Resonant flexural vibrations and dissipative heating of a piezoceramic ring plate with nonuniformly electroded surfaces

The forced flexural vibrations and dissipative heating of a bimorph ring plate are studied. The plate is made of viscoelastic piezoceramics and is polarized across the thickness. The outer surfaces of the plate are nonuniformly electroded, and harmonic electric excitation is applied to the electrodes. The viscoelastic behavior of the material is described using the concept of temperature-dependent complex moduli. The coupled nonlinear problem of thermoviscoelasticity is solved by time iteration using, at each iteration, the discrete-orthogonalization method to integrate the mechanics equations and the explicit finite-difference method to solve the heat-conduction equation with a nonlinear heat source. Numerical calculations demonstrate that by changing the size of the ring electrode we can influence the natural frequency, stress and displacement distributions, dissipative-heating temperature, and amplitude-and temperature-frequency characteristics. With certain boundary conditions, there is an optimal electrode configuration that produces deflections of maximum amplitudes when an electric excitation is applied __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 3, pp. 102–109, March 2006.     

On the structure of a turbulent spot in a heated laminar boundary layer

An artificially generated turbulent spot was investigated experimentally in a heated boundary layer using a rake of mini-thermocouples. Simultaneous temperature traces were used to determine the spot's leading and trailing edge characteristics. The measurements on the centerline of the plate at a constant velocity and variable streamwise positions provided a Re _x range of 2.45–12.6 x 10⁵. At one axial station the free stream velocity was varied and off-axis measurements were obtained.The shape of the interface between the spot and the surrounding laminar flow was described by conventional and conditional histograms. The length of the spot's leading edge (i.e. the overhang) increased linearly with the downstream distance. Off-axis, the length of the overhang decreased slightly towards the wing tips but became larger with respect to the spot's streamwise extent. The trailing edge changed less significantly in the downstream direction.It was shown that when two spots are generated such that the leading edge of the upstream spot is in the calmed region of the downstream spot, the celerity of the upstream spot is decreased and the spots ultimately merge.     

A CFD comparative study of bubble break-up models in a turbulent multiphase jet

In this paper several bubble break-up models are compared. They have been implemented in the CFX-4.4 fluid dynamic commercial code, which uses the population balance equations for describing liquid/gas multi-phase flows. The models have been assessed against published experimental data, obtained for air bubble break-up within a turbulent water jet. The model of Martínez-Bazán, based on purely kinematics arguments, has shown better agreement with the experimental data. The capabilities of using these models coupled to a CFD code for multiphase flow prediction in industrial applications have been demonstrated.     

Kinetic droplet evaporation in a turbulent air jet

Droplet evaporation in a turbulent air jet is considered for conditions such that the evaporation rate is determined by the evaporation kinetics for the individual droplets rather than by the diffusion rate of the air in the jet. Numerical solution of the equations by computer has shown that the mean air speed in the jet has little effect on the droplet evaporation in the range covered. A simplified solution is presented for the dispersal of an evaporating impurity in a jet. Experiments confirm that this solution is correct, and they show that the turbulent pulsations play a large part, with the result that an initially monodisperse system becomes more and more polydisperse away from the jet.     

On the optimal distribution of the flow rate of gas blown through the side walls of the channel of a de plasmotron (plasma generator)

It is well known that the blowing of cold gas through the side walls of the channel of a dc plasmotron (plasma generator) with longitudinal blowing over the arc leads to an increase in the useful power of the plasmotron [1]. The increase is due to the increase in the combustion voltage of the arc and also the decrease in the heat fluxes to the wall of the channel. The present paper solves the problem of the optimal distribution of the flow rate of gas blown through the side walls into the channel of a dc plasmotron of arbitrary shape F(x). The flow in the main channel and in the ducts in the side walls is described by the quasi-one-dimensional gas-dynamic equations investigated qualitatively in [2] and verified experimentally in [3].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 120–124, May–June, 1981.     

Some experiments on the effect of isolated protuberances on flow through tubes

At various locations in the arterial system, plaques, or small relatively isolated protuberances, can develop on the inner wall of the vessel and project into the lumen. A number of investigators have suggested that the development and growth of these protuberances is related to the flow in the vicinity of the protuberance. In this study, the conditions under which the flow separates from an isolated protuberance located in a cylindrical tube were investigated. The critical Reynolds number at which separation first takes place for a given protuberance was determined. A series of tests was performed for steady flow of a Newtonian fluid through a rigid tube in which protuberances of various sizes were inserted. The results of the tests show the effect of the protuberance height and shape on the separation characteristics. In general, the results indicate that separation takes place at relatively small values of the Reynolds number; values that commonly occur in the arterial system, so that this phenomenon may be important in the study of the “coupling” between blood flow and arterial lesions.     

Graphite combustion in a chemical-equilibrium boundary layer

The mechanism of graphite decomposition in a dissociated air stream in the presence of heterogeneous reactions on the surface and nonequilibrium evaporation for the case of a frozen boundary layer is studied in [1, 2]. Examples of the calculation of graphite decomposition in an oxygen stream with equilibrium [3] and nonequilibrium [4] chemical reactions in the boundary layer are presented in [3, 4]. The effect of the chemical reactions in the boundary layer on the rate of mass transfer and on the surface temperature with variation of the external flow parameters (p, T_e) remains unexplained. The present paper is devoted to a study of the mechanism of graphite ablation over a wide range of temperatures and pressures with air flow about the body in the case of an equilibrium boundary layer. The effect of the individual components on the heat and mass transfer processes is investigated.In conclusion, the author wishes to thank N. A. Anfimov for this constant interest and valuable advice, and also I. S. Epifanovskii for fruitful discussion of the results.     

On the macroscopic dynamics induced by a model wave-particle collision operator

The macroscopic dynamics of a kinetic equation involving a model wave-particle collision operator of plasma physics is investigated. The Chapman-Enskog asymptotics is first considered in the framework of a hydrodynamic scaling. The obtained macroscopic model still involves a kinetic variable, the particle energy in the rest frame of the fluid, but shares similarities with the compressible Navier-Stokes equation of gas dynamics. Then a diffusive scaling is examined under the hypothesis of small perturbations of a global equilibrium. In this case, the macroscopic model couples the usual incompressible Navier-Stokes with a diffusion equation for the energy distribution function of the particles, constrained by an extended version of the Boussinesq relation. In both cases, the effect of a Lorentz force term is developed, in the perspective of plasma physical modelling. Received June 16, 1997     

Noether-Type Symmetries and Conservation Laws Via Partial Lagrangians

We show how one can construct conservation laws of Euler-Lagrange-type equations via Noether-type symmetry operators associated with what we term partial Lagrangians. This is even in the case when a system does not directly have a usual Lagrangian, e.g. scalar evolution equations. These Noether-type symmetry operators do not form a Lie algebra in general. We specify the conditions under which they do form an algebra. Furthermore, the conditions under which they are symmetries of the Euler-Lagrange-type equations are derived. Examples are given including those that admit a standard Lagrangian such as the Maxwellian tail equation, and equations that do not such as the heat and nonlinear heat equations. We also obtain new conservation laws from Noether-type symmetry operators for a class of nonlinear heat equations in more than two independent variables.     

On the Realizability of Nonlinear Stress–Strain Relationships for Reynolds Stress Closures

A class of recently developed explicit algebraic stress models based on tensorially quadratic stress--strain relations [7] is subjected to a systematical realizability analysis. It is found that these models, which are of particular interest for their rigorous derivation from linear second-moment closure models, tend to produce inappropriate unrealizable results like negative turbulence energy components, even in simple shear flows. The cause of the defect is identified in conjunction with a set of realizability-furnishing constraints on the model coefficients. With the exception of the silent normal stress component in accelerated flow, the nature and rationale of the explicit algebraic stress model suggested by Gatski and Speziale [7] can be extended to maintain the realizability principle. Results obtained from the corresponding quasi-realizable quadratic eddy-viscosity model are reported in comparison with other nonlinear modelling practices.