PIV Measurements in a Heavy‐Gas Channel

The propagation and dilution behaviour of cryogenic clouds in a heavy‐gas channel is studied by Particle Image Velocimetry (PIV) measurements. Ice particles are used as tracer particles for the flow. These particles are generated automatically during the evaporation of the liquid nitrogen in a release chamber used for generation of the cloud. The density of the seeding is controlled by changing the evaporation conditions during the startup phase. The measurements conducted so far result in detailed velocity vector maps and show clearly a vortex forming in the vicinity of the first backward facing step     

Similarity solution for a cylindrical shock wave in a rotational axisymmetric dusty gas with heat conduction and radiation heat flux

The propagation of shock waves in a rotational axisymmetric dusty gas with heat conduction and radiation heat flux, which has a variable azimuthally fluid velocity together with a variable axial fluid velocity, is investigated. The dusty gas is assumed to be a mixture of non-ideal (or perfect) gas and small solid particles, in which solid particles are continuously distributed. It is assumed that the equilibrium flow-condition is maintained and variable energy input is continuously supplied by the piston (or inner expanding surface). The fluid velocities in the ambient medium are assume to be vary and obey power laws. The density of the ambient medium is assumed to be constant, the heat conduction is express in terms of Fourier’s law and the radiation is considered to be of the diffusion type for an optically thick grey gas model. The thermal conductivity K and the absorption coefficient α_R are assumed to vary with temperature and density. In order to obtain the similarity solutions the angular velocity of the ambient medium is assume to be decreasing as the distance from the axis increases. The effects of the variation of the heat transfer parameter and non-idealness of the gas in the mixture are investigated. The effects of an increase in (i) the mass concentration of solid particles in the mixture and (ii) the ratio of the density of solid particles to the initial density of the gas on the flow variables are also investigated.     

Spherical shock wave generated by a moving piston in mixture of a non-ideal gas and small solid particles under a gravitational field

Self-similar solutions are obtained for one-dimensional isothermal and adiabatic unsteady flows behind a strong spherical shock wave propagating in a dusty gas. The shock is assumed to be driven out by a moving piston and the dusty gas to be a mixture of a non-ideal (or perfect) gas and small solid particles, in which solid particles are continuously distributed. It is assumed that the equilibrium flow-conditions are maintained and variable energy input is continuously supplied by the piston. The medium is under the influence of the gravitational field due to a heavy nucleus at the origin (Roche model). The effects of an increase in the mass concentration of solid particles, the ratio of the density of the solid particles to the initial density of the gas, the gravitational parameter and the parameter of non-idealness of the gas in the mixture, are investigated. It is shown that due to presence of gravitational field the compressibility of the medium at any point in the flow-field behind the shock decreases and all other flow-variables and the shock strength increase. A comparison has also been made between the isothermal and adiabatic flows. It is investigated that the singularity in the density and compressibility distributions near the piston in the case of adiabatic flow are removed when the flow is isothermal.     

Numerical Simulation of Detonation Excitation at Shock Wave Interaction with Dust Cloud in Channel

The study of detonation ability of reactive particle gas mixtures is necessary to prevent industrial explosions in industries where dispersed powders are used. The present paper focuses on numerical simulation of the shock wave interaction with semiinfinite aluminum dust cloud, which is situated inside a plane channel. The cloud fills entirely or partly the channel cross‐section and has initially a rectangular shape. The scenarios of detonation initiation in the cloud are determined depending on the incident shock wave amplitude values. The processes of transformation and spreading of finite width clouds under weak incident shock wave action (when the particles do not ignite) are investigated. The types of an oblique shock wave reflection from the plane of symmetry in the cloud are analyzed. The processes of particle ignition and detonation structure formation at strong incident shock wave action are investigated. Nonstationary periodic fuctuations take place in the detonation flow due to transversal wave effect. Nevertheless the detonation structure established propagates in quasistationary regime. If the incident shock wave is attenuated with a rarefaction wave then the detonation formation fails at clouds of insufficient width.     

Discrete dipole approximation simulations on GPUs using OpenCL—Application on cloud ice particles

The global distribution and climatology of ice clouds are among the main uncertainties in climate modeling and prediction. In order to retrieve ice cloud properties from remote sensing measurements, the scattering properties of all cloud ice particle types must be known. The discrete dipole approximation (DDA) simulates scattering of radiation by arbitrarily shaped particles and is thus suitable for cloud ice crystals. The DDA models the particle as a collection of equal dipoles on a lattice, and is computationally much more expensive than approximations restricted to more regularly shaped particles. On a single computer the calculation for an ice particle of a specific size, for a given scattering plane at one specific wavelength can take several days. We have ported the core routines of the scattering suite “ADDA” to the open computing language (OpenCL), a framework for programming parallel devices like PC graphics cards (graphics processing units, GPUs) or multi-core CPUs. In a typical case we can achieve a speed-up on a GPU as compared to a CPU by a factor of 5 in double precision and a factor of 15 in single precision. Spreading the work load over multiple GPUs will allow calculating the scattering properties even of large cloud ice particles.     

On the linearized system of equations for the condensate–normal fluid interaction at very low temperature

The linearization around one of its equilibrium of a system that describes the correlations between the superfluid component and the normal fluid part of a condensed Bose gas in the approximation of very low temperature and small condensate density is studied. A simple and transparent argument gives a necessary and sufficient condition for the existence of global solutions satisfying the conservation of the total number of particles and energy. The global solutions describe the evolution in time of the density of the thermal cloud and, unlike in previous work, that of the condensate's density. Their convergence to a suitable stationary state is also shown and rates of convergence for the normal fluid and superfluid components are obtained.     

Steady motions of a continuous medium, resonances and Lagrangian turbulence

A method which enables one to establish a non-regularity property of the motion of fluid particles (known as chaotic advection or Lagrangian turbulence) for typical steady flows is developed. The method is based on expanding solutions of the equations of motion of a continuous medium in powers of a small parameter and using the conditions for the destruction of invariant resonant tori when perturbations are added. It is shown that the velocity field, defined as the solution of the Burgers equations, generates a generally non-regular dynamical system. For an ideal barotropic fluid in an irrotational force field, the method proposed yields a well-known necessary condition for chaotization: the velocity field is collinear with its curl. Special attention is given to investigating the chaotization of typical steady flows of a heat-conducting perfect gas.     

Stability diagrams for a heterogeneous ensemble of particles at the collinear libration points of the photogravitational three-body problem

The stability of the collinear libration points in the photogravitational elliptical three-body problem is investigated. The distribution of the inner collinear libration points located between the principal bodies in the system is revealed. A method of finding collinear libration points for particles with specified reduction coefficients is given. Stability diagrams are constructed for an entire heterogeneous ensemble of particles (cloud) at libration points, which, in particular, make it possible to trace cloud subdivision scenarios. The characteristics (the number of clusters, the diameter of each cluster and the distances to the components of a binary system) are determined for a binary star system similar to α–Centauri.     

Zur Beeinflussung des Hagelkornwachstums

Summary To decrease the accretion rate of a growing hailstone its deposit has to be made dry. Under such conditions a spherical form is prefered to an ellipsoidal one. The growth rate of the former is lower than that of the latter to a factor of two. The accretion rate can be slowed down further when the small cloud particles are partially frozen. In a solid state they will mostly be rejected from the surface of the (dry) hailstone and do not contribute to growth.In paragraph 4 calculations are made about the proportion of cloud particlesV which must be frozen to arrive at a dry deposit. The variables are air temperaturet _L , hailstone diameterd, free H₂O-contentw _f , and air pressurep. The results are shown in Figures 1, 2, and 3 and demonstrate the high ratio of cloud droplets which should be frozen to reduce the growth rate noticeably. Figure 4 is valuable for hailstones growing in a cloud model as postulated byLudlam.This decrease in accretion rate will normally lower the hail damage. But there exists another method which produces hailstones with a very high rate of liquid water. Such spongy particles burst as soon as they hit the ground. The conditions for such a procedure are not yet elaborated but are quite dissimilar to those described above.     

Unlimited cumulation under one-dimensional unsteady compression of an ideal gas

Various methods of unlimited cumulation (UC) of an ideal (inviscid and non-heat-conducting) gas subject to one-dimensional unsteady compression by a plane, cylindrical, or spherical piston are considered. The most perfect method, namely, UC with isentropic compression from rest to rest, which is referred to as “ideal” (IUC), is compared with three other methods of UC, which correspond to well-known self-similar solutions of one-dimensional gas compression. The most effective of these is UC with a reflected shock wave, behind which the compressed gas is homogeneous and at rest, as in IUC. The efficiency of various methods of UC is estimated by the ratio of the work done during compression to the work in the case of IUC, the ratio of the internal energy to the total energy of the compressed gas, and the degree of gas homogeneity with respect to the Lagrangian variable. Computations of these characteristics are carried out for a perfect gas with various adiabatic exponents.     

Flow of a dustry gas through a channel with arbitrary time varying pressure gradient

The unsteady flow of a viscous incompressible gas embedded with small spherical particles in a rectangular channel is studied. The flow is produced under the influence of an arbitrary time varying pressure gradient. The exact velocities of the gas and particles are obtained by operational methods. The change in velocity profiles of the gas and particles with time for a constant pressure gradient, have been drawn graphically. It is found that the velocities of the gas and particles are maximum in the central plane of the channel.     

Self-similar convergence of a shock wave in a heat conducting gas

The problem of the convergence of a spherical shock wave (SW) to the centre, taking into account the thermal conductivity of the gas in front of the SW, is considered within the limits of a proposed approximate model of a heat conducting gas with an infinitely high thermal conductivity and a small temperature gradient, such that the heat flux is finite in a small region in front of the converging SW. In this model, there is a phase transition in the surface of the SW from a perfect gas to another gas with different constant specific heat and the heat outflow. The gas is polytropic and perfect behind the SW. Constraints are derived which are imposed on the self-similarity indices as a function of the adiabatic exponents on the two sides of the SW. In front of the SW, the temperature and density increase without limit. In the general case, a set of self-similar solutions with two self-similarity indices exists but, in the case of strong SW close to the limiting compression, there are two solutions, each of which is completely determined by the motion of the spherical piston causing the self-similar convergence of the SW.     

Nonlocal parabolic problems in statistical mechanics

A nonlocal parabolic equation describing the evolution of a cloud of particles is studied.     

Phase transition in an exactly solvable model of interacting bosons

In the formalism of the grand canonical ensemble, we study a model system of a lattice Bose gas with repulsive hard-core interaction on a perfect graph. We show that the corresponding ideal system may undergo a phase transition (Bose-Einstein condensation). For a system of interacting particles, we obtain an explicit expression for pressure in the thermodynamic limit. The analysis of this expression demonstrates that the phase transition does not take place in the indicated system. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 2, pp. 196–205, February, 1997.     

Ideal gas approximation for a two-dimensional rarefied gas under Kawasaki dynamics

In this paper we consider a two-dimensional lattice gas under Kawasaki dynamics, i.e., particles hop around randomly subject to hard-core repulsion and nearest-neighbor attraction. We show that, at fixed temperature and in the limit as the particle density tends to zero, such a gas evolves in a way that is close to an ideal gas, where particles have no interaction. In particular, we prove three theorems showing that particle trajectories are non-superdiffusive and have a diffusive spread-out property. We also consider the situation where the temperature and the particle density tend to zero simultaneously and focus on three regimes corresponding to the stable, the metastable and the unstable gas, respectively.     

Comparison of non-cohesive resolved and coarse grain DEM models for gas flow through particle beds

The Discrete Element Method (DEM) is a widely used approach for modelling granular systems. Currently, the number of particles which can be tractably modelled using DEM is several orders of magnitude lower than the number of particles present in common large-scale industrial systems. Practical approaches to modelling such industrial system therefore usually involve modelling over a limited domain, or with larger particle diameters and a corresponding assumption of scale invariance. These assumption are, however, problematic in systems where granular material interacts with gas flow, as the dynamics of the system depends heavily on the number of particles. This has led to a number of suggested modifications for coupled gas–grain DEM to effectively increase the number of particles being simulated. One such approach is for each simulated particle to represent a cluster of smaller particles and to re-formulate DEM based on these clusters. This, known as a representative or ‘coarse grain’ method, potentially allows the number of virtual DEM particles to be approximately the same as the real number of particles at relatively low computational cost. We summarise the current approaches to coarse grain models in the literature, with emphasis on discussion of limitations and assumptions inherent in such approaches. The effectiveness of the method is investigated for gas flow through particle beds using resolved and coarse grain models with the same effective particle numbers. The pressure drop, as well as the pre and post fluidisation characteristics in the beds are measured and compared, and the relative saving in computational cost is weighed against the effectiveness of the coarse grain approach. In general, the method is found perform reasonably well, with a considerable saving of computational time, but to deviate from empirical predictions at large coarse grain ratios.     

Real gas effects in thermally choked nozzle flows

Real gas effects in condensing nozzle flows are discussed by the virial equation of state truncated after the second virial coefficient. The thermal choking conditions in nozzles previously derived for a perfect condensible vapor are generalized to include real gas effects. For these cases it is shown that the critical amount of heat necessary to thermally choke the flow can be defined explicitly only for the expansion of a pure vapor.Alexander von Humboldt Fellow.The flow Mach number is usually taken as the local frozen Mach number.     

Simulation of aerosol distribution in hyperbolic resonator

Dynamics of the distribution of aerosol particles in acoustic field inside a hyperbolic plane resonator is numerically studied. The exact value of the first resonant frequency, as well as the amplification of gas velocity amplitude are found. The existence of acoustic flow in the form of four Rayleigh and four Schlichting vortices is revealed at first resonant frequency. Dynamics of the initially uniformly distributed particles and their drift at the first resonant frequency is simulated. Five zones of attraction of aerosol particles (acoustic traps) are observed. The influence of entrainment coefficient of particles on their distribution is analyzed.     

Optimal control of a magnetohydrodynamic viscous heat-conducting gas flow

The control problem for a one-dimensional flow of a polytropic viscous heat-conducting perfect gas through an interval is considered. The density of external currents is taken as the control. The existence of an optimal control function is proved. Necessary optimality conditions are derived. The compactness of the set of solutions is established.