Measurement of mean rotation and strain-rate tensors by using stereoscopic PIV

A technique is described for measuring the mean velocity gradient (rate-of-displacement) tensor by using a conventional stereoscopic particle image velocimetry (SPIV) system. Planar measurement of the mean vorticity vector, rate-of-rotation and rate-of-strain tensors and the production of turbulent kinetic energy can be accomplished. Parameters of the Q criterion and negative λ₂ techniques used for vortex identification can be evaluated in the mean flow field. Experimental data obtained for a circular turbulent jet issuing normal to a crossflow in a low speed wind tunnel for a jet-to-crossflow velocity ratio of 3.3 are presented to show the applicability of the proposed technique. The results reveal the presence of a secondary counter-rotating vortex pair (SCVP) which is located within the jet core and has a sense of rotation opposite to that of the primary one (PCVP). Consistency of the measurements is verified by the agreement of data obtained in two perpendicular planes. Accuracy of the data is discussed and algebraic relations for some measurement uncertainties are presented.     

Simple Torsion of Isotropic, Hyperelastic, Incompressible Materials with Limiting Chain Extensibility

The purpose of this research is to investigate the simple torsion problem for a solid circular cylinder composed of isotropic hyperelastic incompressible materials with limiting chain extensibility. Three popular models that account for hardening at large deformations are examined. These models involve a strain-energy density which depends only on the first invariant of the Cauchy–Green tensor. In the limit as a polymeric chain extensibility tends to infinity, all of these models reduce to the classical neo-Hookean form. The main mechanical quantities of interest in the torsion problem are obtained in closed form. In this way, it is shown that the torsional response of all three materials is similar. While the predictions of the models agree qualitatively with experimental data, the quantitative agreement is poor as is the case for the neo-Hookean material. In fact, by using a global universal relation, it is shown that the experimental data cannot be predicted quantitatively by any strain-energy density which depends solely on the first invariant. It is shown that a modification of the strain energies to include a term linear in the second invariant can be used to remedy this defect. Whether the modified strain-energies, which reflect material hardening, are a feasible alternative to the classic Mooney–Rivlin model remains an open question which can be resolved only by large strain experiments. This revised version was published online in August 2006 with corrections to the Cover Date.     

Bifurcation of coisotropic invariant tori under locally Hamiltonian perturbations of integrable systems and nondegenerate deformation of symplectic structure

We study the bifurcation problem for a Cantor set of coisotropic invariant tori in the case where a Liouville-integrable Hamiltonian system undergoes locally Hamiltonian perturbations and, simultaneously, a deformation of the symplectic structure of the phase space. We consider a new case where the deformed symplectic structure generates a nondegenerate matrix of the Poisson brackets of action variables. __________ Translated from Neliniini Kolyvannya, Vol. 9, No. 2, pp. 221–232, April–June, 2006.     

Uniform asymptotics for the linearized Boltzmann equation describing sound wave propagation

The multiple-scale expansionmethod is used for constructing a uniformly applicable asymptotic approximation of the solution of the linearized Boltzmann equation for small Knudsen numbers. The asymptotic expansion is constructed for the particular example of a sound wave generated by a plane oscillation source and dissipating in a half-space. The simplicity of the problem makes it possible clearly to demonstrate the appearance of secular terms in the expansion and the introduction of multiple scales opens the way to eliminating them.     

On the approximate solution of elastic contact problems for a circular annulus

Paper concerns the Boussinesq and Reissner-Sagoci contact problems for a rigid punch in contact with the plane face of an isotropic elastic half-space over a circular annulusbra. It is shown that a simple combination of the interior and exterior Dirichlet and Neumann solutions for a circle, when expressed in terms of oblate spheriodal coordinates, yields extremely accurate approximate solutions provided that 0b/a0.8.     

Transfer of energy from an evaporating drop in a vapor medium

The article considers the temperature distribution around an evaporating drop in a vapor medium. The transfer of energy is effected by molecular thermal conductivity, convection, and radiation. The mean length of the free flight path of the radiation considerably exceeds the characteristic distance at which the temperature changes. The times required for relaxation of the temperature to a steady-state value are determined, as well as the characteristic distances at which the temperature distribution changes.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 74–78, January–February, 1972.The authors thank V. G. Levich for his evaluation of the results obtained.     

FD-method for a nonlinear eigenvalue problem with discontinuous eigenfunctions

An algorithm for the solution of a nonlinear eigenvalue problem with discontinuous eigenfunctions is developed. The numerical technique is based on a perturbation of the coefficients of a differential equation combined with the Adomian decomposition method for the nonlinear term of the equation. The proposed approach provides an exponential convergence rate dependent on the index of the trial eigenvalue and on the transmission coefficient. Numerical examples support the theory. Published in Neliniini Kolyvannya, Vol. 10, No. 1, pp. 126–143, January–March, 2007.     

Stability and nonlinear wavy regimes in downward film flows on a corrugated surface

The linear and nonlinear stability of downward viscous film flows on a corrugated surface to freesurface perturbations is analyzed theoretically. The study is performed with the use of an integral approach in ranges of parameters where the calculated results and the corresponding solutions of Navier-Stokes equations (downward wavy flow on a smooth wall and waveless flow along a corrugated surface) are in good agreement. It is demonstrated that, for moderate Reynolds numbers, there is a range of corrugation parameters (amplitude and period) where all linear perturbations of the free surface decay. For high Reynolds numbers, the waveless downward flow is unstable. Various nonlinear wavy regimes induced by varying the corrugation amplitude are determined. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 1, pp. 110–120, January–February, 2007.     

Bitumen/polyethylene blends: using m-LLDPEs to improve stability and viscoelastic properties

The stability and the rheological properties of blends of a 60/70 penetration-grade bitumen with conventional HDPEs and metallocene catalysed LLDPEs (m-LLDPE) are investigated. Considerably better stability results are obtained using m-LLDPEs instead of conventional polyethylenes, allowing one to avoid phase separation of the emulsion-like system during storage at high temperature. Thermodynamical interaction between bitumen and polyethylene is discarded as a cause of the observed difference, because the solubility parameter is practically the same for all the investigated polyethylenes. The result is explained on the basis of the lower melt elasticity of m-LLDPEs (attributed to their narrow molecular weight distribution), which facilitates the drop breakup during mixing process. The modification of bitumen with any of the m-LLDPEs considered in this work gives a new material with considerably improved viscoelastic properties.     

Investigation of thermogravitational-thermocapillary steady-state convective flow stability at low Prandtl numbers

The stability of gravitational-capillary flow in a square cavity with isothermal vertical and adiabatic horizontal boundaries is investigated. The region of stable regimes in the Grashof number-Marangoni number plane is determined for a fluid with a Prandtl number equal to 0.02. In [1] the stability of steady-state thermogravitational convection regimes in a laterally heated square cavity was numerically investigated. The Galerkin method with a system of coordinate functions constructed as proposed in [2] was used to solve the system of equations of free convection in the Oberbeck-Boussinesq approximation. Below, the variant of the Galerkin method described in [2] is used to investigate the stability of steady-state regimes of free convection flow developing under the combined influence of thermogravitational and thermocapillary forces.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 8–13, March–April, 1990.