Role of nuclei density as a “hidden” parameter in the formation of anomalous zones in a heavy cavitating magma

The formation of zones with anomalously high values of the basic flow characteristics in decompression waves in a heavy cavitating magma with an intense increase in the density of cavitation nuclei is numerically studied within the framework of a mathematical model of multiphase media with a system of kinetic equations. The basic effects leading to the formation of the anomalous zone are identified.     

The Theory of Thin-Walled Rods of Open Profile as a Result of Asymptotic Splitting in the Problem of Deformation of a Noncircular Cylindrical Shell

A new asymptotic approach to the theory of thin-walled rods of open profile is suggested. For the problem of linear static deformation of a noncircular cylindrical shell we consider solutions, which are slowly varying along the axial coordinate. A small parameter is introduced in the equations of the modern theory of shells. Conditions of compatibility for the shell strain measures are employed. The principal terms of the series expansion of the solution are determined from the conditions of solvability for the minor terms. We conclude the procedure with the subsequent solution for the field of displacements. The analysis shows that the known equations of thin-walled rods, which were previously obtained with some approximate methods using hypotheses and approximations of displacements, are asymptotically exact. The presented semi-numerical analysis of the shell equations allows us to estimate the accuracy of the obtained solution. The results of the paper constitute a sound basis to the equations of the theory of thin-walled rods and provide trustworthy information concerning the distribution of stresses in the cross-section.     

Experimental study of the condensation heat transfer characteristics of CO2 in a horizontal microfin tube with a diameter of 4.95?mm

The condensation heat transfer characteristics for CO₂ flowing in a horizontal microfin tube were investigated by experiment with respect to condensation temperature and mass flux. The test section consists of a 2,400?mm long horizontal copper tube of 4.6?mm inner diameter. The experiments were conducted at refrigerant mass flux of 400–800?kg/m²s, and saturation temperature of 20–30?°C. The main experimental results showed that annular flow was highly dominated the majority of condensation flow in the horizontal microfin tube. The condensation heat transfer coefficient increases with decreasing saturation temperature and increasing mass flux. The experimental data were compared against previous heat transfer correlations. Most correlations failed to predict the experimental data. However, the correlation by Cavallini et al. showed relatively good agreement with experimental data in the microfin tube. Therefore, a new condensation heat transfer correlation is proposed with mean and average deviations of 3.14 and ?7.6?%, respectively.     

Is the concept of “average shape” legitimate,for a mixture of inclusions of diverse shapes?

In heterogeneous materials, inhomogeneities (pores, cracks, particles) usually represent a mixture of diverse shapes. In modeling the effective elastic and conductive properties, they are often replaced by identical spheroidal shapes – for which exact solutions are available – that intend to represent certain “average shape” (for cracks, for example, the circular shape is routinely used). We find that, in anisotropic cases of non-random orientations, such a replacement cannot generally be done (with the exception of flat cracks). In other words, the concept of “average spheroid’ is not legitimate, and its use may lead to large errors in predicting the effective properties – information on shape distribution is needed. In cases of overall isotropy, the replacement is possible in certain cases; even in these cases, however, the aspect ratio of the “average shape” may not be intuitively obvious.     

Damköhler-Shelkin Paradox in the Theory of Turbulent Flame Propagation,and a Concept of the Premixed Flame at the Intermediate Asymptotic Stage

We formulated a paradox in the theory of turbulent premixed flame in the flamelet regime: discrepancy between the Damköhler (1940) and Shelkin (1943) estimate of the turbulence flame speed \(U_{t} \sim {u}^{\prime }\) in the case of strong turbulence (\({u}^{\prime }>>S_{L} \)) and numerous experiments that show a strong dependence of U_t on the speed of the instantaneous flame S_L. We name this discrepancy the Damköhler-Shelkin paradox. The first aim of the research is to validate and clarify this estimate, which is based on intuitive considerations, as the paradox must be a statement that seems contradictory to observations but is actually true. We analysed the turbulent flame in the context of the original hyperbolic combustion equation that directly describes the leading edge of the flame, which is a locus of the Zel’dovich “leading points” controlling the speed of the turbulent flame. Analysis of the corresponding characteristic equations results in the expression for speed on the steady-state turbulent flame \(U_{t} ={u}^{\prime }\sqrt {1+(S_{L} /{u}^{\prime })^{2}} \), which is the case when \({u}^{\prime }>>S_{L} \) becomes \(U_{t} \cong {u}^{\prime }\). This result confirms and improves the Damköhler-Shelkin estimate \(U_{t} \sim {u}^{\prime }\). The second aim is to resolve the Damköhler-Shelkin paradox. We explain the discrepancy with observations by the fact that turbulent flames are transient due to insufficient residence time in the real burners to reach statistical equilibrium of wrinkle structures of the random flame surface. We consider the transient flame in the intermediate asymptotic stage when the small-scales wrinkles are in statistical equilibrium, while at the same time the large-scale wrinkles are far from equilibrium. The expressions for the flame speed and width, which we deduce using the dimensional analysis and general properties of the ransom surface, \(U_{t} \sim ({u}^{\prime }S_{L})^{1/2}\) and \(\delta _{t} \sim ({u}^{\prime }Lt)^{1/2}\), show that this transient flame is in fact a turbulent mixing layer travelling with constant speed U_t depending on S_L, the intermediate steady propagation (ISP) flame. Qualitative estimations of the times required for the small-scale and large-scale wrinkles to reach statistical equilibrium show that the turbulent Bunsen- and V-flames correspond to the intermediated asymptotic stage, and the turbulent flames with a complete equilibrium structure of the wrinkled flamelet surface are not attainable under laboratory conditions. We present the results of numerical simulations of the impingent flames, which count in favour of the belief that these flames are also transient.     

Weak in Space, Log in Time Improvement of the Lady?enskaja�CProdi�CSerrin Criteria

In this article we present a Ladyženskaja–Prodi–Serrin Criteria for regularity of solutions for the Navier–Stokes equation in three dimensions which incorporates weak L ^p norms in the space variables and log improvement in the time variable.     

Existence of a Weak Solution to a Nonlinear Fluid–Structure Interaction Problem Modeling the Flow of an Incompressible, Viscous Fluid in a Cylinder with Deformable Walls

We study a nonlinear, unsteady, moving boundary, fluid–structure interaction (FSI) problem arising in modeling blood flow through elastic and viscoelastic arteries. The fluid flow, which is driven by the time-dependent pressure data, is governed by two-dimensional incompressible Navier–Stokes equations, while the elastodynamics of the cylindrical wall is modeled by the one-dimensional cylindrical Koiter shell model. Two cases are considered: the linearly viscoelastic and the linearly elastic Koiter shell. The fluid and structure are fully coupled (two-way coupling) via the kinematic and dynamic lateral boundary conditions describing continuity of velocity (the no-slip condition), and the balance of contact forces at the fluid–structure interface. We prove the existence of weak solutions to the two FSI problems (the viscoelastic and the elastic case) as long as the cylinder radius is greater than zero. The proof is based on a novel semi-discrete, operator splitting numerical scheme, known as the kinematically coupled scheme, introduced in Guidoboni et al. (J Comput Phys 228(18):6916–6937, 2009) to numerically solve the underlying FSI problems. The backbone of the kinematically coupled scheme is the well-known Marchuk–Yanenko scheme, also known as the Lie splitting scheme. We effectively prove convergence of that numerical scheme to a solution of the corresponding FSI problem.     

Limit Design in the Absense of a Given Layout: A Finite Element,Zero-One Programming Approach∗

Limit design in three dimensions is discussed and formulated as a constrained minimax problem in kinematic and geometric variables. A finite element discretization is proposed which, combined with piecewise linearization of the yield surfaces, reduces the minimum weight design to a pair of dual problems in linear mixed zero one programming. The relevant duality theory is shown to be useful for the theoretical frame of the mechanical problem. Various ways of reducing the number of variables and constraints are pointed out, in order to make available algorithms economically applicable to practical situations.     

Relaxation oscillations,subharmonic orbits and chaos in the dynamics of a linear lattice with a local essentially nonlinear attachment

We study the dynamic interactions between traveling waves propagating in a linear lattice and a lightweight, essentially nonlinear and damped local attachment. Correct to leading order, we reduce the dynamics to a strongly nonlinear damped oscillator forced by two harmonic terms. One of the excitation frequencies is characteristic of the traveling wave that impedes to the attachment, whereas the other accounts for local lattice dynamics. These two frequencies are energy-independent; a third energy-dependent frequency is present in the problem, characterizing the nonlinear oscillation of the attachment when forced by the traveling wave. We study this three-frequency strongly nonlinear problem through slow-fast partitions of the dynamics and resort to action-angle coordinates and Melnikov analysis. For damping below a critical threshold, we prove the existence of relaxation oscillations of the attachment; these oscillations are associated with enhanced targeted energy transfer from the traveling wave to the attachment. Moreover, in the limit of weak or no damping, we prove the existence of subharmonic oscillations of arbitrarily large periods, and of chaotic motions. The analytical results are supported by numerical simulations of the reduced order model.     

Influence of vertical heat exchanger tubes,their arrangement and the column diameter on the hydrodynamics in a gas–solid bubbling fluidized bed

The hydrodynamic behavior of a cold-flow gas–solid fluidized bed with an inner diameter of 22 cm is investigated by means of an ultra-fast X-ray tomographic setup. In the case of an exothermal reaction, heat exchanger tubes are required to remove the reaction heat out of the bubbling fluidized bed reactor. For the examined cold-flow model, the heat exchanger tubes are replaced by vertical internals that serve as placeholder. The influence of vertical internals on the bubble properties for different spatial configurations (square and circular arrangements) is investigated in addition to measurements without internals. Furthermore, the hydrodynamic results of the Ø 22 cm column are compared with an available data set which is based on measurements that were conducted in a column with an inner diameter of 14 cm. The objective of this paper is to provide measurement data for the scale-up process as well as for various computer models simulating a bubbling fluidized bed with vertical internals. It was found that the scale-up process from pilot plants to an industrial scale may be simplified if vertical internals are present, independently of the geometric arrangement.     

Comment on the paper “Magnetohydrodynamic effects on natural convection flow of a nanofluid in the presence of heat source due to solar energy,N. Anbuchezhian,K. Srinivasan,K. Chandrasekaran,R. Kandasamy,Meccanica (2013) 48:307–321”

In the above paper a theoretical investigation of MHD convective flow and heat transfer of an incompressible viscous nanofluid past a porous vertical stretching sheet in the presence of variable stream condition is presented. The governing boundary layer equations are transformed by a Lie symmetry group transformation and the ordinary differential equations are solved numerically using Runge–Kutta Gill method.     

Painlevé analysis,auto-Bäcklund transformation and analytic solutions of a (2 $$+$$ + 1)-dimensional generalized Burgers system with the variable coefficients in a fluid

Nonlinear Dynamics - Burgers-type equations are used to describe certain phenomena in gas dynamics, traffic flow, plasma astrophysics and ocean dynamics. In this paper, a (2 $$+$$ 1)-dimensional...     

Comments on the Paper “Non-Darcian Forced-Convection Flow of Viscous Dissipating Fluid over a Flat Plate Embedded in a Porous Medium” by O. Aydin and A. Kaya,Transport in Porous Media,doi:10.1007/s11242-007-9200-x, 2008

In a very recent paper by Aydin and Kaya (Transp. Porous Media (to appear), 2008) the combined effects of viscous dissipation and surface mass flux on the forced-convection boundary-layer flow was considered. However, as the present Note shows, the thermal boundary condition imposed at the outer edge of the boundary-layer by Aydin and Kaya is incompatible with the energy equation, and thus the results of their paper are in error.