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Article
Publication date: 2 October 2017

Sujun Dong, Fanchao Meng, Dechun Guo and Hongling Kang

The time of tightly coupled transient calculation and the accuracy of conventional loosely coupled algorithm make it difficult to meet the engineering design requirements…

Abstract

Purpose

The time of tightly coupled transient calculation and the accuracy of conventional loosely coupled algorithm make it difficult to meet the engineering design requirements for long-term conjugate heat transfer (CHT) problems. The purpose of this paper is to propose a new loosely coupled algorithm with sufficient accuracy and less calculation time on the basis of the quasi-steady flow field. Through this algorithm, it will be possible to reduce the update frequency of the flow field and devise a strategy by which to reasonably determine the update steps.

Design/methodology/approach

In this paper, the new algorithm updates the flow field by solving the steady governing equations in the fluid region and by calculating the transient temperature distribution until the next update of the fluid flow, by means of solving the transient energy equations in the entire computational domain. The authors propose a strategy by which to determine the update step, by using the engineering empirical formula of the Nusselt number, on the basis of the changes of the inlet and outlet boundary conditions.

Findings

Taking a duct heated by an inner forced air flow heating process as an example, the comparison results for the tightly coupled transient calculation by Fluent software shows that the new algorithm is able to significantly reduce the calculation time of the transient temperature distribution with reasonable accuracy. For example, the respective computing times are reduced to 22.8 and 40 per cent, while the duct wall temperature deviations are 7 and 5 per cent, using the two flow update time steps of 100 and 50 s on the variable inlet-flow rate conditions.

Originality/value

The new algorithm outlined in this paper further improves the calculated performance and meets the engineering design requirements for long-term CHT problems.

Details

Engineering Computations, vol. 34 no. 7
Type: Research Article
ISSN: 0264-4401

Keywords

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Article
Publication date: 1 June 1996

M.M. El‐Refaee, M.M. Elsayed, N.M. Al‐Najem and I.E. Megahid

A fast false implicit transient scheme FITS is developed to predict thetwo‐dimensional steady‐state solutions ofbuoyancy‐assisted laminar internal flows. This new scheme…

Abstract

A fast false implicit transient scheme FITS is developed to predict the two‐dimensional steady‐state solutions of buoyancy‐assisted laminar internal flows. This new scheme uses the control volume based on power law technique in conjugation with the alternating direction implicit (ADI) and the successive grid refinement (SGR) procedures to solve the transient vorticity and energy transport equations. The ADI procedure allows the power law, which gives an excellent approximation to the exact 1‐D solution, to be applied locally in one‐dimensional sense for each sweep in the co‐ordinates’ directions. This in turn increased the solution accuracy and hence permits the use of a larger time increment. As a result a remarkable increase in the convergence rate to steady‐state is achieved. The final solution is obtained by successively refining the grid as the solution advances in time. The efficiency of FITS is verified by comparing the present predictions with three steady‐state benchmark solutions: natural convection of a heat generating fluid in a rectangular enclosure, natural convection inside a cavity with two isothermal walls, and a vertical buoyancy‐assisted laminar backward‐facing step flow.

Details

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

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Article
Publication date: 1 January 1992

ZHONG QIN and OLSON

A numerical method is developed for steady and unsteady turbulent flows with significant regions of separation. A finite element formulation of the Navier‐Stokes equations…

Abstract

A numerical method is developed for steady and unsteady turbulent flows with significant regions of separation. A finite element formulation of the Navier‐Stokes equations with a modified Baldwin‐Lomax eddy viscosity closure is used. The method of averaging is employed to obtain a periodic solution of unsteady flow. The formulation is tested on a problem of flow over a backward‐facing step and the results are compared with experimental and other numerical results. The gross features of both steady and unsteady flows are reasonably well predicted by the numerical analysis, at least for the limited range of parameters tested so far.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 2 no. 1
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 6 November 2007

Manab Kumar Das and P. Rajesh Kanna

The purpose of the paper is to study the steady and periodic solution of a lid‐driven cavity flow problem with the gradual increase of Reynolds number (Re) up to 10,000.

Abstract

Purpose

The purpose of the paper is to study the steady and periodic solution of a lid‐driven cavity flow problem with the gradual increase of Reynolds number (Re) up to 10,000.

Design/methodology/approach

The problem is solved by unsteady stream function‐vorticity formulation using the clustered grids. The alternating direction implicit (ADI) method and the central difference scheme have been used for discretization of the governing equations. Total vorticity error and the total kinetic energy have been considered for ensuring the state of flow condition. The midplane velocity distribution and the top wall vortex distribution are compared with the results of other authors and found to show good agreement.

Findings

Kinetic energy variation with time is studied for large time computation. Below 7,500, it becomes constant signifying the flow to be in steady‐state. At Re=10,000, the fluid flow has an oscillating nature. The dimensionless period of oscillation is found to be 1.63. It is demonstrated that the present computation is able to capture the periodic solution after the bifurcation very accurately.

Originality/value

The findings will be useful in conducting a steady and periodic solution of variety of fluid flows or thermally‐driven fluid flows.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 17 no. 8
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 11 January 2011

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

Keywords

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Article
Publication date: 1 February 1998

Seong Ho Cho and Seung O. Park

Computational procedures and results of an upwash jet arising from two opposing plane wall jets based on the Reynolds averaged Navier‐Stokes equations are discussed. For…

Abstract

Computational procedures and results of an upwash jet arising from two opposing plane wall jets based on the Reynolds averaged Navier‐Stokes equations are discussed. For the calculation of the flow, a steady and an unsteady numerical approach were taken. For the steady computation, we adopted various eddy viscosity models(the standard k‐ε model, the RNG k‐ε model and the Bardina’s model) and the Reynolds stress transport model with various diffusion term closures. Results of the steady computation indicated that the jet half‐width was very much underpredicted, and hence the velocity profiles of the upwash jet were in very poor agreement with the experimental data. We found, however, that the velocity profiles nondimensionalized by the jet half width and the maximum velocity appeared to be in good agreement with the experimental data, which could be misleading. When an unsteady approach with an unsteady version of the standard k‐ε eddy viscosity model was taken, a periodic oscillation of the jet was observed. The jet half‐width distribution obtained by taking the time average of the periodic velocity profiles was found to be in much better agreement with the experimental data.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 8 no. 1
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 1 January 1996

K.J. Badcock, I.C. Glover and B.E. Richards

The approximate factorisation‐conjugate gradient squared (AF‐CGS) methodhas been successfully demonstrated for unsteady turbulent aerofoil flows andtransonic inviscid flows

Abstract

The approximate factorisation‐conjugate gradient squared (AF‐CGS) method has been successfully demonstrated for unsteady turbulent aerofoil flows and transonic inviscid flows in two and three dimensions. The method consists of a conjugate gradient solution of the linear system at each step with the ADI approximate factorisation as a preconditioner. In the present paper the method is adapted to obtain rapid convergence for steady aerofoil flows when compared to the basic explicit method. Modifications to the original method are described, convergence criteria are examined and the method is demonstrated for transonic flow including AGARD test case 9 for the RAE2822 aerofoil.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 6 no. 1
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 3 May 2019

Jin-Ping Wang, Jian-Fei Zhang, Zhi-Guo Qu and Wen-Quan Tao

Pressure-based methods have been demonstrated to be powerful for solving many practical problems in engineering. In many pressure-based methods, inner iterative processes…

Abstract

Purpose

Pressure-based methods have been demonstrated to be powerful for solving many practical problems in engineering. In many pressure-based methods, inner iterative processes are proposed to get efficient solutions. However, the number of inner iterations is set empirically and kept fixed during the whole computation for different problems, which is overestimated in some computations but underestimated in other computations. This paper aims to develop an algorithm with adaptive inner iteration processes for steady and unsteady incompressible flows.

Design/methodology/approach

In this work, with the use of two different criteria in two inner iterative processes, a mechanism is proposed to control inner iteration processes to make the number of inner iterations vary during computing according to different problems. By doing so, adaptive inner iteration processes can be achieved.

Findings

The adaptive inner iterative algorithm is verified to be valid by solving classic steady and unsteady incompressible problems. Results show that the adaptive inner iteration algorithm works more efficient than the fixed inner iteration one.

Originality/value

The algorithm with adaptive inner iteration processes is first proposed in this paper. As the mechanism for controlling inner iteration processes is based on physical meaning and the feature of iterative calculations, it can be used in any methods where there exist inner iteration processes. It is not limited for incompressible flows. The performance of the adaptive inner iteration processes in compressible flows is conducted in a further study.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 4
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 18 September 2009

Simon D. Harris, Derek B. Ingham and Ioan Pop

The purpose of this paper is to present a numerical and an analytical study of the fluid flow and heat transfer in the unsteady, laminar boundary layer resulting from the…

Abstract

Purpose

The purpose of this paper is to present a numerical and an analytical study of the fluid flow and heat transfer in the unsteady, laminar boundary layer resulting from the forced convection flow along a semi‐infinite wedge, where the transients are initiated at time t¯ = 0 when the wedge is impulsively started from rest with a uniform velocity and a constant heat flux at the walls of the wedge is suddenly imposed.

Design/methodology/approach

The velocity of the main free stream is written in non‐dimensional form for t > 0 as ue(x) = xm, where x is the non‐dimensional distance along the surface from the leading edge (apex) of the wedge and the constant m is related to the included angle of the wedge πβ by m = β / (2 − β) (0 ≤ m ≤ 1 for physical applications). The wedge and the fluid are assumed to be initially (t¯ = 0) at the same uniform temperature T, so that there is zero heat flux at the surface. A time‐dependent thermal boundary layer is then produced at t¯ = 0 as the zero heat flux at the surface is suddenly changed, and a constant heat flux qw is imposed as the wedge is set into motion. Analytical solutions for the simultaneous development of the momentum and thermal boundary layers are obtained for both small (initial unsteady flow) and large (steady‐state flow) times for several wedge angles (several values of m) and several values of the Prandtl number Pr. These two asymptotic solutions are matched using two specialised numerical procedures.

Findings

The numerical results obtained for the transient fluid velocity and temperature fields concentrate mainly on the case when the Prandtl number Pr = 1 and m = 1 / 5, namely a wedge angle of 60. Required alterations to these parameters are then discussed with reference to variations in Pr and m separately. Further, an engineering empirical expression is presented for the skin friction Cf (τ) Rex1/2 that is valid for all times. The comparison between the empirical formula and the full numerical solution demonstrates that this matching solution can be used with confidence over the whole range of values of the non‐dimensional time τ for each of the values of m presented, and may therefore be used with confidence in engineering applications.

Originality/value

The results of the present work, which have been obtained through many computations, are very important for the advancement of knowledge on this classical problem of fluid mechanics and heat transfer. It is believed that such very detailed solutions have not previously been presented.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 19 no. 8
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 3 April 2007

Victoria Timchenko, John Reizes and Eddie Leonardi

The development of novel cooling techniques is needed in order to be able to substantially increase the performance of integrated electronic circuits whose operations are…

Abstract

Purpose

The development of novel cooling techniques is needed in order to be able to substantially increase the performance of integrated electronic circuits whose operations are limited by the maximum allowable temperature. Air cooled micro‐channels etched in the silicon substrate have the potential to remove heat directly from the chip. For reasonable pressure drops, the flow in micro‐channels is inherently laminar, so that the heat transfer is not very large. A synthetic jet may be used to improve mixing, thereby considerably increasing heat transfer. This paper seeks to address this issue.

Design/methodology/approach

CFD has been used to study the flow and thermal fields in forced convection in a two‐dimensional micro‐channel with an inbuilt synthetic jet actuator. The unsteady Navier‐Stokes and energy equations are solved. The effects of variation of the frequency of the jet at a fixed pressure difference between the ends of the channel and with a fixed jet Reynolds number, have been studied with air as the working fluid. Although the velocities are very low, the compressibility of air has to be taken into account.

Findings

The use of a synthetic jet appreciably increases the rate of heat transfer. However, in the frequency range studied, whilst there are significant changes in the details of the flow, due primarily to large phase changes with frequency, there is little effect of the frequency on the overall rate heat transfer. The rates of heat transfer are not sufficiently large for air to be a useful cooling medium for the anticipated very large heat transfer rates in future generations of microchips.

Research limitations/implications

The study is limited to two‐dimensional flows so that the effect of other walls is not considered.

Practical implications

It does not seem likely that air flowing in channels etched in the substrate of integrated circuits can be successfully used to cool future, much more powerful microchips, despite a significant increase in the heat transfer caused by synthetic jet actuators.

Originality/value

CFD is used to determine the thermal performance of air flowing in micro‐channels with and without synthetic jet actuators as a means of cooling microchips. It has been demonstrated that synthetic jets significantly increase the rate of heat transfer in the micro‐channel, but that changing the frequency with the same resulting jet Reynolds number does not have an effect on the overall rate of heat transfer. The significant effect of compressibility on the phase shifts and more importantly on the apparently anomalous heat transfer from the “cold” air to the “hot” wall is also demonstrated.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 17 no. 3
Type: Research Article
ISSN: 0961-5539

Keywords

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