Langevin Dynamics Simulation of Transport and Aggregation of Soot Nano-particles in Turbulent Flows

The present paper uses Langevin dynamics (LD) to investigate the aggregation of soot nano-particles in turbulent flows. Interparticle forces are included, and the computation of the individual particles by LD is retained even after aggregate formation such that collision events and locations can be based on center-to-center particle distances without invoking any modelling assumptions of aggregate shape and/or collision frequency. We focus on the interactions between the specific hydrodynamic conditions and the particle properties and their effect on the resulting agglomerates’ morphologies. The morphology is characterized by the fractal dimension, D _f . Computations of particle aggregation in homogeneous isotropic turbulence and in shear flows dominated by counter-rotating vortices with a wide range of turbulence intensities and particle sizes indicate that the evolution of the agglomerates’ shapes can be adequately parameterized by the size of the agglomerates and the Knudsen and Péclet numbers, the latter being based on the smallest turbulence scales. The computations further suggest that the shapes of agglomerates of certain sizes are relatively independent of time and relatively insensitive to larger turbulence structures. The fractal dimensions are modelled as functions of radius of gyration, Kn and Pe. The fitted expressions show good agreement with the LD simulations and represent the entire growth process of the agglomerates. A direct comparison of selected aggregates with experimental data shows very good qualitative agreement. A thorough quantitative validation of the evolution of the computed aggregate characteristics is, however, presently hindered by the challenges for and therefore lack of suitable experiments under appropriately controlled conditions.     

Experimental study of shock-accelerated liquid layers

An experimental investigation of a shock wave interacting with one, or several, liquid layer(s) is reported with a motivation towards first wall protection in inertial fusion energy reactor chamber design. A 12.8 mm or 6.4 mm thick water layer is suspended horizontally in a large vertical shock tube in atmospheric pressure argon and subjected to a planar shock wave of strength ranging from M = 1.34 to 3.20. For the single water layer experiments, the shock-accelerated liquid results in a significant increase in end-wall pressure loading (and impulse) compared with tests without water. The end-wall loading can be reduced by more than 50% for a given volume of water when it is divided into more than one layer with interspersed layer(s) of argon. A flash X-ray technique is employed to measure the volume fraction of the shocked water layer and multiple water layers are found to dissipate more energy through the liquid fragmentation process resulting in increased shock mitigation.     

Particle image velocimetry study of the shock-induced single mode Richtmyer–Meshkov instability

Full field particle image velocimetry (PIV) measurements are obtained for the first time in Richtmyer–Meshkov instability shock tube experiments. The experiments are carried out in a vertical shock tube in which the light gas (air) and the heavy gas (SF₆) flow from opposite ends of the shock tube driven section and exit through narrow slots at the interface location. A sinusoidal perturbation is given to the interface by oscillating the shock tube in the horizontal direction. Richtmyer–Meshkov instability is then produced by the interaction with a weak shock wave (M _s  = 1.21). PIV measurements are obtained by seeding the flow with 0.30 μm polystyrene Latex spheres which are illuminated using a double-pulsed Nd:YAG laser. PIV measurements indicate the vorticity to be distributed in a sheet-like distribution on the interface immediately after shock interaction and that this distribution quickly rolls up into compact vortices. The integration of the vorticity distribution over one half wave length shows the circulation to increase with time in qualitative agreement with the numerical study of Peng et al. (Phys. Fluids, 15, 3730–3744, 2003).     

Experimental investigation of a twice-shocked spherical gas inhomogeneity with particle image velocimetry

Results are presented from an experimental investigation into the interaction of a planar shock wave with a vortex ring. A free-falling spherical soap bubble is traversed by the incident shock wave and develops into a vortex ring as a result of baroclinically deposited vorticity (?r×?p 1 0{\nabla\rho\times\nabla p \neq 0}). The vortex ring translates with a velocity relative to the particle velocity behind the shock wave due to circulation. After the shock wave reflects from the tube end wall, it traverses the vortex ring (this process is called “reshock”) and deposits additional vorticity. Planar Mie scattering is used to visualize the atomized soap film at high frame rates (up to 10,000 fps). Particle image velocimetry (PIV) was performed for an argon bubble in nitrogen accelerated by a M = 1.35 shock wave. Circulation was determined from the PIV velocity field and found to agree well with Kelvin’s vortex ring model.     

Analysis of the influence of polymer viscosity on the dispersion of magnesium hydroxide in a polyolefin matrix

The dispersion of Mg(OH)₂ agglomerates at low concentration in a polymer melt was investigated in a transparent counter-rotating shear cell. The influence of the viscosity of the matrix, the initial agglomerate size and the infiltration of the matrix was evaluated. Mg(OH)₂ agglomerates have a low cohesion and a fractal structure. Two dispersive mechanisms already mentioned in the literature were identified: erosion and rupture. Critical conditions for rupture were measured and particle size analysis was performed in order to determine the kinetics of erosion. The infiltration of the matrix, which depends on the viscosity, was found to play a key role on dispersion mechanisms. In contrast to previous works, infiltration is more important with the high viscosity matrix. In infiltrated matrix, rupture was found to occur firstly through plastic deformation of the infiltrated agglomerate, and then the agglomerates split into small fragments. In the low viscosity matrix, fragments produced either by rupture or erosion are small aggregates.     

Particle tracer response across shocks measured by PIV

The experimental approach used for the evaluation of the particle response time across a stationary shock wave is assessed by means of PIV measurements. The study focuses on the experimental requirements for a reliable and unbiased measurement of the particle response time τ _p and length ξ _p based on a single-exponent decaying law. A numerical simulation of the particle response experiment returns the parameters governing the measurement: namely the normalized spatial and temporal resolution, shock strength, and digital resolution. Representing the velocity decay in logarithmic coordinates it is shown that measurements performed with laser pulse separation time up to τ _p and interrogation window up to ξ _p still yield unbiased results for the particle response. A set of experiments on the particle response across a planar oblique shock wave was conducted to verify the results from the numerical assessment. Liquid droplets of DEHS and solid tracer particles of silicon and titanium dioxide with different primary crystal size are compared. The resulting temporal response ranges from 2 to 3 μs, corresponding to values commonly reported in literature, to almost 0.3 μs when particles are properly dehydrated and a filter is applied before injection into the wind tunnel. It is the first experimental evidence of particle tracers with a measured response time lower than 0.4 μs. The same procedure is applied to attempt the measurement of individual particle tracers by particle tracking velocimetry to estimate the spread in the distribution of tracer time response. The latter analysis is limited by the particle image tracking precision error, which biases the results introducing a wider broadening of the particle velocity distribution.     

Static and dynamic compaction of ceramic powders

The static and dynamic compaction of ceramic powders was investigated experimentally using a high-pressure friction-compensated press to achieve static stresses of 1.6 GPa and with a novel gas gun setup to stresses of 5.9 GPa for a tungsten carbide powder. Experiments were performed in the partial compaction region to nearly full compaction. The effects of variables including initial density, particle size distribution, particle morphology, and loading path were investigated in the static experiments. Only particle morphology was found to significantly affect the compaction response. Post-test examination of the powder reveals fracture of the grains as well as breaking at particle edges. In dynamic experiments, steady structured compaction waves traveling at very low velocities were observed. The strain rate within the compaction waves was found to scale nearly linearly with the shock stress, in contrast with many fully dense materials where strain rate scales with stress to the fourth power. Similar scaling is found for data from the literature on TiO₂ powder. The dynamic response of WC powder is found to be significantly stiffer than the static response, probably because deformation in the dynamic case is confined to the relatively narrow compaction wave front. Comparison of new static powder compaction results with shock data from the literature for SiO₂ also reveals a stiffer dynamic response.     

Precursor vacuum-ultraviolet radiation ahead of strong shock waves in a shock tube

The profile and excitation mechanism of vacuum-ultraviolet radiation emitted from shock wave is investigated in a shock tube. For shock wave in argon, the rdiation is due to resonant transition excited by argon-argon collision in the shock front with excitation cross section coefficientS ^*=1.0×10⁻¹⁷ cm²·ev⁻¹ and activation energyE ^*=11.4 ev. For shock wave in air the radition is emitted from a very thin shock layer in which the mechanism ofX ¹∑→b ¹∑ of N₂ is excited with excitation cross sectionQ=2×10⁻¹⁶cm² and activation energyE ^*=12.1 ev. Institute of Mechanics, Academia Sinica     

Numerical simulation of a supersonic gas–solid flow over a blunt body: The role of inter-particle collisions and two-way coupling effects

A supersonic dusty gas flow over a blunt body is considered. The mathematical model of the two-phase gas–particle flow takes into account the inter-particle collisions and the two-way coupling effects. The carrier gas is treated as a continuum, the averaged flow field of which is described by the complete Navier–Stokes equations with additional source terms modeling the reverse action of the dispersed phase. The dispersed phase is treated as a discrete set of solid particles, and its behavior is described by a kinetic Boltzmann-type equation. Particles impinging on the body surface are assumed to bounce from it. Numerical analysis is carried out for the cross-wise flow over a cylinder. The method of computational simulation represents a combination of a CFD-method for the carrier gas and a Monte Carlo method for the “gas” of particles. The dependence of the fine flow structure of the continuous and dispersed phases upon the free stream particle volume fraction α_p∞ and the particle radius r_p is investigated, particularly in the shock layer and in the boundary layer at the body surface. The particle volume fraction α_p∞ is varied from a negligibly low value to the value α_p∞ = 3 × 10⁵ at which inter-particle collisions and two-way coupling effects are simultaneously essential. Particular attention has been given to the particles of radii close to the critical value r_p1, because in this range of particle size the behavior of the particles and their effect on the carrier gas flow are not yet completely understood. An estimate of the turbulent kinetic energy produced by the particles in the shock layer is obtained.     

Interaction of a gasdynamic shock with small disturbances

The stability of shock wave based on the definition of Landau and Lifschitz^[1] is treated in this paper. This is tantamount to solving the problem of interaction of small disturbances with a shock wave. Small disturbances are introduced on both sides of a steady, non-dissipative, plane shock wave. Landau et al.^[1] obtained the stability criterionM ₁>1,M ₂<1 for small disturbances which are travelling in the direction perpendicular to the shock wave. In the present paper, we assume that the small disturbances may be two dimensional, i.e. they may be propagating in the direction inclined to the shock wave. The conclusions obtained are: regardless of whether the incident wave and diverging wave are defined according to the direction of the phase velocity or the group velocity, the shock wave is unstable for some frequencies and longitudinal wave lengths of the disturbances, even if the conditionsM ₁>1,M ₂<1 are fulfilled. Then several experiments are proposed, and the problem of ways to define the incident wave and diverging wave is discussed. The meaning of this problem is illustrated. The same results can be obtained for the steady shock wave in a tube.     

Interaction of a shock with a sphere suspended in a vertical shock tube

Shock wave interaction with a sphere is one of the benchmark tests in shock dynamics. However, unlike wind tunnel experiments, unsteady drag force on a sphere installed in a shock tube have not been measured quantitatively. This paper presents an experimental and numerical study of the unsteady drag force acting on a 80 mm diameter sphere which was vertically suspended in a 300 mm x 300 mm vertical shock tube and loaded with a planar shock wave of M _s = 1.22 in air. The drag force history on the sphere was measured by an accelerometer installed in it. Accelerometer output signals were subjected to deconvolution data processing, producing a drag history comparable to that obtained by solving numerically the Navier-Stokes equations. A good agreement was obtained between the measured and computed drag force histories. In order to interpret the interaction of shock wave over the sphere, high speed video recordings and double exposure holographic interferometric observations were also conducted. It was found that the maximum drag force appeared not at the time instant when the shock arrived at the equator of the sphere, but at some earlier time before the transition of the reflected shock wave from regular to Mach reflection took place. A negative value of the drag force was observed, even though for a very short duration of time, when the Mach stem of the transmitted shock wave relfected and focused at the rear stagnation point of the sphere.Received: 31 March 2003, Accepted: 7 July 2003, Published online: 2 September 2003     

Experimental study on rise velocities of single bubbles in liquid metal under the influence of strong horizontal magnetic fields in a flat vessel

The ascent of single argon bubbles with equivalent diameters (d_eq) between 3.43 and 6.28 mm is investigated at room temperature in a flat, rectangular vessel by means of ultrasound Doppler velocimetry (UDV). GaInSn is used as a working liquid and magnetic flux intensities up to B ≈ 0.918 T are applied. A decelerating effect on the rise velocity is observed at lower, an accelerating effect at medium and a reduction at higher field strengths. Maximum velocities are achieved when the ratio of N/C_D ≈ 1, bubble paths are substantially rectilinear at N/C_D > 2. The mean ascent velocities are compared with literature and data of this work as well as other publications is provided in tables.     

Effect of suspended CuO nanoparticles on mass transfer to a rotating disc electrode

The effect of suspended CuO nanoparticles on the mass transfer to a rotating disc electrode was investigated experimentally, using the electrochemical limiting diffusion current technique. The particle volume fraction was from 0.39% to 1.94%. The rotating speed ranged from 100 to 1000 rpm, which yielded the Reynolds number between 10 and 110, based on the electrochemically active disc radius. The results showed that the addition of the suspended particles increased the limiting current and the plot of log I vs. log ω resulted in linear lines, of which slopes decreased with increasing particle volume fraction. The ratio of Sh/Sh_o ranged from 1 to 1.5. The Sherwood number correlation as function of the Reynolds number and the particle volume fraction was also given.     

Richtmyer–Meshkov instability on a low Atwood number interface after reshock

The Richtmyer–Meshkov instability after reshock is investigated in shock tube experiments at the Wisconsin Shock Tube Laboratory using planar laser imaging and a new high-speed interface-tracking technique. The interface is a mixture of helium and argon (50% each by volume) stratified over pure argon. This interface has an Atwood number of 0.29 and a near single-mode, two-dimensional, standing wave perturbation with an average amplitude of 0.35?cm and a wavelength of 19.4?cm. The incident shock wave of Mach number 1.92 accelerates the interface before reflecting from the shock tube end wall with M =?1.70 and accelerating the interface in the opposite direction. The amplitude growth after reshock is reported for variations in this initial amplitude, and several amplitude growth rate models are compared to the experimental growth rate after reshock. A new growth model is introduced, based on a model of circulation deposition calculated from one-dimensional gas dynamics parameters. This model compares well with the amplitude growth rate after reshock and the circulation over one-half wavelength of the interface after the first shock wave and after reshock.     

On the energy conservation and critical velocities for the propagation of a ＂steady-shock＂ wave in a bar made of cellular material

The propagation of shock waves in a cellular bar is systematically studied in the framework of continuum solids by adopting two idealized material models, viz. the dynamic rigid, perfectly plastic, locking （D-R-PP-L） model and the dynamic rigid, linear hardening plastic, locking （D-R-LHP-L） model, both considering the effects of strain-rate on the material properties. The shock wave speed relevant to these two models is derived. Consider the case of a bar made of one of such material with initial length L 0 and initial velocity v i impinging onto a rigid target. The variations of the stress, strain, particle velocity, specific internal energy across the shock wave and the cease distance of shock wave are all determined analytically. In particular the ＂energy conservation condition＂ and the ＂kinematic existence condition＂ as proposed by Tan et al. （2005） is re-examined, showing that the ＂energy conservation condition＂ and the consequent ＂critical velocity＂, i.e. the shock can only be generated and sustained in R-PP-L bars when the impact velocity is above this critical velocity, is incorrect. Instead, with elastic deformation, strain-hardening and strain-rate sensitivity of the cellular materials being considered, it is appropriate to redefine a first and a second critical impact velocity for the existence and propagation of shock waves in cellular solids. Starting from the basic relations for shock wave propagating in D-R-LHP-L cellular materials, a new method for inversely determining the dynamic stress-strain curve for cellular materials is proposed. By using e.g. a combination of Taylor bar and Hopkinson pressure bar impact experimental technique, the dynamic stress-strain curve of aluminum foam could bedetermined. Finally, it is demonstrated that this new formulation of shock theory in this one-dimensional stress state can be generalized to shocks in a one-dimensional strain state, i.e. for the case of plate impact on cellular materials, by simply making proper replacements of the elastic and plastic constants.     

Axisymmetric shock wave interaction with a cone: a benchmark test

Results of the benchmark test are presented of comparing numerical schemes solving shock wave of M_s = 2.38 in nitrogen and argon interacting with a 43∘ semi-apex angle cone and corresponding experiments. The benchmark test was announced in Shock Waves Vol. 12, No. 4, in which we tried to clarify the effects of viscosity and heat conductivity on shock reflection in conical flows. This paper summarizes results of ten numerical and two experimental applications. State of the art in studies regarding the shock/cone interaction is clarified. PACS 01.50.Kw, 47.15.Pn Communicated by K. Takayama     

A theory of the densification-induced fragmentation in glasses and ceramics under dynamic compression

A boundary of failure which follows a shock front is observed in glasses and ceramics above a critical compressive shock load. This boundary, called the failure wave leaves behind a damaged material with newly evolved properties. These include the Tresca yield behavior and the reduction in sound speed. The evolution of the Mescall zone during long-rod penetration of these materials is associated with this wave. But, the failure wave and this accompanying process of fragmentation under dynamic compression are still not understood. It is known that some brittle solids undergo an irreversible density increase when subjected to high compression. This phenomenon, called densification is linked to the formations of slip lines and cracks in intensely compressed regions of silica glass. It also corresponds directly to the losses in shock wave speeds. Once densified, a region tends to shrink, straining the interface between it and the original solid. Stressed interfaces are unstable and may roughen, causing local cracking. On this basis, the failure wave is idealized as a propagating fracture boundary layer where the solid is comminuted by a process of densification interface roughness. The kinetics for this process are established using the fluctuation dissipation theorem. Shear and tensile modes of fragmentation are studied in plane stress. The theory predicts the powder size in the Mescall zone of silica glass. Nevertheless, this theory still needs experimental verification.     

Constitutive behaviour of anisotropic materials under shock loading

Thermodynamically and mathematically consistent constitutive equations suitable for shock wave propagation in an anisotropic material are presented in this paper. Two fundamental tensors α_ij and β_ij which represent anisotropic material properties are defined and can be considered as generalisations of the Kronecker delta symbol, which plays the main role in the theory of isotropic materials. Using two fundamental tensors α_ij and β_ij, the concept of total generalised “pressure” and pressure corresponding to the thermodynamic (equation of state) response are redefined. The equation of state represents mathematical and physical generalisation of the classical Mie–Grüneisen equation of state for isotropic material and reduces to the Mie–Grüneisen equation of state in the limit of isotropy. Based on the generalised decomposition of the stress tensor, the modified equation of state for anisotropic materials, and the modified Hill criteria, combined with the associated flow rule, a system of constitutive equations suitable for shock wave propagation is formulated. The behaviour of aluminium alloy 7010-T6 under shock loading conditions is considered. A comparison of numerical simulations with existing experimental data shows good agreement of the general pulse shape, Hugoniot Elastic Limits (HELs), and Hugoniot stress levels, and suggests that the constitutive equations are performing satisfactorily. The results are presented and discussed, and future studies are outlined.     

Numerical Study of a Turbulent Flow Compressed by a Weak Shock Wave

Abstract

Modification of a two-dimensional isotropic trbulent flow by passage of a weak shock wave was numerically studied by the explicit spectral collocation method with the fourier series in the ranges of M₁ = 0.14?0.21 and M_s = 1.06?1.14. The density 1 trbulent kinetic energy increased by 10 to 19 % and density fluctuation increased by 14 to 50 % in proportion to the shock wave mach number. The amplification of turbulent kinetic energy did not change by increase of the turbulent Mach number, while that of density fluctuation decreased from1.35 to 1.15%. The argumentation of turbulent kinetic energy appeared at moderate and high wave numbers of energy spectra and resulted in a reduction of the integral scale by3.33 to 5.4%. Modifications mechanisms of turbulent kinetic energy, density fluctuation and vorticity were verified by the transport equations It was shown that the decreased amplification of the density fluctuation In the increased trbulent Mach number attributed to the unchanged production terms and the negative dilatation correlation behind the shock wave.the vorticity-dilatation term was responsible for more than 80 % of the total vorticity production at the shock front.     

Effect of incident shock wave strength on the decay of Richtmyer–Meshkov instability-introduced perturbations in the refracted shock wave

The effect of incident shock wave strength on the decay of interface introduced perturbations in the refracted shock wave was studied by performing 20 different simulations with varying incident shock wave Mach numbers (M ~ 1.1? 3.5). The analysis showed that the amplitude decay can be represented as a power law model shown in Eq.7, where A is the average amplitude of perturbations (cm), B is the base constant (cm^?(E?1), S is the distance travelled by the refracted shockwave (cm), and E is the power constant. The proposed model fits the data well for low incident Mach numbers, while at higher mach numbers the presence of large and irregular late time oscillations of the perturbation amplitude makes it hard for the power law to fit as effectively. When the coefficients from the power law decay model are plotted versus Mach number, a distinct transition region can be seen. This region is likely to result from the transition of the post-shock heavy gas velocity from subsonic to supersonic range in the lab frame. This region separates the data into a high and low Mach number region. Correlations for the power law coefficients to the incident shock Mach number are reported for the high and low Mach number regions. It is shown that perturbations in the refracted shock wave persist even at late times for high incident Mach numbers.