Two-dimensional problem concerning the impact of a rigid body onto a thin elastic plate lying on the surface of a compressible fluid

Institute of Mechanics, Academy of Sciences of the UkrSSR, Kiev. Kiev Autorail Institute. Translated from Prikladnaya Mekhanika, Vol. 27, No. 9, pp. 59–66, September, 1991.     

Coupled analysis of elastic plate-infinite nonhomogeneous layered medium

The static interaction problem between an elastic plate and infinite medium is studied by the semi-numerical (in one direction) and semi-analytical (in two directions) method-semianalytical element method, a simple practical and effective method for coupled analysis between above-ground structure and infinite soil medium with complex material character in engineering.     

Statistical analysis of the hydrodynamic pressure in the near field of compressible jets

This paper is devoted to the statistical characterization of the pressure fluctuations measured in the near field of a compressible jet at two subsonic Mach numbers, 0.6 and 0.9. The analysis is focused on the hydrodynamic pressure measured at different distances from the jet exit and analyzed at the typical frequency associated to the Kelvin–Helmholtz instability. Statistical properties are retrieved by the application of the wavelet transform to the experimental data and the computation of the wavelet scalogram around that frequency. This procedure highlights traces of events that appear intermittently in time and have variable strength. A wavelet-based event tracking procedure has been applied providing a statistical characterization of the time delay between successive events and of their energy level. On this basis, two stochastic models are proposed and validated against the experimental data in the different flow conditions     

Vibrational frequency analysis of finite elastic tube filled with compressible viscous fluid

The vibrational frequency analysis of finite elastic tube filled with compressible viscous fluid has received plenty of attention in recent years. To apply frequency analysis to defect detection for example, it is necessary to investigate the vibrational behavior under appropriate boundary conditions. In this paper, we present a detailed theoretical study of the three dimensional modal analysis of compressible fluid within an elastic cylinder. The dispersion equations of flexural, torsional and longitudinal modes are derived by elastodynamic theory and the unsteady Stokes equation. The symbolic software Mathematica is used in order to find the coupled vibration frequencies. The dispersion equation is deduced and analytically solved. The finite element results are compared with the present method for validation and an acceptable match between them are obtained.     

Numerical simulation of vortical and coherent structures in compressible jet flows

The compressible flows of plane free jets and jets of the intake-stroke of a rectangular piston-engine model are investigated by numerical simulations. The observed vortical structures appear to be the well-known coherent structures of turbulent shear layers. The simulated structures are compared to experimental data by means of density fields and turbulent statistics taken from different authors. The computed flow depends on physical as well as on numerical parameters. The good agreement with the experimental data is obtained by direct simulation without any turbulence model.     

Coupled CFD-DEM simulation of hydrodynamic bridging at constrictions

This paper presents a coupled CFD-DEM approach to simulate the flow of particulate suspensions in the intermediate concentration regime where solid volume concentration is 1% < ϕ < 50%. In particular, hydrodynamic multi-particle bridging during flow through a single constriction in a rectangular channel is studied. It is shown that for neutrally buoyant, monodispersed particulate suspensions, the probability of jamming increases with the particle concentration. There also exists a critical particle concentration (ϕ*) for spontaneous bridging, which depends on the ratio of pore size to particle size, the flow velocity, the particle-fluid density contrast, and the flow geometry leading to the constriction. The ϕ* has a strong dependence on the outlet-to-particle relative size (R_o). For 1.5 ≤ R_o ≤ 2.5, a direct transition from a flowing state to a jammed state was observed. For R_o ≥ 3, the flowing state typically transitioned to a dense state characterized by the accumulation of particles near the constriction before jamming. Increasing the inlet-to-particle relative size (R_ip) lowers ϕ* by increasing the number of particles arriving at the constriction simultaneously. The effect of changing R_ip is more pronounced at high R_o when the probability of bridging is lower. A high fluid velocity increases particle interactions near the constriction and accelerates the onset of bridging. However, no distinct effect of velocity on ϕ* was observed in this study. A higher particle-to-fluid density ratio (ρ_p/ρ_f) increases the probability of bridging and leads to a lower ϕ* in a given constriction geometry. The effect saturates at higher ρ_p/ρ_fwhen gravitational forces completely dominate over viscous drag forces. ϕ* is also found to decrease with increasing angle of constriction convergence (θ) for θ < 30°, but increases beyond that at $\theta ={60}^{\circ }$.     

Spherical inflation of a class of compressible elastic bodies

Using a special model that belongs to a new class of elastic bodies wherein the Cauchy-Green stretch is given in terms of the Cauchy stress and its invariants, within the context of the spherical inflation of a spherical annulus, we show that interesting phenomena like the development of “stress boundary layers” manifest themselves. We consider two cases of boundary value problems, one in which there is a cavity in a sphere and the other in which there is a rigid spherical inclusion in a sphere. We show that in the case of a rigid inclusion, it is possible for a pronounced “stress boundary” layer to develop, in that the values of the stresses within this boundary layer that is adjacent to a spherical inclusion are much larger than external to it. We also show that in the case of both the cavity and a rigid inclusion, the stress concentration is an order of magnitude higher than the increase in the deformation gradient, that is, the stress and the stretch do not scale in a similar manner. While the stress adjacent to a rigid inclusion can be 2500 times the applied radial stress, the maximum stretch, which occurs at the rigid inclusion is about 10. While the variation in the stresses are linear in thin walled annular regions, we find that in thick walled annular regions, the variation of the stresses is non-linear.     

Mechanism of self-oscillations in a supersonic jet impact onto an obstacle 1. Obstacle with a spike

Results of numerical simulations and experimental investigations of self-oscillations arising in the case of impingement of an overexpanded or underexpanded jet onto an obstacle with a spike are reported. The mechanisms of the emergence and maintaining of self-oscillations for overexpanded and underexpanded jets are elucidated. It is demonstrated that self-oscillations are caused by disturbances in a supersonic jet, which induce mass transfer between the supersonic flow and the region between the shock wave and the obstacle. The feedback is ensured by acoustic waves generated by the radial jet on the obstacle. These waves propagate in the gas surrounding the jet, impinge onto the nozzle exit, and initiate disturbances of the supersonic jet parameters. In the overexpanded jet, these disturbances penetrate into the jet core, where they are amplified in oblique shock waves.     

Analogies between linearized and linear problems for compressible elastic bodies

International Applied Mechanics -     

Axially-symmetric problem of the impact of a rigid blunt body onto the surface of an elastic halfspace

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 25, No. 7, pp. 16–24, July, 1989.     

A computational analysis of the hydrodynamic instability of a liquid jet focused into a converging microchannel

The instability of a focused liquid jet is studied by semi-analytical methods and by methods of computational fluid dynamics. The semi-analytical approach relies on earlier work on the instability of an extending liquid thread and is based on the Stokes flow regime and small-amplitude perturbations. The evolution of different excitation modes is evaluated and compared. Through hydrodynamic focusing and the corresponding extensional flow an initially stable mode may become unstable and it depends on the position away from the inlet which mode is to be regarded as the most unstable one. When plotting a hypothetical jet decay length against the excitation wave number, a comparatively broad minimum is exhibited. The CFD simulations based on the volume-of-fluid method show that the jet may break up either in the conical focusing zone or in the attached capillary, depending on the flow velocity. When the deformation of the jet surface reaches a certain amplitude, the jet assumes a “beads-on-a-string” structure instead of a shape derived from a harmonic perturbation. A jet decay within the capillary produces elongated droplets with cusped ends. When comparing the results of the CFD and the semi-analytical model, it turns out that the CFD simulations predict more stable jets with a larger decay length. An analysis of the flow velocity field shows that the increased stability might be due to the interaction of the jet with the channel walls.     

Simulation and analysis of the impact of micron-scale particles onto a rough surface

Normal impact of micron-scale copper particles onto a rough copper surface is investigated in the 25–150 m/s impact velocity range, by the finite element method. Surface roughness is generated numerically and incorporated into the finite element model. Particle size is varied in a range comparable to the magnitude of the standard deviation of the surface roughness. Isotropic hardening with strain rate effects and thermal softening due to plastic heat dissipation are included in the model. Analysis is carried out in plane strain mode and impact of single and multiple particles are modeled. The effects of surface roughness on the mechanics of impact, energy exchange, rebound characteristics of the particle and the residual stresses in the substrate are investigated. Impacts on peaks and valleys cause response similar to oblique impact, affecting the rebound behavior of the particle by changing the rebound direction and increasing the rebound energy of the particle. Impacts also cause surface smoothening by crushing the surface peaks; however, collapse of adjacent peaks can provoke stress concentrations and initiate crack formation. Influence of surface roughness on the aftermath of particle impacts decreases with increasing particle size and impact velocity. For impact velocities higher than 50 m/s, no significant difference is observed between impact on smooth and rough surfaces in terms of residual stress generation in the substrate. In general, it is concluded that the effect of surface roughness should be taken into account for low velocity impacts where only the surface peaks deform, or for small particles with size comparable to the standard deviation of the surface roughness.     

Mechanism of self-oscillations in a supersonic jet impact onto an obstacle. 2. Obstacle with no spike

Results of the numerical solution of the problem of impingement of an overexpanded supersonic jet onto an obstacle are reported. The mass-flow-rate mechanism of self-oscillations is revealed. This mechanism consists of periodic changes in the regimes of gas inflow and outflow from the separation region to the jet around this region. It is shown that the shock-wave structure of the impinging supersonic jet exerts a significant effect on the amplitude of self-oscillations.     

聚能射流侵彻径向扩孔的可压缩模型

聚能射流侵彻厚靶时,对靶材同时进行轴向和径向挤压进而发生轴向侵彻和径向扩孔。本文中基于聚能射流侵彻可压缩模型并结合Szendrei-Held扩孔方程,推导给出考虑弹/靶材料可压缩性的聚能射流扩孔方程。为简化完整可压缩模型繁琐的计算过程,又基于Murnaghan状态方程给出可压缩模型的近似解。与水中聚能射流扩孔的实验研究对比分析,表明该模型预测优于Szendrei-Held扩孔方程。模型分析表明,射流半径、驻点压力、靶材强度、驻点处靶材密度以及聚能射流速度是影响聚能射流扩孔的主要因素。本文模型可以更准确地预测聚能射流侵彻可压缩性较强的靶材的扩孔情况。相关工作可为含液密闭结构干扰聚能射流侵彻提供理论基础。     

Measurements in the field of a spark excited compressible axisymmetric jet

Acoustic phase (ensemble) averaged measurements were performed in a constant temperature, axisymmetric, Mach 0.6 jet of air. These measurements show that the noise directly radiated by the coherent structure in the jet flow field was responsible for the directivity of the acoustic field.List of symbols D nozzle exit diameter - f frequency, Hz - r radial distance from the jet centerline - SPL sound pressure level (ref.: 20 micro pascals) - St Strouhal number, = f D/U - U jet exit velocity - x distance along the jet axis from the nozzle exit - t time - ensemble average quantity     

The structural performance of near-optimized truss core panels

Theoretical studies have indicated that truss core panels with a tetragonal topology support bending and compression loads at lower weight than competing concepts. The goal of this study is to validate this prediction by implementing an experimental protocol that probes the key mechanical characteristics while addressing node eccentricity and structural robustness. For this purpose, panels have been fabricated from a beryllium–copper alloy using a rapid prototyping approach and investment casting. Measurements were performed on these panels in flexure, shear and compression. Numerical simulations were conducted for these same configurations. The measurements reveal complete consistency with the stiffness and limit load predictions, as well as providing a vivid illustration of asymmetric structural responses that arises because the bending behavior of optimized panels is dependent on truss orientation.