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Article
Publication date: 1 April 1994

A. Huerta and F. Casadei

The arbitrary Lagrangian—Eulerian (ALE)formulation, which is already well established in the hydrodynamics andfluid‐structure interaction fields, is extended to materials…

Abstract

The arbitrary Lagrangian—Eulerian (ALE) formulation, which is already well established in the hydrodynamics and fluid‐structure interaction fields, is extended to materials with memory, namely, non‐ linear path‐dependent materials. Previous attempts to treat non‐ linear solid mechanics with the ALE description have, in common, the implicit interpolation technique employed. Obviously, this implies a numerical burden which may be uneconomical and may induce to give up this formulation, particularly in fast‐transient dynamics where explicit algorithms are usually employed. Here, several applications are presented to show that if adequate stress updating techniques are implemented, the ALE formulation could be much more competitive than classical Lagrangian computations when large deformations are present. Moreover, if the ALE technique is interpreted as a simple interpolation enrichment, adequate—in opposition to distorted or locally coarse—meshes are employed. Notice also that impossible computations (or at least very involved numerically) with a Lagrangian code are easily implementable in an ALE analysis. Finally, it is important to observe that the numerical examples shown range from a purely academic test to real engineering simulations. They show the effective applicability of this formulation to non‐linear solid mechanics and, in particular, to impact, coining or forming analysis.

Article
Publication date: 6 November 2023

Qing Liu, Li Wang and Ming Feng

This paper aims to study the clearance compatibility of active magnetic bearing (AMB) and gas bearing (GB) to achieve a single-structured hybrid gas-magnetic bearing (HGMB), which…

Abstract

Purpose

This paper aims to study the clearance compatibility of active magnetic bearing (AMB) and gas bearing (GB) to achieve a single-structured hybrid gas-magnetic bearing (HGMB), which uses a single bearing structure to realize both the functions of gas bearing and magnetic bearing.

Design/methodology/approach

Because the radial clearance size of the AMB is typically ten times larger than that of the GB, radial clearance compatibility of GB and AMB needs to maximize the radial clearance of GB by adjusting structural parameters. Parametric analysis of structural parameters of GB is explored. Furthermore, a general structural design principle based on static analysis, rotordynamic performance and system stability is established for the single-structured HGMB.

Findings

Load capacity is vastly reduced due to the enlarged radial clearance of the GB. A minimum clearance needs to be ensured by increasing the bearing diameter or width to compensate for the reduced load capacity, yet indirectly raising the bearing load. Increased bearing load is conducive to stability, yet it raises the risk of rotor abrasion. In addition, excessively large bearing diameter leads to system instability, and inappropriate bearing width affects critical speeds. A general structural design principle is established and the designed HGMB–rotor processes optimal performances.

Originality/value

A single-structured HGMB is proposed to address the urgent demand for high-speed, cryogenic turboexpanders with frequent starts/stops. This design applies a single-bearing structure to realize the characteristics of both GB and AMB, greatly simplifying the implementation, reducing air friction loss and raising critical speeds. This paper provides a fresh perspective on the development of cryogenic turboexpanders for hydrogen liquefaction. It theoretically validates the feasibility and provides a design guide for a single-structured HGMB system.

Details

Industrial Lubrication and Tribology, vol. 75 no. 10
Type: Research Article
ISSN: 0036-8792

Keywords

Article
Publication date: 1 May 1930

J.W. Maccoll

THIS paper aims at giving the most important results of modern German research upon the motion of incompressible fluids. Before dealing with the latest developments, I have…

Abstract

THIS paper aims at giving the most important results of modern German research upon the motion of incompressible fluids. Before dealing with the latest developments, I have thought it advisable to give a short account of the older researches upon which the present work is based. It is hoped that this résumé will give a fairly complete survey of the methods that have led to the present insight into the hydrodynamical mechanism.

Details

Aircraft Engineering and Aerospace Technology, vol. 2 no. 5
Type: Research Article
ISSN: 0002-2667

Article
Publication date: 5 May 2015

Xi Ye, Longquan Sun and Fuzhen Pang

The purpose of this paper is to research the interaction between multiple bubbles and their noise radiation considering the influence of compressibility. The influences of bubble…

Abstract

Purpose

The purpose of this paper is to research the interaction between multiple bubbles and their noise radiation considering the influence of compressibility. The influences of bubble spacing, initial inner pressure, buoyance and phase difference are presented with different bubbles arrangements.

Design/methodology/approach

Based on wave equation, the new boundary integral equation considering the compressibility is given by the matching between prophase and anaphase approximation of bubble motion and solved with boundary element method. The time-domain characteristics of noise induced by multiple bubbles are obtained by the moving boundary Kirchhoff integral equation. With the surface discretization and coordinate transformation, the bubbles surface is treated as a moving deformable boundary and noise source, and the integral is implemented on the surface directly.

Findings

Numerical results show the manner of jet generation will be affected by the phase difference between bubbles. With the increasing of phase difference, the directive property of noise becomes obvious. With the enlargement of initial inner pressure, the sound pressure will arise at the early stage of expanding, and the increasing of buoyance parameter will reduce the sound pressure after the generation of jet. Since the consideration of compressibility, the oscillation amplitude of bubbles will be weakened.

Originality/value

The paper could provide the reference for the research about the dynamics and noise characteristics of multiple bubbles in compressible fluid. And the new method based on boundary integral equation to simulate the multiple bubbles motion and noise radiation is presented.

Details

Engineering Computations, vol. 32 no. 3
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 4 September 2019

Mithun Kanchan and Ranjith Maniyeri

The purpose of this paper is to perform two-dimensional numerical simulation involving fluid-structure interaction of flexible filament. The filament is tethered to the bottom of…

Abstract

Purpose

The purpose of this paper is to perform two-dimensional numerical simulation involving fluid-structure interaction of flexible filament. The filament is tethered to the bottom of a rectangular channel with oscillating fluid flow inlet conditions at low Reynolds number. The simulations are performed using a temporal second-order finite volume-based immersed boundary method (IBM). Further, to understand the relation between different aspect ratios i.e. ratio of filament length to channel height (Len/H) and fixed channel geometry ratio, i.e. ratio of channel height to channel length (H/Lc) on mixing and pumping capabilities.

Design/methodology/approach

The discretization of governing continuity and Navier–Stokes equation is done by finite-volume method on a staggered Cartesian grid. SIMPLE algorithm is used to solve fluid velocity and pressure terms. Two cases of oscillatory flow conditions are used with the flexible filament tethered at the center of bottom channel wall. The first case is sinusoidal oscillatory flow with phase shift (SOFPS) and second case is sinusoidal oscillatory flow without phase shift (SOF). The simulation results are validated with filament dynamics studies of previous researchers. Further, parametric analysis is carried to study the effect of filament length (aspect ratio), filament bending rigidity and Reynolds number on the complex deformation and behavior of flexible filament interacting with nearby oscillating fluid motion.

Findings

It is found that selection of right filament length and bending rigidity is crucial for fluid mixing scenarios. The phase shift in fluid motion is also found to critically effect filament displacement dynamics, especially for rigid filaments. Aspect ratio, suitable for mixing applications is dependent on channel geometry ratio. Symmetric deformation is observed for filaments subjected to SOFPS condition irrespective of bending rigidity, whereas medium and low rigidity filaments placed in SOF condition show severe asymmetric behavior. Two key findings of this study are: symmetric filament conformity without appreciable bending produces sweeping motion in fluid flow, which is highly suited for mixing application; and asymmetric behavior shown by the filament depicts antiplectic metachronism commonly found in beating cilia. As a result, it is possible to pin point the type of fluid motion governing fluid mixing and fluid pumping. The developed computational model can, thus, successfully demonstrate filament-fluid interaction for a wide variety of similar problems.

Originality/value

The present study uses a temporal second-order finite volume-based IBM to examine flexible filament dynamics for various applications such as fluid mixing. Also, it highlights the relationship between channel geometry ratio and filament aspect ratio and its effect on filament sweep patterns. The study further reports the effect of filament displacement dynamics with or without phase shift for inlet oscillating fluid flow condition.

Details

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

Keywords

Article
Publication date: 1 December 1930

N.A.V. Piercy

WE found, on experimental grounds in Article I, that the field of air‐flow past a short body of low resistance shape, such as an aerofoil, comprises two dissimilar parts: (a) a…

Abstract

WE found, on experimental grounds in Article I, that the field of air‐flow past a short body of low resistance shape, such as an aerofoil, comprises two dissimilar parts: (a) a thin boundary layer enveloping the body and dominated by viscous effects, and (b) a motion outside the boundary layer in which viscosity is much less important. It will be remembered that in the external motion occur the large pressure changes, which, transmitted through the boundary layer, account for nearly all the lift and for part of the drag. These pressures we observed to be calculable from the velocities without appreciable error by Bernoulli's equation. In the present Article we confine attention to this external flow, assuming it to be steady, incompressible, and inviscid. Its dependence upon (a), already discussed to some extent, we ignore; the boundary layer is conceived to be everywhere very thin, so that the only role it plays is to allow of relative velocity at the surface of the body. The assumptions made, excepting that of incompressibility, will appear drastic, and it will not be surprising if some of our deductions prove discordant with experimental fact. Nevertheless, they lead to a theory which finds many applications and uses in real fluid motion, and, in particular, gives an intimate view of aerofoil flow that is very close to the truth. It is convenient to develop our reasoning in analytical terms and for simplicity to restrict the flow to two dimensions (Article 1, §5). But the engineer will find special scope in this part of aerodynamics for graphical methods in the solution of particular problems.

Details

Aircraft Engineering and Aerospace Technology, vol. 2 no. 12
Type: Research Article
ISSN: 0002-2667

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 laminar…

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

Keywords

Article
Publication date: 1 June 1960

H.L. Price

An examination is made of the way in which the ground resonance properties of a helicopter depend on the fuselage damping, blade damping, drag hinge offset, inter‐blade spring…

Abstract

An examination is made of the way in which the ground resonance properties of a helicopter depend on the fuselage damping, blade damping, drag hinge offset, inter‐blade spring stiffness, blade mass and angular velocity of the rotor as specified by the parameters λƒ, λβ, Λ1, Λ2, Λ3 and Ω respectively. A direct method of drawing stability boundaries in the (Ω, λβ) plane is developed, and the geometry of these boundaries as the remaining parameters vary is studied theoretically at length. Arising out of the geometry, the validity of Coleman's criterion for stability is examined, and it is shown that the requirement that the product λƒ,λβ should have a certain minimum value is not itself sufficient to ensure stability for all Ω. The condition can be made sufficient by a proper and unique choice of the individual values of ?f and ??, and these values are found in terms of Λ1, Λ2, and Λ3. All other cases of stability require a larger value of the product λƒ, λβ. An alternative criterion for stability is developed which gives the minimum value of λƒ capable of ensuring stability for all Ω. This, and the preceding criterion, are mathematically exact, and follow from Coleman's equations of motion as applied to the case of a helicopter on isotropic supports. A brief account is also given of the case of a rotor having inter‐blade friction damping as against the viscous damping previously assumed.

Details

Aircraft Engineering and Aerospace Technology, vol. 32 no. 6
Type: Research Article
ISSN: 0002-2667

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 both the…

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

Keywords

Article
Publication date: 5 August 2021

Gladys Tharapatla, Pamula Rajakumari and Ramana G.V. Reddy

This paper aims to analyze heat and mass transfer of magnetohydrodynamic (MHD) non-Newtonian fluids flow past an inclined thermally stratified porous plate using a numerical…

Abstract

Purpose

This paper aims to analyze heat and mass transfer of magnetohydrodynamic (MHD) non-Newtonian fluids flow past an inclined thermally stratified porous plate using a numerical approach.

Design/methodology/approach

The flow equations are set up with the non-linear free convective term, thermal radiation, nanofluids and Soret–Dufour effects. Thus, the non-linear partial differential equations of the flow analysis were simplified by using similarity transformation to obtain non-linear coupled equations. The set of simplified equations are solved by using the spectral homotopy analysis method (SHAM) and the spectral relaxation method (SRM). SHAM uses the approach of Chebyshev pseudospectral alongside the homotopy analysis. The SRM uses the concept of Gauss-Seidel techniques to the linear system of equations.

Findings

Findings revealed that a large value of the non-linear convective parameters for both temperature and concentration increases the velocity profile. A large value of the Williamson term is detected to elevate the velocity plot, whereas the Casson parameter degenerates the velocity profile. The thermal radiation was found to elevate both velocity and temperature as its value increases. The imposed magnetic field was found to slow down the fluid velocity by originating the Lorentz force.

Originality/value

The novelty of this paper is to explore the heat and mass transfer effects on MHD non-Newtonian fluids flow through an inclined thermally-stratified porous medium. The model is formulated in an inclined plate and embedded in a thermally-stratified porous medium which to the best of the knowledge has not been explored before in literature. Two elegance spectral numerical techniques have been used in solving the modeled equations. Both SRM and SHAM were found to be accurate.

Details

World Journal of Engineering, vol. 20 no. 1
Type: Research Article
ISSN: 1708-5284

Keywords

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