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Article
Publication date: 1 October 2004

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

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Article
Publication date: 10 December 2019

Bahador Abolpour and Rahim Shamsoddini

Increasing the temperature of gas flows passing through hot tubes is one of the industrial interests. Operations in the gas phase with high temperature variations involve…

Abstract

Purpose

Increasing the temperature of gas flows passing through hot tubes is one of the industrial interests. Operations in the gas phase with high temperature variations involve engineers with the compressible fluids problems. The paper aims to discuss this issue.

Design/methodology/approach

In this study, a mathematical three-dimensional turbulent model is applied for investigating the heat transfer and laminar gas flow inside the thermal developing zone of a hot tube. The Favre Averaged Navier–Stokes and energy equations and also the Reynolds Stress Model are numerically solved to obtain the fluid velocity and temperature profiles inside this the tube. This model is validated using the experimental data and also well-known formulas in this science.

Findings

Finally, effects of inlet volumetric flow rate, heating conditions of the tube wall and tube angle on the temperature and velocity distributions of the gaseous phase inside this zone are investigated.

Originality/value

The compressible laminar gas flow and also heat transfer in the thermal developing zone of a hot tube is studied using a three-dimensional turbulent model.

Details

Multidiscipline Modeling in Materials and Structures, vol. 16 no. 3
Type: Research Article
ISSN: 1573-6105

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Article
Publication date: 7 November 2016

Ying Chen, Chuanjing Lu, Xin Chen, Jie Li and Zhaoxin Gong

Ultrahigh-speed projectile running in water with the velocity close to the speed of sound usually causes large supercavity. The computation of such transonic cavitating…

Abstract

Purpose

Ultrahigh-speed projectile running in water with the velocity close to the speed of sound usually causes large supercavity. The computation of such transonic cavitating flows is usually difficult, thus high-speed model reflecting the compressibility of both the liquid and the vapor phases should be introduced to model such flow. The purpose of this paper is to achieve a model within an in-house developed solver to simulate the ultrahigh-speed subsonic supercavitating flows.

Design/methodology/approach

An improved TAIT equation adjusted by local temperature is adopted as the equation of state (EOS) for the liquid phase, and the Peng-Robinson EOS is used for the vapor phase. An all-speed variable coupling algorithm is used to unify the computations and regulate the convergence at arbitrary Mach number. The ultrahigh-speed (Ma=0.7) supercavitating flows around circular disk are investigated in contrast with the case of low subsonic (Ma=0.007) flow.

Findings

The characteristic physical variables are reasonably predicted, and the cavity profiles are compared to be close to the experimental empirical formula. An important conclusion in the compressible cavitating flow theory is verified by the numerical result that, at any specific cavitation number the cavity’s size and the drag coefficient both increase along with the rise of Mach number. On the contrary, it is found as well that the cavity’s slenderness ratio decreases when Mach number goes up. It indicates that the compressibility has different influences on the length and the radius of the supercavity.

Originality/value

A high-speed model reflecting the compressibility of both the liquid and the vapor phases was suggested to model the ultrahigh-speed supercavitating flows around underwater projectiles.

Details

Engineering Computations, vol. 33 no. 8
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 13 June 2019

Arthur Piquet, Boubakr Zebiri, Abdellah Hadjadj and Mostafa Safdari Shadloo

This paper aims to present the development of a highly parallel finite-difference computational fluid dynamics code in generalized curvilinear coordinates system. The…

Abstract

Purpose

This paper aims to present the development of a highly parallel finite-difference computational fluid dynamics code in generalized curvilinear coordinates system. The objectives are to handle internal and external flows in fairly complex geometries including shock waves, compressible turbulence and heat transfer.

Design/methodology/approach

The code is equipped with high-order discretization schemes to improve the computational accuracy of the solution algorithm. Besides, a new method to deal with the geometrical singularities, so-called domain decomposition method (DDM), is implemented. The DDM consists of using two different meshes communicating with each other, where the base mesh is Cartesian and the overlapped one a hollow cylinder.

Findings

The robustness of the present implemented code is appraised through several numerical test cases including a vortex advection, supersonic compressible flow over a cylinder, Poiseuille flow, turbulent channel and pipe flows. The results obtained here are in an excellent agreement when compared to the experimental data and the previous direct numerical simulation (DNS). As for the DDM strategy, it was successful as simulation time is clearly decreased and the connection between the two subdomains does not create spurious oscillations.

Originality/value

In sum, the developed solver was capable of solving, accurately and with high-precision, two- and three-dimensional compressible flows including fairly complex geometries. It is noted that the data provided by the DNS of supersonic pipe flows are not abundant in the literature and therefore will be available online for the community.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 1
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 22 March 2013

Nima Tajallipour, Vimal Kumar and Marius Paraschivoiu

The purpose of this paper is to investigate a large‐eddy simulation, using low order numerical discretization and upwinding schemes on unstructured grids, for a turbulent…

Abstract

Purpose

The purpose of this paper is to investigate a large‐eddy simulation, using low order numerical discretization and upwinding schemes on unstructured grids, for a turbulent free jet at Mach number 0.95. The accuracy and stability performance is discussed for the finite element/volume upwinding numerical code used.

Design/methodology/approach

This code is equipped with a self‐adaptive upwinding method which has been previously developed to reduce the numerical dissipation of applied low order flux calculation on unstructured elements using Roe's scheme. Herein, this method is used to numerically investigate a high Reynolds, compressible turbulent free jet and compare the results with a recently published set of experimental data. The effect of grid size is also investigated. A reasonable good agreement with the experimental measurements is obtained.

Findings

Based on the results, it is concluded that the developed self‐adaptive upwinding scheme provides a considerably better emulation of the flow regime in comparison to the full‐upwinding scheme. Different case studies have been carried out to assess the performance of self‐adaptive upwinding method and the effect of the subgrid model.

Originality/value

This paper presents an original research on self‐adaptive upwinding scheme and the effect of the subgrid model on a compressible turbulent free jet.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 23 no. 2
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 1 April 1993

S. SOLTANI, K. MORGAN and J. PERAIRE

An upwind unstructured grid cell‐centred scheme for the solution of the compressible Euler and Navier‐Stokes equations in two dimensions is presented. The algorithm…

Abstract

An upwind unstructured grid cell‐centred scheme for the solution of the compressible Euler and Navier‐Stokes equations in two dimensions is presented. The algorithm employs a finite volume formulation. Calculation of the inviscid fluxes is based on the approximate Riemann solver of Roe. Viscous fluxes are obtained from solution gradients computed by a variational recovery procedure. Higher order accuracy is achieved through performing a monotonic linear reconstruction of the solution over each cell. The steady state is obtained by a point implicit time integration of the unsteady equations using local time stepping. For supersonic inviscid flow an alternative space marching algorithm is proposed. This latter approach is applicable to supersonic flow fields containing regions of local subsonic flow. Numerical results are presented to show the performance of the proposed scheme for inviscid and viscous flows.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 3 no. 4
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 31 May 2011

S. Askari, M.H. Shojaeefard and K. Goudarzi

The purpose of this paper is to carry out a comprehensive study of compressible flow over double wedge and biconvex airfoils using computational fluid dynamics (CFD) and…

Abstract

Purpose

The purpose of this paper is to carry out a comprehensive study of compressible flow over double wedge and biconvex airfoils using computational fluid dynamics (CFD) and three analytical models including shock and expansion wave theory, Busemann's second‐order linearized approximation and characteristic method (CHM).

Design/methodology/approach

Flow over double‐wedge and biconvex airfoils was investigated by the CFD technique using the Spalart‐Allmaras turbulence model for computation of the Reynolds stresses. Flow was considered compressible, two dimensional and steady. The no slip condition was applied at walls and the Sutherland law was used to calculate molecular viscosity as a function of static temperature. First‐order upwind discretization scheme was used for the convection terms. Finite‐volume method was used for the entire solution domain meshed by quadratic computational cells. Busemann's theory, shock and expansion wave technique and CHM were the analytical methods used in this work.

Findings

Static pressure, static temperature and aerodynamic coefficients of the airfoils were calculated at various angles of attack. In addition, aerodynamic coefficients of the double‐wedge airfoil were obtained at various free stream Mach numbers and thickness ratios of the airfoil. Static pressure and aerodynamic coefficients obtained from the analytical and numerical methods were in excellent agreement with average error of 1.62 percent. Variation of the static pressure normal to the walls was negligible in the numerical simulation as well as the analytical solutions. Analytical static temperature far from the walls was consistent with the numerical values with average error of 3.40 percent. However, it was not comparable to the numerical temperature at the solid walls. Therefore, analytical solutions give accurate prediction of the static pressure and the aerodynamic coefficients, however, for the static temperature; they are only reliable far from the solid surfaces. Accuracy of the analytical aerodynamic coefficients is because of accurate prediction of the static pressure which is not considerably influenced by the boundary layer. Discrepancies between analytical and numerical temperatures near the walls are because of dependency of temperature on the boundary layer and viscous heating. Low‐speed flow near walls causes transformation of the kinetic energy of the free stream into enthalpy that leads to high temperature on the solid walls; which is neglected in the analytical solutions.

Originality/value

This paper is useful for researchers in the area of external compressible flows. This work is original.

Details

Engineering Computations, vol. 28 no. 4
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 29 July 2014

Haiming Huang, Guo Huang, Xiaoliang Xu and Weijie Li

Relevant analyses are presented on the base of the compressible vortex method for simulating the development of two or three co-rotating vortices with different…

Abstract

Purpose

Relevant analyses are presented on the base of the compressible vortex method for simulating the development of two or three co-rotating vortices with different characteristic Mach numbers. The paper aims to discuss this issue.

Design/methodology/approach

In addition to having vorticity and dilatation properties, the vortex particles also carry density, enthalpy, and entropy. Taking co-rotating vortices in two-dimensional unsteady compressible flow for an example, truncation of unbounded domains via a nonreflecting boundary condition was considered in order to make the method computationally efficient.

Findings

For two identical vortices, the effect of the vortex Mach number on merging process is not evident; if two vortices have the same circulation rather than different radiuses, the vorticity and dilatation fields of the vortex under a vortex Mach number will be absorbed by the vortex under a higher vortex Mach number. For three vortices, if the original arrangement of the vortices is changed, the evolvement of the vorticity and dilatation fields is different.

Originality/value

The paper reveals new mechanism of the three co-rotating vortices by a feasible compressible vortex method.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 24 no. 6
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 1 March 1993

J.F. MILTHORPE

A simple convection algorithm for simulation of time‐dependent supersonic and hypersonic flows of a perfect but viscous gas is described. The algorithm is based on…

Abstract

A simple convection algorithm for simulation of time‐dependent supersonic and hypersonic flows of a perfect but viscous gas is described. The algorithm is based on conservation and convection of mass, momentum and energy in a grid of rectangular cells. Examples are given for starting flow in a shock‐tube and oblique shocks generated by a wedge, at Mach numbers up to 30.4. Good comparisons are achieved with well‐known perfect gas flows.

Details

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

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Article
Publication date: 1 July 2005

C.G. Thomas and P. Nithiarasu

To improve inviscid compressible flow solution.

Abstract

Purpose

To improve inviscid compressible flow solution.

Design/methodology/approach

A local element‐size calculation procedure in the streamline direction and a local variable smoothing approach are employed to improve inviscid compressible flow solution. The characteristic based split approach is used as basic solution procedure to demonstrate the employed improvements.

Findings

Results show that employing the element size in the streamline direction improves the solution accuracy in the transonic flow region. The nodal variable smoothing is very effective below a Mach number of 0.85 and produces results without any spatial oscillations.

Originality/value

This paper fills the gap by suggesting novel procedures to study Mach number range between zero and supersonic flow.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 15 no. 5
Type: Research Article
ISSN: 0961-5539

Keywords

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