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Article
Publication date: 6 June 2016

Ashraf Muhammad, Ali J Chamkha, S Iqbal and Masud Ahmad

The purpose of this paper is to report a numerical solution for the problem of steady, two dimensional boundary layer buoyant flow on a vertical magnetized surface, when…

Abstract

Purpose

The purpose of this paper is to report a numerical solution for the problem of steady, two dimensional boundary layer buoyant flow on a vertical magnetized surface, when both the viscosity and thermal conductivity are assumed to be temperature-dependent. In this case, the motion is governed by a coupled set of three nonlinear partial differential equations, which are solved numerically by using the finite difference method (FDM) by introducing the primitive variable formulation. Calculations of the coupled equations are performed to investigate the effects of the different governing parameters on the profiles of velocity, temperature and the transverse component of magnetic field. The effects of the thermal conductivity variation parameter, viscosity variation parameter, magnetic Prandtl number Pmr, magnetic force parameter S, mixed convection parameter Ri and the Prandtl number Pr on the flow structure and heat transfer characteristics are also examined.

Design/methodology/approach

FDM.

Findings

It is noted that when the Prandtl number Pr is sufficiently large, i.e. Pr=100, the buoyancy force that driven the fluid motion is decreased that decrease the momentum boundary layer and there is no change in thermal boundary layer is noticed. It is also noted that due to slow motion of the fluid the magnetic current generates which increase the magnetic boundary layer thickness at the surface. It is observed that the momentum boundary layer thickness is increased, thermal and magnetic field boundary layers are decreased with the increase of thermal conductivity variation parameter =100. The maximum boundary layer thickness is increased for =100 and there is no change seen in the case of thermal boundary layer thickness but magnetic field boundary layer is deceased. The momentum boundary layer thickness shoot quickly for =40 but is very smooth for =50.There is no change is seen for the case of thermal boundary layer and very clear decay for =40 is noted.

Originality/value

This work is original research work.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 26 no. 5
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 1 May 1993

MICHAEL J. NUSCA

An aerothermodynamic design code for axisymmetric projectiles has been developed using a viscous‐inviscid interaction scheme. Separate solution procedures for the inviscid…

Abstract

An aerothermodynamic design code for axisymmetric projectiles has been developed using a viscous‐inviscid interaction scheme. Separate solution procedures for the inviscid and the viscous (boundary layer) fluid dynamic equations are coupled by an iterative solution procedure. Non‐equilibrium, equilibrium and perfect gas boundary layer equations are included. The non‐equilibrium gas boundary layer equations assume a binary mixture (two species; atoms and molecules) of chemically reacting perfect gases. Conservation equations for each species include finite reaction rates applicable to high temperature air. The equilibrium gas boundary layer equations assume infinite rate reactions, while the perfect gas equations assume no chemical reactions. Projectile near‐wall and surface flow profiles (velocity, pressure, density, temperature and heat transfer) representing converged solutions to both the inviscid and viscous equations can be obtained in less than two minutes on minicomputers. A technique for computing local reverse flow regions is included. Computations for yawed projectiles are accomplished using a coordinate system transformation technique that is valid for small angle‐of‐attack. Computed surface pressure, heat transfer rates and aerodynamic forces and moments for 1.25 &le Mach No. &le 10.5 are compared to wind tunnel and free flight measurements on flat plate, blunt‐cone, and projectile geometries such as a cone‐cylinder‐flare.

Details

Engineering Computations, vol. 10 no. 5
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 28 October 2013

Lelanie Smith, Oliver Oxtoby, A. Malan and Josua Meyer

– The purpose of this paper is to introduce a unique technique to couple the two-integral boundary layer solutions to a generic inviscid solver in an iterative fashion.

Abstract

Purpose

The purpose of this paper is to introduce a unique technique to couple the two-integral boundary layer solutions to a generic inviscid solver in an iterative fashion.

Design/methodology/approach

The boundary layer solution is obtained using the two-integral method to solve displacement thickness point by point with a local Newton method, at a fraction of the cost of a conventional mesh-based, full viscous solution. The boundary layer solution is coupled with an existing inviscid solver. Coupling occurs by moving the wall to a streamline at the computed boundary layer thickness and treating it as a slip boundary, then solving the flow again and iterating. The Goldstein singularity present when solving boundary layer equations is overcome by solving an auxiliary velocity equation along with the displacement thickness.

Findings

The proposed method obtained favourable results when compared with the analytical solutions for flat and inclined plates. Further, it was applied to modelling the flow around a NACA0012 airfoil and yielded results similar to those of the widely used XFOIL code.

Originality/value

A unique method is proposed for coupling of the boundary layer solution to the inviscid flow. Rather than the traditional transpiration boundary condition, mesh movement is employed to simulate the boundary layer thickness in a more physically meaningful way. Further, a new auxiliary velocity equation is presented to circumvent the Goldstein singularity.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 23 no. 8
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 1 March 1962

G.V. Lachmann

Since the end of the Second World War, many spectacular advances have been made in aeronautics, thanks chiefly to the development of more powerful and economical jet…

Abstract

Since the end of the Second World War, many spectacular advances have been made in aeronautics, thanks chiefly to the development of more powerful and economical jet engines. As to the parasitic drag of manned aircraft, progress has been confined to reducing unfavourable compressibility effects (area rule, Whitcombe bodies); methods to suppress separation have been developed but no new methods to reduce the drag resulting from turbulent boundary layers developing over the exposed surfaces have as yet found practical application.

Details

Aircraft Engineering and Aerospace Technology, vol. 34 no. 3
Type: Research Article
ISSN: 0002-2667

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Article
Publication date: 1 September 1955

T.R. Nonweiler

WRITING an introduction to an article by Mr S. B. Gates on Trailing‐Edge Flaps, which appeared in these columns in 1937, the Editor felt constrained to admit his…

Abstract

WRITING an introduction to an article by Mr S. B. Gates on Trailing‐Edge Flaps, which appeared in these columns in 1937, the Editor felt constrained to admit his bewilderment over the number and variety of types of high‐lift aid which then existed. Without intending any disrespect, I imagine that the progress of years must have added to his embarrassment. It has certainly added to the number of devices in use and under test.

Details

Aircraft Engineering and Aerospace Technology, vol. 27 no. 9
Type: Research Article
ISSN: 0002-2667

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Article
Publication date: 8 July 2019

Massoud Tatar, Mojtaba Tahani and Mehran Masdari

In this paper, the applicability of shear stress transport k-ω model along with the intermittency concept has been investigated over pitching airfoils to capture the…

Abstract

Purpose

In this paper, the applicability of shear stress transport k-ω model along with the intermittency concept has been investigated over pitching airfoils to capture the laminar separation bubble (LSB) position and the boundary layer transition movement. The effect of reduced frequency of oscillations on boundary layer response is also examined.

Design/methodology/approach

A two-dimensional computational fluid dynamic code was developed to compute the effects of unsteadiness on LSB formation, transition point movement, pressure distribution and lift force over an oscillating airfoil using transport equation of intermittency accompanied by the k-ω model.

Findings

The results indicate that increasing the angle of attack over the stationary airfoil causes the LSB size to shorten, leading to a rise in wall shear stress and pressure suction peak. In unsteady cases, both three- and four-equation models are capable of capturing the experimentally measured transition point well. The transition is delayed for an unsteady boundary layer in comparison with that for a static airfoil at the same angle of attack. Increasing the unsteadiness of flow, i.e. reduced frequency, moves the transition point toward the trailing edge of the airfoil. This increment also results in lower static pressure suction peak and hence lower lift produced by the airfoil. It was also found that the fully turbulent k-ω shear–stress transport (SST) model cannot capture the so-called figure-of-eight region in lift coefficient and the employment of intermittency transport equation is essential.

Practical implications

Boundary layer transition and unsteady flow characteristics owing to airfoil motion are both important for many engineering applications including micro air vehicles as well as helicopter blade, wind turbine and aircraft maneuvers. In this paper, the accuracy of transition modeling based on intermittency transport concept and the response of boundary layer to unsteadiness are investigated.

Originality/value

As a conclusion, the contribution of this paper is to assess the ability of intermittency transport models to predict LSB and transition point movements, static pressure distribution and aerodynamic lift variations and boundary layer flow pattern over dynamic pitching airfoils with regard to oscillation frequency effects for engineering problems.

Details

Aircraft Engineering and Aerospace Technology, vol. 91 no. 8
Type: Research Article
ISSN: 1748-8842

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Article
Publication date: 6 May 2020

S. Das, R.R. Patra and R.N. Jana

The purpose of this study is to present the significance of Joule heating, viscous dissipation, magnetic field and slip condition on the boundary layer flow of an…

Abstract

Purpose

The purpose of this study is to present the significance of Joule heating, viscous dissipation, magnetic field and slip condition on the boundary layer flow of an electrically conducting Boussinesq couple-stress fluid induced by an exponentially stretching sheet embedded in a porous medium under the effect of the magnetic field of the variable kind. The heat transfer phenomenon is accounted for under thermal radiation, Joule and viscous dissipation effects.

Design/methodology/approach

The governing nonlinear partial differential equations are transformed to the nonlinear ordinary differential equations (ODEs) by using some appropriate dimensionless variables and then the consequential nonlinear ODEs are solved numerically by making the use of the well-known shooting iteration technique along with the standard fourth-order Runge–Kutta integration scheme. The impact of emerging flow parameters on velocity and temperature profiles, streamlines, local skin friction coefficient and Nusselt number are described comprehensively through graphs and tables.

Findings

Results reveal that the velocity profile is observed to diminish considerably within the boundary layer in the presence of a magnetic field and slip condition. The enhanced radiation parameter is to decline the temperature field. The slip effect is favorable for fluid flow.

Originality/value

Till now, slip effect on Boussinesq couple-stress fluid over an exponentially stretching sheet embedded in a porous medium has not been explored. The present results are validated with the previously published study and found to be highly satisfactory.

Details

Multidiscipline Modeling in Materials and Structures, vol. 16 no. 5
Type: Research Article
ISSN: 1573-6105

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Article
Publication date: 1 December 1948

N.A.V. Piercy, L.G. Whitehead and R.A. Tyler

THE greatly increased transition Reynolds numbers now attained in the boundary layers of cylinders having favourably shaped sections have renewed interest in the solution…

Abstract

THE greatly increased transition Reynolds numbers now attained in the boundary layers of cylinders having favourably shaped sections have renewed interest in the solution of the equations of steady flow in a thin boundary layer. It is familiar that the scries solutions of Blasius and Hiemenz, improved by Howarth (ref. 1), and of Falkner (ref. 2) become severely restricted in range when applied to cylinders having other than bluff sections. But it appears that a series solution of substantially greater range is possible, at least for symmetrical flow, provided that the nose of the section is rounded. This problem forms the subject of Section I of the present paper.

Details

Aircraft Engineering and Aerospace Technology, vol. 20 no. 12
Type: Research Article
ISSN: 0002-2667

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Article
Publication date: 15 February 2020

Yunpeng Wang and Roger E. Khayat

The purpose of this study is to examine theoretically the axisymmetric flow of a steady free-surface jet emerging from a tube for high inertia flow and moderate surface…

Abstract

Purpose

The purpose of this study is to examine theoretically the axisymmetric flow of a steady free-surface jet emerging from a tube for high inertia flow and moderate surface tension effect.

Design/methodology/approach

The method of matched asymptotic expansion is used to explore the rich dynamics near the exit where a stress singularity occurs. A boundary layer approach is also proposed to capture the flow further downstream where the free surface layer has grown significantly.

Findings

The jet is found to always contract near the tube exit. In contrast to existing numerical studies, the author explores the strength of upstream influence and the flow in the wall layer, resulting from jet contraction. This influence becomes particularly evident from the nonlinear pressure dependence on the upstream distance, as well as the pressure undershoot and overshoot at the exit for weak and strong gravity levels, respectively. The approach is validated against existing experimental and numerical data for the jet profile and centerline velocity where good agreement is obtained. Far from the exit, the author shows how the solution in the diffusive region can be matched to the inviscid far solution, providing the desired appropriate initial condition for the inviscid far flow solution. The location, at which the velocity becomes uniform across the jet, depends strongly on the gravity level and exhibits a non-monotonic behavior with respect to gravity and applied pressure gradient. The author finds that under weak gravity, surface tension has little influence on the final jet radius. The work is a crucial supplement to the existing numerical literature.

Originality/value

Given the presence of the stress singularity at the exit, the work constitutes a superior alternative to a computational approach where the singularity is typically and inaccurately smoothed over. In contrast, in the present study, the singularity is entirely circumvented. Moreover, the flow details are better elucidated, and the various scales involved in different regions are better identified.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 10
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 11 October 2018

Yang Zhang, Jianfeng Zou, Jiahua Xie, Xiaoyue Li, Zhenhai Ma and Yao Zheng

When a reflected shock interacts with the boundary layer in a shock tube, the shock bifurcation occurs near the walls. Although the study of the shock bifurcation has been…

Abstract

Purpose

When a reflected shock interacts with the boundary layer in a shock tube, the shock bifurcation occurs near the walls. Although the study of the shock bifurcation has been carried out by many researchers for several decades, little attention has been devoted to investigate the instability pattern of the bifurcation. This research work aims to successfully capture the asymmetry of the whole flow field, and attempt to achieve the instability mechanism of the shock bifurcation by a direct numerical simulation of the reflected shock wave/boundary layer interaction at Ma = 1.9. In addition, the reason for the formation of the bifurcated structure is also explored.

Design/methodology/approach

The spatial and temporal evolution of the shock bifurcation is obtained by solving the two-dimensional compressible Navier–Stokes equations using a seventh-order accurate weighted essentially non-oscillatory (WENO) scheme and a three-step Runge–Kutta time advancing approach.

Findings

The results show that the formation of shock bifurcation is mainly because of the shock/gradient field interaction, and the height of the bifurcated foot increases with the growth of the shock intensity and the gradient field. The unsteady asymmetry of the upper and bottom shock bifurcated structures is because of the vortex shedding with high frequency in the rear recirculation zone, which leads to the fluctuation of the recirculation area. The vortex shedding process behind the bifurcated structure closely resembles the Karman vortex street formed by the flow around the cylinder. The dimensionless vortex shedding frequency varies between 0.01 and 0.02. In comparison to the scenario at Ma = 1.9, the occurring time of instability is delayed and the upper and bottom bifurcated feet intersect in a relatively short time at Ma = 3.5. The region behind the bifurcated shock is a transitional flow field containing obvious cell structures and “isolated islands.”

Originality/value

This paper discovers an unsteady flow pattern of the shock bifurcation, and the mechanism of this instability in the reflected shock/boundary layer interaction is revealed in detail.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 28 no. 10
Type: Research Article
ISSN: 0961-5539

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