Dynamic instabilities in {1 1 1} silicon

The phenomena occurring during rapid crack propagation in brittle single crystals was studied by cleaving strip-like silicon specimens along the {1 1 1} low-energy cleavage plane under bending. The experiments reveal phenomena associated with rapid crack propagation in brittle single crystals not previously reported, and new crack path instabilities in particular. In contrast to amorphous materials, the observed instabilities are generated at relatively low velocity, while at high velocity the crack path remains stable. The experiments demonstrate that crack velocity in single crystals can attain the theoretical limit. No evidence for mirror, mist, and hackle instabilities, typical in amorphous materials, was found. The important role played by the atomistic symmetry of the crystals on controlling and generating the surface instabilities is explained; the importance of the velocity and orientation-dependent cleavage energy is discussed. The surface instabilities are generated to satisfy minimum energy dissipation considerations. These findings necessitate a new approach to the fundamentals of dynamic crack propagation in brittle single crystals.     

Swept-Wing Boundary Layer Receptivity to a Steady Free-Stream Vortex Disturbance

A single trailing vortex developed behind a micro-wing immersed in a free stream was used to study the vortex receptivity of a swept-wing boundary layer. As a result of the interaction, longitudinal-velocity disturbances develop in the boundary layer. On the swept wing, disturbance transformation occurs near the leading edge and is accompanied by the formation of a wave packet consisting of waves typical of cross-flow instability. Disturbances with other characteristics are also detected. These disturbances may be attributable to distributed boundary-layer receptivity to the free-stream vortex disturbance considered.     

Experimental study of nonlinear processes in a swept-wing boundary layer at the mach number M=2

Results of experiments aimed at studying the linear and nonlinear stages of the development of natural disturbances in the boundary layer on a swept wing at supersonic velocities are presented. The experiments are performed on a swept wing model with a lens-shaped airfoil, leading-edge sweep angle of 45°, and relative thickness of 3%. The disturbances in the flow are recorded by a constant-temperature hot-wire anemometer. For determining the nonlinear interaction of disturbances, the kurtosis and skewness are estimated for experimentally obtained distributions of the oscillating signal over the streamwise coordinate or along the normal to the surface. The disturbances are found to increase in the frequency range from 8 to 35 kHz in the region of their linear development, whereas enhancement of high-frequency disturbances is observed in the region of their nonlinear evolution. It is demonstrated that the growth of disturbances in the high-frequency spectral range (f > 35 kHz) is caused by the secondary instability.     

Linear Stability Analysis of a Viscous Liquid Sheet in a High-Speed Viscous Gas

Air-assisted atomizers in which a thin liquid sheet is deformed under the action of a high-speed air flow are extensively used in industrial applications, e.g., in aircraft turbojet injectors. Primary atomization in these devices is a consequence of the onset and growth of instabilities on the air/liquid interfaces. To better understand this process, a temporal linear instability analysis is applied to a thin planar liquid sheet flowing between two semi-infinite streams of a high-speed viscous gas. This study includes the full viscous effects both in the liquid and gas basic states and perturbations. The relevant dimensionless groups entering the non-dimensional Orr–Sommerfeld equations and boundary conditions are the liquid and gas stream Reynolds numbers, the gas to liquid momentum flux ratio, the gas/liquid velocity ratio, the Weber number and the equivalent gas boundary layer to liquid sheet thickness ratio. Growth rates and temporal frequencies as a function of the wave number, varying the different dimensionless parameters are presented, together with neutral stability curves. From the results of this parametric study it is concluded that when the physical properties of gas and liquid are fixed, the momentum flux ratio is especially relevant to determine the instability conditions. It is also observed that the gas boundary layer thickness strongly influences the wave propagation, and acts by damping sheet oscillation frequency and growth. This is especially important because viscosity in the basic gas velocity profile has always been ignored in instability analysis applied to the geometry under study. This revised version was published online in July 2006 with corrections to the Cover Date.     

Delayed die swell

The experiments reported here establish that there is a general critical condition associated with die swell which we call delayed die swell. This condition is defined by a critical speed which is the area-averaged velocity, the extrusion velocity, at the exit of the pipe when the swell is first delayed. The delayed swell ratio and delay distance first increase for larger, post-critical values of the extrusion velocity; then the increases are terminated either by instabilities or by smoothing. The maximum post-critical velocity at the pipe exit was always greater than the shear wave speed measured on the shear-wave-speed meter. The post critical area averaged velocity at the position of maximum swell before termination was always less than the shear wave speed. There were always points in the region of swelling where the ratio of the local velocity to the shear wave speed, the viscoelastic Mach number, was unity. The swelling of the jet is a nonlinear phenomenon which we suggest is finally terminated either by instability or when the variations of the velocity, vorticity and stress field are reduced to zero by the inward propagation of shear waves from the free surface of the jet. This propagation is generated by discontinuous “initial” data along χ in which the prescribed values of velocity at the boundary change from no-slip in the pipe to no-shear in the jet. The measurements raise the possibility that the delay may be associated with a change of type from supercritical to subcritical flow.     

Local stability effects of plasma actuation on a zero pressure gradient boundary layer

The effects of plasma actuation in a flat plate boundary layer with zero pressure gradient have been simulated. Based on these simulations, non-dimensional parameters and a combined wall jet/boundary layer model of the velocity profile have been developed. A parametric study using local linear stability analysis has been performed to examine the hydrodynamic stability of the velocity profiles created through this model. Convective and absolute instability mechanisms are found to be important, some of which have not been previously documented. Neutral stability curves have been computed for the different instabilities, and when put in terms of the shape factor, they still compare favorably with reported canonical results, indicating that the critical Reynolds number is primarily a function of the shape factor. These results are also discussed in relation to existing experimental results as well as with respect to their implementation.     

Experimental and numerical study of the stability of a pre-separated flow on an airfoil

The problem of the origin and evolution of two-dimensional waves of unstable disturbances in the boundary layer on an airfoil in the region of adverse pressure gradient in the preseparation flow region is solved numerically. The stability of the experimental velocity profiles, including the inflected profiles, is studied. As a result of the calculations, the boundaries of the instability region and the parameters of the maximally unstable disturbances (frequency, growth rate, wavelength, and propagation velocity) are determined for each velocity profile. The characteristics obtained in the present work are in good agreement with the real experimental parameters of instability waves. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 126–132, January–February, 1999.     

Surface instability and primary atomization characteristics of straight liquid jet sprays

Using the detailed numerical simulation data of primary atomization, the liquid surface instability development that leads to atomization is characterized. The numerical results are compared with a theoretical analysis of liquid–gas layer for a parameter range close to high-speed Diesel jet fuel injection. For intermittent and short-duration Diesel injection, the aerodynamic surface interaction and transient head formation play an important role. The present numerical setting excludes nozzle disturbances to primarily investigate this interfacial instability mechanism and the role of jet head. The first disturbed area is the jet head region, and the generated disturbances are fed into the upstream region through the gas phase. This leads to the viscous boundary layer instability development on the liquid jet core. By temporal tracking of surface pattern development including the phase velocity and stability regime and by the visualization of vortex structures near the boundary layer region, it is suggested that the instability mode is the Tollmien–Schlichting (TS) mode similar to the turbulent transition of solid-wall boundary layer. It is also demonstrated that the jet head and the liquid core play an interacting role, thus the jet head cannot be neglected in Diesel injection. In this study, this type of boundary layer instability has been demonstrated as a possible mechanism of primary atomization, especially for high-speed straight liquid jets. The effect of nozzle turbulence is a challenging but important issue, and it should be examined in the future.     

Tollmien-Schlichting wave generation by flow turbulence

The problem of freestream-turbulence-generated instability waves in the flat-plate boundary layer is solved on the basis of a nonlinear turbulence model admitting the deviation of the speed of propagation of vortex disturbances from the flow velocity. The solution obtained well describes the experimental dependence of the laminar-turbulent transition Reynolds number on the freestream turbulence degree.     

A numerical study of the frontal region of gravity currents propagating on a free-slip boundary

We investigate numerically the three-dimensional flow near the head of gravity currents propagating along a free-slip boundary. The simulations show that two states are possible: a high-mixing state, where the flow departs from the analytic inviscid solution 0.5 channel heights downstream of the front location, and with characteristics similar to the ones observed for purely two-dimensional simulations; and a low-mixing state, where billows are weaker and appear further downstream. To access the high-mixing state, it is necessary to add a source of perturbation upstream of the head in the form of turbulence. At high values of the Reynolds number, the intensity of rms turbulent fluctuations necessary to switch to the high-mixing state is small (0.5% of the speed of propagation) and may explain why the low-mixing state has so far eluded experimental detection. In the low-mixing state, the flow becomes three-dimensional near the front due to centrifugal instabilities caused by the curved streamlines. This instability of the outer flow is coupled to overturning instabilities that develop within the heavy fluid in the head, and suppresses the formation of billows. This complex behavior, which feeds on the interplay of streamline curvature and stratification, should be considered a good model to understand how instabilities occur in other types of strongly nonlinear stratified flows.      

薄膜沿加热平板下落的稳定性分布

本文分析了薄膜沿加热平板下落的稳定性。在时间模式下，发现流动的不稳定性是由表面波不稳定和加毛细不稳定构成的，同时当流体的热扩散越大以及界面热量损失越小时，热毛细不稳定越剧烈，在时空模式下，流动随着Marangoni数的增大。流动有可能从对流不稳定过渡到绝对不稳定，这一结论尚待实验验证。     

Response of the boundary layer developing over a blunt-nosed flat plate to free-stream non-uniformities

The response of the boundary layer on a flat plate with blunt nose to infinitesimally small non-uniformity in the freestream velocity along the span has been studied. The non-uniformity was shown to excite boundary-layer disturbances similar to streaks or Klebanoff modes generally observed in experiments conducted with a high level of free-stream turbulence. The boundary layer disturbances have a predominantly streamwise velocity component and exhibit transient growth. In contrast to streaks generated by streamwise vortices impinging on the sharp nose of a plate, the disturbances produced by free-stream non-uniformity interaction with a blunt nose have a different level of growth. Their maximal amplification scales with the Reynolds number, based on the size of nose bluntness and is almost independent of the spanwise period of disturbances. This difference was shown to be caused by additional amplification of disturbances via vortex lines stretching around the leading edge.     

Liquid jet in a high Mach number air stream

The instability of circular liquid jet immersed in a coflowing high velocity air stream is studied assuming that the flow of the viscous gas and liquid is irrotational. The basic velocity profiles are uniform and different. The instabilities are driven by Kelvin–Helmholtz instability due to a velocity difference and neckdown due to capillary instability. Capillary instabilities dominate for large Weber numbers. Kelvin–Helmholtz instability dominates for small Weber numbers. The wavelength for the most unstable wave decreases strongly with the Mach number and attains a very small minimum when the Mach number is somewhat larger than one. The peak growth rates are attained for axisymmetric disturbances (n = 0) when the viscosity of the liquid is not too large. The peak growth rates for the first asymmetric mode (n = 1) and the associated wavelength are very close to the n = 0 mode; the peak growth rate for n = 1 modes exceeds n = 0 when the viscosity of the liquid jet is large. The effects of viscosity on the irrotational instabilities are very strong. The analysis predicts that breakup fragments of liquids in high speed air streams may be exceedingly small, especially in the transonic range of Mach numbers.     

The onset of Görtler vortices in laminar boundary layer flow over a slightly concave wall

The onset of convective instability in the laminar boundary layer over the slightly curved wall is analyzed theoretically and compared with the existing experimental data. A new set of stability equations are derived by the propagation theory considering the relative instability under the linear stability theory. In this analysis the disturbances are assumed to have the form of longitudinal vortices and also to grow themselves in streamwise direction. The critical position to mark the onset of Görtler instability is obtained as a function of the Görtler number, where disturbances at the critical state are mainly confined to the hydrodynamic boundary layer. Comparing the theoretical predictions with available experimental and other theoretical results, the present predictions follow experimental trends fairly well with slightly higher critical Görtler numbers than those from the local stability theory. The propagation theory commanding the local eigenvalue analysis is successful to obtain stability conditions reasonably in Görtler vortex problems, relaxing the limitations by the conventional analyses.     

CFD modelling of the cross-flow through normal triangular tube arrays with one tube undergoing forced vibrations or fluidelastic instability

A CFD methodology involving structure motion and dynamic re-meshing has been optimized and applied to simulate the unsteady flow through normal triangular cylinder arrays with one single tube undergoing either forced oscillations or self-excited oscillations due to damping-controlled fluidelastic instability. The procedure is based on 2D URANS computations with a commercial CFD code, complemented with user defined functions to incorporate the motion of the vibrating tube. The simulation procedure was applied to several configurations with experimental data available in the literature in order to contrast predictions at different calculation levels. This included static conditions (pressure distribution), forced vibrations (lift delay relative to tube motion) and self-excited vibrations (critical velocity for fluidelastic instability). Besides, the simulation methodology was used to analyze the propagation of perturbations along the cross-flow and, finally, to explore the effect on the critical velocity of the Reynolds number, the pitch-to-diameter ratio and the degrees of freedom of the vibrating cylinder.     

Acoustic Field Effect on Laminar Turbulent Transition on a Swept Wing in the Favorable Pressure Gradient Region

The development of disturbances in a three-dimensional boundary layer on a swept wing model is studied both under natural conditions and for artificial excitation of traveling waves by an acoustic field. It is found that steady-state streamwise structures are formed in the three-dimensional boundary layer; under natural conditions a wave packet leading to turbulence is detected. When the flow is exposed to the action of an acoustic field at a frequency from the wave packet, disturbances whose velocity along the streamwise structures is equal to 0.55 of the oncoming flow velocity are formed, while the laminar-turbulent transition is displaced upstream.     

Statistical laws of the pressure fluctuations in a hypersonic turbulent boundary layer

The results of measuring the pressure fluctuations on the wall of the nozzle of a hypersonic wind tunnel beneath a developed turbulent boundary layer are presented for the Mach number M_∞ = 7.5. On the basis of a statistical analysis, it is shown that the action of the turbulent flow is dynamically similar to the propagation of a random sequence of wave packets with continuously distributed temporal and spatial scales. Low-frequency disturbances are associated with large-scale structures of long duration that propagate at a mean-statistical velocity similar in value to the outer flow velocity. The continuous generation of weakly-correlated small-scale disturbances ensuring the maintenance and development of turbulence occurs chiefly in the inner region of the boundary layer. Spectral estimates of the power generated by the turbulent flow in the wall region of the boundary layer are presented.     

Interaction between an unsteady pressure disturbance and a hypersonic boundary layer

The development of disturbances in a hypersonic boundary layer on a cooled surface is investigated in the case in which the characteristic velocity of disturbance propagation is small but greater than the flow velocity in the wall region of the three-layer disturbed zone with interaction. The nonlinear boundary value problem formulated involves a single similarity parameter that characterizes the contribution made by the main, on average either subsonic or supersonic, region of the boundary layer to the generation of the pressure disturbance. In the linear approximation, an analytical solution and an algebraic dispersion equation are derived. It is shown that only waves exponential in time and in the streamwise coordinate can propagate downstream when themain region of the undisturbed boundary layer is subsonic on average.     

LOCAL AND GLOBAL INSTABILITY OF FLUID-CONVEYING PIPES ON ELASTIC FOUNDATIONS

We investigate the relationship between the local and global bending motions of fluid-conveying pipes on an elastic foundation. The local approach refers to an infinite pipe without taking into account its finite ends, while in the global approach we consider a pipe of finite length with a given set of boundary conditions. Several kinds of propagating disturbances are identified from the dispersion relation, namely evanescent, neutral and unstable waves. As the length of the pipe is increased, the global criterion for instability is found to coincide with local neutrality, whereby a local harmonic forcing only generates neutral waves. For sets of boundary conditions that give rise only to static instabilities, the criterion for global instability of the long pipe is that static neutral waves exist. Conversely, for sets of boundary conditions that allow dynamic instabilities, the criterion for global instability of the long pipe corresponds to that for the existence of neutral waves of finite nonzero frequency. These results are discussed in relation with the work of Kulikovskii and other similar approaches in hydrodynamic stability theory.     

Experimental investigations of controlled transition of a laminar separation bubble in an axisymmetric diffuser

The instability of a pressure-induced laminar separation bubble is examined experimentally on an axisymmetric diffuser for a Reynolds number range 7,800 ≤ ≤ 11,400 for an inlet pipe diameter D ₁ (50 mm) and as mean input flow velocity 4.2 m/s ≤ u _m ≤ 6.1 m/s. A characterization of the base flow shows a wide-spread separation at the smooth diverging contour which gives rise to a massive amplification of instabilities. Controlled disturbances are introduced by means of a slot and a membrane actuator to trigger the transition, and the receptivity of the perturbations to the laminar boundary layer is evaluated. Different axisymmetric and azimuthal disturbances are applied in order to study their influence on the laminar–turbulent transition. The measurements show a clear dependence of the transition scenario and the reattachment length on the actuation mode.