Taylor Wave Research Articles

The thermodynamics of C-J deflagration

The mechanisms of detonation instability, detonation quenching, deflagration-to-detonation transition, and thermodynamics of C-J deflagration are fundamental issues of combustion theory. In this paper, these mechanisms are discussed by analyzing the convective flux and heat release flux of one-dimensional numerical simulation. The governing equations are Euler equation with overall one-step chemical reaction kinetics. The mixture is stochiometric H2-air mixture at 1atm and 300K.The activation energy is increased to trigger the instability of C-J detonation. The numerical results show that the detonation instability is induced by the von Neumann spike. The von Neumann spike produces unsteady rarefaction wave, which is determined by the slope of von Neumann spike. The detonation is extinguished to a C-J deflagration abruptly under critical activation energy at one-time step because the strength of rarefaction wave is stronger than heat release under this critical condition. The C-J deflagration propagates with a relative constant velocity about half of C-J detonation velocity. The gas temperature and pressure behind the leading shock wave of C-J deflagration is too low to ignite the mixture. The Taylor wave from the end-wall ceases the mixture behind the leading shock, increases its temperature and decreases its pressure. As a result, combustion takes place at the contact surface with almost constant pressure. Therefore, the C-J deflagration is of constant-pressure combustion and this mechanism makes it propagate downstream with a relatively constant velocity for a long distance.

The threshold of instability of Taylor–Couette flow of a Newtonian fluid in quasi-periodic modulation with two immense frequencies using spectral Chebychev collocation methods

This study investigates the dynamic flow of a Newtonian fluid through two coaxial cylinders, each rotating at speeds Ω1(t)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\Omega }_{1}(t)$$\\end{document} (inner cylinder) and Ω2(t)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\Omega }_{2}(t)$$\\end{document} (outer cylinder). We derive equations of motion for disturbances in balance, yielding a controlled system characterized by parameters such as Taylor number, wave number, frequency ratio, and interior cylinder frequency. We introduce numerical techniques for solving this system, employing spectral Chebychev collocation for spatial resolution and a combined approach of Floquet theory and Runge–Kutta method for temporal resolution. Our refined approach enables comprehensive analysis of fluid dynamics within the rotating coaxial cylinders, showcasing the interplay of various control parameters.

Effects of strain rate on spall damage and deformation mechanisms of Mg–3Al–1Zn alloy under Taylor wave loading

Effects of strain rate on spall damage and deformation mechanisms of Mg–3Al–1Zn alloy under Taylor wave loading

Evolution of turbulent mixing driven by implosion in spherical geometry

The interface instability and turbulent mixing of perturbed multi-modes Air/SF6 interface driven by implosion in spherical geometry are numerically investigated. The results show the complex evolving laws and physical mechanisms of turbulent mixing. After the incident imploding shock, the transmitted shock wave moves towards the centre and bounces off outward to produce the second impact, which is a combination of reshock and Taylor wave rather than a single one like in planar case, and forms the loading/unloading effects. The following rebound impacts repeat this assembled loading/unloading process. In the whole process, the turbulent mixing zone (TMZ) growth is closely related to the multiple loading/unloading features. The Richtmyer-Meshkov instability (RMI), Rayleigh-Taylor instability (RTI), Rayleigh-Taylor stabilization (RTS) and Bell-Plesset (BP) effects coexist, and the competition mechanism results in the TMZ width growing in an oscillatory way. The statistics properties of TMZ are highly related to the multiple shocks process. The fluids mixing across TMZ is asymmetrical but behaves in a self-similar way. The evolution of TMZ has a high degree anisotropy, especially around the two edges of TMZ, the turbulent flow is also highly intermittent. When the turbulent mixing develops fully the energy spectra approach k -1 scaling law at the inertial subrange.

Experimental Investigations on the Deformation and Breakup of Hundred-Micron Droplet Driven by Shock Wave

This study examines the process of a 240 µm droplet breakup under a shock wave through experiments using a double-pulse laser holographic test technique on a shock tube. The technique allowed for high-resolution data to be obtained at the micron-nanosecond level, including the Weber number distribution of deformation and breakup modes for droplets of different sizes and loads. Results were compared with larger droplets at the same Weber number, revealing that higher Weber numbers result in more difficulty in droplet breakup, longer deformation times, and increased deformation behavior. At low Weber numbers within the critical range, changes in droplet diameter affect the Rayleigh–Taylor waves and alter the droplet’s characteristics. The study also investigates the laws and reasons behind windward displacement variation for hundred-micron droplets at different Weber numbers over time.

Improved Exponential Phase Mask for Generating Defocus Invariance of Wavefront Coding Systems

Wavefront coding is an effective way to extend the depth of field of optical imaging systems. The invariant defocusing imaging feature can be obtained by adding a phase mask with a suitable form to the aperture of a typical optical system. Traditional exponential phase mask defocusing optical characteristics exhibit strong invariance in the frequency domain, but the point spread function (PSF) variation is significant in the image plane To reduce PSF position deviation, we presented an improved exponential phase mask. The phase function of the improved mask is obtained by analyzing the relationship between Taylor expansion and wave aberration. Numerical analysis and imaging simulation are used to evaluate the performance of the proposed phase mask to that of other standard phase masks. The simulation results show that the improved exponential phase mask has a stronger defocus invariance of the modulation transfer function (MTF), and the position deviation of the PSF has been effectively controlled.

A practical simulation of a hexanitrohexaazaisowurtzitane (CL-20) sphere detonated underwater with the Taylor wave solution and modified Tait parameters

The modified ghost fluid method (MGFM) has been one of the most popular and successful algorithms for coping with the numerical calculation of multi-medium flows, especially for the interaction between strong discontinuities and material interfaces. To apply the advanced algorithm to an underwater explosion simulation, first, the uniform distribution of the state of the detonation products, which is the most generally used initial condition in an explosion simulation, is replaced by the analytic solution of the Taylor wave. The Tait equation is, then, expanded to a broader pressure coverage of up to 100 GPa to match the initial state at the discontinuity. One-dimensional Euler equations with source terms governing the explosion flow are discretized with the fifth-order weighted essentially non-oscillatory scheme in space and the third-order Runge–Kutta scheme in time. The gas–water interface is tracked with the level set equations, and the intermediate states are resolved and defined by following the MGFM. In addition to the comparative studies among diverse numerical cases, experimental data were offered as a calibration in this work. The temporal and spatial distribution characteristics of the energy and flow variables were comprehensively discussed. Studies and analysis showed that (1) the novelly achieved parameters B = 710.8 MPa and γ = 5.22 for the Tait equation of state were highly recommended for any application involving transient loads. (2) The explosion flow field produced by the Taylor wave model was closer to the nature of physical reality. (3) Without considering the details, the stationary wave model was not entirely unacceptable as an initial condition for roughly simulating an explosion effect. The most important thing was that one had to ensure that the initial energy was equivalent to the Taylor wave case.

Numerical investigations of interface instability and turbulent mixing driven by implosion

The interface instability and turbulent mixing of perturbed Air/SF6 interface driven by implosion in spherical convergent geometry are numerically investigated by the use of in-house compressible hydrodynamic code (multi-viscous flow and turbulence). The results revealed the complex evolving laws and physical mechanisms of interface instability and turbulent mixing due to the evolution of complex waves in this case. The RM instability is induced when the perturbed Air/SF6 interface is driven by the incident shock wave. And the perturbed interface accelerates toward the center, thereafter RT instability occurs. Then the perturbed interface slows down and decelerates towards the center, and the RT stabilization appears and suppresses the development of the interface instability and turbulent mixing. When the RT stabilization acts an absolutely dominant role, the growth of the turbulent mixing zone (TMZ) width is restrained completely, and its width in turn reduces. After the rebound of transmitted shock waves, the secondary loading from heavy fluid to light fluid is a combination of quasi-isentropic ramp wave, shock wave and Taylor wave in time series. The loading of quasi-isentropic ramp wave also contributes to the RT stabilization mechanism, the drive of rebound shock wave was seen to have induced the RM instability too, and the impact of Taylor wave resulted in RT instability once again. In the following, the reflected wave moves toward the center and bounces, the third loading process is the same as the secondary one; the TMZ width repeats the same growth laws. The Bell-Plesset (BP) effect which belongs to the conergent geometry can promote the development of TMZ. In the spherical converegent geometry, the competition mechanism among the RM instability, RT instability, BP effect and RT stabilization controls the evolution of interface instability and turbulent mixing. The distributions of turbulent kinetic energy indicate that TMZ evolves asymmetrically along the radial direction. The distributions of three direction components of turbulent kinetic energy and energy spectra also exhibit the evolution of TMZ as strong anisotropy.

Influence of Taylor waves on standing windows of oblique detonation wave

An oblique detonation wave stabilized over a body has been studied due to the ongoing development of high-speed propulsion systems, such as oblique detonation wave engines and ram accelerators. Standing window of oblique detonation wave reflects the degree of standing difficulty. Firstly, Shock relations coupled with chemical equilibrium are solved to draw detonation polar diagrams between oblique detonation angle and wedge angle by iterative algorithm. In these diagrams, the wedge angle detaching from the wedge nose is referred as the maximum wedge angle θιηॉκ and forming CJ detonation in the direction normal to the oblique detonation wave is referred as the minimum wedge angle θख़τ. The region between the two wedge angles is regarded as the standing windows. G. Emanuel holds that Taylor waves follow the oblique detonation wave as the wedge angle is smaller than θख़τ. Based on reactive Euler equation, wedge-induced oblique detonation is simulated in this paper. For the case of the wedge angle below θख़τ, Taylor waves change post-detonation wave flow field to maintain standing oblique detonation wave. Therefore, the standing window becomes wider.

Influence of flow shear on localized Rayleigh–Taylor and resistive drift wave instabilities

AbstractThe impact of velocity shear on the localized solutions of Rayleigh–Taylor (RT) and resistive drift wave (DW) instabilities has been investigated. Slab geometry is used, and the plasma density gradient is assumed to have a finite spatial structure. It demonstrates that the velocity shear has quite different effects on these instabilities: while it stabilizes RT instability and causes tilting of the eddies of equipotential contour, it has a very mild impact on the resistive DW instability and simply shifts the eddies with no tilting.

Spray dynamics simulations for pulsatile injection at different ambient pressure and temperature conditions

A numerical study on the transient characteristics of a pulsatile, iso-octane spray issuing from a pressure-swirl atomizer is presented. The effects of system pressure and temperature, as well as the initial fuel temperature on spray dispersion and evaporation, are highlighted. The computations were carried out using ANSYS FLUENT-15.0, assuming the spray dispersion to be axisymmetric. Gas phase turbulence is simulated using the renormalized group k- ε model, while the discrete phase model is used for tracking fuel droplets. The linear instability sheet atomization model is adopted for the primary breakup of the liquid sheet, and the Taylor Analogy Breakup and Wave Breakup models are adopted for the secondary breakup, depending upon the operating conditions. The drag force on the droplet is evaluated, after incorporating the effects of evaporation and neighbouring droplets, along with droplet shape distortion. The significance of droplet collision on the evolution of droplet size distribution is examined. The local mean drop sizes and spray penetration length are in agreement with the experimental results of the literature. The predicted results indicate that the spray is narrower and penetrates less at higher ambient pressure. In this respect, the additional force on droplets due to local static pressure gradient is examined in detail. The effect of ambient conditions on the spray evaporation process is studied based on the spatio-temporal evolution of the equivalence ratio of the mixture of fuel vapour and air.

Energy-optimal strokes for multi-link microswimmers: Purcell's loops and Taylor's waves reconciled

Micron-scale swimmers move in the realm of negligible inertia, dominated by viscous drag forces. In this paper, we formulate the leading-order dynamics of a slender multi-link (N-link) microswimmer assuming small-amplitude undulations about its straight configuration. The energy-optimal stroke to achieve a given prescribed displacement in a given time period is obtained as the largest eigenvalue solution of a constrained optimal control problem. Remarkably, the optimal stroke is an ellipse lying within a two-dimensional plane in the (N – 1)-dimensional space of joint angles, where N can be arbitrarily large. For large N, the optimal stroke is a traveling wave of bending, modulo edge effects. If the number of shape variables is small, we can consider the same problem when the prescribed displacement in one time period is large, and not attainable with small variations of the joint angles. The fully nonlinear optimal control problem is solved numerically for the cases N = 3 (Purcell’s three-link swimmer) and N = 5 showing that, as the prescribed displacement becomes small, the optimal solutions obtained using the small-amplitude assumption are recovered. We also show that, when the prescribed displacements become large, the picture is different. For N = 3 we recover the non-convex planar loops already known from previous studies. For N = 5 we obtain non-planar loops, raising the question of characterizing the geometry of complex high-dimensional loops.

Experimental and Computational Damage and Ejecta Studies of Pb Explosively Shock Loaded to $$P_{SL} \approx 32$$ P S L ≈ 32 - to 40-GPa

We report results from an experiment on Pb that we explosively shock loaded to $$P_{SL} \approx 32$$ - and 43-GPa, in a single experiment. These $$P_{SL}$$ caused the Pb sample to isentropically release to either a liquid or mixed solid–liquid phase post-shock. The post-shock sample damage and dynamics were diagnosed with proton radiography, which gave quantitative damage data within three distinct regions. The first region is the particle (ejecta) cloud, where we observed that total areal mass ejected from the shocked Pb surface is in-dependent of the peak $$P_{SL}$$ for unsupported (Taylor wave) shockwave loading. The second region, which exhibits spall and cavitation, distends and disperses as the shocked coupon self-similarly expands subsequent to the shockwave impulse and the release into tension. The third region includes undamaged, full density Pb sample. We report quantitative observations from all three regions, and we used the data to evaluate and validate damage and ejecta models, which satisfactorily describe the observed experimental dynamics.

High-order implicit finite difference schemes for the two-dimensional Poisson equation

In this paper, a new family of high-order finite difference schemes is proposed to solve the two-dimensional Poisson equation by implicit finite difference formulas of (2M+1) operator points. The implicit formulation is obtained from Taylor series expansion and wave plane theory analysis, and it is constructed from a few modifications to the standard finite difference schemes. The approximations achieve (2M+4)-order accuracy for the inner grid points and up to eighth-order accuracy for the boundary grid points. Using a Successive Over-Relaxation method, the high-order implicit schemes have faster convergence as M is increased, compensating the additional computation of more operator points. Thus, the proposed solver results in an attractive method, easy to implement, with higher order accuracy but nearly the same computation cost as those of explicit or compact formulation. In addition, particular case M=1 yields a new compact finite difference schemes of sixth-order of accuracy. Numerical experiments are presented to verify the feasibility of the proposed method and the high accuracy of these difference schemes.

A compact laboratory device for accelerating thin strikers

We describe a method for accelerating a thin (~1 mm thick) striker with a diameter of 35 mm in a shock tube channel up to velocities above to ~275 m/s under the pressure of detonation products of acetylene–oxygen fuel mixture. Impact of this striker on a ~1-cm-thick water layer generates a nonstationary decaying shock wave (Taylor wave) with amplitude of ~0.2 GPa on escape from the free surface.

Computational fluid dynamics analysis of the initial stages of a VHTR air-ingress accident using a scaled-down model

An air-ingress accident is considered to be one of the design basis accidents of a very high-temperature gas-cooled reactor (VHTR). The air-ingress accident is initiated, in its worst-case scenario, by a complete break of the hot duct in what is referred to as a double-ended guillotine break. This leads to an initial loss of the primary helium coolant via depressurization. Following the depressurization process, the air–helium mixture in the reactor cavity could enter the reactor core via the hot duct and hot exit plenum. In the event that air ingresses into the reactor vessel, the high-temperature graphite structures in the reactor core and hot plenum will chemically react with the air, which could lead to damage of in-core graphite structures and fuel, release of carbon monoxide and carbon dioxide, core heat up, failure of the structural integrity of the system, and eventually the release of radionuclides to the environment.Studies in the available literature focus on the phenomena of the air ingress accident that occur after the termination of the depressurization, such as density-driven stratified flow, molecular diffusion, and natural circulation. However, a recent study shows that flow reversal could occur due to Taylor wave expansion near the end of the depressurization, which could affect subsequent stages of the air ingress accident scenario. Therefore, to properly understand and evaluate the depressurization effects, numerical simulations are performed for the double-ended guillotine break of the Gas Turbine-Modular Helium Reactor (GT-MHR) cross vessel with a computational fluid dynamics (CFD) tool, ANSYS FLUENT.A benchmark and error quantification study of the depressurization shows that the ANSYS FLUENT model can predict the depressurization problem with relatively low uncertainty. In addition, the computational results show that the depressurization of a double-ended guillotine break behaves as an isentropic process. The observed flow oscillations near the end of the depressurization promote mixing of helium gas and air near the break. The results of the CFD analyses also show that the density-driven stratified flow, which is postulated to be the next stage of the air-ingress accident scenario, is strongly dependent on the density difference between the air–helium mixture in the containment and the helium in the reactor vessel. Therefore, the flow oscillations near the end of the depressurization stage may have a minor, yet notable, effect to slow down the air ingress due to density-driven stratified flow by decreasing the bulk density of the gas mixture in the containment through the addition of helium and increasing the bulk density in the reactor vessel through the addition of air.

Electrical conductivity distribution during detonation of a TATB-based explosive

The distribution of electrical conductivity upon detonation of a TATB-based explosive (C6H6N6O6) is obtained for two densities (1.3 and 1.8 g/cc). A peak of width of about 0.1 µs detected in all profiles is in good agreement with the duration of the chemical reaction zone known from the literature. An extended electrical conductivity region is observed in the Taylor wave.

気体デトネーション駆動型ガス銃を用いた飛行体加速実験

The gaseous detonation driven gas gun was developed for accelerating the projectile to a supersonic speed. The gas gun was simply consisted of two straight stainless-steel tubes. The one was the detonation tube and the other was the launch tube. The detonation tube was 50 mm inside diameter with 2180 or 4280 mm long, and the launch tube was 5 mm inside diameter with 1040 mm long. Chapman-Jouguet detonation wave was initiated in the detonation tube, and the projectile was accelerated in the launch tube via combustion products behind the detonation wave. The spherical projectile of 4.76 mm diameter was made of high-density polyethylene with 52 mg mass. The driver mixture was stoichiometric hydrogen-oxygen premixed gas with initial pressure ranging from 120 to 450 kPa. The gas gun was successfully operated, and the maximum projectile velocity of 1400 m/s was obtained for the conditions that the detonation tube was 4280 mm long and the initial pressure of the driver gas was 450 kPa. The results of the longer detonation tube demonstrated that the projectile velocity was 1.15 - 1.25 times higher than the case of shorter detonation tube. This velocity change of the projectile could be explained by the pressure increase at the inlet of the launch tube by using longer detonation tube. The reason of the pressure increase has a possibility that the length of Taylor wave behind the detonation wave becomes longer for the case of longer detonation tube.

Instability of the free boundary of a water layer accelerated by a Taylor wave

The instability of the free boundary of a thin (1 mm) water layer under the action of a Taylor wave (80 MPa), which is created by a laser pulse, has been experimentally studied. The experimental results demonstrate the capabilities of the laser Doppler method for the continuous recording of a flying object (PDV method) [O. T. Strand, D. R. Goosman, and C. Martinez, Rev. Sci. Instrum. 77, 0831081 (2006)] for studying this problem.

Efficient GPGPU implementation of a lattice Boltzmann model for multiphase flows with high density ratios

We present the development of a Lattice Boltzmann Method (LBM) for the numerical simulation of multiphase flows with high density ratios, such as found in ocean surface wave and air–sea interaction problems, and its efficient implementation on a massively parallel General Purpose Graphical Processing Unit (GPGPU). The LBM extends Inamuro’s et al.’s (2004) multiphase method by solving the Cahn–Hilliard equation on the basis of a rigorously derived diffusive interface model. Similar to Inamuro et al., instabilities resulting from high density ratios are eliminated by solving an additional Poisson equation for the fluid pressure. We first show that LBM results obtained on a GPGPU agree well with standard analytic benchmark problems for: (i) a two-fluid laminar Poiseuille flow between infinite plates, where numerical errors exhibit the expected convergence as a function of the spatial discretization; and (ii) a stationary droplet case, which validates the accuracy of the surface tension force treatment as well as its convergence with increasing grid resolution. Then, simulations of a rising bubble simultaneously validate the modeling of viscosity (including drag forces) and surface tension effects at the fluid interface, for an unsteady flow case. Finally, the numerical validation of more complex flows, such as Rayleigh–Taylor instability and wave breaking, is investigated. In all cases, numerical results agree well with reference data, indicating that the newly developed model can be used as an accurate tool for investigating the complex physics of multiphase flows with high density ratios. Importantly, the GPGPU implementation proves highly efficient for this type of models, yielding large speed-ups of computational time. Although only two-dimensional cases are presented here, for which computational effort is low, the LBM model can (and will) be implemented in three-dimensions in future work, which makes it very important using an efficient solution.