A THEORETICAL ANALYSIS OF THE FLOW DISTURBANCE INDUCED BY A SPHERE OSCILLATING IN INCOMPRESSIBLE FLUID

为了改进基于不可压缩流场的声类比法的气动声数值预测方法,首先要明确扰动在可压缩和不可压缩流体媒介中的传播特性. 推导了震荡小球在不可压缩流体中产生的小扰动的理论解,分析其速度场与压力场的特点,并与可压缩情况的解进行比较. 结果显示,速度场中包含传播速度为无穷大和有限值的分量;而压力场只有传播速度为无穷大的分量. 当流体黏性趋于零或小球震荡频率趋于无穷大时,其流场与经典声学中震荡小球声辐射问题的近场声一致,这表明震荡小球产生的近场扰动为不可压缩流场,即伪声.     

Fluid flow and fluid shear stress in canaliculi induced by external mechanical loading and blood pressure oscillation

The paper studies the problem of fluid flow and fluid shear stress in canaliculi when the osteon is subject to external mechanical loading and blood pressure oscillation. The single osteon is modeled as a saturated poroelastic cylinder. Solid skeleton is regarded as a poroelastic transversely isotropic material. To get near-realistic results, both the interstitial fluid and the solid matrix are regarded as compressible. Blood pressure oscillation in the Haverian canal is considered. Using the poroelasticity theory, an analytical solution of the pore fluid pressure is obtained. Assuming the fluid in canaliculi is incompressible, analytical solutions of fluid flow velocity and fluid shear stress with the Navier-Stokes equations of incompressible fluid are obtained. The effect of various parameters on the fluid flow velocity and fluid shear stress is studied.     

水/气多介质问题的界面处理方法

针对不可压缩可压缩水/气多介质问题, 提出一种新的界面处理方法。在可压缩水/气界面处构造Riemann问题, 在水中设音速趋于无穷大, 求解Riemann问题得到不可压缩可压缩水/气界面处流体的准确流动状态; 然后以此状态结合GFM(ghost fluid method)方法分别为2种流体定义界面边界条件, 将两相流问题转化为单相流问题计算, 通过求解level set方程来跟踪界面的位置。对各种不同的界面边界条件定义方法进行了比较, 数值模拟结果表明算法能准确地捕捉各类间断的位置, 证明了算法的有效性和稳健性。     

One-dimensional flow of a fluid through a porous skeleton with consideration of the Darcy and frontal pressure interaction forces

The problem of one-dimensional steady flow of a compressible fluid through a solid porous skeleton made of an incompressible material is formulated and numerically solved with consideration of the Darcy and frontal pressure interaction forces.     

A matrix-free high-order discontinuous Galerkin compressible Navier-Stokes solver: A performance comparison of compressible and incompressible formulations for turbulent incompressible flows

Both compressible and incompressible Navier-Stokes solvers can be used and are used to solve incompressible turbulent flow problems. In the compressible case, the Mach number is then considered as a solver parameter that is set to a small value, M ≈0.1, in order to mimic incompressible flows. This strategy is widely used for high-order discontinuous Galerkin (DG) discretizations of the compressible Navier-Stokes equations. The present work raises the question regarding the computational efficiency of compressible DG solvers as compared to an incompressible formulation. Our contributions to the state of the art are twofold: Firstly, we present a high-performance DG solver for the compressible Navier-Stokes equations based on a highly efficient matrix-free implementation that targets modern cache-based multicore architectures with Flop/Byte ratios significantly larger than 1. The performance results presented in this work focus on the node-level performance, and our results suggest that there is great potential for further performance improvements for current state-of-the-art DG implementations of the compressible Navier-Stokes equations. Secondly, this compressible Navier-Stokes solver is put into perspective by comparing it to an incompressible DG solver that uses the same matrix-free implementation. We discuss algorithmic differences between both solution strategies and present an in-depth numerical investigation of the performance. The considered benchmark test cases are the three-dimensional Taylor-Green vortex problem as a representative of transitional flows and the turbulent channel flow problem as a representative of wall-bounded turbulent flows. The results indicate a clear performance advantage of the incompressible formulation over the compressible one.     

Solution of the inverse boundary-value problem of aerohydrodynamics with allowance for a boundary layer

The problem of constructing the contour of a wing profile in a viscous (incompressible or compressible) flow from the velocity distribution, given in terms of the arc abscissa, is solved in the approximation of boundary layer theory. The solvability conditions are obtained. Numerical calculations are carried out. Wing profile contours are constructed from velocity distributions that ensure the nonseparation of the flow. The effect of viscosity and compressibility on the solution of the problem is considered.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 28–32, July–August, 1989.The authors are grateful to G. Yu. Stepanov for useful discussions.     

配置点谱方法-人工压缩法(SCM-ACM)求解同心圆筒内流体流动

发展了配置点谱方法SCM(Spectral collocation method)和人工压缩法ACM(Artificial compressibility method)相结合的SCM-ACM数值方法,计算了柱坐标系下稳态不可压缩流动N-S方程组。选取典型的同心圆筒间旋转流动Taylor-Couette流作为测试对象,首先,采用人工压缩法获得人工压缩格式的非稳态可压缩流动控制方程;再将控制方程中的空间偏微分项用配置点谱方法进行离散,得到矩阵形式的代数方程;编写了SCM-ACM求解不可压缩流动问题的程序;最后,通过与公开发表的Taylor-Couette流的计算结果对比,验证了求解程序的有效性。结果证明,本文发展的SCM-ACM数值方法能够用于求解圆筒内不可压缩流体流动问题,该方法既保留了谱方法指数收敛的特性,也具有ACM形式简单和易于实施的特点。本文发展的SCM-ACM数值方法为求解柱坐标下不可压缩流体流动问题提供了一种新的选择。     

Axisymmetric oscillations of two spherical shells in a compressible fluid

To find the interaction between spherical shells at the frequency of their free oscillations in a fluid, we examine the problem of axisymmetric oscillations of two identical spherical shells under the assumption that the shell centers of curvature do not coincide. The solution is found for the cases of a compressible and an incompressible fluid by the series method with reduction to an infinite system of linear equations. A mathematical justification of the method used is presented.     

Incompressible fluid flow past a circular cylinder with linear relation between the vorticity and the stream function

Incompressible fluid flow with a linear relationship between the vorticity and the stream function past a circular cylinder is studied.Vortical flows about profiles have been considered in several studies [1–15], but in all these studies with the exception of [15] a constant vorticity was assumed (in [15] an approximate solution is found of the problem of incompressible fluid flow about a Zhukovskii profile with parabolic distribution of the velocities in the approaching stream).A freestream velocity profile similar to that considered below occurs, for example, in a planar jet (laminar or turbulent), in the wake behind a bluff body, in the boundary layer along an infinite plane [4,13], in turbulent jet flows with reverse fluid currents [16]. A similar situation also arises in the flow past an array of cylinders with large spacing which is located in the wake of another array.The author wishes to thank V. E. Davidson for posing the problem and for guidance in its solution.     

Evaluation of integral forces and pressure fields from planar velocimetry data for incompressible and compressible flows

The approach to determine pressure fields and integral loads from planar velocimetry data is discussed, in relation to the implementation for incompressible and compressible flows around two-dimensional objects. The method relies upon the application of control-volume approaches in combination with the deduction of the pressure field from the experimental data, by making use of the flow constitutive equations. In this paper the implementation for two specific application areas is addressed. The first is time-mean pressure field and force evaluation from velocity ensemble statistics, as obtained from time-uncorrelated PIV acquisition, for incompressible flow. Two test cases are considered for this flow regime: the unsteady vortical flow around a square section cylinder at incidence, as well as the force characterization of a low-speed airfoil. The second topic considers the extension of the method to steady compressible flow, with the supersonic flow around a bi-convex airfoil as experimental test case. As in this flow regime the density appears as an extra unknown in the momentum equation, additional flow equations need to be invoked. A convenient approach for this was found, using the gas law and the adiabatic flow condition, with which the pressure-integration procedure becomes essentially the same as for the incompressible case.     

Simulation of Single-Phase Multicomponent Flow Problems in Gas Reservoirs by Eulerian–Lagrangian Techniques

Over the past two decades most discussions of the simulation of miscible displacement in porous media were related to incompressible flow problems; recently, however, attention has shifted to compressible problems. The first goal of this paper is the derivation of the governing equations (mathematical models) for a hierarchy of miscible isothermal displacements in porous media, starting from a very general single-phase, multicomponent, compressible flow problem; these models are then compared with previously proposed models. Next, we formulate an extension of the modified method of characteristics with adjusted advection to treat the transport and dispersion of the components of the miscible fluid; the fluid displacement must be coupled in a two-stage operator-splitting procedure with a pressure equation to define the Darcy velocity field required for transport and dispersion, with the outer stage incorporating an implicit solution of the nonlinear parabolic pressure equation and an inner stage for transport and diffussion in which the mass fraction equations are solved sequentially by first applying a globally conservative Eulerian–Lagrangian scheme to solve for transport, followed by a standard implicit procedure for including the diffusive effects. The third objective is a careful investigation of the underlying physics in compressible displacements in porous media through several high resolution numerical experiments. We consider real binary gas mixtures, with realistic thermodynamic correlations, in homogeneous and heterogeneous formations.     

Effect of proximity of barrier on lifting force produced by vertical solid jets

The effect of proximity to the ground on the lifting force generated by a vertical solid jet is studied in connection with development of vertical takeoff and landing devices and of air cushion devices. Such a study was made in [1 ] for planar flow by an incompressible ideal fluid. There a generalization of the results obtained on a compressible fluid was made by the approximation method. In the present work the planar problem of streamline flow past a dihedral barrier of a gas jet emerging from a channel with parallel walls was solved by the Chaplygin-Fal'kovich method [2, 3], The results of [1, 4–9] follow as a particular case from the solution obtained. Calculations were carried out clarifying the effect of the proximity of a barrier and the lifting effect of a fluid on flow characteristics at subsonic speeds.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 123–131, September–October, 1971.     

On the problem of vortex interaction with a plane

We consider the well-known problem of the interaction of a vortex filament with a perpendicular plane in a viscous incompressible fluid. In this study, the vortex filament is represented by a semi-infinite rotating needle. Different models are considered: a zero-radius needle and fixed and movable in the axial direction needles of a finite radius. The ranges of the existence of the solution are found, and the correspondence of the flow around a finite-radius needle to that around a zero-radius needle, as the needle radius decreases, is studied.     

The penetration of a jet into a channel

The method of S. A. Chaplygin [1], as generalized by S. V. Fal'kovich [2] to the case of a few characteristic velocities, is used to solve the two-dimensional problem of the penetration of a subsonic jet of compressible fluid flowing at an angle from a slit into a stream of the same fluid bounded by parallel walls. The problem is solved for the case of an incompressible fluid by passing to the asymptotic limit. Using the tables of [3] the compression coefficient is calculated for a stream of gas merged with an incompressible fluid.     

A model for the bulk viscosity of a non-Newtonian fluid

A model for the bulk viscosity of a non-Newtonian fluid is presented. An elementary two-phase cell containing an incompressible non-Newtonian fluid and a gas bubble is compared with a one-phase cell consisting of a corresponding compressible non-Newtonian fluid. The rates of work of both cells are set equal to one another. The deformation histories of both cells are represented by the density history. From the extra stress an expression for the bulk viscosity of the compressible non-Newtonian fluid is derived. The material data are expressed in terms of the known properties of the two-phase flow.     

The lifting force action on a contour in a plane homogeneous vortex flow of an incompressible ideal fluid

The plane problem of homogeneous vortex flows of an incompressible inviscid fluid around a contour is considered. A method is developed for contours having a center or an axis of symmetry for calculating the lifting force acting on the contour which reduces the problem of determining the lifting force to an ordinary problem of a potential flow of a fluid around the given contour.     

Domain Decomposition Methods for Sensitivity Analysis of a Nonlinear Aeroelasticity Problem

Abstract

We consider the nonlinear aeroelasticity problem of the interaction between a viscous, incompressible fluid and Lin elastic solid undergoing large displacement. The non-linearities of the problem formulation include the solid and fluid governing equations. as well as thc dependence of the How geometry on the solid deformation. The resulting coupling is thus two-way. We develop domain-decomposition methods for solution and sensitivity analysis of the coupled problem. The domain decomposition is in the form of a block-Gauss-Seidel-like prcconditioncr that decomposes ihc coupled-domain problem into distinct nonovcrlapping fluid and solid subdotnain problems. The preconditioner thus enables exploitation or single-domain algorithms for solid and fluid mechanics discretization and solution. On the other hand, two-way fluid-solid coupling is retained within the residuals, which is essential for correct sensitivities. Sensitivities of field quantities can be found with little additional work beyond that required for solving the coupled fluid-solid system. The methodology developed here is illustrated by the solution of a problem of viscous incompressible flow about an infinite clastic cylinder. Sensitivities of the resulting velocity and displacement fields with respect to elastic modulus and fluid viscosity are computed.     

Impact of a strip of compressible liquid on a barrier

The exact solution of the plane problem of the impact of a finite liquid strip on a rigid barrier is obtained in the linearized formulation. The velocity components, the pressure and other elements of the flow are determined by means of a velocity potential that satisfies a two-dimensional wave equation. The final expressions for them are given in terms of elementary functions that clearly reflect the wave nature of the motion. The exact solution has been thoroughly analyzed in numerous particular cases. It is shown directly that in the limit the solution of the wave problem tends to the solution of the analogous problem of the impact of an incompressible strip obtained in [1]. A logarithmic singularity of the velocity parallel to the barrier in the corner of the strip is identified. A one-dimensional model of the motion, which describes the behavior of the compressible liquid in a thin layer on impact and makes it possible to obtain a simple solution averaging the exact wave solution, is proposed. Inefficient series solutions are refined and certain numerical data on the impact characteristics for a semi-infinite compressible liquid strip, previously considered in [2–4] in connection with the study of the earthquake resistance of a dam retaining water in a semi-infinite basin, are improved. The solution obtained can be used to estimate the forces involved in the collision of solids and liquids. It would appear to be useful for developing correct and reliable numerical methods of solving the nonlinear problems of fluid impact on solids often examined in the literature [5].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 138–145, November–December, 1990.The results were obtained by the author under the scientific supervision of B. M. Malyshev (deceased).     

Reservoir fluid flow through vertical fracture of thick stratum with underlying fluid interface

An exact solution is obtained for the problem of steady-state filtration of a heavy dense incompressible fluid in a thin, infinitely deep, inclined reservoir having a crack of given depth along the reservoir rise. The region of filtration of the lighter liquid (oil) has an impermeable upper boundary in the form of a horizontal fault line. Below the filtration region there is a free boundary, below which lies the region of stationary fluid (bottom water). The interface of the fluids, the fissure profile, and the reservoir fluid flow rate are determined from the solution of the problem on the basis of the given parameters (permeability of the reservoir and of the material filling the fissure, viscosity of the filtering fluid, specific weight of the upper and lower fluids, depth of the fissure, pressure differential between a point at the fissure and a point at the interface of the fluids). In the case when the thin reservoir is a vertical filtering layer, the considered flow is interpreted as the motion of the reservoir fluid through a vertical fissure of a thick reservoir (half-space) in the presence of an underlying fluid interface. The problem is solved in finite form with the aid of known analytic functions using integrals of the Cauchy type. The fundamental solution is first found of the special problem of flow with a point singularity. The fundamental solution is also of independent importance as an extension of the solution of certain known problems [1–4].