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Article
Publication date: 1 June 1996

P.G. Tucker and C.A. Long

Semi‐implicit, second order temporal and spatial finite volumecomputations of the flow in a differentially heated rotating annulus arepresented. For the regime considered…

Abstract

Semi‐implicit, second order temporal and spatial finite volume computations of the flow in a differentially heated rotating annulus are presented. For the regime considered, three cyclones and anticyclones separated by a relatively fast moving jet of fluid or “jet stream” are predicted. Two second order methods are compared with, first order spatial predictions, and experimental measurements. Velocity vector plots are used to illustrate the predicted flow structure. Computations made using second order central differences are shown to agree best with experimental measurements, and to be stable for integrations over long time periods (>1000s). No periodic smoothing is required to prevent divergence.

Details

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

Keywords

Article
Publication date: 1 April 1994

C.A. Long and P.G. Tucker

A heated rotating cavity with an axial throughflow of cooling air isused as a model for the flow in the cylindrical cavities between adjacentdiscs of a high‐pressure…

Abstract

A heated rotating cavity with an axial throughflow of cooling air is used as a model for the flow in the cylindrical cavities between adjacent discs of a high‐pressure gas‐turbine compressor. In an engine the flow is expected to be turbulent, the limitations of this laminar study are fully realised but it is considered an essential step to understand the fundamental nature of the flow. The three‐dimensional, time‐dependent governing equations are solved using a code based on the finite volume technique and a multigrid algorithm. The computed flow structure shows that flow enters the cavity in one or more radial arms and then forms regions of cyclonic and anticyclonic circulation. This basic flow structure is consistent with existing experimental evidence obtained from flow visualization. The flow structure also undergoes cyclic changes with time. For example, a single radial arm, and pair of recirculation regions can commute to two radial arms and two pairs of recirculation regions and then revert back to one. The flow structure inside the cavity is found to be heavily influenced by the radial distribution of surface temperature imposed on the discs. As the radial location of the maximum disc temperature moves radially outward, this appears to increase the number of radial arms and pairs of recirculation regions (from one to three for the distributions considered here). If the peripheral shroud is also heated there appear to be many radial arms which exchange fluid with a strong cyclonic flow adjacent to the shroud. One surface temperature distribution is studied in detail and profiles of the relative tangential and radial velocities are presented. The disc heat transfer is also found to be influenced by the disc surface temperature distribution. It is also found that the computed Nusselt numbers are in reasonable accord over most of the disc surface with a correlation found from previous experimental measurements.

Details

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

Keywords

Article
Publication date: 1 November 1997

P.G. Tucker

Presents three non‐isothermal, time dependent, three dimensional examples having cylindrical geometries to show the significant effort of numerical precision and…

Abstract

Presents three non‐isothermal, time dependent, three dimensional examples having cylindrical geometries to show the significant effort of numerical precision and dissipation on rotating flow predictions. The examples are relevant to turbomachinery design and geophysical studies. Discusses the relationship between numerical precision, numerical dissipation and co‐ordinate system angular velocity. Compares predictions made in stationary and rotating co‐ordinate systems, using contour plots of dimensionless stream function and temperature. Shows that wrong, axisymmetric solutions are predicted if the co‐ordinate system is not selected to minimize relative tangential velocities/Peclet numbers, thereby increasing numerical precision and reducing dissipation.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 7 no. 7
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 20 July 2010

C.‐B. Liu, P. Nithiarasu and P.G. Tucker

The purpose of this paper is to numerically solve Eikonal and Hamilton‐Jacobi equations using the finite element method; to use both explicit Taylor Galerkin (TG) and…

Abstract

Purpose

The purpose of this paper is to numerically solve Eikonal and Hamilton‐Jacobi equations using the finite element method; to use both explicit Taylor Galerkin (TG) and implicit methods to obtain shortest wall distances; to demonstrate the implemented methods on some realistic problems; and to use iterative generalized minimal residual method (GMRES) method in the solution of the equations.

Design/methodology/approach

The finite element method along with both the explicit and implicit time discretisations is employed. Two different forms of governing equations are also employed in the solution. The Eikonal equation in its original form is used in the explicit Taylor Galerkin discretisation to save computational time. For implicit method, however, the convection‐diffusion form in its conservation form is used to maintain spatial stability.

Findings

The finite element solution obtained is both accurate and smooth. As expected the implicit method is much faster than the explicit method. Though the proposed finite element solution procedures in serial is slower than the standard search procedure, they are suitable to be used in a parallel environment.

Originality/value

The finite element procedure for Eikonal and Hamilton‐Jacobi equations are attempted for the first time. Though the finite volume and finite difference‐based computational fluid dynamics (CFD) solvers have started employing differential equations for wall distance calculations, it is not common for finite element solvers to use such wall distance calculations. The results presented here clearly show that the proposed methods are suitable for unstructured meshes and finite element solvers.

Details

Engineering Computations, vol. 27 no. 5
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 20 July 2020

Paul G. Tucker

The purpose of this paper is to outline the extensive multi-scale and multi-physics challenges when simulating future aircraft and offer strategies to help deal with some…

Abstract

Purpose

The purpose of this paper is to outline the extensive multi-scale and multi-physics challenges when simulating future aircraft and offer strategies to help deal with some of these challenges.

Design/methodology/approach

To help with the multi-scale challenges, in a hierarchical, zonal fashion both the handling of turbulence and geometry is considered.

Findings

Such modelling of geometry is necessary to help deal with the increasingly coupled nature of many aerodynamic problems more economically and the drive towards considering ever increasing levels of geometrical complexity/scale.

Originality/value

The proposed unified framework could be exploited all the way, through initial fast preliminary design to final numerical test involving various bespoke combinations of hierarchical components.

Details

Engineering Computations, vol. 38 no. 3
Type: Research Article
ISSN: 0264-4401

Keywords

Abstract

Details

Functional Structure and Approximation in Econometrics
Type: Book
ISBN: 978-0-44450-861-4

Article
Publication date: 4 December 2017

Chunbao Liu, Weiyang Bu, Dong Xu, Yulong Lei and Xuesong Li

This paper aims to improve performance prediction and to acquire more detailed flow structures so as to analyze the turbulence in complex rotor-stator flow.

Abstract

Purpose

This paper aims to improve performance prediction and to acquire more detailed flow structures so as to analyze the turbulence in complex rotor-stator flow.

Design/methodology/approach

Hydraulic retarder as typical fluid machinery was numerically investigated by using hybrid Reynolds-averaged Navier–Stokes (RANS)/large eddy simulation (LES) models CIDDES Algebraic Wall-Modeled Large Eddy Simulation (LES) (WMLES) S-Ω and dynamic hybrid RANS/LES (DHRL). The prediction results were compared and analyzed with a RANS model shear stress transport (SST) k-omega which was a recommended choice in engineering.

Findings

The numerical results were verified by experiment and indicated that the predicted values for three hybrid turbulence models were more accurate. Then, the transient flow field was further analyzed visually in terms of turbulence statistics, Reynolds number, pressure-streamline, vortex structure and eddy viscosity ratio. The results indicated that HRL approaches could capture unsteady flow phenomena.

Practical implications

This study achieves both in performance prediction improvement and better flow mechanism understanding. The computational fluid dynamics (CFD) could be used instead of flow visualization to a certain extent. The improved CFD method, the fine computational grid and the reasonable simulation settings jointly enhance the application of CFD in the rotor-stator flow.

Originality/value

The improvement was quite encouraging compared with the reported literatures, contributing to the CFD playing a more important role in the flow machinery. DHRL provided the detailed explanation of flow transport between rotor and stator, which was not reported before. Through it, the flow mechanism can be better understood.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 27 no. 12
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 11 January 2008

A.K. Arnold, P. Nithiarasu and P.G. Tucker

This paper seeks to numerically model electro‐osmotic flow (EOF) through microchannels using a finite element‐based unstructured mesh solution methodology.

Abstract

Purpose

This paper seeks to numerically model electro‐osmotic flow (EOF) through microchannels using a finite element‐based unstructured mesh solution methodology.

Design/methodology/approach

The finite element method (FEM) combined with the characteristic‐based split (CBS) algorithm is used to solve the coupled Navier‐Stokes equations in order to simulate EOFs. The Laplace and Poisson‐Boltzmann equations are solved explicitly a priori to the solution of the fluid dynamic equations. The external electric field and internal potential values are then used to construct the source terms of the fluid dynamics equations.

Findings

Proposed methodology works excellently on unstructured meshes for both two‐ and three‐dimensional flow problems. The results obtained for benchmark channel flow problems show an excellent agreement with analytical and experimental data.

Originality/value

The idea of using the FEM and the CBS algorithm to solve the governing equations of EOFs is proposed. This particular method of solving these equations is unprecedented. In addition to benchmark examples, a problem of practical importance is also solved in this paper.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 18 no. 1
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 6 November 2017

J.I. Ramos

The purpose of this paper is to develop a new finite-volume method of lines for one-dimensional reaction-diffusion equations that provides piece-wise analytical solutions…

Abstract

Purpose

The purpose of this paper is to develop a new finite-volume method of lines for one-dimensional reaction-diffusion equations that provides piece-wise analytical solutions in space and is conservative, compare it with other finite-difference discretizations and assess the effects of the nonlinear diffusion coefficient on wave propagation.

Design/methodology/approach

A conservative, finite-volume method of lines based on piecewise integration of the diffusion operator that provides a globally continuous approximate solution and is second-order accurate is presented. Numerical experiments that assess the accuracy of the method and the time required to achieve steady state, and the effects of the nonlinear diffusion coefficients on wave propagation and boundary values are reported.

Findings

The finite-volume method of lines presented here involves the nodal values and their first-order time derivatives at three adjacent grid points, is linearly stable for a first-order accurate Euler’s backward discretization of the time derivative and has a smaller amplification factor than a second-order accurate three-point centered discretization of the second-order spatial derivative. For a system of two nonlinearly-coupled, one-dimensional reaction-diffusion equations, the amplitude, speed and separation of wave fronts are found to be strong functions of the dependence of the nonlinear diffusion coefficients on the concentration and temperature.

Originality/value

A new finite-volume method of lines for one-dimensional reaction-diffusion equations based on piecewise analytical integration of the diffusion operator and the continuity of the dependent variables and their fluxes at the cell boundaries is presented. The method may be used to study heat and mass transfer in layered media.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 27 no. 11
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 28 June 2021

Anuj Kumar Shukla and Anupam Dewan

Convective heat transfer features of a turbulent slot jet impingement are comprehensively studied using two different computational approaches, namely, URANS (unsteady…

Abstract

Purpose

Convective heat transfer features of a turbulent slot jet impingement are comprehensively studied using two different computational approaches, namely, URANS (unsteady Reynolds-averaged Navier–Stokes equations) and SAS (scale-adaptive simulation). Turbulent slot jet impingement heat transfer is used where a considerable heat transfer enhancement is required, and computationally, it is a quite challenging flow configuration.

Design/methodology/approach

Customized OpenFOAM 4.1, an open-access computational fluid dynamics (CFD) code, is used for SAS (SST-SAS k-ω) and URANS (standard k-ε and SST k-ω) computations. A low-Re version of the standard k-ε model is used, and other models are formulated for good wall-refined calculations. Three turbulence models are formulated in OpenFOAM 4.1 with second-order accurate discretization schemes.

Findings

It is observed that the profiles of the streamwise turbulence are under-predicted at all the streamwise locations by SST k-ω and SST SAS k-ω models, but follow similar trends as in the reported results. The standard k-ε model shows improvements in the predictions of the streamwise turbulence and mean streamwise velocity profiles in the zone of outer wall jet. Computed profiles of Nusselt number by SST k-ω and SST-SAS k-ω models are nearly identical and match well with the reported experimental results. However, the standard k-ε model does not provide a reasonable profile or quantification of the local Nusselt number.

Originality/value

Hybrid turbulence model is suitable for efficient CFD computations for the complex flow problems. This paper deals with a detailed comparison of the SAS model with URANS and LES for the first time in the literature. A thorough assessment of the computations is performed against the results reported using experimental and large eddy simulations techniques followed by a detailed discussion on flow physics. The present results are beneficial for scientists working with hybrid turbulence models and in industries working with high-efficiency cooling/heating system computations.

Details

Engineering Computations, vol. 38 no. 10
Type: Research Article
ISSN: 0264-4401

Keywords

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