Effect of the porosity and particle size of materials on sound-wave velocity

Methods were developed to measure longitudinal and transverse sound velocities in porous materials — various Zn-S mixtures and KBr samples. It is shown that, on exposure to ultrasound with a wavelength far exceeding the pore size in pressed samples, a porous body behaves as a continuous medium. Sound velocity in a porous material was found to depend on the quantitative ratio of vacuum, air, and toluene in the pores. Bulk sound velocities estimated using an additive method agree with experimental data within an error not more than 10%. It was found that removal of moisture traces from porous samples led to significant absorption of sound waves. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 121–127, July–August, 2009.     

Variational approach to constructing hyperbolic models of two-velocity media

A generalized Hamilton variational principle of the mechanics of two-velocity media is proposed, and equations of motion for homogeneous and heterogeneous two-velocity continua are formulated. It is proved that the convexity of internal energy ensures the hyperbolicity of the one-dimensional equations of motion of such media linearized for the state of rest. In this case, the internal energy is a function of both the phase densities and the modulus of the difference in velocity between the phases. For heterogeneous media with incompressible components, it is shown that, in the case of low volumetric concentrations, the dependence of the internal energy on the modulus of relative velocity ensures the hyperbolicity of the equations of motion for any relative velocity of motion of the phases. the present location of work: Universite of Aix-Marseille III, Marseille 13397 Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 5, pp. 39–54, September–October, 1998.     

Detonability of THDCPD-exo–air mixtures

In the frame of industrial risk and propulsive application, the detonability study of JP10–air mixtures was performed. The simulation and measurements of detonation parameters were performed for THDCPD-exo/air mixtures at various initial pressure (1 bar < P ₀ < 3 bar) and equivalence ratio (0.8 < Φ < 1.6) in a heated tube (T ₀ ~ 375 K). Numerical simulations of the detonation were performed with the STANJAN code and a detailed kinetic scheme of the combustion of THDCPD. The experimental study deals with the measurements of detonation velocity and cell size λ. The measured velocity is in a good agreement with the calculated theoretical values. The cell size measurements show a minimum value for Φ ~ 1.2 at every level of initial pressure studied and the calculated induction length L _i corresponds to cell size value with a coefficient k = λ/L _i = 24 at P ₀ = 1 bar. Based on the comparison between the results obtained during this study and those available in the literature on the critical initiation energy E _c, critical tube diameter d _c and deflagration to detonation transition length L _DDT, we can conclude that the detonability of THDCPD–air mixtures corresponds to that of hydrocarbon–air mixtures.

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This paper is based on the work presented at the 33rd International Pyrotechnics Seminar, IPS 2006, Fort Collins, July 16–21, 2006.     

Stability for the 3D Navier–Stokes Equations with Nonzero far Field Velocity on Exterior Domains

Concerning to the non-stationary Navier–Stokes flow with a nonzero constant velocity at infinity, just a few results have been obtained, while most of the results are for the flow with the zero velocity at infinity. The temporal stability of stationary solutions for the Navier–Stokes flow with a nonzero constant velocity at infinity has been studied by Enomoto and Shibata (J Math Fluid Mech 7:339–367, 2005), in L ^p spaces for p ≥ 3. In this article, we first extend their result to the case \frac32 < p{\frac{3}{2} < p} by modifying the method in Bae and Jin (J Math Fluid Mech 10:423–433, 2008) that was used to obtain weighted estimates for the Navier–Stokes flow with the zero velocity at infinity. Then, by using our generalized temporal estimates we obtain the weighted stability of stationary solutions for the Navier–Stokes flow with a nonzero velocity at infinity.     

Reflection of shock waves from a solid boundary in a mixture of condensed materials 2. Nonequilibrium approximation

The process of reflection of shock waves from a solid wall in a two-component mixture of condensed materials is numerically studied with account of the difference in velocities and pressures of the components within the framework of mechanics of heterogeneous media. It is shown that a shock wave (SW) of the dispersed type with monotonic velocity profiles. A dispersed SW with a nonmonotonic velocity profile in the light component and a monotonic velocity profile in the heavy component is reflected by an SW of the dispersed-frozen type. When a frozen-dispersed SW is reflected, its type is either preserved, or changed to the dispersed-frozen structure depending on the initial parameters of the mixture. A dispersed-frozen SW is reflected by an SW of the same type with slight changes in the velocity and pressure profiles. A frozen SW of the two-front configuration can be reflected as an SW of the dispersed-frozen type or a frozen SW of the two-wave configuration. It is shown that a boundary layer is formed near the wall, where the volume concentration and the density of the light component exceed the corresponding values behind the reflected SW. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 6, pp. 3–10, November–December, 1999.     

Near-ground tornado-like vortex structure resolved by particle image velocimetry (PIV)

The near-ground flow structure of tornadoes is of utmost interest because it determines how and to what extent civil structures could get damaged in tornado events. We simulated tornado-like vortex flow at the swirl ratios of S = 0.03–0.3 (vane angle θ_v = 15°–60°), using a laboratory tornado simulator and investigated the near-ground-vortex structure by particle imaging velocimetry. Complicated near-ground flow was measured in two orthogonal views: horizontal planes at various elevations (z = 11, 26 and 53 mm above the ground) and the meridian plane. We observed two distinct vortex structures: a single-celled vortex at the lowest swirl ratio (S = 0.03, θ_v = 15°) and multiple suction vortices rotating around the primary vortex (two-celled vortex) at higher swirl ratios (S = 0.1–0.3, θ_v = 30°–60°). We quantified the effects of vortex wandering on the mean flow and found that vortex wandering was important and should be taken into account in the low swirl ratio case. The tangential velocity, as the dominant velocity component, has the peak value about three times that of the maximum radial velocity regardless of the swirl ratio. The maximum velocity variance is about twice at the high swirl ratio (θ_v = 45°) that at the low swirl ratio (θ_v = 15°), which is contributed significantly by the multiple small-scale secondary vortices. Here, the results show that not only the intensified mean flow but greatly enhanced turbulence occurs near the surface in the tornado-like vortex flow. The intensified mean flow and enhanced turbulence at the ground level, correlated with the ground-vortex interaction, may cause dramatic damage of the civil structures in tornadoes. This work provides detailed characterization of the tornado-like vortex structure, which has not been fully revealed in previous field studies and laboratory simulations. It would be helpful in improving the understanding of the interaction between the tornado-like vortex structure and the ground surface, ultimately leading to better predictions of tornado-induced wind loads on civil structures.     

Method for identification of the filled polymer material relaxation kernel in millisecond time range

The filled polymer materials exhibit viscoelastic properties in a wide time range including the millisecond range (∼10⁻²–10 ms) characteristic of different shock loadings of structures made of these materials. We propose a method for the identification of the filled polymer material relaxation kernel in the millisecond time range; this method is based on a shock loading test of a cylindrical sample made of this material. In this test, the disk indenter acceleration is measured by using a piezotransducer. The test scheme does not impose any rigid constraints on the sample dimensions. In particular, it is possible to use samples of typical dimensions of the order of 10 cm, for which the conditions that the sample material is representative of the structure material are necessarily satisfied. The relaxation kernel parameters are identified by numerical minimization of the theoretically predicted indenter velocity deviation from the velocity-time dependence obtained by integrating the acceleration transducer readings. The minimization problem is solved by using a genetic algorithm. The problem of theoretical prediction of the indenter velocity is solved numerically by using a reduced computational scheme whose parameters are chosen from the minimum condition for the deviation from the prediction obtained in the framework of the detailed computational scheme. The use of the reduced computational scheme permits decreasing the computational costs by 3–4 orders of magnitude compared with the detailed computational scheme, which is a necessary condition for the practical applicability of the genetic algorithm in identification problems. We present examples of relaxation kernel identification in the range of 0.1–10ms from the results of the test where the disk indenter raised to the height of 1m falls on the sample end surface.     

Full-field measurements of flow through a scaled metal foam replica

Open-celled foam geometries show great promise in heat/mass transfer, chemical treatment, and enhanced mixing applications. Flow measurements on these geometries have consisted primarily of observations of the upstream and downstream effects the foam has on the velocity field. Unfortunately, these observations give little insight into the flow inside the foam. We have performed quantitative flow measurements inside a scaled replica of a metal foam, ϕ = 0.921, D _Cell = 2.5 mm, by Magnetic Resonance Velocimetry to better understand the fluid motion inside the foam and give an alternative method to determine the foam cell and pore sizes. Through these 3-D, spatially resolved measurements of the flow field for a cell Reynolds number of 840, we have shown that the transverse motion of the fluid has velocities 20–30% of the superficial velocity passing through the foam. This strong transverse motion creates and dissipates streamwise jets with peak velocities 2–3 times the superficial velocity and whose coherence length is strongly correlated to the cell size of the foam. This complex fluid motion is described as “mechanical mixing” and is attributed to the geometry of the foam. A mechanical dispersion coefficient, D _M, was formed which demonstrates the transverse dispersion of this geometry to be 14 times the kinematic viscosity and 10 times the thermal diffusivity of air at 20°C and 1 atm.     

Edge Finishing Effects on the Impact Behavior of Chopped GFRP Composites

The low velocity and low energy impact response of two common sheet mold compound (SMC) material systems—SMC-R27, and SMC-R37—were investigated. In addition to characterizing the low velocity impact response and failure progression of the material systems, the edge effects of diamond saw cutting, waterjet cutting and abrasive waterjet cutting were investigated using optical microscopy and contact surface profilometry. Impact force–time and displacement–time responses were measured and used to characterize energy absorption capabilities and potential correlation to post processing operation and fiber volume fraction. Pre and post-impact edge surface micrographs were examined to relate the failure behavior on the machined surfaces. Experiments and measurements all show that the failure zone size and growth behavior are clearly dependent on the edge finishing process.     

Large eddy simulation of compressible channel flow

Astract The present study is a contribution to the analysis of wall-bounded compressible flows, including a special focus on wall modeling for compressible turbulent boundary layer in a plane channel. large eddy simulation (LES) of fully developed isothermal channel flows at Re = 3,000 and Re = 4,880 with a sufficient mesh refinement at the wall are carried out in the Mach number range 0.3 ≤ M ≤ 3 for two different source term formulations: first the classical extension of the incompressible configuration by Coleman et al. (J. Fluid Mech. 305:159–183, 1995), second a formulation presently derived to model both streamwise pressure drop and streamwise internal energy loss in a spatially developed compressible channel flow. It is shown that the second formulation is consistent with the spatial problem and yields a much stronger cooling effect at the wall than the classical formulation. Based on the present LES data bank, compressibility and low Reynolds number effects are analysed in terms of coherent structure and statistics. A study of the universality of the structure of the turbulence in non-hypersonic compressible boundary layers (M≤5) is performed in reference to Bradshaw (Annu. Rev. Fluid. Mech. 9:33–54, 1977). An improvement of the van Driest transformation is proposed; it accounts for both density and viscosity changes in the wall layer. Consistently, a new integral wall scaling (y ^c+) which accounts for strong temperature gradients at the wall is developed for the present non-adiabatic compressible flow. The modification of the strong Reynolds analogy proposed by Huang et al. (J. Fluid Mech. 305:185–218, 1995) to model the correlation between velocity and temperature for non-adiabatic wall layers is assessed on the basis of a Crocco–Busemann relation specific to channel flow. The key role of the mixing turbulent Prandtl number Pr _m is pointed out. Results show very good agreement for both source formulations although each of them involve a very different amount of energy transfer at the wall. The present work was performed within the framework of the French–German research initiative “large eddy simulation of complex flows’ (UR 507). The computing resources were provided by IDRIS-France. The authors gratefully acknowledge the financial support from the Centre National de la Recherche Scientifique (CNRS), the Centre d’été Mathématique de Recherche Avancée en Calcul Scientifique (CEMRACS) and the Direction Générale de l’Armement (DGA/D4S).     

Effect of energy dissipation on the shaped-charge flow regime

Convergence of a viscous shaped-charge liner to the symmetry axis is described. It is shown that energy dissipation has a significant effect on the process considered. Convergence at small angles can lead to a strong phase explosion of the metastable liquid of the inner, strongly heated, layers of the liner, which is comparable toTNT explosion. An increase in the angle of convergence results in a weak phase “explosion,” which leads to different behavior of shaped-charge jets for different types of linear material. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 4, pp. 3–11, July–August, 2000.     

Hamiltonian structure for a neutrally buoyant rigid body interacting with N vortex rings of arbitrary shape: the case of arbitrary smooth body shape

We present a (noncanonical) Hamiltonian model for the interaction of a neutrally buoyant, arbitrarily shaped smooth rigid body with N thin closed vortex filaments of arbitrary shape in an infinite ideal fluid in Euclidean three-space. The rings are modeled without cores and, as geometrical objects, viewed as N smooth closed curves in space. The velocity field associated with each ring in the absence of the body is given by the Biot–Savart law with the infinite self-induced velocity assumed to be regularized in some appropriate way. In the presence of the moving rigid body, the velocity field of each ring is modified by the addition of potential fields associated with the image vorticity and with the irrotational flow induced by the motion of the body. The equations of motion for this dynamically coupled body-rings model are obtained using conservation of linear and angular momenta. These equations are shown to possess a Hamiltonian structure when written on an appropriately defined Poisson product manifold equipped with a Poisson bracket which is the sum of the Lie–Poisson bracket from rigid body mechanics and the canonical bracket on the phase space of the vortex filaments. The Hamiltonian function is the total kinetic energy of the system with the self-induced kinetic energy regularized. The Hamiltonian structure is independent of the shape of the body, (and hence) the explicit form of the image field, and the method of regularization, provided the self-induced velocity and kinetic energy are regularized in way that satisfies certain reasonable consistency conditions.      

Numerical modelling of film cooling with and without mist injection

Two-phase CFD calculations, using a Lagrangian model and commercial code Fluent 6.2.16, were employed to calculate the gas and droplet flows and film cooling effectiveness with and without mist on a flat plate. Two different three dimensional geometries are generated and the effects of the geometrical shape, size of droplets, mist concentration in the coolant flow and temperature of mainstream flow for different blowing ratios are studied. A cylindrical and laterally diffused hole with a streamwise angle of 30° and spanwise angle of 0° are used. The diameter of film cooling (d) hole, and the hole length to diameter ratio (L/d) for both of geometries are 10 mm and 4, respectively. Also the blowing ratio ranges from 1.0 to 2.0, and the mainstream Reynolds number based on the mainstream velocity and hole diameter (Re _d) is 6,219. The results are shown for different droplets diameters (1–10 μm), concentrations (1–5%) and mainstream temperatures (350–500 K). The centreline effectiveness and distribution of effectiveness on the surface of cooling wall are presented.     

Production of nanomaterials by vaporizing ceramic targets irradiated by a moderate-power continuous-wave CO<Subscript>2</Subscript> laser

The efficiency of utilization of CO ₂ laser energy for vaporization of Al ₂ O ₃ ceramics is evaluated using a mathematical model for the interaction of laser radiation with materials. It is shown that the calculated efficiency of radiation-energy utilization is not higher than 15% at a radiation power density of 10⁵ W/cm ² on the target. On the experimental facility designed for the synthesis of nanopowders, a vaporization rate of 1 g/h was achieved for Al ₂ O ₃, which corresponds to a 3% efficiency of radiation-energy utilization. The dependence of the characteristic particle size of a zirconium oxide nanopowder on helium pressure in the range of 0.01–1.00 atm was studied. Results of experiments on vaporization of multicomponent materials (LaNiO ₃ and the Tsarev meteorite) are given. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 172–184, March–April, 2007.     

Effect of the grain size on the macroscopic response of aluminum to shock loading

Shock tests of two lots of a 1420 aluminum-lithium alloy are performed. The mean grain size is 24 μm in the first lot and 1.6 μm in the second lot obtained by the method of equal-channel angular pressing. Two characteristics of dynamic strength of the material were determined in experiments on the high-velocity impact of flat samples: threshold of dynamic stability with respect to compression on the fore front of the compression pulse and spall strength of the material. The materials of both types have an identical threshold of dynamic stability with respect to compression, whereas the spall strength of the microcrystalline alloy is 20% greater than the spall strength of the polycrystalline alloy. The reason is the consumption of energy on structure formation in the coarse-grain material in passing to a larger-scale structural level (in the case with a fine-grain material, such a structure is available in the initial state). The experiments reveal the presence of a second plastic front whose amplitude is approximately 10% of the first plastic front. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 135–146, November–December, 2007.     

Rheological properties of binary associating polymers

Dynamics of associating polymer solutions above the reversible gelation point are studied. Each macromolecule consists of a soluble backbone (B) and a small fraction of specific strongly interacting groups (A or C stickers) attached to B. A mixture of B–A and B–C associating polymers with 1:1 stoichiometric ratio is considered. As a result of AC association, the polymers reversibly gelate above the overlap concentration. It is shown that (1) the network strands are linear complexes (double chains) of B–A and B–C; (2) “diffusion” of the network junction points is characterized by an apparent activation energy, which can be significantly higher than the energy of one AC bond; (3) most importantly, the randomness of sticker distribution along the chain can significantly slow down the network relaxation leading to a markedly non-Maxwellian viscoelastic behavior. The theory elucidates the most essential features of rheological behavior of polysaccharide associating systems (with A = adamantyl moiety, C = β-cyclodextrin, B = either chitosan or hyaluronan) including similar behavior of G ^′ and G ^″ in a wide frequency range, strong temperature dependence of the characteristic frequency ω _x , and an extremely strong effect of added free stickers (fC) on the dynamics. This paper was presented at Annual European Rheology Conference (AERC) held in Hersonisos, Crete, Greece, April 27–29, 2006.     

Modelling detonation waves in condensed energetic materials: multiphase CJ conditions and multidimensional computations

A hyperbolic multiphase flow model with a single pressure and a single velocity but several temperatures is proposed to deal with the detonation dynamics of condensed energetic materials. Temperature non-equilibrium effects are mandatory in order to deal with wave propagation (shocks, detonations) in heterogeneous mixtures. The model is obtained as the asymptotic limit of a total non-equilibrium multiphase flow model in the limit of stiff mechanical relaxation only (Kapila et al. in Phys Fluids 13:3002–3024, 2001). Special attention is given to mass transfer modelling, that is obtained on the basis of entropy production analysis in each phase and in the system (Saurel et al. in J Fluid Mech 607:313–350, 2008). With the help of the shock relations given in Saurel et al. (Shock Waves 16:209–232, 2007) the model is closed and provides a generalized ZND formulation for condensed energetic materials. In particular, generalized CJ conditions are obtained. They are based on a balance between the chemical reaction energy release and internal heat exchanges among phases. Moreover, the sound speed that appears at sonic surface corresponds to the one of Wood (A textbook of sound, G. Bell and Sons LTD, London, 1930) that presents a non-monotonic behaviour versus volume fraction. Therefore, non-conventional reaction zone structure is observed. When heat exchanges are absent, the conventional ZND model with conventional CJ conditions is recovered. When heat exchanges are involved interesting features are observed. The flow behaviour presents similarities with non ideal detonations (Wood and Kirkwood in J Chem Phys 22:1920–1924, 1950) and pathological detonations (Von Neuman in Theory of detonation waves, 1942; Guenoche et al. in AIAA Prog Astron Aeronaut 75: 387–407, 1981). It also present non-conventional behaviour with detonation velocity eventually greater than the CJ one. Multidimensional resolution of the corresponding model is then addressed. This poses serious difficulties related to the presence of material interfaces and shock propagation in multiphase mixtures. The first issue is solved by an extension of the method derived in Saurel et al. (J Comput Phys 228(5):1678–1712, 2009) in the presence of heat and mass transfers. The second issue poses the difficult mathematical question of numerical approximation of non-conservative systems in the presence of shocks associated to the physical question of energy partition among phases for a multiphase shock. A novel approach is used, based on extra evolution equations used to retain the information of the material initial state. This method insures convergence in the post-shock state. Thanks to these various theoretical and numerical ingredients, one-dimensional and multidimensional unsteady detonation waves computations are done, eventually in the presence of material interfaces. Convergence of the numerical hyperbolic solver against ZND multiphase solution is reached. Material interfaces, shocks, detonations are solved with a unified formulation where the same equations are solved everywhere with the same numerical scheme.     

The velocity of ultrasound in low-carbon steel deformed at the low yield limit

The variation of a thin structure upon deformation of low-carbon steel at the yield limit is analyzed. The character of the interrelationship between the stage nature of a plastic flow of low-carbon steel and the velocity of ultrasound in it is established. It is shown that the velocity of ultrasound is a parameter for obtaining additional data on the development of plastic flow. The structural changes that exert an effect on the velocity of ultrasound in the deformation that corresponds to the yield site are studied. Institute of Strength and Materials Science Physics, Siberian Division, Russian Academy of Sciences, Tomsk 634021. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 3, pp. 197–201, May–June, 2000.     

Effects of coincidence window and measuring volume size on laser Doppler velocimetry measurement of turbulence

The effects of coincidence window and measuring volume size on two-component laser velocimeter measurement of turbulence in an isothermal liquid flow through a concentric annular channel were studied. Three different coincidence windows (100–500 μs) and three different measuring volume sizes (diameter, 5–9 wall units; spanwise length, 24–91 wall units) were used in a flow of Reynolds number 31,500 and data density spanning the high end of intermediate to the low end of high (3–6). While no significant effects of the coincidence window and measuring volume size were found on the time-mean velocity and turbulence intensities, the streamwise Reynolds shear stress measured near a wall was found to be markedly affected by both. The smallest feasible measuring volume along with an appropriate coincidence window provides good measurement of the shear stress. Received: 8 September 1999/Accepted: 11 July 2000