The propagation mechanism of high speed turbulent deflagrations

The propagation regimes of combustion waves in a 30 cm by 30 cm square cross–sectioned tube with an obstacle array of staggered vertical cylindrical rods (with BR=0.41 and BR=0.19) are investigated. Mixtures of hydrogen, ethylene, propane, and methane with air at ambient conditions over a range of equivalence ratios are used. In contrast to the previous results obtained in circular cross–sectioned tubes, it is found that only the quasi–detonation regime and the slow turbulent deflagration regimes are observed for ethylene–air and for propane–air. The transition from the quasi–detonation regime to the slow turbulent deflagration regime occurs at (where D is the tube “diameter” and is the detonation cell size). When , the quasi–detonation velocities that are observed are similar to those in unobstructed smooth tubes. For hydrogen–air mixtures, it is found that there is a gradual transition from the quasi–detonation regime to the high speed turbulent deflagration regime. The high speed turbulent deflagration regime is also observed for methane–air mixtures near stoichiometric composition. This regime was previously interpreted as the “choking” regime in circular tubes with orifice plate obstacles. Presently, it is proposed that the propagation mechanism of these high speed turbulent deflagrations is similar to that of Chapman–Jouguet detonations and quasi-detonations. As well, it is observed that there exists unstable flame propagation at the lean limit where . The local velocity fluctuates significantly about an averaged velocity for hydrogen–air, ethylene–air, and propane–air mixtures. Unstable flame propagation is also observed for the entire range of high speed turbulent deflagrations in methane–air mixtures. It is proposed that these fluctuations are due to quenching of the combustion front due to turbulent mixing. Quenched pockets of unburned reactants are swept downstream, and the subsequent explosion serves to overdrive the combustion front. The present study indicates that the dependence on the propagation mechanisms on obstacle geometry can be exploited to elucidate the different complex mechanisms of supersonic combustion waves. Received 5 November 2001 / Accepted 12 June 2002 / Published online 4 November 2002 Correspondence to: J. Chao (e-mail: jenny.chao@mail.mcgill.ca) An abridged version of this paper was presented at the 18th Int. Colloquium on the Dynamics of Explosions and Reactive Systems at Seattle, USA, from July 29 to August 3, 2001.     

Near-resonance highly nonlinear gas oscillations in tubes

Near-resonance highly nonlinear ideal perfect gas oscillations in tubes are studied numerically for boundary conditions of various types. The oscillations are initiated by weak periodic perturbations at one end of the tube. As distinct from earlier studies [1–10], the oscillation amplitudes were not assumed to be small and the entropy increase at the shock waves formed was taken into account. Periodic flow regimes result as a limit of the solution of a Cauchy problem for one-dimensional time-dependent gasdynamic equations. The frequency responses of the oscillations under consideration are determined for boundary conditions of various types. It is shown that in specific cases the attainment of a periodic regime is accompanied by the appearance of long-wave modulations. The “repeated resonance” effect is revealed. This is due to the change in the tube's natural acoustic frequency, which takes place during the heating of the gas in the tube by the shock waves traveling in it. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 150–157, July–August, 1994.     

The shock–vortex interaction patterns affected by vortex flow regime and vortex models

We have used a third-order essentially non-oscillatory method to obtain numerical shadowgraphs for investigation of shock–vortex interaction patterns. To search different interaction patterns, we have tested two vortex models (the composite vortex model and the Taylor vortex model) and as many as 47 parametric data sets. By shock–vortex interaction, the impinging shock is deformed to a S-shape with leading and lagging parts of the shock. The vortex flow is locally accelerated by the leading shock and locally decelerated by the lagging shock, having a severely elongated vortex core with two vertices. When the leading shock escapes the vortex, implosion effect creates a high pressure in the vertex area where the flow had been most expanded. This compressed region spreads in time with two frontal waves, an induced expansion wave and an induced compression wave. They are subsonic waves when the shock–vortex interaction is weak but become supersonic waves for strong interactions. Under a intermediate interaction, however, an induced shock wave is first developed where flow speed is supersonic but is dissipated where the incoming flow is subsonic. We have identified three different interaction patterns that depend on the vortex flow regime characterized by the shock–vortex interaction.      

Derivation of the Zakharov Equations

This article continues the study, initiated in [27, 7], of the validity of the Zakharov model which describes Langmuir turbulence. We give an existence theorem for a class of singular quasilinear equations. This theorem is valid for prepared initial data. We apply this result to the Euler–Maxwell equations which describes laser-plasma interactions, to obtain, in a high-frequency limit, an asymptotic estimate that describes solutions of the Euler–Maxwell equations in terms of WKB approximate solutions, the leading terms of which are solutions of the Zakharov equations. Due to the transparency properties of the Euler–Maxwell equations evidenced in [27], this study is carried out in a supercritical (highly nonlinear) regime. In such a regime, resonances between plasma waves, electromagnetric waves and acoustic waves could create instabilities in small time. The key of this work is the control of these resonances. The proof involves the techniques of geometric optics of JOLY, MéTIVIER and RAUCH [12, 13]; recent results by LANNES on norms of pseudodifferential operators [14]; and a semiclassical paradifferential calculus.     

On Nonlinear Baroclinic Waves and Adjustment of Pancake Dynamics

Three-dimensional nonhydrostatic Euler–Boussinesq equations are studied for Bu=O(1) flows as well as in the asymptotic regime of strong stratification and weak rotation. Reduced prognostic equations for ageostrophic components (divergent velocity potential and geostrophic departure/thermal wind imbalance) are analyzed. We describe classes of nonlinear anisotropic ageostrophic baroclinic waves which are generated by the strong nonlinear interactions between the quasi-geostrophic modes and inertio-gravity waves. In the asymptotic regime of strong stratification and weak rotation we show how switching on weak rotation triggers frontogenesis. The mechanism of the front formation is contraction in the horizontal dimension balanced by vertical shearing through coupling of large horizontal and small vertical scales by weak rotation. Vertical slanting of these fronts is proportional to μ^−1/2 where μ is the ratio of the Coriolis and Brunt–V?is?l? parameters. These fronts select slow baroclinic waves through nonlinear adjustment of the horizontal scale to the vertical scale by weak rotation, and are the envelope of inertio-gravity waves. Mathematically, this is generated by asymptotic hyperbolic systems describing the strong nonlinear interactions between waves and potential vorticity dynamics. This frontogenesis yields vertical “gluing” of pancake dynamics, in contrast to the independent dynamics of horizontal layers in strongly stratified turbulence without rotation. Received 8 April 1997 and accepted 29 March 1998     

Active Control of Wave Instabilities in Three-Dimensional Compressible Flows

In many fluid flows of practical importance transition is caused by the linear growth of wave instabilities, such as Tollmien–Schlichting waves, which eventually grow to a finite size at which stage secondary instabilities come into play. If transition is to be delayed or even avoided in such flows, then the linear growth of the disturbances must be prevented since control in the nonlinear regime would be a considerably more difficult task. Here a strategy for active control of two-dimensional incompressible and compressible Tollmien–Schlichting waves and its use in controlling the more practically relevant problem of crossflow instability which arises in swept-wing flows is discussed. The control is through an active suction/blowing distribution at the wall though the same result could be achieved by variable wall heating. In order to control the instability it is assumed that the wall shear stress and pressure are known from measurements. It is shown that, certainly at finite Reynolds numbers, it is sufficient to know the flow properties at a finite number of points along the wall. The cases of high and finite Reynolds numbers are discussed using asymptotic and numerical methods respectively. It is shown that a control strategy can be developed to stop the growth of all two-dimensional Tollmien–Schlichting waves at finite and large Reynolds numbers. Some discussion of nonlinear effects in the presence of active control is given and the possible control of other instability mechanisms investigated. Received 1 May 1998 and accepted 24 September 1998     

A double-front structure of detonation wave as the result of phase transitions

Using thermochemical code calculations, we show that the nanographite–nanodiamond phase transition, which may occur in the detonation products of a number of carbon containing explosives, can affect the detonation properties and can cause a specific detonation regime with some unusual peculiarities. Among them, we first note the failure of the Chapman–Jouguet condition and the presence of the sonic plane, where the Mach number is equal to unity, in a detonation product expansion wave at a lower pressure than that at the Chapman–Jouguet point. The peculiarities of this detonation regime are demonstrated by the example of TNT, HNS, and RDX. The computed detonation velocities are in excellent agreement with experiments over a wide range of initial charge densities for all of the investigated explosives. The results of this work allow one to explain, e.g., contradictory experimental data on the detonation pressure and on the length of the reaction zone for TNT. We believe that some other solid–solid, solid–liquid, and liquid–liquid phase transformations in the detonation products may also cause a detonation regime with the same features as shown here for the nanographite–nanodiamond transition. We suggest a computational study that should facilitate proposing detonation experiments strongly arguing in favor of the model presented. PACS 47.40.-x; 47.40.Rs; 64.70.-p; 64.70.Kb; 05.70.-a; 05.70-.CeThis paper was based on the work that was presented at the 19th International Colloquium on the Dynamics of Explosions and Reactive Systems, Hakone, Japan, July 27–August 1, 2003.     

Modelling of in-plane wave propagation in a plate using spectral element method and Kane–Mindlin theory with application to damage detection

This paper presents results of experimental and numerical analyses of in-plane waves propagating in a 5 mm-thick steel plate in the frequency range of 120–300 kHz. For such a thickness/frequency ratio, extensional waves reveal dispersive character. To model in-plane wave propagation taking into account the thickness-stretch effect, a novel 2D spectral element, based on the Kane–Mindlin theory, was formulated. An application of in-plane waves to damage detection is also discussed. Experimental investigations employing a laser vibrometer demonstrated that the position and length of a defect can precisely be identified by analysing reflected and diffracted waves.     

Seismic efficiency of a contact explosion and a high-velocity impact

The seismic energy transferred to an elastic half-space as a result of a contact explosion and a meteorite impact on a planet’s surface is estimated. The seismic efficiency of the explosion and impact are evaluated as the ratio of the energy of the generated seismic waves to the energy of explosion or the kinetic energy of the meteorite. In the case of contact explosions, this ratio is in the range of 10⁻⁴–10⁻³. In the case of wide-scale impact effects, where the crater in the planet’s crust is produced in the gravitational regime, a formula is derived that relates the seismic efficiency of an impact to its determining parameters. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 3–12, March–April, 2007.     

Large Time Well-posedness of the Three-Dimensional Capillary-Gravity Waves in the Long Wave Regime

In the regime of weakly transverse long waves, given long-wave initial data, we prove that a non-dimensionalized water wave system in an infinite strip under the influence of gravity and surface tension on the upper free interface has a unique solution on [0, T/ e{0, T/ \varepsilon} ] for some e{\varepsilon} independent of constant T. We shall prove in the subsequent paper (Ming et al., The long wave approximation to the three-dimensional capillary gravity waves, 2011) that on the same time interval, these solutions can be accurately approximated by sums of solutions of two decoupled Kadomtsev–Petviashvili (KP) equations.     

Experimental technique for generating fast high-density shock waves with phased linear explosive shock tubes

The sequential detonation of a layer of explosive surrounding a pressurized tube can be used to generate fast, high-density shock waves by means of a piston-like implosive pinch travelling at the detonation velocity of the explosive. A novel technique has been developed to extend the regime of operation to piston velocities greater than the detonation velocity of known explosives. This technique consists of cutting a slit in the tamper of a conventional explosive shock tube and introducing a phased detonation wave into the explosive cladding. Preliminary results indicate that quasi-steady shocks can be generated in helium with velocities between 13–17 km/s for initial fill pressures of 6.9 MPa.     

Waves in a heavy two-layer liquid excited by an oscillating sphere

An approximate solution of an initial-boundary-value problem appropriate for the semiaxist>0 (t is time) is constructed for a system of integrodifferential equations which describes the waves excited in an initially stationary unbounded heavy two-layer fluid by a vertically oscillating sphere located at a distance from the interface that is significantly greater than its radius. The shape of the steady-state wave is found by passing to the limit as time increases indefinitely. The wave resistance experienced by the sphere during the transient process and in the steady-state regime is studied as a function of frequency. Nizhnii Novgorod. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 120–133, March–April, 1998.     

Reflection of plane waves in thermoelastic microstructured materials under the influence of gravitation

This paper presents an analysis of wave propagation in a microstretch elastic medium in the context of the Green–Naghdi (GN) theory. Moreover, the dissipation and the influence of gravity on reflected waves have also been investigated. In the present article, five reflected waves propagate into the medium for any incident wave. The problem is solved numerically, and the amplitude ratios are graphically represented allowing for a comparison between the simple GN theory and the case in which one considers the effect of gravity on waves.     

Vortices for a Rotating Toroidal Bose–Einstein Condensate

We construct local minimizers of the Gross–Pitaevskii energy, introduced to model Bose–Einstein condensates (BEC) in the Thomas–Fermi regime which are subject to a uniform rotation. Our sample domain is taken to be a solid torus of revolution in with starshaped cross-section. We show that for angular speeds ω_ε = O(|ln ε|) there exist local minimizers of the energy which exhibit vortices, for small enough values of the parameter ε. These vortices concentrate at one or several planar arcs (represented by integer multiplicity rectifiable currents) which minimize a line energy, obtained as a Γ-limit of the Gross–Pitaevskii functional. The location of these limiting vortex lines can be described under certain geometrical hypotheses on the cross-sections of the torus.     

Numerical modeling the dynamics of flow in explosion above a surface

The hydrodynamics of processes occurring in explosion of condensed explosives in air is considered. The physical model, computation technique, and results of simulation of a two-dimensional hydrodynamic flow arising in explosion of cylindrical charges are discussed. In this case, the explosions are considered at some distance above the ground. To close the gas-dynamics equations, the Jones–Wilkins–Lee equation of state is used. The results of calculation allow one to obtain a detailed space–time pattern of the arising flow and to study the origination, propagation, and subsequent attenuation of shock waves. Cylindrical charges of the same mass but with different diameter-to-length ratios are considered. It is shown that the charge shape can render essential influence on dynamics of flow and the parameters of shock waves (in the near and medium fields of explosion).     

August Toepler — The first who visualized shock waves

The scientific investigation of the nature of shock waves started 130 years ago with the advent of the schlieren method which was developed in the period 1859–1864 by August Toepler. At the very beginning applied to the visualization of heat and flow phenomena, he immediately turned to air shock waves generated by electric sparks, andsubjectively studied the propagation, reflection and refraction of shock waves. His new delay circuit in the microsecond time regime for the first time made it possible to vary electrically the delay time between a spark generating a shock wave and a second spark acting as a flash light source in his chlieren setup. In 1870 Toepler, together with Boltzmann, applied Jamin's interferometric refractometer and extended the visualization to very weak sound waves at the threshold of hearing. Toepler's pioneering schlieren method stimulated Ernst Mach and his team toobjectively investigate the nature of shock waves: they improved Toepler's time delay circuit; continued the study on the reflection of shock waves; introduced shadowgraphy as a modification of the schlieren method; photographed the propagation of shock waves generated by an electric spark and by supersonic projectiles, and improved interferometry. Based on a large number of original documents the paper illuminates the concomitant circumstances of the invention of the schlieren method and its first applications by others. Although the schlieren method is only one of the many methods I had to use, it is a very important one, and I believe that you will enjoy the results as much as I do. Ernst Mach     

Breaking of gravity waves in the motion of a vertical plate in a two-layer liquid

Results of experimental studies of surface and internal waves generated by translational motion of a vertical plate covering the entire cross section of the channel are discussed. It is found that the waves do not break at the critical propagation speeds predicted by the linear theory or the first approximation of shallow water theory. Breaking begins only at higher propagation speeds, at which the stabilizing effect of wave dispersion ceases. Quantitative information is given that can be used to test mathematical models and numerical methods. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 5, pp. 11–18, September–October, 1998.     

PIV- and LDV-measurements of baroclinic wave interactions in a thermally driven rotating annulus

Already in the 1950s, an elegant laboratory experiment had been designed to understand how the atmospheric circulation transports heat from equatorial to polar latitudes. It consists of a cooled inner and heated outer cylinder mounted on a rotating platform, mimicking the heated tropical and cooled polar regions of the earth’s atmosphere. Depending on the strength of the heating and the rate of rotation, different flow regimes had been identified: wave-regimes that can be classified by pro-grade propagating waves of different wavenumbers and quasi-chaotic regimes where waves and small-scale vortices coexist. In the present paper, we will use multivariate statistical techniques to understand better the variability of the heated rotating flow (i) in the transition region between regular waves with zonal wave number 3 and 4 and (ii) in the transition region to the quasi-chaotic regime. The former regime is studied by applying the complex empirical orthogonal function (CEOF) method to particle image velocimetry data, the latter by applying the multichannel singular spectrum analysis (M-SSA) to laser Doppler velocimetry (LDV) data. In the annulus, interactions between the dominant mode and the so-called weaker modes, explaining less variance than the dominant mode, can lead to low-frequency amplitude and wave structure vacillations. The CEOF analysis reveals the coexistence of a dominant and a weak mode in the 3-4 wave transition region. This finding confirms earlier ideas on wave dispersion in transition regions between regular waves. Increasing the annulus’ rotation leads to a growth of the weak mode until this mode becomes the dominant one. No coexistence of modes could be found for the regular 4-wave regime but a slight structural vacillation was present. The M-SSA was applied to LDV data corresponding with much faster annulus rotation for which the flow becomes more irregular. The analysis reveals a coexistence of a dominant 4 mode and a much weaker 5 mode for this regime. Our results complement previous observations recovered primarily by thermocouple arrangements.     

On the Asymptotic Regimes and the Strongly Stratified Limit of Rotating Boussinesq Equations

Asymptotic regimes of geophysical dynamics are described for different Burger number limits. Rotating Boussinesq equations are analyzed in the asymptotic limit of strong stratification in the Burger number of order one situation as well as in the asymptotic regime of strong stratification and weak rotation. It is shown that in both regimes the horizontally averaged buoyancy variable is an adiabatic invariant (approximate conservation law) for the full Boussinesq system. Spectral phase shift corrections to the buoyancy time scale associated with vertical shearing of this invariant are deduced. Statistical dephasing effects induced by turbulent processes on inertial-gravity waves are evidenced. The “split” of the energy transfer of the vortical and the wave components is established in the Craya–Herring cyclic basis. As the Burger number increases from zero to infinity, we demonstrate gradual unfreezing of energy cascades for ageostrophic dynamics. This property is related to the nonlinear geostrophic adjustment mechanism which is the capacity of ageostrophic dynamics to transfer energy to small scales. The energy spectrum and the anisotropic spectral eddy viscosity are deduced with an explicit dependence on the anisotropic rotation/stratification time scale which depends on the vertical aspect ratio parameter. Intermediate asymptotic regime corresponding to strong stratification and weak rotation is analyzed where the effects of weak rotation are accounted for by an asymptotic expansion with full control (saturation) of vertical shearing. The regularizing effect of weak rotation differs from regularizations based on vertical viscosity. Two scalar prognostic equations for ageostrophic components (divergent velocity potential and geostrophic departure) are obtained. Received 23 January 1997 and accepted 11 July 1997