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Nigel Peake - One of the best experts on this subject based on the ideXlab platform.
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The unsteady lift on a swept blade tip
Journal of Fluid Mechanics, 1994Co-Authors: Nigel PeakeAbstract:Highly swept blades are now commonly used in modern aeroengines, and in this paper we solve a model problem of relevance to the understanding and prediction of noise generation by the interaction between incident vortical disturbances and such a blade. In order to include the potentially significant effects of the blade-tip region, we consider a (semi-Infinite Span) quarter-plane aligned at a non-zero sweep angle to supersonic mean flow, with a single harmonic gust incident on the quarterplane from upstream. The solution is completed using a novel application of the Wiener–Hopf technique, in which the usual factorisation is carried out with respect to two independent complex variables separately, and closed-form expressions for the practically important lift per unit Span are derived for both the subsonic and the supersonic leading-edge regimes. The dependence of the unsteady response on the sweep angle and the gust wavenumbers is examined, and in particular we demonstrate that the magnitude of the effects of the tip region is significantly reduced by increasing the blade sweep or by considering gusts of higher frequency. It also becomes clear that the magnitude of the unsteady response can be either decreased or increased by sweeping the blade, in a way which proves highly dependent on the particular values of the flow parameters. In addition, we consider the two critical values of the gust trace speed along the leading edge which correspond to the sonic velocities in the two Spanwise directions, and for which the chordwise oscillation of the unsteady lift distribution on an Infinite-Span blade vanishes. In these two cases, the lift per unit Span (integrated over the Infinite chord) is clearly singular, but we demonstrate that the effect of including the blade tip is to smooth out just one of these singularities, and replace it instead by a relatively large, but finite, value.
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The interaction between a steady jet flow and a supersonic blade tip
Journal of Fluid Mechanics, 1993Co-Authors: Nigel PeakeAbstract:The potentially high level of noise generated by modern counter-rotation propellers has attracted considerable interest and concern, and one of the most potent mechanisms involved is the unsteady interaction between the tip vortex shed from the tips of the forward blade row and the rear row. In this paper a model problem is considered, in which the tip vortex is represented by a jet of constant axial velocity, which is convected at right angles to itself by a uniform supersonic mean flow, and which is cut by a rigid airfoil with its chord aligned along the mean flow direction. Ffowcs Williams & Guo have previously considered this problem for an Infinite-Span airfoil and a circular jet; in this paper we extend their analysis to include the effects of the presence of the second-row blade tip on the interaction, by considering a semi-Infinite-Span airfoil. As a first attempt, the case of a highly compact jet, represented by a delta-function upwash on the airfoil, is considered, and both the total lift on the airfoil and the radiation are investigated. The presence of the airfoil corner and side edge is seen to cause the lift to decay in time from its Infinite-Span value towards zero, due to a Spanwise motion round the side edge; whilst the radiation is shown to be composed of two Signals, the first received directly from the interaction between the jet and the leading edge, and the second resulting from the diffraction of sound waves emanating from the leading edge by the side edge. The effect of choosing a more diffuse upwash distribution is then considered, in which case it becomes clear that the first signal has a considerably larger amplitude, and shorter duration, than the second, diffracted signal.
Daoud Ait-kadi - One of the best experts on this subject based on the ideXlab platform.
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Age replacement policies for two-component systems with stochastic dependence
Journal of Quality in Maintenance Engineering, 2015Co-Authors: Zouheir Malki, Daoud Ait-kadi, Mohamed-salah OualiAbstract:Purpose – The purpose of this paper is to investigate age replacement policies for two-component parallel system with stochastic dependence. The stochastic dependence considered, is modeled by a one-sided domino effect. The failure of component 1 at instant t may induce the failure of component 2 at instant t+τ with probability p 1→2. The time delay τ is a random variable with known probability density function h p 1→2 (.). The system is considered in a failed state when both components are failed. The proposed replacement policies suggest to replace the system upon failure or at age T whichever occurs first. Design/methodology/approach – In the first policy, costs and durations associated with maintenance activities are supposed to be constant. In the second replacement policy, the preventive replacement cost depends on the system’s state and age. The expected cost per unit of time over an Infinite Span is derived and numerical examples are presented. Findings – In this paper and especially in the second...
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Optimal replacement policies for two-component parallel system with stochastic dependence
2013Co-Authors: Zouheir Malki, Daoud Ait-kadi, Mohamed-salah OualiAbstract:In this paper, age replacement policies for two-component parallel system with stochastic dependence are investigated. The stochastic dependence considered, is modeled by a one-sided domino effect. The failure of component 1 at instant t may induce the failure of component 2 at instant t + τ with a given probability. The time delay is a random variable with known probability density function. The system is considered in a failed state when both components are failed. The proposed replacement policies suggest to replace the system upon failure or at age T whichever occurs first. In the first policy, costs and durations associated with maintenance activities are supposed to be constant. In the second replacement policy, the preventive replacement cost depends on the system's state and age. The expected cost per unit of time over an Infinite Span is derived and numerical examples are presented. The mathematical model can be used to analyze the stochastic dependence on the performance of the system.
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Optimal periodic replacement strategy using new and used items
Journal of Decision Systems, 2003Co-Authors: Daoud Ait-kadi, Mohamed Anouar Jamali, Abdelhakim ArtibaAbstract:An optimal block replacement strategy using new and used items is presented. The preventive replacement using new items are performed at T, 2T,… regardless of the age and the states of the operating items. At failure, the failed item is replaced by a used one whose age is x. Two analytical models are proposed to determine the optimal couple (T*, x*), which minimizes the total expected cost per unit of time over an Infinite Span or maximizes the steady state availability of the item. The residual lifetime must be greater or equal to some proportion γ of the replacement cycle of length T. Optimal strategies are derived for an item whose lifetime is distributed according to Gamma (λ, 2). The proposed replacement strategy seems quite performant and easy to implement.
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Spare provisioning strategy for preventively replaced systems subjected to random failure
International Journal of Production Economics, 2001Co-Authors: Anis Chelbi, Daoud Ait-kadiAbstract:Abstract A jointly optimal periodic replacement and spare parts provisioning strategy is discussed. This strategy is completely defined once the replacement period T, the replenishment cycle R=kT (k=1, 2, …) , and the ordering point s are determined. The optimal strategy (T * , R * , s * ) , if it exists, is one which minimizes the total expected cost (replenishment cost+spare parts inventory management cost) per time unit over an Infinite Span. A numerical algorithm is proposed to find the optimal strategy. The system lifetime distribution, the probability distribution of the demand during the lead-time and the costs associated to the replenishment and the spare parts inventory management are supposed to be known. Some numerical results are presented.
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An optimal inspection strategy for randomly failing equipment
Reliability Engineering & System Safety, 1999Co-Authors: Anis Chelbi, Daoud Ait-kadiAbstract:Abstract This paper addresses the problem of generating optimal inspection strategies for randomly failing equipment where imminent failure is not obvious and can only be detected through inspection. Inspections are carried out following a condition-based procedure. The equipment is replaced if it has failed or if it shows imminent signs of failure. The latter state is indicated by measuring certain predetermined control parameters during inspection. Costs are associated with inspection, idle time and preventive or corrective actions. An optimal inspection strategy is defined as the inspection sequence minimizing the expected total cost per time unit over an Infinite Span. A mathematical model and a numerical algorithm are developed to generate an optimal inspection sequence. As a practical example, the model is applied to provide a machine tool operator with a time sequence for inspecting the cutting tool. The tool life time distribution and the trend of one control parameter defining its actual condition are supposed to be known.
Oleg N. Kirillov - One of the best experts on this subject based on the ideXlab platform.
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Membrane flutter induced by radiation of surface gravity waves on a uniform flow
Journal of Fluid Mechanics, 2020Co-Authors: Joris Labarbe, Oleg N. KirillovAbstract:We consider stability of an elastic membrane being on the bottom of a uniform horizontal flow of an inviscid and incompressible fluid of finite depth with free surface. The membrane is simply supported at the leading and the trailing edges which attach it to the two parts of the horizontal rigid floor. The membrane has an Infinite Span in the direction perpendicular to the direction of the flow and a finite length in the direction of the flow. For the membrane of Infinite length we derive a full dispersion relation that is valid for arbitrary depth of the fluid layer and find conditions for the flutter of the membrane due to emission of surface gravity waves. We describe this radiation-induced instability by means of the perturbation theory of the roots of the dispersion relation and the concept of negative energy waves and discuss its relation to the anomalous Doppler effect.
Christoph J. Mack - One of the best experts on this subject based on the ideXlab platform.
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Global stability of swept flow around a parabolic body: features of the global spectrum
Journal of Fluid Mechanics, 2011Co-Authors: Christoph J. Mack, Peter J. SchmidAbstract:The global temporal stability of three-dimensional compressible flow about a yawed parabolic body of Infinite Span is investigated using an iterative eigenvalue technique in combination with direct numerical simulations. The computed global spectrum provides a comprehensive picture of the temporal perturbation dynamics of the flow, and a wide and rich variety of modes has been uncovered for the investigated parameter choices: stable and unstable boundary-layer modes, different types of stable and unstable acoustic modes, and stable wavepacket modes have been found. A parameter study varying the Spanwise perturbation wavenumber and the sweep Reynolds number reproduced a preferred Spanwise length scale and a critical Reynolds number for a boundary-layer or acoustic instability. Convex leading-edge curvature has been found to have a strongly stabilizing effect on boundary-layer modes but only a weakly stabilizing effect on acoustic modes. Furthermore, for certain parameter choices, the acoustic modes have been found to dominate the boundary-layer modes. © 2011 Cambridge University Press.
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Global stability of swept flow around a parabolic body: connecting attachment-line and crossflow modes
Journal of Fluid Mechanics, 2008Co-Authors: Christoph J. Mack, Peter J. Schmid, Jörn SesterhennAbstract:The global linear stability of a three-dimensional compressible flow around a yawed parabolic body of Infinite Span is investigated using an iterative eigenvalue method in conjunction with direct numerical simulations. The computed global spectrum shows an unstable branch consisting of three-dimensional boundary layer modes whose amplitude distributions exhibit typical characteristics of both attachment-line and crossflow modes. In particular, global eigenfunctions with smaller phase velocities display a more pronounced structure near the stagnation line, reminiscent of attachment-line modes while still featuring strong crossflow vortices further downstream. This analysis establishes a link between the two prevailing instability mechanisms on a swept parabolic body which, so far, have only been studied separately and locally. A parameter study shows maximum modal growth for a Spanwise wavenumber of β = 0.213, suggesting a preferred disturbance length scale in the sweep direction.
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Global stability of swept flow around a parabolic body: Connecting attachment-line and crossflow modes
Journal of Fluid Mechanics, 2008Co-Authors: Christoph J. Mack, Peter Schmid, Jörn SesterhennAbstract:The global linear stability of a three-dimensional compressible flow around a yawed parabolic body of Infinite Span is investigated using an iterative eigenvalue method in conjunction with direct numerical simulations. The computed global spectrum shows an unstable branch consisting of three-dimensional boundary layer modes whose amplitude distributions exhibit typical characteristics of both attachment-line and crossflow modes. In particular, global eigenfunctions with smaller phase velocities display a more pronounced structure near the stagnation line, reminiscent of attachment-line modes while still featuring strong crossflow vortices further downstream. This analysis establishes a link between the two prevailing instability mechanisms on a swept parabolic body which, so far, have only been studied separately and locally. A parameter study shows maximum modal growth for a Spanwise wavenumber of ß = 0.213, suggesting a preferred disturbance length scale in the sweep direction. © 2008 Cambridge University Press.
Pijush K. Kundu - One of the best experts on this subject based on the ideXlab platform.
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Chapter 14 – Aerodynamics
Fluid Mechanics, 2016Co-Authors: Pijush K. KunduAbstract:Aerodynamics is the branch of fluid mechanics that deals with the fluid dynamic forces and moments that act on moving objects. Lift and drag, the aerodynamic force components perpendicular and parallel to the oncoming fluid velocity, are both the result of viscous effects within a fluid flow. For two-dimensional (Infinite Span) airfoils at low or moderate angles of attack (up to ∼15°), lift may be predicted by ideal flow analysis when the effect of viscosity is represented by choosing the foil's circulation so that the aft flow-separation point occurs at the foil's trailing edge. For finite-Span wings, trailing vortices aligned with the oncoming flow develop downstream of each wing tip and induce a downward vertical velocity at the wing. This induced velocity locally changes the angle of attack along the wing in a manner that rotates the lift force backward to produce a drag force known as induced drag. Fish, birds, and sailboats use aerodynamic lift forces for propulsion and maneuvering.