Fundamentals of rotating detonations

A rotating detonation propagating at nearly Chapman–Jouguet velocity is numerically stabilized on a two-dimensional simple chemistry flow model. Under purely axial injection of a combustible mixture from the head end of a toroidal section of coaxial cylinders, the rotating detonation is proven to give no average angular momentum at any cross section, giving an axial flow. The detonation wavelet connected with an oblique shock wave ensuing to the downstream has a feature of unconfined detonation, causing a deficit in its propagation velocity. Due to Kelvin–Helmholtz instability existing on the interface of an injected combustible, unburnt gas pockets are formed to enter the junction between the detonation and oblique shock waves, generating strong explosions propagating to both directions. Calculated specific impulse is as high as 4,700 s.      

Centrifugal instability and the rib vortices in the cylinder wake

The physical mechanism for generation of streamwise vortices (or rib vortices) in the cylinder wake is numerically investigated with a finite-difference scheme. Rayleigh's theory of centrifugal instability for inviscid axisymmetric flow is extended to analyze the 2-D primary flows. Accordingly, an analytical dimensionless groupRay=−(r/v _θ)∂v _θ/∂r−1 is derived, wherev _θ represents the velocity of a fluid element relative to the oncoming flow,r is the local curvature radius of the element pathline. Centrifugal instability occurs whenRay>0. Stability analyses are carried out with this discriminant for primary flows at different time levels in a half shedding period of the von Kármán (or vK) vortices. Unstable areas are identified and the locations of rib vortices are coincident well with the unstable areas within the first wavelength of vK vortices behind the cylinder. The numerical results also show that rib vortices experience amplification in this region. It is apparent that centrifugal instability plays an important role in the generation of rib vortices in the cylinder wake. The project spported by the National Natural Science Foundation of China     

A design of a two-dimensional,supersonic KH experiment on OMEGA-EP

An experiment meant to investigate the evolution of single mode Kelvin–Helmholtz (KH) instability in the supersonic regime is presented and theoretically analyzed. This experiment is intended to provide a direct measurement of the two-dimensional vortex evolution so that the high-Mach-number effects can be measured. The proposed design takes advantage of the ability of OMEGA-EP to drive experiments for up to 30 ns to produce steady conditions for KH that endure long enough to observe substantial growth. KH growth for the proposed design has been analyzed using two-dimensional numerical simulations. The results were compared to synthetic temporal KH numerical simulations using non-dimensional scaling in the low and high Mach number regime. The comparisons show that the growth in the high Mach number regime is expected to be suppressed by up to a factor of two. The effects of two-dimensional rarefactions from the lateral boundaries of the experimental system were also investigated. It was found that they introduce no major uncertainties or hazards to the experiment. We produced simulated radiographs, which show that the proposed experimental system will enable observation of the KH structures. An experiment of this kind has not yet been performed, and therefore would serve to validate numerical results and analytical models presented here and in the literature.     

The instability of water-mud interface in viscous two-layer flow with large viscosity contrast

The temporal instability of parallel viscous two-phase mixing layers is extended to current-fluid mud by considering a composite error function velocity profile. The influence of viscosity ratio, Reynolds number, and Froude number on the instability of the system are discussed and a new phenomenon never discussed is investigated based on our numerical results. It is shown that viscosity can enlarge the unstable wave number range, cause new instability modes, and certainly reduce the growth rate of Kelvin—Helmholtz (K—H) instability.     

Trailing-edge dynamics of a morphing NACA0012 aileron at high Reynolds number by high-speed PIV

Particle image velocimetry (piv) measurements are made at the trailing edge of a piezoelectric actuated aileron in order to investigate the physical effect on the flow via high-frequency low-amplitude actuation at high Reynolds numbers. The measurements at different actuation frequencies show the modification of the primary frequency components of the flow with the actuation frequency. A statistical analysis reveals the reduction of the Reynolds stress components which increases with the actuation frequency. Proper orthogonal decomposition (pod) analysis shows the modification of the spatial modes illustrating the vortex breakdown in the shear-layer and the reduction of the temporal mode spectral energy depending on the actuation. It has been shown that a specific low amplitude actuation frequency produces a significant reduction of the predominant shear-layer frequency.     

Large eddy simulations in low-pressure turbines: Effect of wakes at elevated free-stream turbulence

The transition of a separated shear layer over a flat plate, in the presence of periodic wakes and elevated free-stream turbulence (FST), is numerically investigated using Large Eddy Simulation (LES). The upper wall of the test section is inviscid and specifically contoured to impose a streamwise pressure distribution over the flat plate to simulate the suction surface of a low-pressure turbine (LPT) blade. Two different distributions representative of a ‘high-lift’ and an ‘ultra high-lift’ turbine blade are examined. Results obtained from the current LES compare favourably with the extensive experimental data previously obtained for these configurations. The LES results are then used to further investigate the flow physics involved in the transition process.In line with experimental experience, the benefit of wakes and FST obtained by suppressing the separation bubble, is more pronounced in ‘ultra high-lift’ design when compared to the ‘high-lift’ design. Stronger ‘Klebanoff streaks’ are formed in the presence of wakes when compared to the streaks due to FST alone. These streaks promoted much early transition. The weak Klebanoff streaks due to FST continued to trigger transition in between the wake passing cycles.The experimental inference regarding the origin of Klebanoff streaks at the leading edge has been confirmed by the current simulations. While the wake convects at local free-stream velocity, its impression in the boundary layer in the form of streaks convects much slowly. The ‘part-span’ Kelvin–Helmholtz structures, which were observed in the experiments when the wake passes over the separation bubble, are also captured. The non-phase averaged space-time plots manifest that reattachment is a localized process across the span unlike the impression of global reattachment portrayed by phase averaging.     

Wall slip and extrudate instability of 4-arm star polybutadienes in capillary flow

This paper presents experimental research on wall slip and extrusion instability behavior of a series of monodisperse 4-arm star polybutadienes (PBD) of different molecular weights during fast capillary flow. The star PBDs reveal a slope of 3.0 in the capillary flow curve, showing a faster non-linear response than linear PBDs. The global stick-slip transition of star PBD is weaker than linear PBD of the same molecular weight, as indicated by a smaller extrapolation length b of star PBD. The sharkskin fracture takes place without a global stick-slip transition for a star PBD with molecular weight of 200 K, suggesting the sharkskin instability may not originate from an oscillating stick-slip transition at die exit. The flow splitting, i.e., the phenomenon that the extrudate breaks into two or more branches after the die exit, is observed in star PBDs with molecular weights higher than 200 K. The flow splitting, accompanied by a precession motion, is found to be an exit instability behavior. The flow splitting is related to the long bulk relaxation time of the star polymers and more likely to occur in a solid-like state, where the storage modulus G is higher than the loss modulus G. A rotating-breaking hypothesis is proposed to explain the flow splitting and sharkskin instability behavior of star PBDs based on a stretch induced rupture at die exit in a rotating pattern.     

Convective instability in a rapidly rotating fluid layer in the presence of a non-uniform magnetic field

Magnetoconvective instabilities in a rapidly rotating, electrically conducting fluid layer heated from below in the presence of a non-uniform, horizontal magnetic field are investigated. It was first shown by Chandrasekhar that an overall minimum of the Rayleigh number may be reached at the onset of magnetoconvection when a uniform basic magnetic field is imposed. In this paper, we show that the properties of instability can be quite different when a non-uniform basic magnetic field is applied. It is shown that there is an optimum value of the Elsasser number provided that the basic magnetic field is a monotonically decreasing or increasing function of the vertical coordinate. However, there exist no optimum values of the Elsasser number that can give rise to an overall minimum of the Rayleigh number at the onset of magnetoconvection if the imposed basic magnetic field has an inflexion point. The project supported by the National Natural Science Foundation of China (40174026 and 40074041)     

Instabilité d'une nappe de vorticité étirée instationnaireInstability of an unsteady stretched vortex layer

We consider how the Kelvin–Helmholtz instability is affected by an external hyperbolic strain flow. The basic flow being unsteady, the inviscid evolution of perturbations is studied within the framework of a non-normal analysis in which the maximum amplification is computed for any given time. A positive or negative stretching is shown to enhance or reduce, respectively, the instability even for weak stretching rates. To cite this article: T. Gomez, M. Rossi, C. R. Mecanique 331 (2003).     

Ablative Rayleigh–Taylor instability in the limit of an infinitely large density ratio

The instability of ablation fronts strongly accelerated toward the dense medium under the conditions of inertial confinement fusion (ICF) is addressed in the limit of an infinitely large density ratio. The analysis serves to demonstrate that the flow is irrotational to first order, reducing the nonlinear analysis to solve a two-potential flows problem. Vorticity appears at the following orders in the perturbation analysis. This result simplifies greatly the analysis. The possibility for using boundary integral methods opens new perspectives in the nonlinear theory of the ablative RT instability in ICF. A few examples are given at the end of the Note. To cite this article: P. Clavin, C. Almarcha, C. R. Mecanique 333 (2005).