Euler–Lagrange simulation of high pressure shock waves

This paper presents the numerical simulation of overdriven detonation (or O.D.D.) that occurs when a high velocity object impacts an explosive. The pressure and the velocity at this state are higher than those of the Chapman–Jouguet (C–J) state. First, before the simulation of this event, a study of PBX air blast by using multi-material Eulerian method is presented. Pressure peaks are computed for several distances from the explosive. Second, the O.D.D. phenomenon is modeled by the Euler–Lagrange penalty coupling, which permits to couple a Lagrangian mesh of the flyer plate to multi-material Eulerian mesh of explosives and air. This coupling gives us the high detonation velocities in the acceptor explosive and demonstrates that it is able to handle shock–structure interaction problems.     

Aerodynamic characteristics of solid particles�� acceleration by shock waves

In this study, the interaction of a planar shock wave with a group of particles has been investigated using high-speed photography and dynamic pressure measurements. Experiments were carried out in a horizontal circular shock tube. The influence of the particle loading ratio, particle diameter, driving gas and shock wave Mach number on the acceleration was studied. It was found that the higher the particle loading ratio, the greater was the particle velocity. This is due to the higher driving pressure. Helium and nitrogen gases play quite different roles in acceleration. Pressure multiplication during shock wave interaction with particles also appears. Based on the experimental results, the discussion regarding partial quantitative velocities and accelerations of particle groups, as well as the attenuation factors when shock waves pass through the particles, is given.     

A self-similar solution of exponential shock waves in non-ideal magnetogasdynamics

A self similar method is used to analyze numerically the one-dimensional, unsteady flow of a strong cylindrical shock wave driven by a piston moving with time according to an exponential law in a plasma of constant density. The plasma is assumed to be a non-ideal gas with infinite electrical conductivity permeated by an axial magnetic field. Numerical solutions in the region between the shock and the piston are presented for the cases of adiabatic and isothermal flow. The general behaviour of density, velocity, and pressure profiles remains unaffected due to presence of magnetic field in non-ideal gas. However, there is a decrease in values of density, velocity and pressure in case of magnetogasdynamics as compared to non-magnetic case. It may be noted that the effect of magnetic field on the flow pattern is more significant in case of isothermal flow as compared to adiabatic flow. The effect of non-idealness, specific heat exponent and magnetic field strength on the variation of shock strength across the shock front is also investigated.     

Numerical investigation of interactions between shock waves and thermal inhomogeneities after “multipoint” energy emission

This paper discusses a possible mechanism for the various anomalous phenomena induced by spatially inhomogeneous energy emission. Two gas-dynamical models of multipoint energy emission in an ideal compressible gas have been numerically investigated using a second-order difference scheme. It is shown that qualitatively different scenarios are possible depending on the initial parameters.     

“Non-free” interaction of plane shock waves and the boundary layer in the neighborhood of the leading edge of a plate with slip

The interaction between a normally impinging shock wave and the boundary layer on a plate with slip is studied in the neighborhood of the leading edge using various experimental methods, including special laser technology, to visualize the supersonic conical gas flows. It is found that in the “non-free” interaction, when the leading edge impedes the propagation of the boundary layer separation line upstream, the structure of the disturbed flow is largely identical to that in the developed “free” interaction, but with higher parameter values and gradients in the leading part of the separation zone. The fundamental property of developed separation flows, namely, coincidence of the values of the pressure “plateau” in the separation zone and the pressure behind the oblique shock above the separation zone of the turbulent boundary layer, is conserved. Moscow. e-mail: ostap@inmech.msu.su. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 57–69, May–June, 2000. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 97-01-00099).     

Three-dimensional magnetohydrodynamic description of the process of collision of a solar wind shock wave and the Earth’s bow shock

The propagation of a solar wind shock wave along the surface of the Earth’s bow shock is investigated within the framework of an ideal magnetohydrodynamic model in the three-dimensional non-plane-polarized formulation. The most characteristic values of the solar wind parameters and the interplanetary magnetic field strength are considered for the plane front of a solar wind shock wave moving at various velocities along the Sun-Earth radius. The global three-dimensional pattern of the interaction is constructed as a function of the angle of inclination of the surface of the bow shock to the solar wind velocity and the azimuthal angle along the curve of intersection of the fronts of the interacting shock waves. The evolution of the flow developed in the neighborhood of the bow shock is investigated and the parameters of the medium and magnetic field are calculated.     

Reflection and transmission of regular waves at a surface-pitching slotted barrier

The interactions between regular surface waves and a surface-pitching slotted barrier are investigated both analytically and experimentally.A quasi-linear theory is developed using the eigenfunction expansion method.The energy dissipation within the barriers is modeled by a quadratic friction factor,and an equivalent linear dissipation coefficient,which is depth-varying,wave-height dependent,is introduced to linearize the matching condition at the surface-pitching barrier.By comparing the theoretical results with laboratory experiments,it is shown that the present method can satisfactorily predict the variation of the reflection and transmission coefficients with wave height.     

Lumps and rogue waves of generalized Nizhnik–Novikov–Veselov equation

In this paper, via generalized bilinear forms, we consider the (\(2+1\))-dimensional bilinear p-Sawada–Kotera (SK) equation. We derive analytical rational solutions in terms of positive quadratic functions. Through applying the dependent transformation, we present a class of lump solutions of the (\(2+1\))-dimensional SK equation. Those rationally decaying solutions in all space directions exhibit two kinds of characters, i.e., bright lump wave (one peak and two valleys) and bright–dark lump wave (one peak and one valley). In addition, we also obtain three families of bright–dark lump wave solutions to the nonlinear p-SK equation for \(p=3\).     

Collision of an interplanetary shock wave with the Earth’s bow shock. Hydrodynamic parameters and magnetic field

Hydrodynamic parameters and magnetic field generated in each of the waves in neighborhood of the Earth’s bow shock when an interplanetary shock wave impinges on it and propagates along its surface are found in the three-dimensional non-plane-polarized formulation within the framework of the ideal magnetohydrodynamic model. The interaction pattern is constructed in the quasi-steady-state formulation as a mosaic of exact solutions, obtained by means of a computer, to the Riemann problem of breakdown of a discontinuity between the states downstream of the impinging wave and the bow shock on the traveling line of intersection of their fronts. The calculations are carried out for typical parameters of the quiescent solar wind and the interplanetary magnetic field in the Earth’s orbit when the plane front of a shock wave moves along the Sun-Earth radius with various given velocities. The solutions obtained can be used to interpret measurements carried out by spacecraft in the solar wind and in neighborhood of the Earth’s magnetosphere.     

Biomechanical evaluation of heel elevation on load transfer — experimental measurement and finite element analysis

In spite of ill-effects of high heel shoes, they are widely used for women. Hence, it is essential to understand the load transfer biomechanics in order to design better fit and comfortable shoes. In this study, both experimental measurement and finite element analysis were used to evaluate the biomechanical effects of heel height on foot load transfer. A controlled experiment was conducted using custom-designed platforms. Under different weight-bearing conditions, peak plantar pressure, contact area and center of pressure were analyzed. A three-dimensional finite element foot model was used to simulate the high-heel support and to predict the internal stress distributions and deformations for different heel heights. Results from both experiment and model indicated that heel elevations had significant effects on all variables. When heel elevation increased, the center of pressure shifted from the midfoot region to the forefoot region, the contact area was reduced by 26% from 0 to 10.2 cm heel and the internal stress of foot bones increased. Prediction results also showed that the strain and total tension force of plantar fascia was minimum at 5.1 cm heel condition. This study helps to better understand the biomechanical behavior of foot, and to provide better suggestions for design parameters of high heeled shoes.     

The monotonicity and critical periods of periodic waves?of?the �� 6 field model

In this paper, we study the relationship between period and energy of periodic traveling wave solutions for the ?? ⁶ field model. The various topological phase portraits with periodic annulus are given by using standard phase portrait analytical technique. Some analytic behaviors (convexity, monotonicity and number of critical periods) of the period functions associated with periodic waves are investigated. We prove that the period function has exactly one critical period under certain conditions. Moreover, the numerical simulation is made. The results show that our theoretical analysis agrees with the numerical simulation.     

An example of stick–slip and stick–slip–separation waves

The dynamical problem of a brake-like mechanical system composed of an elastic cylindrical tube with Coulomb's friction in contact with a rigid and rotating cylinder is considered. This model problem enables us to give an example of non-trivial periodic solutions in the form of stick–slip or stick–slip–separation waves propagating on the contact surface. A semi-analytical analysis of stick–slip waves is obtained when the system of governing equations is reduced by condensation to a simpler system involving only the contact displacements. This reduced system, of only one space variable in addition to time, can be solved almost analytically and gives some interesting informations on the existence and the characteristics of stick–slip waves such as the wave numbers on the circumference, stick and slip proportions, wave celerities, tangential and normal forces. It is shown in particular that the stick–slip–separation solutions would occur for small normal pressures or high rotational speeds. Since the analytical discussion becomes cumbersome in this case, a second approach based on numerical analysis by the finite element method is performed. The existence and the characteristics of stick–slip and stick–slip–separation waves are discussed numerically.     

The phenomena of shock wave reflection — a review of unsolved problems and future research needs

Although the phenomenon of shock wave reflection was discovered more than a hundred years ago, active research related to this phenomenon still goes on in many countries in the world (e.g., Australia, Canada, China, Germany, Israel, Japan, Poland, Russia and United States of America). As a matter of fact the research activity increased so drastically in the past decade and a half that a special scientific meeting dedicated to better understanding the reflection phenomena of shock waves, namely The International Mach Reflection Symposium was initiated in 1981 and was held since then in the major research centers actively involved in the research of shock wave reflections. In the present paper the status of the research of the phenomenon of shock wave reflection will be discussed in general, and unresolved problems and future research needs will be pointed out.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Ageing and collapse of bentonite gels—effects of Li,Na, K and Cs ions

The state of bentonite gels at the start of the ageing experiment must be well-defined, and this required the gels to be at a constant surface chemistry condition. This is achieved by allowing the freshly prepared gels to rest for a day. At this state, the yield stress is constant, provided that the gel is at an equilibrium breakdown state after stirring prior to each measurement. This point is also the yield stress at zero aged time. Ageing study then commenced, and the behaviour is generally characterised by an increasing yield stress with wait time. Alkali metal ion type and concentration affect the gel ageing and stability behaviour significantly. The ageing behaviour is most pronounced at low salt concentrations for the smallest and most strongly hydrated cations, Li ⁺and Na ⁺. The yield stress at any given aged time and its rate of increase are generally larger. Coarsening of these suspensions was observed. The opposite is true for the weakly hydrated K ⁺and Cs ⁺ions. At high concentrations of 0.5 and 1.0 M Cs, K and Na ions, the gels became unstable over time and phase-separated. The stability time of these weak gels was found to increase with decreasing cation size, Na > K > Cs. This stability time displayed a very strong quantitative correlation with the hydration bond length. Coarsening was also expected, but not observed due to the lack of integrity of these weak aggregates during particle size measurement. The recovery or ageing behaviour was fitted with both the Nguyen–Boger and Leong models.     

Vector solitons and rogue waves of the matrix Lakshmanan–Porsezian–Daniel equation

Nonlinear Dynamics - With the Darboux-dressing transformation, we study the vector solitons and rogue waves of the matrix Lakshmanan–Porsezian–Daniel equation. Firstly, we show the...     

Nanoscale Poiseuille flow and effects of modified Lennard–Jones potential function

Numerical simulation of Poiseuille flow of liquid Argon in a nanochannel using the non-equilibrium molecular dynamics simulation (NEMD) is performed. The nanochannel is a three-dimensional rectangular prism geometry where the concerned numbers of Argon atoms are 2,700, 2,550 and 2,400 at 102, 108 and 120 K. Poiseuille flow is simulated by embedding the fluid particles in a uniform force field. An external driving force, ranging from 1 to 11 PN (Pico Newton), is applied along the flow direction to inlet fluid particles during the simulation. To obtain a more uniform temperature distribution across the channel, local thermostating near the wall are used. Also, the effect of other mixing rules (Lorenthz–Berthelot and Waldman–Kugler rules) on the interface structure are examined by comparing the density profiles near the liquid/solid interfaces for wall temperatures 108 and 133 K for an external force of 7 PN. Using Kong and Waldman–Kugler rules, the molecules near the solid walls were more randomly distributed compared to Lorenthz–Berthelot rule. These mean that the attraction between solid–fluid atoms was weakened by using Kong rule and Waldman–Kugler rule rather than the Lorenthz–Berthelot rule. Also, results show that the mean axial velocity has symmetrical distribution near the channel centerline and an increase in external driving force can increase maximum and average velocity values of fluid. Furthermore, the slip length and slip velocity are functions of the driving forces and they show an arising trend with an increase in inlet driving force and no slip boundary condition is satisfied at very low external force (<1 PN).     

An experimental study on effects of solid concentration and ζ-potential on pseudoplastic flow of suspensions

The pseudoplastic flow of suspensions, alumina or styrene-acrylamide copolymer particles in water or an aqueous solution of glycerin has been studied by the step-shear-rate method. The relation between the shear rate,D, and the shear stress,, in the step-shear-rate measurements, where the state of dispersion was considered to be constant, was expressed as = AD ^1/2 +CD. The effective solid volume fraction,ø _F, andA were dependent on the shear rate and expressed byø _F =aD ^b andA = D . Combining the above relations, the steady flow curve was expressed by = D ^{1/2 +} + ₀ (1 – a D ^b/0.74)^–1.85 D, where ₀ is the viscosity of the medium.With an increase in solid volume fraction and a decreases in the absolute value of the-potential, the flow behavior of the suspensions changed from Newtonian ( = = b = 0), slightly pseudoplastic ( = b = 0), pseudoplastic ( = 0) to a Bingham-like behavior.The change in viscosity of the medium had an effect on the change in the effective volume fraction.