Impermeability Condition Research Articles

Dynamic Analysis of Anisotropic Cylindrical Shells Containing Flowing Fluid

This paper deals with the study of dynamic behavior of anisotropic cylindrical shells, based on refined shell theory, subjected simultaneously to an internal and external fluid. In the present theory, the transverse shear deformation effect is taken into account, therefore, the equations of motion are determined with displacements and transverse shear as independent variables. The solution is divided into three parts: In Section 2, the displacement functions are derived from the exact solution of refined shell equations based on orthogonal curvilinear coordinates. The mass and stiffness matrices of each structural element are derived by exact analytical integration. In Section 3, the velocity potential, Bernoulli’s equation and impermeability condition have been applied to the shell fluid interface to obtain an explicit expression for fluid pressure which yields three forces (inertial, centrifugal, Coriolis). Numerical examples are given in Section 4 for the free vibration of laminated composite and isotropic materials for both open and closed circular cylindrical shells. Reasonable agreement is found with other theories and experiments.

An algorithm for velocity calculation in close proximity to body surfaces in panel methods

To model incompressible flow over a body of arbitrary geometry when using vortex methods, it is necessary to construct an irrotational field to impose the impermeability condition at the surface of the object. In order to achieve this impermeability, this paper uses a boundary integral equation based on the single-layer representation for the velocity potential. Specifically, we formulate this exterior Neumann problem in terms of a source/sink boundary integral equation. The solution to this integral equation is then coupled with an interpolation procedure which smoothes the transition between near-wall and interior regimes. We describe the numerical scheme embedding this strategy and discuss its accuracy and efficiency. For validation purposes, we consider the potential and vortical flow over a circular cylinder, for which an analytical solution and the commonly used method of images are available.

A low-shear turbulent boundary layer

This paper describes experimental results measured in a low-shear turbulent boundary layer. The low-shear condition is exerted after the boundary layer reaches Reθ≂2000 and has the effect of removing the inner layer; thus, these are the first results to show the behavior of an outer-layer-only turbulent boundary layer. The removal of the inner layer causes the gradual decay of the turbulent stresses over eleven boundary-layer thicknesses (roughly 20 large-eddy length scales) of streamwise distance, with the decay beginning at the wall and propagating into the outer flow with increasing downstream distance. However, the structure of the outer layer is little affected by the perturbation, as demonstrated by stress (anisotropy) ratios, quadrant analysis, and spectral measurements. Although the lack of near-wall production implies this flow must eventually decay into isotropic turbulence, this decay occurs relatively slowly because the dissipation is also greatly reduced with the decrease in near-wall shear. In addition, the outer-layer production is significant in maintaining the turbulence level. These results show that, once formed, the outer-layer characteristics are not explicitly dependent on the presence of the inner layer. These results are compared with similar studies of isotropic turbulence near a shear-free wall. Very close to the wall the two flows both show that the normal-stress components respond differently to the presence of the wall. However, away from the wall the isotropic results underpredict the distance to which the tangential stresses are damped by the impermeability condition at the wall. Finally, the results show general similarities to those in a boundary layer just downstream of reattachment, after a similar low-shear condition over the separation bubble. This raises the possibility that many of the important features of the reattaching flow can be captured by the present, simpler experiment.

Effective permeability of the boundary of a domain

Let u be a solution of the Laplace equation in a boilnded domain Ω in R n whose boundary consists of two disjoint surfaces λ0 and λ1. On λ1 u satisfies a Dirichlet boundary condition, whereas on Λ0 u satisfies the impermeability condition ∂u/∂n = 0 ever3 where except on m, small “holes” λ, separated from one another by distance of older of magnitude ε. and u= O on the holes. In this paper wr study the effective periwabilitv of the surface λ0as ε→0.

Aspects of Modeling Partially Cavitating Flows

A method for calculating partially cavitating flows is presented. This method respects the impermeability condition on the profile in the vicinity of the cavity. The difficulties inherent in a scheme which gives a solution depending on the internal field organization, when the cavity is open, are analyzed. Several closure models are compared with the experimental results. This comparison shows the great variety of models that would have to be considered in order to give a proper account of the t(ac) law for three types of geometry. The pressure recovery study for one of the three geometries shows that pressure recovery can be simulated by a distribution of sinks distributed immediately downstream of the cavity, followed by a positive flux zone farther downstream. Validated by means of a finite-element calculation, the method proves its capability to take into account the effect of nonparallel confining walls placed very close around a foil of very small relative thickness.

Wave propagation in a waveguide with discontinuous wall impedance

Nonlocally reacting porous liners are used extensively in ducts to achieve sound absorption. We consider wave propagation in a duct in which the boundary condition on one wall jumps from the impermeability condition to one exhibiting bulk reaction. The bulk‐reacting boundary condition of Bliss [J. Acoust. Soc. Am. 71, 533–545 (1982)] is used to model the behavior of the liner. There are three regions in the duct in which the fluid exhibits different overall behavior; two “outer” regions and one “inner” region in which a fast transition occurs in wave character. The method of matched asymptotic expansions will be used to obtain a solution that is uniformly valid throughout the three regions. [Work supported by the National Science Foundation.]

The interaction between vortex-array representations of free-stream turbulence and semi-infinite flat plates

Free-stream turbulence is modelled by a low-intensity array of vortices where the vorticity is distributed continuously throughout the flow. This vorticity approaches and convects along a semi-infinite flat plate and the structure of the free-stream disturbances is altered by the impermeability condition at the plate. The analysis consists of tracking the vorticity as it convects with the uniform mean flow, determining the stream function induced by that vorticity field without imposing the impermeability condition, and finally superimposing an irrotational flow field which effects impermeability. The bisecting of a vortex as it encounters the plate yields a pair of vortices which rotate in the same direction. The combined heights of these vortices are less than the height of the original vortex. Small segments of a vortex which has been cut by the plate, but not through its centre, are completely absorbed by neighbouring vortices. Far from the leading edge in any direction, the disturbance pressure is O(ρq2), where q is the characteristic disturbance speed, and the streamline patterns convect with the mean flow. Near the leading edge, the fluctuating pressure is O(ρqU∞) because of unsteady vortex distortion and the velocity correlations reveal that Taylor's hypothesis is not valid. These correlations are based on averages over time and over all possible orientations of the vortex array. Vortex structures based on iso-vorticity contours are sometimes quite different from the structures based on disturbance streamlines.

Disturbances in a Boundary Layer Introduced by a Low Intensity Array of Vortices

To acquire insight into the role of free-stream turbulence on laminar-turbulent transition, the interaction between a boundary layer and an array of single-wavenumber vortices convected at the mean free-stream velocity is studied analytically and numerically. For small amplitudes, the effect of a spectrum can be obtained by superposition. The flow field is taken to be the sum of the steady laminar field (Blasius) plus a flow field ascribable to the effects of the vortex array. This latter flow field is further subdivided into the portion that exists in the absence of the plate (the vortex array itself) plus a flow field representing the alteration to that array due to the shearing mean flow and no-slip and impermeability conditions at the plate surface. This last portion of the flow field is described by a nonhomogeneous Orr–Sommerfeld equation with phase speed unity and real wavenumber. The forcing function depends on the mean flow and on the free-stream disturbance array. The problem is not an eigenvalue problem. The mathematical system is solved numerically via expansion in Chebyshev polynomials. Disturbance velocities, vorticity, energy, pressure, and Reynolds stresses are obtained over a range of wavenumbers, Reynolds numbers, and vortex positions relative to the plate. The results show that the disturbances are greatly damped near the wall. Far from the wall the disturbances approach the values existing if the plate were absent. A phase shift across the viscous sublayer yields a Reynolds stress as in stability theory, but this stress is small relative to the Reynolds stress near the boundary layer edge. Disturbance amplitudes may grow or decay depending on the parameters and the position in the boundary layer.

On the plate paradox of sapondzhyan and babuška

We consider flows of an incompressible Navier–Stokes fluid in a tubular domain with Navier’s slip boundary condition imposed on the impermeable wall. We focus on several implementational issues associated with this type of boundary conditions within the framework of the standard Taylor-Hood mixed finite element method and present the computational results for flows in a tubular domain of finite length with one inlet and one outlet. In particular, we present the details regarding variants of the Nitsche method concerning the incorporation of the impermeability condition on the wall. We also find that the manner in which the normal to the boundary is numerically implemented influences the nature of the computational results. As a benchmark, we set up steady flows in a tube of finite length and compare the computational results with the analytical solutions. Finally, we identify various quantities of interest, such as the dissipation, wall shear stress, vorticity, pressure drop, and provide their precise mathematical definitions. We document how well these quantities are computationally approximated in the case of the benchmark.Although the geometry of the benchmark is simple, the correct computational results require careful selection of numerical methods and surprisingly non-trivial computational resources. Our goal is to test, using the setting with a known analytical solution, a robust computational tool that would be suitable for computations on real complex geometries that have relevance to problems in engineering and medicine. The model parameters in our computations are chosen based on flows in large arteries.

Quelques aspects des écoulements presque horizontaux à deux dimensions en plan et non permanent, application aux estuaires

Quelques aspects des écoulements presque horizontaux à deux dimensions en plan et non permanent, application aux estuaires