Finite-amplitude shear horizontal waves propagating in a pre-stressed layer between two half-spaces

The propagation of finite-amplitude time-harmonic shear horizontal waves, in a pre-stressed compressible elastic layer of finite thickness embedded between two identical compressible elastic half-spaces, is investigated. This is accomplished by combining finite-amplitude linearly polarized inhomogeneous transverse plane wave solutions in the half-spaces and finite-amplitude linearly polarized unattenuated transverse plane wave solutions in the layer. The layer and half-spaces are made of different pre-stressed compressible neo-Hookean materials. The dispersion relation which relates wave speed and wavenumber is obtained in explicit form. The special case where the interfaces between the layer and the half-spaces are principal planes of the left Cauchy–Green deformation tensor is also investigated. Numerical results are presented showing the variation of the shear horizontal wave speed with the pre-stress and the propagation angle.     

Finite-amplitude Love waves in a pre-stressed compressible elastic half-space with a double surface layer

The dispersive behavior of finite-amplitude time-harmonic Love waves propagating in a pre-stressed compressible elastic half-space overlaid with two compressible elastic surface layers of finite thickness is investigated. The half-space and layers are made of different pre-stressed compressible neo-Hookean materials. The dispersion relation which relates wave speed and wavenumber is obtained in explicit form. Results for the energy density and energy flux of the waves are also presented. The special case where the interfaces between the layers and the half-space are principal planes of the left Cauchy–Green deformation tensor is also investigated. Numerical results are presented showing the variation of the Love wave speed with the pre-stress and the propagation angle.     

Separation at the interface of non-linearly elastic spinning tube-rigid shaft subjected to circumferential shear

Separation at the interface of homogeneous, isotropic, compressible, hyperelastic, spinning cylindrical tube-rigid shaft subjected to circumferential shear is investigated within the context of the finite elasticity theory. The compressible, hyperelastic spinning tube with a uniform wall thickness is assumed to be tautly fitted to a rigid shaft along its inner curved surface. The outer surface of the tube is subjected to a constant uniformly distributed circumferential shearing stress while the rigid shaft is assumed to spin with an angular speed. The state when a separation occurs at the interface of the shaft and the tube is investigated. The critical values are given for slightly compressible rubbers and nearly incompressible rubbers.     

Investigation of the stability for inviscid compressible swirling flow between concentric cylinders

The temporal stability on inviscid compressible swirling flow between two concentric cylinders is investigated. First, a linearized differential equation is derived. Two stability criteria are derived for compressible swirling flow by an analytic method analogous to Ludwieg ’s method. A finite-difference numerical method is then used to solve the eigenvalue problem of this differential equation, to get temporal growth rate and to check these stabilitv criteria derived. Finally.The effect of compressibility for stability is disscused.     

Interaction of isotropic turbulence with a normal shock wave

The evolution of incompressible and compressible isotropic 2-d turbulent fields interacting with a normal shock wave up to Mach numbers of 2.4 was investigated by means of direct numerical simulation using an ENO scheme. A comparison of statistics with linear analysis results is presented. Vorticity amplification in the DNS agrees well with the linear theory. Energy spectra are enhanced more in the small scales than in the large scales for incoming incompressible turbulence. The amplification rate for initially compressible turbulence is comparatively small.     

Inelastic analysis of plastic compressible materials using the viscoplastic model

In this study the theory of viscoplasticity is employed to provide a unified approach to the problems of plasticity and creep. For plastic compressible materials, the viscoplasticity equation is formulated and the effective range of the equation is discussed. The Drucker-Prager potential is used to describe the plastic compressible yielding and the strength-differential effect. The influence of the strength-differential effect is investigated for a pressurized cylinder.     

The dynamics of a compressible viscous liquid (review). II

This article is the second part of a review of the dynamics of rigid and elastic bodies in a compressible viscous liquid in a linearized formulation. The following processes are investigated: the forced harmonic vibrations of rigid bodies in moving and resting compressible viscous liquids, the nonstationary motion of rigid bodies in a compressible viscous liquid at rest, the movement of rigid bodies in a resting compressible viscous liquid under the action of radiation forces that are due to the interaction with propagating acoustic harmonic waves, the propagation of harmonic waves in thin-walled cylindrical elastic shells containing a compressible viscous liquid, and the propagation of harmonic waves in hydroelastic systems consisting of a resting compressible viscous liquid and elastic compressible or incompressible bodies with initial stresses. Publications concerning the above problems are analyzed. S.P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 3, pp. 3–30, March, 2000.     

On the Invariance of Compressible Navier–Stokes and Energy Equations Subject to Density-Weighted Filtering

The scale invariance properties of compressible Navier–Stokes and energy equations subject to density-weighted filtering are investigated. Scale or filter invariance forms of compressible moment equations require that two forms of generalized central second-order moments be defined—(1) product of two density-weighted sub-filter fluctuations and (2) product of one density-weighted and one un-weighted sub-filter fluctuation. The evolution equations for all required first and second order filtered moments are derived. These results provide the theoretical underpinning for variable-resolution calculations of reacting and compressible turbulent flows.     

Shocklets in compressible flows

The mechanism of shocklets is studied theoretically and numerically for the stationary fluid, uniform compressible flow, and boundary layer flow. The conditions that trigger shock waves for sound wave, weak discontinuity, and Tollmien-Schlichting （T-S） wave in compressible flows are investigated. The relations between the three types of waves and shocklets are further analyzed and discussed. Different stages of the shocklet formation process are simulated. The results show that the three waves in compressible flows will transfer to shocklets only when the initial disturbance amplitudes are greater than the certain threshold values. In compressible boundary layers, the shocklets evolved from T-S wave exist only in a finite region near the surface instead of the whole wavefront.     

Improvements to compressible Euler methods for low‐Mach number flows

In the present study improvements to numerical algorithms for the solution of the compressible Euler equations at low Mach numbers are investigated. To solve flow problems for a wide range of Mach numbers, from the incompressible limit to supersonic speeds, preconditioning techniques are frequently employed. On the other hand, one can achieve the same aim by using a suitably modified acoustic damping method. The solution algorithm presently under consideration is based on Roe's approximate Riemann solver [Roe PL. Approximate Riemann solvers, parameter vectors and difference schemes. Journal of Computational Physics 1981; 43 : 357–372] for non‐structured meshes. The numerical flux functions are modified by using Turkel's preconditioning technique proposed by Viozat [Implicit upwind schemes for low Mach number compressible flows. INRIA, Rapport de Recherche No. 3084, January 1997] for compressible Euler equations and by using a modified acoustic damping of the stabilization term proposed in the present study. These methods allow the compressible Euler equations at low‐Mach number flows to be solved, and they are consistent in time. The efficiency and accuracy of the proposed modifications have been assessed by comparison with experimental data and other numerical results in the literature. Copyright © 2000 John Wiley & Sons, Ltd.     

Saturated Elastic Porous Solids: Incompressible,Compressible and Hybrid Binary Models

Constitutive models for a general binary elastic-porous media are investigated by two complementary approaches. These models include both constituents treated as compressible/incompressible, a compressible solid phase with an incompressible fluid phase (hybrid model of first type), and an incompressible solid phase with a compressible fluid phase (hybrid model of second type). The macroscopic continuum mechanical approach uses evaluation of entropy inequality with the saturation condition always considered as a constraint. This constraint leads to an interface pressure acting in both constituents. Two constitutive equations for the interface pressure, one for each phase, are identified, thus closing the set of field equations. The micromechanical approach shows that the results of Didwania and de Boer can be easily extended to general binary porous media.     

用激波管研究超音速气固两相流

在激波管里进行了可压缩性气固两相流的实验研究。测量了激波通过颗粒群时的压力的衰减过程。用纹影仪拍摄了激波与颗粒群相互干涉的照片。试验了颗粒群的不同构造对压力衰减的影响。指出了激波反射、聚焦等非线性气动因素是可压缩性气固两相流的关键问题。     

Calculation of flow-induced residual stresses in injection moulded products

Flow-induced residual stresses that arise during the injection moulding of amorphous thermoplastic polymers are calculated in both the filling and post-filling stage. To achieve this a compressible version of the Leonov model is employed. Two techniques are investigated. First a direct approach is used where the pressure problem is formulated using the viscoelastic material model. Secondly, generalized Newtonian material behaviour is assumed, and the resulting flow kinematics is used to calculate normal stresses employing the compressible Leonov model. The latter technique gives comparable results, while reducing the computational cost significantly.     

可压缩自由剪切流混合转捩大涡模拟

针对湍流气动光学效应与冲压发动机气体混合机理问题,开展了可压缩混合层流动空间模式大涡模拟和时间模式直接数值模拟研究.通过对流场(包含亚/亚混合、超/亚混合两种情况)失稳、转捩直至完全湍流的空间发展过程的研究表明,对流Mach数0.4状态下流场失稳以二维最不稳定扰动为主;非线性发展中,基频涡对并及展向涡撕裂主控流动转捩,流场发生混合转捩;转捩后脉动流场基本达到局部各向同性,此时,湍流Mach数低于0.3,流动压缩性可近似忽略.     

High-order ghost-point immersed boundary method for viscous compressible flows based on summation-by-parts operators

A high-order immersed boundary method is devised for the compressible Navier-Stokes equations by employing high-order summation-by-parts difference operators. The immersed boundaries are treated as sharp interfaces by enforcing the solid wall boundary conditions via flow variables at ghost points. Two different interpolation schemes are tested to compute values at the ghost points and a hybrid treatment is used. The first method provides the bilinearly interpolated flow variables at the image points of the corresponding ghost points and the second method applies the boundary condition at the immersed boundary by using the weighted least squares method with high-order polynomials. The approach is verified and validated for compressible flow past a circular cylinder at moderate Reynolds numbers. The tonal sound generated by vortex shedding from a circular cylinder is also investigated. In order to demonstrate the capability of the solver to handle complex geometries in practical cases, flow in a cross-section of a human upper airway is simulated.     

Boundary-layer flows with swirl and large suction

The effect of large suction on laminar compressible boundary-layer flows with swirl is investigated by employing the perturbation method. The resulting equations have been solved by analytical methods. The result shows that the skin-friction and mass transfer parameter are well in agreement with the values obtained by quasi-linearization technique at large suction and the present investigation implies to obtain the parameters at large suction.     

Taylor instability in the discontinuity between two fluids in an electromagnetic field

The gravitational instability of the discontinuity between two compressible (or incompressible) fluids is investigated. The fluids are exposed to an electromagnetic field, and one of them is nonconducting, while the other has a finite conductivity. The magnetic Reynolds number is assumed to be small. It is shown that in contrast to the cases investigated in [1, 2], where compressible, infinitely conducting fluids were considered on both sides of the discontinuity, in the present case the electromagnetic field is not able to stabilize the discontinuity and the perturbations can propagate in fixed directions. The presence of walls inhibits the perturbation growth [2, 3], while their conductivity does not affect the instability of the discontinuity. The greatest perturbation growth is found to occur in a wave propagating along the magnetic field, when the electromagnetic field does not influence these perturbations in the case of incompressible fluids, but does influence them in the compressible case.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 24–28, September–October, 1976.The author wishes to express his appreciation to A. A. Barmin and A. G. Kulikovskii for suggesting the problem and for their continued interest in the work.     

Compressible and confined vortex flow

The internal compressible flow of a thin vortex chamber was investigated experimentally by measuring the radial distribution of temperature and pressure, from which the velocity field was calculated. The bulk of the internal vortex was found to be described by u_θr^0.69 = constant. The total resistance of the vortex chamber to the flow was also investigated in the context of fluidic vortex diode behavior under conditions of compressible and choked flow. It was found that the vortex chamber choked at an upstream-to-downstream pressure ratio of about 6 and in doing so passed a mass flow rate of 28% of the equivalent one-dimensional ideal nozzle. The resistance of vortex chambers is known to be strongly influenced by the presence of reversed flow in the exit due to vortex breakdown. Schlieren photography of the swirling exhaust flow was used to show that, while vortex breakdown does occur, it can only do so after the flow has become subsonic downstream of the exit and cannot therefore influence the vortex chamber resistance.     

Calculation of residual stresses in injection molded products

Both flow- and thermally-induced residual stresses which arise during the injection molding of amorphous thermoplastic polymers are calculated in the filling and post-filling stage. To achieve this, a compressible version of the Leonov model is employed. Two techniques to calculate flow-induced residual stresses are investigated. First, a direct approach is developed where the pressure problem is formulated using the viscoelastic material model. Second, generalized Newtonian material behavior is assumed in formulating the pressure problem, and the resulting flow kinematics is used to calculate normal stresses employing the compressible Leonov model. The latter technique gives comparable results, while reducing the computational cost significantly.