A three-dimensional PSME model for rotating flows in an annular cavity

A pseudospectral matrix-element (PSME) numerical model is described for the simulation of rotating flows in a three-dimensional annular cavity. Temporal discretisation is implemented using a second-order semi-implicit scheme. Modified compressibility is invoked to handle the coupling between velocity and pressure while maintaining the incompressibility constraint. The governing continuity and Navier–Stokes momentum equations and boundary conditions are discretised using Chebyshev and Fourier collocation formulae. The model is validated against numerical results from alternative schemes and experimental data on rotating flows in an annular cavity. A base flow regime and instability patterns are observed, in accordance with other previously published investigations. It is demonstrated that the PSME model provides an accurate representation of rotating flows in an annular cavity.     

Modelling the slight compressibility of anisotropic soft tissue

In order to avoid the numerical difficulties in locally enforcing the incompressibility constraint using the displacement formulation of the Finite Element Method, slight compressibility is typically assumed when simulating transversely isotropic, soft tissue. The current standard method of accounting for slight compressibility of hyperelastic soft tissue assumes an additive decomposition of the strain-energy function into a volumetric and a deviatoric part. This has been shown, however, to be inconsistent with the linear theory for anisotropic materials. It is further shown here that, under hydrostatic tension or compression, a transversely isotropic cube modelled using this additive split is simply deformed into another cube regardless of the size of the deformation, in contravention of the physics of the problem. A remedy for these defects is proposed here: the trace of the Cauchy stress is assumed linear in both volume change and fibre stretch. The general form of the strain-energy function consistent with this model is obtained and is shown to be a generalisation of the current standard model. A specific example is used to clearly demonstrate the differences in behaviour between the two models in hydrostatic tension and compression.     

A high-order discontinuous Galerkin method for the incompressible Navier-Stokes equations on arbitrary grids

A high-order discontinuous Galerkin (DG) method is proposed in this work for solving the two-dimensional steady and unsteady incompressible Navier-Stokes (INS) equations written in conservative form on arbitrary grids. In order to construct the interface inviscid fluxes both in the continuity and in the momentum equations, an artificial compressibility term has been added to the continuity equation for relaxing the incompressibility constraint. Then, as the hyperbolic nature of the INS equations has been recovered, the local Lax-Friedrichs (LLF) flux, which was previously developed in the context of hyperbolic conservation laws, is applied to discretize the inviscid term. Unlike the traditional artificial compressibility method, in this work, the artificial compressibility is introduced only for the construction of the inviscid numerical fluxes; therefore, a consistent discretization of the INS equations is obtained, irrespective of the amount of artificial compressibility used. What is more, as the LLF flux can be obtained directly and straightforward, no numerical iteration for solving an exact Riemann problem is entailed in our method. The viscous term is discretized by the direct DG method, which was developed based on the weak formulation of the scalar diffusion problems on structured grids. The performance and the accuracy of the method are demonstrated by computing a number of benchmark test cases, including both steady and unsteady incompressible flow problems. Due to its simplicity in implementation, our method provides an attractive alternative for solving the INS equations on arbitrary grids.     

Turbulence modelling and role of compressibility on oil spilling from a damaged double hull tank

The viscosity plays an important role, and a multiphase solver is necessary to numerically simulate the oil spilling from a damaged double hull tank (DHT). However, it is uncertain whether turbulence modelling is necessary, which turbulence model is suitable; and what the role of compressibility of the fluids is. This paper presents experimental and numerical investigations to address these issues for various cases representing different scenarios of the oil spilling, including grounding and collision. In the numerical investigations, various approaches to model the turbulence, including the large eddy simulation (LES), direct numerical simulation and the Reynolds average Navier–Stokes equation (RANS) with different turbulence models, are employed. Based on the investigations, it is suggested that the effective Reynolds numbers corresponding to both oil outflow and water inflow shall be considered when classifying the significance of the turbulence and selecting the appropriate turbulence models. This is confirmed by new lab tests considering the axial offset between the internal and the external holes on two hulls of the DHT. The investigations conclude for numerically simulating oil spilling from a damaged DHT that when the effective Re is smaller the RANS approaches should not be used and LES modelling should be employed; while when the effective Reynolds numbers is large, the RANS models may be used as they can give similar results to LES in terms of the height of the mixture in the ballast tank and discharge but costing much less CPU time. The investigation on the role of the compressibility of the fluid reveals that the compressibility of the fluid may be considerable in a small temporal‐spatial scale but plays an insignificant role on macroscopic process of the oil spilling. Copyright © 2016 John Wiley & Sons, Ltd.     

Some recent developments on integrity assessment of pipes and elbows. Part II: Experimental investigations

Integrity assessment of piping components is very essential for safe and reliable operation of power plants. Over the last several decades, considerable work has been done throughout the world to develop a methodology for integrity assessment of pipes and elbows, appropriate for the material involved. However, there are scope of further development/improvement of issues, particularly for pipe bends, that are important for accurate integrity assessment of piping. Considering this aspect, a comprehensive Component Integrity Test Program was initiated in 1998 at Reactor Safety Division (RSD) of Bhabha Atomic Research Centre (BARC), India in collaboration with MPA, Stuttgart, Germany through Indo-German bilateral project. In this program, both theoretical and experimental investigations were undertaken to address various issues related to the integrity assessment of pipes and elbows. The important results of the program are presented in this two-part paper. In the part II of the paper, the experimental investigations are discussed. Part I covered the theoretical investigations. Under the experimental investigations, fracture mechanics tests have been conducted on pipes and elbows of 200–400 mm diameter with various crack configurations and sizes under different loading conditions. Tests on small tensile and three point bend specimens, machined from the tested pipes, have also been done to evaluate the actual stress–strain and fracture resistance properties of pipe/elbow material. The load–deflection curve and crack initiation loads predicted by non-linear finite element analysis matched well with the experimental results. The theoretical collapse moments of throughwall circumferentially cracked elbows, predicted by the recently developed equations, are found to be closer to the test data compared to the other existing equations. The role of stress triaxialities ahead of crack tip is also shown in the transferability of J–resistance curve from specimen to component.     

The plastic compressibility of 7075-T651 aluminum-alloy plate

The change in volume, and therefore the change in mass density, of an aluminum alloy was measured in uniaxial tension using clip-on extensometers. The experimental data do not agree with the assumption of plastic incompressibility found in the classical theories of plasticity. In fact, the elastic and plastic volume changes are of the same order of magnitude. Plastic anisotropy is thought to be the prime cause of this plastic compressibility.     

Modelling Slight Compressibility for Hyperelastic Anisotropic Materials

In order to avoid the numerical difficulties in locally enforcing the incompressibility constraint using the displacement formulation of the Finite Element Method, slight compressibility is typically assumed when simulating the mechanical response of nonlinearly elastic materials. The current standard method of accounting for slight compressibility of hyperelastic materials assumes an additive decomposition of the strain-energy function into a volumetric and an isochoric part. A new proof is given to show that this is equivalent to assuming that the hydrostatic stress is a function of the volume change only and that uniform dilatation is a possible solution to the hydrostatic stress boundary value problem, with therefore no anisotropic contribution to the mechanical response. An alternative formulation of slight compressibility is proposed, one that does not suffer from this defect. This new model generalises the standard model by including a mixed term in the volume change and isochoric response. Specific models of slight compressibility are given for isotropic, transversely isotropic and orthotropic materials.     

Compressible and incompressible constituents in anisotropic poroelasticity: The problem of unconfined compression of a disk

The governing equations for the theory of anisotropic poroelastic materials with incompressible constituents undergoing small deformations are developed from the theory of anisotropic poroelastic materials without the constituent incompressibility constraint. The development of the constituent specific incompressibility constraint is accomplished by restricting the elastic constants rather than by introducing Lagrange multipliers, the conventional method. The advantage of the approach is insight into the nature of the elastic response that characterizes incompressible poroelasticity. An application of the theory to the unconfined compression of a circular porous disk is presented to illustrate the effects of compressibility vs. incompressibility and transverse isotropy vs. isotropy.     

Experimental Investigation of Wheel/Rail Rolling Contact at Railhead Edge

Wheel-rail rolling contact at railhead edge, such as a gap in an insulated rail joint, is a complex problem; there are only limited analytical, numerical and experimental studies available on this problem in the academic literature. This paper describes experimental and numerical investigations of railhead strains in the vicinity of the edge under the contact of a loaded wheel. A full-scale test rig was developed to cyclically apply wheel/rail rolling contact load to the edge zone of the railhead. An image analysis technique was employed to determine the railhead vertical, lateral and shear strain components. The vertical strains determined using the image analysis method have been validated with the strain gauge measurements and used for the calibration of a 3D nonlinear Finite Element Model (FEM) that simulates the wheel/rail contact at the railhead edge and use suitable boundary conditions commensurate to the experimental setup. The FEM was then used to determine other states of strains.     

The Effects of Compressibility on Inhomogeneous Deformations for a Class of Almost Incompressible Isotropic Nonlinearly Elastic Materials

Experimental data for simple tension suggest that there is a power–law kinematic relationship between the stretches for large classes of slightly compressible (or almost incompressible) non-linearly elastic materials that are homogeneous and isotropic. Here we confine attention to a particular constitutive model for such materials that is of generalized Varga type. The corresponding incompressible model has been shown to be particularly tractable analytically. We examine the response of the slightly compressible material to some nonhomogeneous deformations and compare the results with those for the corresponding incompressible model. Thus the effects of slight compressibility for some basic nonhomogeneous deformations are explicitly assessed. The results are fundamental to the analytical modeling of almost incompressible hyperelastic materials and are of importance in the context of finite element methods where slight compressibility is usually introduced to avoid element locking due to the incompressibility constraint. It is also shown that even for slightly compressible materials, the volume change can be significant in certain situations.      

Transformations of graphite and boron nitride in shock waves

Peculiarities of shock adiabat of graphite are attributed to the graphite–diamond transformation. However only a very small amount of diamond can be recovered from pure shocked graphite with a density approaching the theoretical value. In order to interpret this fact, accessible data concerning the behaviour of graphite under static and dynamic load have been analysed. An additional peculiarity of the shock adiabat of graphite has been found at 12 GPa by analysing compressibility data. It has been attributed to shearing in the basal planes that paves the way for deformation of the planes. An isotherm of cold compression of graphite can be constructed on the basis of the results from theoretical modelling published in the literature. Another isotherm, fitting experimental data, has been proposed. An isotherm for graphitic boron nitride has been also proposed. The isotherms have been used in the interpretation of the peculiarities of shock adiabats. It has been shown that the so-called “mixed-phase” region is an apparent compressibility curve. Energy evaluations based on the isotherms have proved that the peculiarities of the shock adiabat of graphite correspond to the formation of hexagonal instead of cubic diamond. Similarly the formation of the wurtzite modification of BN is responsible for the peculiarities of the shock adiabat of BN. Literature data concerning the mechanism of the polymorphous transformations of graphite and BN in shock waves have been reviewed. On the basis of proposed isotherms of cold compression, the activation energy has been appraised and an equation of kinetics proposed. The equation has been analysed by comparing results of theoretical modelling and accessible experimental data. Received 11 March 1993 / Accepted 15 September 1993     

Brain tissue deforms similarly to filled elastomers and follows consolidation theory

Slow, large deformations of human brain tissue—accompanying cranial vault deformation induced by positional plagiocephaly, occurring during hydrocephalus, and in the convolutional development—has surprisingly received scarce mechanical investigation. Since the effects of these deformations may be important, we performed a systematic series of in vitro experiments on human brain tissue, revealing the following features. (i) Under uniaxial (quasi-static), cyclic loading, brain tissue exhibits a peculiar nonlinear mechanical behaviour, exhibiting hysteresis, Mullins effect and residual strain, qualitatively similar to that observed in filled elastomers. As a consequence, the loading and unloading uniaxial curves have been found to follow the Ogden nonlinear elastic theory of rubber (and its variants to include Mullins effect and permanent strain). (ii) Loaded up to failure, the “shape” of the stress/strain curve qualitatively changes, evidencing softening related to local failure. (iii) Uniaxial (quasi-static) strain experiments under controlled drainage conditions provide the first direct evidence that the tissue obeys consolidation theory involving fluid migration, with properties similar to fine soils, but having much smaller volumetric compressibility. (iv) Our experimental findings also support the existence of a viscous component of the solid phase deformation.Brain tissue should, therefore, be modelled as a porous, fluid-saturated, nonlinear solid with very small volumetric (drained) compressibility.     

Evaporation heat transfer and flow characteristics of R-134a flowing through internally grooved tubes

This article describes experimental investigations of the heat transfer coefficient and pressure drop of R-134a flowing inside internally grooved tubes. The test tubes are one smooth tube and four grooved tubes. All test tubes are made from type 304 stainless steel, have an inner diameter of 7.1 mm, are 2,000 mm long and are installed horizontally. The test section is uniformly heated by a DC power supply to create evaporation conditions. The groove depth of all grooved tubes is fixed at 0.2 mm. The experimental conditions are conducted at saturation temperatures of 20, 25 and 30°C, heat fluxes of 5, 10 and 15 kW/m², and mass fluxes of 300, 500 and 700 kg/m² s. The effects of groove pitch, mass flux, heat flux, and saturation temperature on heat transfer coefficient and frictional pressure drop are discussed. The results illustrate that the grooved tubes have a significant effect on the heat transfer coefficient and frictional pressure drop augmentations.     

Simulation of jet disintegration in a supercritical reactor

This work deals with the simulation of jet disintegration in supercritical conditions. In this validation case, nitrogen at 140 K is injected into a reactor at 298 K in conditions of turbulent flow. The simulation results are confronted with experimental data from literature. The simulation also compares the use of incompressible and compressible models in order to justify the compressibility assumption frequently used in literature. Both models fit well the experimental results indicating that in the investigated conditions, compressibility effects can be neglected.     

Measurement of the Dynamic Bulk and Shear Response of Soft Human Tissues

Traditionally, Kolsky bars are used to study the dynamic response of hard materials in uniaxial compression, tension or torsion. We present modifications to the technique that allow loading of a soft tissue specimen in (a) hydrostatic compression and (b) simple shear. The first modification is designed to determine the pressure vs. volume behavior of each material, and thence to extract a measure of the dynamic compressibility or equivalently of the bulk modulus. The second modification is designed to develop the shear stress versus shear strain behavior for a near-simple shear experiment. The critically important questions of the proper acquisition of human tissue samples and protocols for appropriate experimentation have also been addressed. The experimental techniques and the results are discussed in detail and the results compared to finite element simulations. We present examples of the dynamic response of typical tissue simulants as well as human liver and stomach tissues.     

Theory of a gas bearing with spiral grooves,taking account of the effects of slip and of local compressibility

The theory of a spiral bearing with a quasi-incompressible lubricant, proposed by Whipple [1], and expanded in [2–4], deviates from experimental investigations, particularly with large values of the compressibility parameter and intermediate values of the Knudsen numbers. Investigations carried out in simplified models of a spiral bearing [6, 7] have shown that the compressibility of a gas layer lowers its bearing capacity. This effect manifests itself even more strongly with intermediate values of the Knudsen number. Therefore, attempts to take account of the effect of slip within the framework of the theory of a quasi-incompressible layer [8] do not achieve their purpose. The proposed theory of a spiral bearing takes account of the combined influence of both effects, and is in agreement with experiment.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 84–93, September–October, 1971.The authors thank V. Idel'son, who carried out the required calculations at the Computational Center of the Siberian Branch of the Academy of Sciences of the USSR.     

Modeling gas dynamic particle interaction in rarefied gas flows

In the case of slow, so-called creeping viscous flow a considerable amount of information on the interaction between individual particles or groups of particles has been obtained theoretically by means of the Stokes equations [1]. Regimes in which it is necessary to take inertia, compressibility and the rarefaction of the medium into account (see, for example, [2]) have received much less attention, especially from the experimental standpoint. As a rule, previous experiments have involved freely falling particles in a viscous fluid, but the experimental possibilities of determining the forces and moments exerted on a particle by a liquid or gas at small Reynolds numbers can be considerably expanded by investigating subsonic, flows of rarefied gas obtained with the aid of porous media. The results of such studies of the flow past a spherical particle and its interaction with another particle are presented in this paper.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 152–157, January–February, 1987.     

A Rational Procedure for the Experimental Evaluation of the Elastic Coefficients in a Linearized Formulation of Biphasic Media with Compressible Constituents

This article illustrates the specialization to infinitesimal perturbations of the geometrically nonlinear formulation describing the macroscopic dynamic behavior of biphasic media presented in (Serpieri and Rosati J Mech Phys Solids 59(4):841–862, 2011) where, based on Lagrangian mechanics arguments, a consistent mathematical theory of fluid-saturated poroelastic material is developed accounting for the property that both constituent materials are microscopically compressible. The primary contribution of this work is the employment of the linearized model in the development of a general procedure for the determination of the relevant elastic coefficients on the basis of the data provided by a set of experimental measures analogous to the one originally considered by Biot and Willis consisting of a shear test, an unjacketed compressibility test and two jacketed tests in which drainage is either completely allowed or prevented. The linearization of the formulation is first presented for a generic configuration in which both phases are undergoing a generic motion. Subsequently, a specific study is presented on the case that the media is motionless, homogeneous, and isotropic in the reference configuration, which is typical of common experimental set-ups for static tests. A numerical example is shown and a general relation between the elastic coefficients and Biot’s constant is derived which consistently accounts for the compressibility of all materials.     

Interior ballistics of a powder-driven pulsed water cannon

Results of theoretical and experimental studies of the interior ballistics of a powder-driven pulsed cannon are presented. The liquid flow in the facility is considered in quasistationary and nonstationary formulations. Conditions for the applicability of the quasistationary approximation are determined. The effect of the compressibility of the liquid on the performance of the pulsed cannon is evaluated. Calculation results are compared with experimental data obtained on a particular installation. Donetsk State University, Donetsk 83055, Ukraine. Translated from Prikladaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 3, pp. 118–124, May–June, 2000.     

Experimental investigations of the compressibility of argillaceous soils subjected to underground explosions

The results of experimental investigations of the compressibility of argillaceous soils (loess loams, loams, and clays) subjected to underground explosions are discussed. The data concerning the deformation at the shock-wave front, and their comparison with data concerning residual deformations indicate that the viscoplastic soil properties strongly influence the soil compressibility for short-term loads originating from underground explosions. The conclusions which were previously drawn in [1] are qualitatively and quantitatively confirmed.