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We consider an incompressible viscous fluid flowing through a cylindrical pipe with rough wall. Motivated by the applications, we assume the periodicity of the roughness in the longitudinal direction and that the flow is governed by the prescribed pressure drop between pipe’s ends. The goal of the paper is to investigate the effects of the corrugated boundary on the fluid flow by taking into account the effects of inertia as well. Starting from the Navier–Stokes system and employing the average boundary roughness as the small parameter, we propose a higher-order correction of the standard Hagen–Poiseuille velocity via boundary layer analysis. Using the obtained result we propose the new formula for the Darcy–Weisbach friction coefficient.

The application of textured bearing surfaces results in a more complex lubricant flow pattern compared to smooth bearing surfaces. In order to capture the more complex flow pattern and possible inertia effects in the vicinity of the surface pockets, the NavierStokes equations should be used to model the flow between textured surfaces instead of the Reynolds equation. In this paper a multi-scale method is presented where the fluid flow in a single micro-scale texture unit cell is modelled using the NavierStokes equations, the results of which are then averaged to flow factors to be used in a novel texture averaged Reynolds equation on the macro-scale bearing level. Depending on the local flow conditions the non-linear inertia effects in the flow can either contribute or detract from the local load capacity of the lubricant film. Some results from the micro-scale calculations are presented, followed by the method developed to average these results to the macro-scale. The resulting flow-factors are presented and a load correction term is introduced. Although the method presented does not put restrictions to the texture dimensions, the texture unit cell dimensions are chosen equal to those in an experimental polymer water lubricated bearing. In a follow-up paper these results will be used to determine the efficiency of surface texturing in a lubricated journal bearing application. © 2010 Elsevier Ltd.

Water lubricated bearings and squeeze film dampers exhibit large lubricant inertia forces on the order of viscous forces. To model these bearings, the traditional Reynolds equation is not adequate. An extended Reynolds equation is developed in this study which takes into account the turbulence and inertia effects: both convective and temporal. The most complete form of the temporal inertia effect model is developed and applies to the turbulent regime, consisting of primary and secondary temporal inertia terms. The convective inertia model follows Constantinescu's approach. The turbulence model is also based on Constantinescu's model and is tuned using CFD analysis. To apply the proposed model to fixed geometry cylindrical water bearings, a computer code named SLEEVEBRG is developed. This program is also capable of satisfying the circumferential periodicity constraint associated with cylindrical bearings. The numerical results show significant convective and temporal inertia effects in water bearings. Convective inertia effects increase the load capacity of the bearing. The temporal inertia, resulting in effective added mass coefficients, exhibits destabilizing effects, while the convective inertia effects serve to improve stability of the bearing. The secondary temporal inertia reduces the added mass terms, thus increasing the stability of the bearing. Squeeze film dampers are designed with numerous different configurations. Features such as supply and discharge holes, end seals, and grooves contribute into the dynamic characteristics of squeeze film dampers. Grooves are shown, contrary to previous perceptions, to generate a considerable amount of dynamic pressure. To capture their effects, an effective groove depth approach is adopted in this work. Additionally, an applicable extended Reynolds equation is developed which includes temporal inertia and also takes into account the contribution of the holes. A computer code named MAXSFD is developed accordingly. Four different configurations are analyzed and results are compared against experimentally obtained data. It is found that in general two distinct effective groove depths are required to match the experimental added mass and damping values. This indicates that different amounts of lubricant trapped in the groove contribute to the added mass and damping characteristics of squeeze film dampers. In open end squeeze film dampers, the ratio of the two effective grooves is nearly two, and for sealed squeeze film dampers the ratio is approximately one long and one and half for short SFD. The numerical observations prove that secondary temporal inertia plays a minor role in the determination of the added mass coefficients. The results are compared against an older squeeze film damper code SQFDAMP [1], which underpredicts the damping values and lacks the added mass prediction capability.

International audience; The Couette viscometer is a well-known problem of fluid mechanics, well-suited for the verification of numerical methods. The aim of this work is to extend the classical steady state mechanical solution obtained in fluid mechanics, both to strongly-coupled thermomechanical problems in the case of laminar and incompressible fluid flows, and to solid-type nonlinear behaviours. Extended solutions will allow for the verification of new formulations of a mixed P1+/P1 finite element developed both in fluid and solid mechanics, within a temperature/velocity/pressure formulation coupled with an implicit (backward) Euler algorithm in time. In the present Part I, we address the case of the laminar flow of incompressible fluids with inertia effects and thermomechanical coupling. The verification performed on the reference solutions developed clearly evidence the good behaviour of the fluid finite element. The extension to solid-type nonlinear behaviours for strongly-coupled thermomechanical problems will be the subject of Part II.

The dip coating of a fiber of small radius is studied via a finite element solution of the Navier-Stokes equations. The coating speed is selected within the range corresponding to the visco-capillary and visco-inertial regimes. Predictions obtained within the range of the visco-capillary regime are in very good agreement with the Landau?Levich law and with published experiments, whereas those obtained within the visco-inertial regime--that is, at coating speeds typical of industrial applications--match published experimental data. Fil: Campana, Diego Martin. Universidad Nacional de Entre Ríos. Facultad de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química (i); Argentina Fil: Ubal, Sebastian. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico Para la Industria Química (i); Argentina. Universidad Nacional de Entre Rios; Argentina Fil: Giavedoni, Maria Delia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico Para la Industria Química (i); Argentina Fil: Saita, Fernando Adolfo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química (i); Argentina

The response of concrete up to complete failure in tension is represented in the load deformation relation. The characteristic parameters are the ultimate strength, stiffness in the ascending branch and the fracture energy. All these parameters depend on concrete composition and environmental conditions, as discussed in the previous chapters. The observed response of concrete at macro-level is determined by the damage initiation and damage accumulation mechanisms at meso- and micro-scale levels. The failure process is governed by (i) the stress condition, (ii) the mechanisms governing microcrack nucleation, propagation and obscuration of critical flaws, (iii) the ability to absorb energy in fracture, and (iv) the energy flow from the surrounding material into the fracture zone. In dynamics, all four conditions vary in time and depend on the loading rate. This chapter discusses the background and mechanisms of the rate-dependent behaviour of concrete, focusing on the effects of (i) inertia and limited cracking velocity at material level, (ii) concrete composition at meso-level, and (iii) moisture content and pore distribution. The available experimental data on dynamic strength and fracture energy are presented and related to response mechanisms for the different loading rate regimes. © 2013 Woodhead Publishing Limited All rights reserved.

The response of concrete up to complete failure in tension is represented in the load deformation relation. The characteristic parameters are the ultimate strength, stiffness in the ascending branch and the fracture energy. All these parameters depend on concrete composition and environmental conditions, as discussed in the previous chapters. The observed response of concrete at macro-level is determined by the damage initiation and damage accumulation mechanisms at meso- and micro-scale levels. The failure process is governed by (i) the stress condition, (ii) the mechanisms governing microcrack nucleation, propagation and obscuration of critical flaws, (iii) the ability to absorb energy in fracture, and (iv) the energy flow from the surrounding material into the fracture zone. In dynamics, all four conditions vary in time and depend on the loading rate. This chapter discusses the background and mechanisms of the rate-dependent behaviour of concrete, focusing on the effects of (i) inertia and limited cracking velocity at material level, (ii) concrete composition at meso-level, and (iii) moisture content and pore distribution. The available experimental data on dynamic strength and fracture energy are presented and related to response mechanisms for the different loading rate regimes. © 2013 Woodhead Publishing Limited All rights reserved.

Quantitative identification of Apparent wall slip (AWS) effect, accompanying the flow of colloidal dispersions in confined geometries, requires a specific modification of common viscometric methods. Essential distinction between common and AWS viscometry is outlined – including theoretical background, calibration, data acquisition, and downstream data treatment – and demonstrated for a class of rotational viscometers.

This article is concerned with finite element approximations for yield stress fluid flows through a sudden planar expansion. The mechanical model is composed by mass and momentum balance equations, coupled with the Bingham viscoplastic model regularized by Papanastasiou (1987) equation. A multi-field Galerkin least-squares method in terms of stress, velocity and pressure is employed to approximate the flows. This method is built to circumvent compatibility conditions involving pressure-velocity and stress-velocity finite element subspaces. In addition, thanks to an appropriate design of its stability parameters, it is able to remain stable and accurate in high Bingham and Reynolds flows. Numerical simulations concerning the flow of a regularized Bingham fluid through a one-to-four sudden planar expansion are performed. For creeping flows, yield stress effects on the fluid dynamics of viscoplastic materials are investigated through the ranging of Bingham number from 0.2 to 100. In the sequence, inertia effects are accounted for ranging the Reynolds number from 0 to 50. The numerical results are able to characterize accurately the morphology of yield surfaces in high Bingham flows subjected to inertia.

This paper discusses the practical implementation of decentralized velocity feedback on a thin rectangular panel using sixteen triangularly shaped piezoceramic patch actuators with the base edges uniformly distributed along the perimeter of the panel and accelerometer sensors located at the tips of the actuators. In the first part of the paper, the sensor–actuator open loop frequency response function of one feedback loop is modelled and analysed in order to study the principal stability properties of a single control unit. In particular an elemental model is developed for studying the bending excitation and passive stiffness and inertia effects produced by the triangular piezoceramic actuator and for investigating the resilient effect of the clamping frame that holds the panel. The simulated frequency response function is validated experimentally and contrasted with that obtained from a conventional model of the bending excitation produced by triangularly shaped distributed transducers. In the second part of the paper, the stability and control performance of sixteen decentralized feedback loops are investigated experimentally. Six rectangular panels have been built and equipped with accelerometer sensors and piezoceramic triangular actuators of various geometries such that the effects of the base width, height and base area can be examined.

The application of textured bearing surfaces results in a more complex lubricant flow pattern compared to smooth bearing surfaces. In order to capture the more complex flow pattern and possible inertia effects in the vicinity of the surface pockets, the NavierStokes equations should be used to model the flow between textured surfaces instead of the Reynolds equation. In this paper a multi-scale method is presented where the fluid flow in a single micro-scale texture unit cell is modelled using the NavierStokes equations, the results of which are then averaged to flow factors to be used in a novel texture averaged Reynolds equation on the macro-scale bearing level. Depending on the local flow conditions the non-linear inertia effects in the flow can either contribute or detract from the local load capacity of the lubricant film. Some results from the micro-scale calculations are presented, followed by the method developed to average these results to the macro-scale. The resulting flow-factors are presented and a load correction term is introduced. Although the method presented does not put restrictions to the texture dimensions, the texture unit cell dimensions are chosen equal to those in an experimental polymer water lubricated bearing. In a follow-up paper these results will be used to determine the efficiency of surface texturing in a lubricated journal bearing application. © 2010 Elsevier Ltd.

WOS; International audience; A model of dynamic damage by void nucleation and growth is proposed for elastic–viscoplastic materials sustaining intense loading. The model is dedicated to ductile materials for which fracture is caused by microvoiding. The material contains potential nucleation sites where microvoids are generated when the local pressure overcomes the nucleation pressure. A probability density function is adopted to describe the fluctuation of the nucleation pressure within the material. The void growth is described by using a hollow sphere model where micro-inertia effects are accounted for. The matrix weakening due to void growth is also included. The model has been first tested under uniaxial deformation. When the strain rate is assumed constant, the pressure inside the material has nearly a linear response up to a maximum. An analytical expression for the maximum pressure is proposed. Finite element simulations of plate impact tests have been carried out and compared to experiments on tantalum. From simulations based on the proposed model, an increase of the spall strength is observed with higher shock intensities. Therefore, the relationship between the velocity pullback and spall strength usually assumed in the literature (based on the acoustic approach) seems to be inadequate. Velocity profiles are simulated for different flyer thicknesses and different impact velocities with close agreement with experiments.

International audience; This paper is concerned with the influence of apparatus inertia effects in controlled stress rheometry. As evidenced on creep experiments, the coexistence of apparatus inertia and viscoelasticity leads to a coupling frequency. For weak gels, this coupling frequency is typically between 1 and 100 Hz. Therefore, frequency sweeps around and above this coupling frequency also corresponds to an effective shear stress sweep evolution due to a non-trivial resonant effect. In other words, frequency sweep experiments are not made at constant shear stress. The detailed modelling and analysis of this inertia effect on a typical weak gel shows a clear and fundamental limitation for its characterization using a controlled stress rheometer. Also, alternative approaches to standard rheometer software analysis are proposed to take this coupling effect into account.

The mechanical face seals ensure the sealing of rotating shafts. The increase in operating conditions led to the development of gas face seals functioning without face contact, separated by a thin fluid film. Friction between the ring of the face seal, and thus wear, is avoided.The bibliographical study reveals that few work on the gas faces seals with high pressures were carried out. The characteristics of a flow at high pressure are examined and the important points of the model are defined: real gases, inertia effects, thermal effects, choked flow. With high pressures, the behaviour of the gas differs from that of a perfect gas, a real gas model is thus developed. The equation of Reynolds for a compressible fluid is modified in order to take into account the inertia effects. The thermal effects in the flow are also introduced into the model. The choked flow at the exit of fluid film is solved by an original method. The solid distortions and the thermal coupling are taken into account by the method of the influence coefficients. The finite element method is used for the discretization of the equations and an iterative algorithm allows the determination of the fields of pressure and temperature. The comparison with an analytical solution and experimental data validates the model. The influence of the model of gas is presented. The parametric study undertaken with the numerical model makes it possible to study the influence of the inertia effects on the flow compared to the dominated viscous flow. Finally, the coupling between fluid and solids is studied. This analysis shows that the face distortions influence the behaviour of the face seals., Les garnitures mécaniques assurent l'étanchéité d'arbres tournants. L'augmentation des contraintes de fonctionnement a conduit au développement de garnitures à gaz fonctionnant sans contact des faces, séparées par un film fluide de très faible épaisseur. Le frottement entre les anneaux de la garniture, et donc l'usure, est évité.L'étude bibliographique révèle que peu de travaux sur les garnitures pour gaz à hautes pressions ont été réalisés. Les caractéristiques d'un écoulement à haute pression sont examinées et les points-clefs du modèle sont définis : gaz réels, effets d'inertie, effets thermiques, écoulement bloqué. A hautes pressions, le comportement du gaz diffère de celui d'un gaz parfait, un modèle de gaz réel est donc développé. L'équation de Reynolds pour un fluide compressible est modifiée afin de prendre en compte les effets d'inertie. Les effets thermiques dans l'écoulement sont également introduits dans le modèle. L'écoulement bloqué à la sortie du film fluide est résolu grâce à une méthode originale. Les déformations des solides et le couplage thermique sont pris en compte par la méthode des coefficients d'influence. La méthode des éléments finis est utilisée pour la discrétisation des équations et un algorithme itératif permet la détermination des champs de pression et de température. La comparaison avec une solution analytique et des données expérimentales permet de valider le modèle. L'influence du modèle du gaz est présentée. L'étude paramétrique menée avec le modèle numérique permet d'étudier l'influence des effets d'inertie sur l'écoulement par rapport au cas purement visqueux. Finalement, le couplage fluide-solides est étudié. Cette analyse montre que les déformations des faces influencent notablement le comportement des garnitures.

This paper deals with the modelling of viscoelastic flows in transient regimes using the Modified Phan Tien and Tanner (MPTT) model. This model is the most recent one which can predict stress overshoot in unsteady shear flow and is based on the description of the liquid microstructure rather than empirical and mathematical developments. Here, the analysis of the squeeze film between parallel plates is presented. It is an alternative in quantifying and understanding the two main factors which may enhance the carrying capacity (inertia effect and viscoelastic behavior) situation which can occur, for instance, in the case of overloading in journal bearings. A boundary element method is used here to model such complex flow. The main factors have been extracted and the restrictions due to a rough estimate of the lubricant's flow are shown. Presented as a Society of Tribologlsts and Lubrication Engineers paper at the ASME/STLE Tribology Conference in Lahaina, Hawaii, October 16–20, 1994

By using a C0continuous, QUAD-4 shear flexible shell element, based on the field consistency principle, the non-linear free flexural vibrations of thin circular cylindrical shells have been studied. The formulation is general in the sense that it includes anisotropy, transverse shear deformation, in-plane and rotary inertia effects. Primarily, an attempt is made to clarify the existing controversies in the prediction of the non-linear behaviour of isotropic circular cylindrical shells through a finite element formulation with dynamic response analysis. The non-linear governing equations are solved by using a Wilson-θ numerical integration scheme with θ = 1·4. For each time step, modified Newton–Raphson iterations are employed to achieve equilibrium at the end of that time step. Detailed numerical results are presented for various parameters for the isotropic shell. The present study also brings out the participation of the asymmetric contraction mode with the asymmetric mode.