A free boundary problem arising in oil production

For a stable two-phase free boundary problem arising in oil production, we prove the existence of a weak solution and the continuity of the free boundary.

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Sommario Si prova un teorema di esistenza di una soluzione debole per un problema stazionario a contorno libero a due fasi che interessa la produzione di petrolio. Si dimostra inoltre la continuità del contorno libero.

     

Stability of conical shells made of composites with one plane of elastic symmetry

The paper proposes a technique for stability analysis of anisotropic laminated thin shells of revolution made of a composite with one plane of symmetry. The technique is used for numerical analysis of truncated cones made of binder-impregnated filaments continuously wound along geodesic lines. It is shown that the effect of low symmetry on the critical loads depends not only on the number of laminas, but also on the cone angle __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 6, pp. 93–101, June 2007.     

Effect of the shear layer on the etching behavior of 6060 aluminum extrusion alloys

The occurrence of preferential grain etching (PGE) during alkaline etching of aluminum extrusion alloys from the 6XXX series is often linked to the presence of certain impurity elements such as zinc, causing an undesired etching appearance. In the presented work, an additional culprit in this context is identified, which has not been investigated yet. A clear relation between PGE and the presence of a subsurface shear layer is identified for extruded Al 6060 alloys containing 0.02 and 0.06 wt% Zn. This shear layer can be distinguished from the bulk of the metal by its difference in crystallographic texture as visualized by electron backscatter diffraction (EBSD). For the Zn enriched alloy, the <111>//ND grains are etched away faster than grains with other orientations, resulting in the grainy appearance typical for PGE. Independent of the Zn content in the alloy, once the shear layer is removed and <111>//ND grains are practically absent on the new surface, the depths variations caused by preferential etching disappear. Instead, the surface of the alloy is attacked uniformly by the caustic etch bath.     

非线性欧拉方程组的完美匹配层吸收边界条件

对于非线性Euler方程,提出一类基于完美匹配层(PML)技术的吸收边界条件。首先对线性化的Euler方程设计出PML公式,然后将线性化Euler方程中的通量函数替换成相对应的非线性通量函数,得到非线性的PML方程。考虑到PML方程中包含有一个刚性的源项,文中采用一种隐显Runge-Kutta方法来求解空间半离散后得到的ODE系统。数值实验表明设计的非线性PML吸收边界条件优于传统的特征边界条件。     

Unsteady three-dimensional boundary layer flow due to a permeable shrinking sheet

The unsteady viscous flow over a continuously permeable shrinking surface is studied. Similarity equations are obtained through the application of similar transformation techniques. Numerical techniques are used to solve the similarity equations for different values of the unsteadiness parameter, the mass suction parameter, the shrinking parameter and the Prandtl number on the velocity and temperature profiles as well as the skin friction coefficient and the Nusselt number. It is found that, different from an unsteady stretching sheet, dual solutions exist in a certain range of mass suction and unsteadiness parameters.     

The Collocation Method and the Splitting Extrapolation for the First Kind of Boundary Integral Equations on Polygonal Regions

In this paper, the collocation methods are used to solve the boundary integral equations of the first kind on the polygon. By means of Sidi's periodic transformation and domain decomposition, the errors are proved to possess the multi-parameter asymptotic expansion at the interior point with the powers $h_{i}^{3}(i=1,...,d)$, which means that the approximations of higher accuracy and a posteriori estimation of the errors can be obtained by splitting extrapolations. Numerical experiments are carried out to show that the methods are very efficient.     

Constrained large-eddy simulation of supersonic turbulent boundary layer over a compression ramp

A supersonic turbulent boundary layer over a compression ramp is numerically investigated using the constrained large-eddy simulation (CLES) method. The compression corner is characterised by a deflection angle of 24°. The free-stream Mach number is Ma_∞ = 2.9, and the Reynolds number based on the momentum thickness of inlet boundary layer is Re_θ = 2300. The mean and statistical quantities, such as mean velocity, wall pressure and Reynolds stresses, are thoroughly analysed and compared with those from traditional large-eddy simulation (LES), experimental measurement and direct numerical simulation (DNS). It turns out that CLES can predict the friction coefficient, wall-pressure distribution, size of separation bubble, Reynolds stresses, etc. more accurately than traditional LES, and the results are in reasonable agreement with the experimental and/or DNS data. Also discussed are the effects of specific parameterisations of the Reynolds constraint and interfacial positions separating the constrained and unconstrained regions on the performance of the CLES method.     

Multi-scale interactions in a compressible boundary layer

The properties of spectral subranges of scales in a boundary layer at Mach=2.3 and friction Reynolds number Reτ = 570 are investigated by analysing DNS data. One major aim is to examine whether footprinting and modulation of small-scale near-wall motions by outer large structures, observed at high Reynolds numbers, also pertain to this low-Reynolds-number case, or whether the logarithmic layer simply contains a continuous hierarchy of motions without specific outer scales playing a distinctive role. To this end, the spectrum of scales is decomposed into modes by application of the “Empirical Mode Decomposition”. The properties of different scales are then investigated by means of spectra, maps of isotropy/anisotropy parameters, the premultiplied derivative of the second-order structure function, correlation coefficients and joint probability density function (PDF), the last constructed from conditionally sampled data for the small-scale motions within the large-scale footprints. A clear commonality is identified between interactions in high-Reynolds-number channel flow and the present low-Reynolds-number boundary layer.     

Analysis of turbulent axisymmetric inner near wake

An analysis is presented describing the characteristics of mean velocity profile in the axisymmetric turbulent inner near-wake flow behind a body of revolution. The near wake is developing under zero streamwise pressure gradient and the upstream turbulent boundary layer is fully developed. It is shown that the boundary layer condition that exists at the trailing edge can be used to describe the mean velocity profiles in the inner near wake. It is shown that the logarithmic layer of the upstream turbulent boundary layer continues to be valid for some more distance in the near wake, and as the streamwise distance is increased, the logarithmic layer is slowly getting destroyed. It is also shown that the central line velocity exhibits a logarithmic behaviour for large streamwise distance. Results of the analysis have been validated using available experimental data.     

Legendre Pseudospectral Approximation of Boussinesq Systems and Applications to Wave Breaking

In this paper, we propose a spectral projection of a regularized Boussinesq system for wave propagation on the surface of a fluid. The spectral method is based on the use of Legendre polynomials, and is able to handle time-dependent Dirichlet boundary conditions with spectral accuracy.The algorithm is applied to the study of undular bores, and in particular to the onset of wave breaking connected with undular bores. As proposed in [2], an improved version of the breaking criterion recently introduced in [5] is used. This tightened breaking criterion together with a careful choice of the relaxation parameter yields rather accurate predictions of the onset of breaking in the leading wave of an undular bore.