Large time behavior to the system of incompressible non-Newtonian fluids in R

In this paper, the authors study the large time behavior for the weak solutions to a class system of the incompressible non-Newtonian fluids in R². It is proved that the weak solutions decay in L² norm at (1+t)^−1/2 and the estimate for the decay rate is sharp in the sense that it coincides with the decay rate of a solution to the heat equation.     

Void fraction measurement by X-ray absorption

An X-ray tube and scintillation detectors were mounted on test pipes containing static voids of air–water mixture. Due to fluctuations in the X-ray tube output, void fraction measurements were carried out by using two detectors, one as a reference and the other as a void monitor. The intensity of a narrow (30–100 kV) X-ray beam transmitted through test pipes of different I.D. was measured to obtain the void fraction. The uncertainty in measuring static void fraction, was found to decrease as the void fraction increases, and to increase as X-ray energy increases. It was found that for a certain test-section pipe diameter, there exist an optimum X-ray energy that gives a minimum uncertainty in void fraction measurement.     

On flow and stability of a Newtonian fluid past a rotating plane

An exact solution is given for the steady flow of a Newtonian fluid occupying the halfspace past the plane z=0 uniformly rotating about a fixed normal axis (Oz). This solution is obtained in a velocity field of the form considered by Berker [2] and can be deduced as a limiting case, as h+, of the solution to the problem relative to the strip 0zh imposing at z=h either the adherence boundary conditions or the free surface conditions. Furthermore, the stability of this flow, subject to periodic disturbances of finite amplitude, is studied using the energy method and the result is compared with those corresponding to stability of flows in the strip 0zh.

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Sommario In questa nota si mostra che-oltre alla calssica soluzione di von Karman [1] — esiste, per opportuni valori del gradiente di pressione all'infinito, una soluzione esatta per il moto stazionario di un fluido Newtoniano posto nel semispazio limitato dal piano z=0 uniformemente rotante attorno ad un asse ad esso perpendicolare (Oz). Tale soluzione, ottenuta sulla scia del lavoro di Berker [2], si può dedurre anche come limite, per h+, della soluzione del problema relativo alla striscia 0zh quando sul piano z=h si assegnano o le condizioni di aderenza o le condizioni di frontiera libera. Si studia poi la stabilità di tale moto rispetto a perturbazioni spazialmente periodiche di ampiezza finita col metodo dell'energia e si confronta il risultato ottenuto con quelli relativi alla stabilità dei moti nella striscia 0zh.

     

Squeeze flow of a power-law fluid between two rigid spheres with wall slip

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Solution of the plane stress problems of strain-hardening materials described by power-law using the complex pseudo-stress function

In the present paper,the compatibility equation for the plane stress problems of power-law materials is transformed into a biharmonic equation by introducing the so-calledcomplex pseudo-stress function,which makes it possible to solve the elastic-plastic planestress problems of strain hardening materials described by power-law using the complexvariable function method like that in the linear elasticity theory.By using this generalmethod,the close-formed analytical solutions for the stress,strain and displacementcomponents of the plane stress problems’of power-law materials is deduced in the paper,which can also be used to solve the elasto-plastic plane stress problems of strain-hardeningmaterials other than that described by power-law.As an example,the problem of a power-law material infinite plate containing a circular hole under uniaxial tension is solved byusing this method,the results of which are compared with those of a known asymptoticanalytical solution obtained by the perturbation method.     

On a nonlocal Cahn-Hilliard/Navier-Stokes system with degenerate mobility and singular potential for incompressible fluids with different densities

We consider a diffuse interface model describing flow and phase separation of a binary isothermal mixture of (partially) immiscible viscous incompressible Newtonian fluids having different densities. The model is the nonlocal version of the one derived by Abels, Garcke and Grün and consists in a inhomogeneous Navier-Stokes type system coupled with a convective nonlocal Cahn-Hilliard equation. This model was already analyzed in a paper by the same author, for the case of singular potential and non-degenerate mobility. Here, we address the physically more relevant situation of degenerate mobility and we prove existence of global weak solutions satisfying an energy inequality. The proof relies on a regularization technique based on a careful approximation of the singular potential. Existence and regularity of the pressure field is also discussed. Moreover, in two dimensions and for slightly more regular solutions, we establish the validity of the energy identity. We point out that in none of the existing contributions dealing with the original (local) Abels, Garcke Grün model, an energy identity in two dimensions is derived (only existence of weak solutions has been proven so far).     

基于波尔兹曼方法研究幂律流体的椭圆柱绕流

基于格子波尔兹曼方法(lattice Boltzmann method) 和幂律流体本构方程, 建立二维流动模型, 将充分发展的速度分布与理论解进行对比, 吻合良好. 对幂律流体的圆柱绕流进行模拟, 采用了反弹格式的无滑移圆柱边界, 并使用应力积分法计算阻力系数, 分析了稳态圆柱绕流时, 阻力系数随幂律指数n 以及雷诺数Re 的变化规律. 分析了椭圆横轴/纵轴长度比和幂律指数n, 对压力系数Cp 和黏度系数Cv 的影响. 得到的变化规律与有限元方法规律一致, 验证了格子波尔兹曼模型的可行性.     

Numerical modeling and investigation of viscoelastic fluid–structure interaction applying an implicit partitioned coupling algorithm

We investigate the interaction between a viscoelastic Oldroyd-B fluid and an elastic structure via simulations applying an implicit partitioned coupling algorithm. Simulations are done for a flow through a channel with a flexible wall and a lid-driven cavity flow with flexible bottom. In addition, we make use of a mass–spring–dashpot prototype model to study the dynamic interaction problem. Both the simulation results and the analysis of the prototype model show that there are obvious differences in the fluid–structure interaction if the fluids are viscoelastic instead of purely viscous. These differences appear in the deformation of the solid at stationary state and in the equilibrium position, amplitude, frequency as well as phase shift of the oscillation. Moreover, we investigate the influence of numerical and physical parameters on the implicit partitioned coupling algorithm for simulation of viscoelastic fluid–structure interaction problems.     

Numerical solutions to regularized long wave equation based on mixed covolume method

The mixed covolume method for the regularized long wave equation is developed and studied. By introducing a transfer operator γh , which maps the trial function space into the test function space, and combining the mixed finite element with the finite volume method, the nonlinear and linear Euler fully discrete mixed covolume schemes are constructed, and the existence and uniqueness of the solutions are proved. The optimal error estimates for these schemes are obtained. Finally, a numerical example is provided to examine the efficiency of the proposed schemes.