Modal scattering at an impedance transition in a lined flow duct

An explicit Wiener-Hopf solution is derived to describe the scattering of duct modes at a hard-soft wall impedance transition in a circular duct with uniform mean flow. Specifically, we have a circular duct r = 1, - ∞ < x < ∞ with mean flow Mach number M > 0 and a hard wall along x < 0 and a wall of impedance Z along x > 0. A minimum edge condition at x = 0 requires a continuous wall streamline r = 1 + h(x, t), no more singular than h = Ο(x1/2) for x ↓ 0. A mode, incident from x < 0, scatters at x = 0 into a series of reflected modes and a series of transmitted modes. Of particular interest is the role of a possible instability along the lined wall in combination with the edge singularity. If one of the "upstream" running modes is to be interpreted as a downstream-running instability, we have an extra degree of freedom in the Wiener-Hopf analysis that can be resolved by application of some form of Kutta condition at x = 0, for example a more stringent edge condition where h = Ο(x3/2) at the downstream side. The question of the instability requires an investigation of the modes in the complex frequency plane and therefore depends on the chosen impedance model, since Z = Z (ω) is essentially frequency dependent. The usual causality condition by Briggs and Bers appears to be not applicable here because it requires a temporal growth rate bounded for all real axial wave numbers. The alternative Crighton-Leppington criterion, however, is applicable and confirms that the suspected mode is usually unstable. In general, the effect of this Kutta condition is significant, but it is particularly large for the plane wave at low frequencies and should therefore be easily measurable. For ω → 0, the modulus fends to |R001| → (1 + M)/(1 -M) without and to 1 with Kutta condition, while the end correction tends to ∞ without and to a finite value with Kutta condition. This is exactly the same behaviour as found for reflection at a pipe exit with flow, irrespective if this is uniform or jet flow.

Two Bifurcation Transition Processes in Floating Half Zone Convection of Larger Prandtl Number Fluid

Processes of the onset oscillation in the thermocapillaxy convection under the Earth's gravity are investigated by the numerical simulation and experiments in a floating half zone of large Prandtl number with different volume ratio. Both computational and experimental results show that the steady and axisymmetric convection turns to the oscillatory convection of m=1 for the slender liquid bridge, and to the oscillatory convection before a steady and 3D asymmetric state for the case of a fat liquid bridge. It implies that, there are two critical Marangoni numbers related, respectively, to these two bifurcation transitions for the fat liquid bridge. The computational results agree with the results of ground-based experiments.

Damage Localization, Sensitivity of Energy Release and the Catastrophe Transition

Large earthquakes can be viewed as catastrophic ruptures in the earth’s crust. There are two common features prior to the catastrophe transition in heterogeneous media. One is damage localization and the other is critical sensitivity; both of which are related to a cascade of damage coalescence. In this paper, in an attempt to reveal the physics underlying the catastrophe transition, analytic analysis based on mean-field approximation of a heterogeneous medium as well as numerical simulations using a network model are presented. Both the emergence of damage localization and the sensitivity of energy release are examined to explore the inherent statistical precursors prior to the eventual catastrophic rupture. Emergence of damage localization, as predicted by the mean-field analysis, is consistent with observations of the evolution of damage patterns. It is confirmed that precursors can be extracted from the time-series of energy release according to its sensitivity to increasing crustal stress. As a major result, present research indicates that the catastrophe transition and the critical point hypothesis (CPH) of earthquakes are interrelated. The results suggest there may be two cross-checking precursors of large earthquakes: damage localization and critical sensitivity.

Glass Transition and Thermal Stability of Hard Magnetic Bulk NdAlFeCo Metallic Glass

Glass transition and thermal stability of bulk Nd60Al10Fe20Co10 metallic glass were investigated by means of dynamic mechanical thermal analysis (DMTA), differential scanning calorimetry (DSC), X-ray diffraction (XRD) and scanning electronic microscopy (SEM). The glass transition temperature, not revealed by DSC, is alternatively determined by DMTA via storage modulus E' and loss modulus E" measurement to be 498 K at a heating rate of 0.167 K s (-1). The calculated reduced glass transition temperature (T-g/T-m) is 0.63. The large value of T-g/T-m of this alloy is consistent with its good glass-forming ability. The crystallization process of the metallic glass is concluded as follows: amorphous --> amorphous + metastable FeNdAl phase --> amorphous + primary delta-FeNdAl phase --> primary delta-phase + eutectic delta-phase + Nd3Al + Nd3Co. The appearance of hard magnetism in this alloy is ascribed to the presence of amorphous phase with highly relaxed structure. The hard magnetism disappeared after the eutectic crystallization of the amorphous phase. (C) 2002 Elsevier Science B.V. All rights reserved.

Direct Numerical Simulation Of Hypersonic Boundary-Layer Transition Over A Blunt Cone

Direct numerical simulation of transition How over a blunt cone with a freestream Mach number of 6, Reynolds number of 10,000 based on the nose radius, and a 1-deg angle of attack is performed by using a seventh-order weighted essentially nonoscillatory scheme for the convection terms of the Navier-Stokes equations, together with an eighth-order central finite difference scheme for the viscous terms. The wall blow-and-suction perturbations, including random perturbation and multifrequency perturbation, are used to trigger the transition. The maximum amplitude of the wall-normal velocity disturbance is set to 1% of the freestream velocity. The obtained transition locations on the cone surface agree well with each other far both cases. Transition onset is located at about 500 times the nose radius in the leeward section and 750 times the nose radius in the windward section. The frequency spectrum of velocity and pressure fluctuations at different streamwise locations are analyzed and compared with the linear stability theory. The second-mode disturbance wave is deemed to be the dominating disturbance because the growth rate of the second mode is much higher than the first mode. The reason why transition in the leeward section occurs earlier than that in the windward section is analyzed. It is not because of higher local growth rate of disturbance waves in the leeward section, but because the growth start location of the dominating second-mode wave in the leeward section is much earlier than that in the windward section.

Ductile To Brittle Transition In Dynamic Fracture Of Brittle Bulk Metallic Glass

We report an unusual transition from a locally ductile to a pure brittle fracture in the dynamic fracture of brittle Mg65Cu20Gd10 bulk metallic glass. The fractographic evolution from a dimple structure to a periodic corrugation pattern and then to the mirror zone along the crack propagation direction during the dynamic fracture process is discussed within the framework of the meniscus instability of the fracture process zone. This work might provide an important clue in understanding of the energy dissipation mechanism for dynamic crack propagation in brittle glassy materials. (C) 2008 American Institute of Physics.

Features of the supercritical transition in the wake of a circular cylinder

The features of the wake behind a uniform circular cylinder at Re = 200, which is just beyond the critical Reynolds number of 3-D transition, are investigated in detail by direct numerical simulations by solving 3-D incompressible Navier-Stokes equations using mixed spectral-spectral-element method. The high-order splitting algorithm based on the mixed stiffly stable scheme is employed in the time discretization. Due to the nonlinear evolution of the secondary instability of the wake, the spanwise modes with different wavelengths emerge. The spanwise characteristic length determines the transition features and global properties of the wake. The existence of the spanwise phase difference of the primary vortices shedding is confirmed by Fourier analysis of the time series of the spanwise vorticity and attributed. to the dominant spanwise mode. The spatial energy distributions of various modes and the velocity profiles in the near wake are obtained. The numerical results indicate that the near wake is in 3-D quasi-periodic laminar state with transitional behaviors at this supercritical Reynolds number.

Numerical exploration of new features on three-dimensional transition of a cylinder wake

The three-dimensional transition of the wake flow behind a circular cylinder is studied in detail by direct numerical simulations using 3D incompressible N-S equations for Reynolds number ranging from 200 to 300. New features and vortex dynamics of the 3D transition of the wake are found and investigated. At Re = 200, the flow pattern is characterized by mode A instability. However, the spanwise characteristic length of the cylinder determines the transition features. Particularly for the specific spanwise characteristic length linear stable mode may dominate the wake in place of mode A and determine the spanwise phase difference of the primary vortices shedding. At Re = 250 and 300 it is found that the streamwise vortices evolve into a new type of mode - "dual vortex pair mode" downstream. The streamwise vortex structures switch among mode A, mode B and dual vortex pair mode from near wake to downstream wake. At Re = 250, an independent low frequency f(m) in addition to the vortex shedding frequency f(s) is identified. Frequency coupling between f(m) and f(s) occurs. These result in the irregularity of the temporal signals and become a key feature in the transition of the wake. Based on the formation analysis of the streamwise vorticity in the vicinity of cylinder, it is suggested that mode A is caused by the emergence of the spanwise velocity due to three dimensionality of the incoming flow past the cylinder. Energy distribution on various wave numbers and the frequency variation in the wake are also described.