Acceleration of the pressure correction method for a rotating Navier-Stokes problem

The behaviour of the pressure correction method is studied for the solution of the incompressible steady-state Navier-Stokes and continuity equations in a rotating cylindrical-polar co-ordinate system, the specific problem being that of laminar source-sink flow between two corotating discs. Modifications to improve the linearization and the handling of the rotation terms are introduced, and we compare three extended pressure correction schemes and also the use of a multigrid algorithm in part of the calculation procedure as a linear solver.     

New Statement of the elasticity problem for a layer

The problem on the equilibrium of an inhomogeneous anisotropic elastic layer is considered. The classical statement of the problem in displacements consists of three partial differential equations with variable coefficients for the three displacements and of three boundary conditions posed at each point of the boundary surface. Sometimes, instead of the statement in displacements, it is convenient to use the classical statement of the problem in stresses [1] or the new statement of the problem in stresses proposed by B. E. Pobedrya [2]. In the case of the problem in stresses, it is necessary to find six components of the stress tensor, which are functions of three coordinates. The choice of the statement of the problem depends on the researcher and, of course, on the specific problem. The fact that there are several statements of the problem makes for a wider choice of the method for solving the problem. In the present paper, for a layer with plane boundary surfaces, we propose a new statement of the problem, which, in contrast to the other two statements indicated above, can be called a mixed statement. The problem for a layer in the new statement consists of a system of three partial differential equations for the three components of the displacement vector of the midplane points. The system is coupled with three integro-differential equations for the three longitudinal components of the stress tensor. Thus, in the new statement, just as in the other statements in stresses, one should find six functions. In the new statement, three of these functions (the displacements of the midplane points) are functions of two coordinates, and the other three functions (the longitudinal components of the stress tensor) are functions of three coordinates. It is shown that all equations in the new statement are the Euler equations for the Reissner functional with additional constraints. After the problem is solved in the new statement, three components of the displacement vector and three transverse components of the stress tensor are determined at each point of the layer. The new statement of the problem can be used to construct various engineering theories of plates made of composite materials.     

Development of an unsteady pressure measurement method

Experimental Techniques - Aerodynamic phenomena such as wakes behind bluff bodies are inherently unsteady. Thus, many aerodynamic experiments require the measurement of unsteady or dynamic flow...     

Numerical modeling of viscoelastic counter flows using the pressure correction method

Counter flows of a viscoelastic fluid described by the rheological Oldroyd model in crossshaped channels are investigated. The modeling is based on the pressure correction method in a convenient-in-use form and with a simple topology of the computation grid and formally proved convergence. It is shown that, starting from certain threshold values of the Weissenberg numbers, the flow pattern in the stabilization stage exhibits considerable changes following two different mechanisms, depending on the Reynolds number. In particular, at low Reynolds numbers (less than 0.1) the flows involve vortex-like structures near the central point, where at the same time anomalies in normal stress distributions are observable. The similarity of these structures with the elastic instability phenomena, which were previously observed in the experimental realizations of the counter flows of this type and in other processes, is shown. To demonstrate the numerical procedure convergence, the results of calculations with different computation grid steps varied on a wide range are presented. In the context of the problem considered the general features of elastic instability are discussed.     

Displacement measurement along a line by the diffractographic method

The diffractographic method, a recently developed experimental technique, has been extended to solve the problem of determining the displacement information along the length of a beam. The method, which uses the diffraction of monochromatic light through a variable aperture whose size is a function of the beam displacement, demonstrates that this displacement along a line technique offers a new and accurate method occupying the unique position between point detectors and whole-field procedures.     

Numerical modeling of three-dimensional viscous flows using a space-marching method with pressure iterations

A method of calculating steady three-dimensional compressible and incompressible flows on the basis of simplified Navier-Stokes equations is examined. Some calculation results are presented. These relate to the problem of supersonic flow past blunt bodies and to incompressible channel flows.Based on paper read at the Seventh Congress on Theoretical and Applied Mechanics, Moscow, August I991. Presented by V. I. Polezhaew.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.5, pp. 132–147, September–October, 1992.     

Improvement of a pressure gradient method and its application to an unsteady flow problem

The pressure gradient method using velocity components and components of a pressure gradient as dependent variables has been modified to solve incompressible Newtonian fluid flow problems numerically. Applying this modified method to unsteady-state development of flow in a circular cavity shows that, at least for the case of a low Reynolds number flow, relative errors produced by the proposed method are smaller for most time intervals than those produced by the primitive velocity-pressure variable method and by the standard pressure gradient method. Also it is found that the modified and standard pressure gradient methods can be applied to the unsteady circular cavity flow at a moderate Reynolds number of at least up to 200.     

Precise integration method for LQG optimal measurement feedback control problem

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一种求解三维声腔声压分布问题的无网格法

利用传统有限元法求解声压分布问题常常受到污染误差和色散误差的困扰.加权最小二乘无网格法(MWLS)是一种基于移动最小二乘(MLS)近似的无网格方法,求解声腔声压分布问题具有低色散、高精度的特点.然而传统的MLS近似有时容易产生病态矩阵,利用加权正交基函数构建改进的移动最小二乘(IMLS)近似,得到的系统方程为非病态的.论文基于改进的加权最小二乘无网格法(IMWLS)求解三维声腔内部声压分布.计算得到的声压分布和声压频响曲线都与参考值十分吻合,峰值误差和污染误差都比FEM的小,计算成本相比无单元伽辽金法显著降低.计算结果表明IMWLS相比传统的FEM,能在更高的频段内达到高精度,并且相比EFGM能大幅提高计算效率.     

Numerical solution of a free surface problem by a boundary element method

This paper describes a method for the numerical solution of a Riabouchinsky cavity flow. Application of a boundary element method leads to a system of non-linear equations. The mild singularity appearing at the separation point is treated with the introduction of a curved boundary element, which satisfies the exact behaviour of the free boundary in that neighbourhood.     

Reynolds stress, mean velocity, and dynamic static pressure measurement by a four-hole pressure probe

An improved version of the four-hole directional pressure probe, or Cobra probe, is described, in which the frequency response has been extended to 1.5 kHz. The probe measures all three orthogonal mean and turbulent velocity components at a point in the flow field. The probe also resolves the local mean and turbulent components of static pressure, allowing moments between the fluctuating velocity components and pressure to be determined. The techniques developed to allow the improved frequency response and the use of the probe in turbulent, developed pipe flow (a calibration flow) are described. Also given are the turbulent pressure-velocity correlations, which show a high degree of anticorrelation for one velocity component.     

Statement of the two-body problem in the parameters of the extended Galilei group

The classical mechanical problem on the motion on a system of two or several bodies is stated in terms of parameters of the 13-parameter extended Galilean group (translations, rotations, boosts, and gravitational transformations) without using such traditional notions as “point” and “force.”     

Solution of the laminar duct flow problem by a boundary integral equation method

Summary A boundary integral equation method is proposed for approximate numerical and exact analytical solutions to fully developed incompressible laminar flow in straight ducts of multiply or simply connected cross-section. It is based on a direct reduction of the problem to the solution of a singular integral equation for the vorticity field in the cross section of the duct. For the numerical solution of the singular integral equation, a simple discretization of it along the cross-section boundary is used. It leads to satisfactory rapid convergency and to accurate results. The concept of hydrodynamic moment of inertia is introduced in order to easily calculate the flow rate, the main velocity, and the fRe-factor. As an example, the exact analytical and, comparatively, the approximate numerical solution of the problem of a circular pipe with two circular rods are presented. In the literature, this is the first non-trivial exact analytical solution of the problem for triply connected cross section domains. The solution to the Saint-Venant torsion problem, as a special case of the laminar duct-flow problem, is herein entirely incorporated.     

Solution of the linearized couette-flow problem in a rarefied gas by the integral-diffusion method

In ordinary diffusion theory the transfer of properties is determined by the local gradients of the corresponding fields. As the mean free path increases, the flux density becomes an integral quantity and is determined by a neighborhood of the point under consideration of the order of a few mean free paths. In a previous article [1], the author proposed a model for a one-dimensional transfer process in linear rarefield-gas problems based on the analogy with radiative transfer. The same approach, though without directional averaging, is used in the present paper to analyze the linearized Couette flow problem. The solution obtained here has the properties of the solution obtained by more exact methods based on the solution of the Boltzmann equation [3-4].Nomenclature p_xy shear stress - c mean thermal velocity of molecules - 2/3 A mean free path - d half-width of channel - ±w₀ plate velocity - c nonequilibriumvalue of momentum flux density - y transverse coordinate - ratio of specific heats - W dimensionless velocity - P_xy shear stress scaled with respect to the shear stress in free-molecule flow - Y dimensionless coordinate - W₁(y) velocity distribution according to Millikan's solution - coefficient of viscosity - R Reynolds number - K Knudsen number     

Deformation measurement during powder compaction by a scanning-moiré method

The mechanical behavior of powders during compaction has been studied in previous papers. It has been shown that a moiré method may be used to determine the resulting strain distribution. Some difficulties were encountered, however, in the method used. In the present paper, therefore, an image-processing system employing a personal computer to analyze the moiré pattern is introduced. Many strain distributions obtained in this way from moiré-fringe patterns are presented. Further, using this image-processing system, a scanning-moiré technique is developed in which the master grating is replaced by the scanning lines of a television camera. The use of image processing in conjunction with the mismatch technique allows measurement of both small and large strains from one image picture.Paper was presented at 1982 SESA Spring Meeting held in Oahu and Maui, HI on May 23–28.     

Aerodynamics of indirect thrust measurement by the impulse method

The aerodynamic aspects of indirect thrust measurement by the impulse method have been studied both experimentally and numerically. The underlying basic aerodynamic principle is outlined, the phenomena in subsonic, supersonic and arc-heated jets are explored, and factors affecting the accuracy of the method are studied and discussed. Results show that the impulse method is reliable for indirect thrust measurement if certain basic requirements are met, and a simple guideline for its proper application is given.