incorporated in its…

Abstract

Purpose

As the penalized vortex-in-cell (pVIC) method is based on the vorticity-velocity form of the Navier–Stokes equation, the pressure variable is not incorporated in its solution procedure. This is one of the advantages of vorticity-based methods such as pVIC. However, dynamic pressure is an essential flow property in engineering problems. In pVIC, the pressure field can be explicitly evaluated by a pressure Poisson equation (PPE) from the velocity and vorticity solutions. How to specify far-field boundary conditions is then an important numerical issue. Therefore, this paper aims to robustly and accurately determine the boundary conditions for solving the PPE.

Design/methodology/approach

This paper introduces a novel non-iterative method for specifying Dirichlet far-field boundary conditions to solve the PPE in a bounded domain. The pressure field is computed using the velocity and vorticity fields obtained from pVIC, and the solid boundary conditions for pressure are also imposed by a penalization term within the framework of pVIC. The basic idea of our approach is that the pressure at any position can be evaluated from its gradient field in a closed contour because the contour integration for conservative vector fields is path-independent. The proposed approach is validated and assessed by a comparative study.

Findings

This non-iterative method is successfully implemented to the pressure calculation of the benchmark problems in both 2D and 3D. The method is much faster than all the other methods tested without compromising accuracy and enables one to obtain reasonable pressure field even for small computation domains that are used regardless of a source distribution (the right-hand side in the Poisson equation).

Originality/value

The strategy introduced in this paper provides an effective means of specifying Dirichlet boundary conditions at the exterior domain boundaries for the pressure Poisson problems. It is very efficient and robust compared with the conventional methods. The proposed idea can also be adopted in other fields dealing with infinite-domain Poisson problems.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 28 no. 3
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 1 September 1998

Asuquo B. Ebiana

A computational procedure based on a hybrid Lagrangian‐Eulerian discrete‐vortical element formulation and conformal transformation schemes are employed in this study to…

Abstract

A computational procedure based on a hybrid Lagrangian‐Eulerian discrete‐vortical element formulation and conformal transformation schemes are employed in this study to simulate the interaction of an air jet with swirling air flow inside a two‐dimensional cylinder. Such an investigation is of importance to many flow‐related industrial and environmental problems, such as mixing, cooling, combustion and dispersion of air‐borne or water‐borne contaminants because of the role of vortices in the global transport of matter and heat. The basis for the simulation is discussed and numerical results compared with theoretical results for the velocity field and streamfunction obtained by the method of images. The swirling air motion and the features of a real jet are well simulated and numerical results are validated by predictions of theory to within 20 per cent. To illustrate the merging and interaction processes of vortices and the formation of large eddies, velocity vectors, particle trajectories and streamline contours are presented.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 8 no. 6
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 14 October 2019

Nagesh Babu Balam and Akhilesh Gupta

Modelling accurately the transient behaviour of natural convection flow in enclosures been a challenging task because of a variety of numerical errors which have limited…

Abstract

Purpose

Modelling accurately the transient behaviour of natural convection flow in enclosures been a challenging task because of a variety of numerical errors which have limited achieving the higher order temporal accuracy. A fourth-order accurate finite difference method in both space and time is proposed to overcome these numerical errors and accurately model the transient behaviour of natural convection flow in enclosures using vorticity–streamfunction formulation.

Design/methodology/approach

Fourth-order wide stencil formula with appropriate one-sided difference extrapolation technique near the boundary is used for spatial discretisation, and classical fourth-order Runge–Kutta scheme is applied for transient term discretisation. The proposed method is applied on two transient case studies, i.e. convection–diffusion of a Gaussian Pulse and Taylor Vortex flow having analytical solution.

Findings

Error magnitude comparison and rate of convergence analysis of the proposed method with these analytical solutions establish fourth-order accuracy and prove the ability of the proposed method to truly capture the transient behaviour of incompressible flow. Also, to test the transient natural convection flow behaviour, the algorithm is tested on differentially heated square cavity at high Rayleigh number in the range of 103-108, followed by studying the transient periodic behaviour in a differentially heated vertical cavity of aspect ratio 8:1. An excellent comparison is obtained with standard benchmark results.

Research limitations/implications

The developed method is applied on 2D enclosures; however, the present methodology can be extended to 3D enclosures using velocity–vorticity formulations which shall be explored in future.

Originality/value

The proposed methodology to achieve fourth-order accurate transient simulation of natural convection flows is novel, to the best of the authors’ knowledge. Stable fourth-order vorticity boundary conditions are derived for boundary and external boundary regions. The selected case studies for comparison demonstrate not only the fourth-order accuracy but also the considerable reduction in error magnitude by increasing the temporal accuracy. Also, this study provides novel benchmark results at five different locations within the differentially heated vertical cavity of aspect ratio 8:1 for future comparison studies.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 3
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 9 April 2019

Mohammad Mortezazadeh and Liangzhu (Leon) Wang

The purpose of this paper is the development of a new density-based (DB) semi-Lagrangian method to speed up the conventional pressure-based (PB) semi-Lagrangian methods.

Abstract

Purpose

The purpose of this paper is the development of a new density-based (DB) semi-Lagrangian method to speed up the conventional pressure-based (PB) semi-Lagrangian methods.

Design/methodology/approach

The semi-Lagrangian-based solvers are typically PB, i.e. semi-Lagrangian pressure-based (SLPB) solvers, where a Poisson equation is solved for obtaining the pressure field and ensuring a divergence-free flow field. As an elliptic-type equation, the Poisson equation often relies on an iterative solution, so it can create a challenge of parallel computing and a bottleneck of computing speed. This study proposes a new DB semi-Lagrangian method, i.e. the semi-Lagrangian artificial compressibility (SLAC), which replaces the Poisson equation by a hyperbolic continuity equation with an added artificial compressibility (AC) term, so a time-marching solution is possible. Without the Poisson equation, the proposed SLAC solver is faster, particularly for the cases with more computational cells, and better suited for parallel computing.

Findings

The study compares the accuracy and the computing speeds of both SLPB and SLAC solvers for the lid-driven cavity flow and the step-flow problems. It shows that the proposed SLAC solver is able to achieve the same results as the SLPB, whereas with a 3.03 times speed up before using the OpenMP parallelization and a 3.35 times speed up for the large grid number case (512 × 512) after the parallelization. The speed up can be improved further for larger cases because of increasing the condition number of the coefficient matrixes of the Poisson equation.

Originality/value

This paper proposes a method of avoiding solving the Poisson equation, a typical computing bottleneck for semi-Lagrangian-based fluid solvers by converting the conventional PB solver (SLPB) to the DB solver (SLAC) through the addition of the AC term. The method simplifies and facilitates the parallelization process of semi-Lagrangian-based fluid solvers for modern HPC infrastructures, such as OpenMP and GPU computing.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

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