The cavitated bifurcation problem in a solid sphere composed of two compressible hyper-elastic materials is examined. The
bifurcation solution for the composed sphere under a uniform radial tensile boundary dead-load is obtained. The bifurcation
curves and the stress contributions subsequent to the cavitation are given. The right and left bifurcation as well as the
catastrophe and concentration of stresses are analyzed. The stability of solutions is discussed through an energy comparison.
Project supported by the National Natural Science Foundation of China (No. 19802012). 相似文献
Exact analytical solutions for a class of unsteady unidirectional flows of an incompressible second-order fluid are constructed. The flows are generated impulsively from rest by motion of a plate or two plates or by sudden application of a pressure gradient. Expressions for velocity, flux and skin friction are obtained for both large and small times. It is found that large and small times solutions are dependent on the coefficient of viscoelasticity. The solutions corresponding to Newtonian fluids can be easily obtained from those for fluids of second order by letting the viscoelastic parameter to be zero. 相似文献
The purpose of this Note is to propose new diffusive capillary models of Korteweg type and discuss their mathematical properties. More precisely, we introduce viscous models which provide some additional information on the behavior of the density close to vacuum. We actually prove that if some compatibility conditions between diffusion and capillarity are satisfied, some extra regularity information on a quantity involving the density is available. We obtain a non-trivial equality deduced from the special structure of the momentum equation. This Note generalizes to some extent the authors' previous works on the Korteweg model (with constant capillary coefficient) and on the shallow water equation. To cite this article: D. Bresch, B. Desjardins, C. R. Mecanique 332 (2004).相似文献
Similarity solutions for the flow of a non-ideal gas behind a strong exponential shock driven out by a piston (cylindrical
or spherical) moving with time according to an exponential law are obtained. Similarity solutions exist only when the surrounding
medium is of constant density. Solutions are obtained, in both the cases, when the flow between the shock and the piston is
isothermal or adiabatic. It is found that the assumption of zero temperature gradient brings a profound change in the density
distribution as compare to that of the adiabatic case. Effects of the non-idealness of the gas on the flow-field between the
shock and the piston are investigated. The variations of density-ratio across the shock and the location of the piston with
the parameter of non-idealness of the gas are also obtained. 相似文献
It is well-known that certain fluids are birefringent and when flows are viewed in polarised light interference fringes are observed. The fringes are caused by a phase shift in the light passing through the fluid and are proportional to the integral of the maximum shear strains in the fluid. In order to understand what is happening within the three dimensional flow and overcome the difficulties due to this integration, additional computational or experimental information is needed.
In this work, a commercially available computer code (Fluent) is used for the first time to model the flows. The flow data are then exported to a spreadsheet where the shear rates are integrated across the field and then banded for graphical output. The results from this are then compared to results generated from birefringent flow experiments and the agreement is found to be good since the modelled fringes show the same patterns as those in the experiment. This novel use of computational and experimental techniques together will allow quantitative analysis of three-dimensional flows in the future.
Currently, there are still a lot of empirical variables involved in fitting the computational fringes to the experiment, but the results of this preliminary study show that this is a promising approach to this type of problem. 相似文献
On the basis of a numerical analysis of the non-Navier-Stokes gas-dynamic equations for slow non-isothermal gas flows, the nonlinear thermomolecular pressure difference effect due to a large temperature gradient along the lateral surface of a capillary is investigated. It is shown that the magnitude of the effect is substantially different from the values calculated using the Navier-Stokes equations. For two models of molecular interaction (Maxwell molecules and hard spheres), the possibility of a quasi-one-dimensional interpretation of the effect for experimental estimation purposes is demonstrated. The solutions of the relaxation kinetic equation for flow in a plane capillary at small Knudsen numbers and the gas-dynamic equations for slow non-isothermal flows are compared and the range of their applicability is estimated. 相似文献
We present a direct numerical simulation by the lattice gas method of the three-dimensional non-stationary incompressible flow at a Reynolds number of 74, past a circular cylinder, with a uniform incident flow. We describe the three-dimensional structure and the time-evolution of the wake, which leads to an oblique vortex shedding situation.We also present early results on measurements of drag coefficients for spheres and cylinders at a Reynolds number of 20. 相似文献
Local viscoplastic-flow and damage processes in a deformable medium induced by the collapse of dispersed vapor-gas bubbles in the near-wall layer of a cavitating fluid in the presence of propagating shock waves are investigated. The study is based on a generalized model developed for describing nonlinear deformations and flow of damageable media and on the results obtained earlier for local fluid flows induced by limiting transitions of vapor-gas bubbles. 相似文献