Incompressible Medium Research Articles

Lyapunov instability of the stationary flows of polymeric fluid with constant flow rate

AbstractWe study a rheological Pokrovski‐Vinogradov model for the flows of solutions and melts of incompressible viscoelastic polymeric medium in case of a flow in an infinite plane channel with perforated walls. We prove the linear Lyapunov instability of the base solution with the constant flow rate in a perturbation class, periodic with respect to the variable, changing along the channel wall.

Models for predicting the test medium temperature during hydrotesting pipe segments based on measured ambient and pipe wall temperatures

Strength and leak tests of newly constructed or modified pipeline sections or piping assemblies are required by code. This is often conducted by pressurizing incompressible medium, such as water, water-methanol or water-propylene glycol (PG) mixtures while the system is sealed. Major challenges are invariably encountered with leak tests, which rely on correlating changes in the test pressure to the test fluid temperature (DP/DT) to discern if a leak exists. Often, the temperature variations are never correlated to pressure variations for several reasons: 1) access to the test fluid temperature is not available for several reasons outlined in the paper, therefore, the measured external pipe wall temperature is taken instead and is assumed to be equal to the test fluid inside the pipe, 2) the pipe wall temperature variations are generally significant due to variation in the ambient temperature or wind speed (in the case of exposed pipe), 3) the pipe section may not be restrained from axial movement, 4) tables and calculations of DP/DT are readily available for pure water and often erroneously assumed to be applicable to other test media such as mixtures of water-methanol or water-PG, which are vastly different than pure water, and 5) some pipe sections may be partially exposed to ambient and partially buried. The present work addresses these factors via development of high-fidelity models based on governing equations that accounts for the respective effects in a more fundamental manner. It was found that it is paramount to use the correct test medium isothermal bulk modulus and its coefficient of volumetric thermal expansion at the test conditions as these two parameters have the most significant influence on DP/DT. Due to these properties, water-PG was shown to result in the highest DP/DT, which poses the greatest challenges during hydrotesting in the field. Additionally, it was found that the difference between the pipe external wall temperature and the test fluid average temperature for the case of exposed pipe increases as Biot number increases. The developed thermal transient models were compared to three field hydrotests of different pipe sizes, namely DN900, DN150 and DN50, all above ground subject to cross wind and variations in ambient air temperatures.

Averaging of turbulent micropolar media: turbulent couple-stress, heat flux, and energy.

The equations governing turbulent flow of micropolar incompressible media are studied using the Reynolds decomposition. The average force-stress is augmented by the Reynolds stress of the same form as in classical continuum mechanics, while the average couple-stress is augmented by a new turbulent couple-stress. Additionally, the average heat flux and internal energy density are modified from the expressions known in classical turbulent fluids. On this basis, the entropy inequality is examined in both classical and micropolar continuum settings.

Waves Propagation at an Interface of Two Liquid Saturated Porous Solid Half Spaces

This manuscript is concerned with reflected and refracted elastic waves when transverse waves are incident at the interface between two fluid-saturated porous solid half-spaces. Perfect and imperfect both types of contact of the interfaces are discussed. It has observed that for a specific model the behaviour of different reflected, refracted waves and the ratio of their amplitudes depend on the physical properties of the medium, angle of emergence, the porosity of the fluid, the porosity of fluid drenched incompressible porous medium and stiffness of imperfect boundary. The computer numerically results for this model have been presented graphically by taking a particular case of empty porous solid.

Mixed Convection Fluid Flow Over a Vertical Cone Saturated Porous Media with Double Dispersion and Injection/Suction Effects

This study reflects the combined impact of double dispersion and injection/suction on mixed convection flow over a vertical cone in an incompressible viscous fluid-saturated porous medium. The governing equations of the model are non-dimensionalized throughout the appropriate transformations and received non-similarity equations are solved numerically via bivariate Chebyshev spectral collocation quasi-linearization method. Computations are reported here graphically to analyze the impact of governing parameters at the different stream-wise locations on the velocity, temperatures, and concentration profiles, like Prandtl number, Schmidt number, buoyancy parameter, injection and suction parameter, thermal dispersion, and Solutal dispersion parameters. Skin friction, heat, and mass transfer rates are also reported in graphical and tabular form. To establish the efficiency of the adopted numerical technique, we have made a comparison with the earlier published results and found them to be of great consent. The residual analysis study also illustrated, which proves the convergence of the present results.

On attached masses of panels oscillating in incompressible medium

The paper discusses small oscillations of a panel in an incompressible medium. Air can be considered an incompressible medium during modal tests of solar array panels for spacecraft deployed on the ground in a lab environment. A panel is represented as a two-sided boundary surface. Conditions are determined for applicability of the potential motion of the medium. Calculation of the attached mass is reduced to the solution of the Neumann boundary value problem. To solve the boundary value problem, the method of boundary elements is used in the piecewise constant approximation variant, which provides a solution of the hypersingular boundary integral equation. Numerical solutions are obtained for the three fundamental modes of rectangular panels. The obtained numerical values are refined using non-linear Shanks transformation. Dependence of attached mass on panel elongation and the amount of the gap between its fragments is studied. For any in-plane oscillation mode of a panel fragment, the attached mass is determined using the principle of linear superposition. An estimate is given of the effect of the distance from the panel to the wall on the attached mass value. Key words: oscillations, incompressible medium, air, attached mass, rectangular panels, boundary elements method.

ON ATTACHED MASSES OF PANELS OSCILLATING IN INCOMPRESSIBLE MEDIUM

The paper discusses small oscillations of a panel in an incompressible medium. Air can be considered an incompressible medium during modal tests of solar array panels for spacecraft deployed on the ground in a lab environment. A panel is represented as a two-sided boundary surface. Conditions are determined for applicability of the potential motion of the medium. Calculation of the attached mass is reduced to the solution of the Neumann boundary value problem. To solve the boundary value problem, the method of boundary elements is used in the piecewise constant approximation variant, which provides a solution of the hypersingular boundary integral equation. Numerical solutions are obtained for the three fundamental modes of rectangular panels. The obtained numerical values are refined using non-linear Shanks transformation. Dependence of attached mass on panel elongation and the amount of the gap between its fragments is studied. For any in-plane oscillation mode of a panel fragment, the attached mass is determined using the principle of linear superposition. An estimate is given of the effect of the distance from the panel to the wall on the attached mass value. Key words: oscillations, incompressible medium, air, attached mass, rectangular panels, boundary elements method.

Safety-enhanced control strategy of a power soft robot driven by hydraulic artificial muscles

Power soft robots—defined as novel robots driven by powerful soft actuators, achieving both powerfulness and softness—are potentially suitable for complex collaborative tasks, and an approach to actuating a power soft robot is the McKibben artificial muscle. This study aims to show the potential of hydraulic artificial muscles to be implemented in a power soft robot with high safety, including higher stability against sudden load separation or impact disturbance, and appropriate dynamic compliance. The stability of a manipulator arm driven by hydraulic muscle actuators is experimentally proven to be higher than that of pneumatic muscle actuators when the stored elastic energy is instantaneously released. Therefore, the hydraulic muscle actuator is a better candidate for actuating a power soft robot. By taking advantage of the incompressible liquid medium and the compliant structure of a hydraulic muscle, a second-order impedance control strategy with a braking method is proposed to improve dynamic compliance without sacrificing the safety features of hydraulic muscles. The results show that the manipulator can be easily shifted by a several-kilogram-level external force and react safely against sudden load change with low angular velocity by the proposed impedance control.

Shock waves in an incompressible anisotropic elastoplastic medium with hardening and their structures

Shock waves and their structures in an incompressible anisotropic elastoplastic medium with hardening are studied. It is assumed that the processes in the structure are determined by stress relaxation, which ensures medium hardening. It is found that a shock adiabat can consist not only of one-dimensional, but also of two-dimensional branches.

Study on Fluid Descends Vertically on Static Fluid Using Moving Particle Semi-Implicit Method

The process of fluid descend vertically on static fluid has been studied through experiment and simulation by using Moving Particle Semi-Implicit (MPS) method. MPS has been developed by Koshizuka and Oka (1996). MPS method is a particle method based on the Lagrangian calculation for incompressible medium and does not rely on grid system. This study has been done by doing simulation first then validated by experiment. Water and cooking oil were used in the experiment. This study was carried out to analyze distance and density influence in the height of static fluid bursting process. The experiments were conducted in an acrylic box with the dimension 150 mm x 40 mm x 30 mm and a bottle with height of 100 mm and the nozzle of bottle was 26 mm. The distance between nozzle and surface of fluid inside box is varied for 100 mm and 200 mm. The results show that in the same height, water will be more difficult to be moved than cooking oil because water has bigger density. The distance between nozzle and fluid surface inside the box will affect at the pressure which is received by the fluid. Higher distance will create higher pressure so that fluid inside the box will be moved easier and more fluid will split out to the box. It also gives some influence in the final condition of remaining fluid in the acrylic box.

Free boundary limit of a tumor growth model with nutrient

Both compressible and incompressible porous medium models are used in the literature to describe the mechanical properties of living tissues. These two classes of models can be related using a stiff pressure law. In the incompressible limit, the compressible model generates a free boundary problem of Hele-Shaw type where incompressibility holds in the saturated phase.Here we consider the case with a nutrient. Then, a badly coupled system of equations describes the cell density number and the nutrient concentration. For that reason, the derivation of the free boundary (incompressible) limit was an open problem, in particular a difficulty is to establish the so-called complementarity relation which allows to recover the pressure using an elliptic equation. To establish the limit, we use two new ideas. The first idea, also used recently for related problems, is to extend the usual Aronson-Bénilan estimate in L∞ to an L2 setting. The second idea is to derive a sharp uniform L4 estimate on the pressure gradient, independently of the space dimension.

Parameter Robust Preconditioning by Congruence for Multiple-Network Poroelasticity

The mechanical behavior of a poroelastic medium permeated by multiple interacting fluid networks can be described by a system of time-dependent partial differential equations known as the multiple-network poroelasticity (MPET) equations or multiporosity/multipermeability systems. These equations generalize Biot's equations, which describe the mechanics of the one network case. The efficient numerical solution of the MPET equations is challenging, in part due to the complexity of the system and in part due to the presence of interacting parameter regimes. In this paper, we present a new strategy for efficiently and robustly solving the MPET equations numerically. In particular, we discuss an approach to formulating finite element methods and associated preconditioners for the MPET equations based on simultaneous diagonalization of the element matrices. We demonstrate the technique for the multicompartment Darcy equations, with large exchange variability, and the MPET equations for a nearly incompressible medium with large exchange variability. The approach is based on designing transformations of variables that simultaneously diagonalize (by congruence) the equations' key operators and subsequently constructing parameter-robust block diagonal preconditioners for the transformed system. The proposed approach is supported by theoretical considerations as well as by numerical results.

АНАЛИТИЧЕСКИЕ И ЧИСЛЕННЫЕ ИССЛЕДОВАНИЯ СВОБОДНЫХ КОЛЕБАНИЙ ЦИЛИНДРИЧЕСКИХ ОБОЛОЧЕК С АКУСТИЧЕСКОЙ СРЕДОЙ

The research materials are related to the problem of ensuring vibration resistance of pipelines exposed to dynamic loads, for which increased vibration is the main cause of damage. The solution to this problem involves studying the parameters of free vibrations of the structure. The paper solves the problem of determining the natural frequencies and forms of vibrations of a section of a circular cylindrical shell filled with an medium considered in the acoustic approximation. The results of studies of the parameters of free vibrations were obtained both by the analytical method of shell theory based on the Kirchhoff-Love hypotheses, and using the finite element complex of engineering analysis ANSYS. It is shown that the influence of the medium density on the parameters of free vibrations of the shell depends on the ratio of the shell thickness to its radius it turns out to be significant only for the shape of vibrations associated with bending deformation, and insignificant for forms associated with deformations of the middle layer. A comparative analysis of the results of calculations obtained for models of compressible and incompressible medium shows that when solving the problem of determining the parameters of free vibrations of the shell, the compressibility of the medium can be neglected. At the same time, to solve practical problems that require taking into account the full spectrum of natural frequencies of the shell–medium system, a compressible medium model should be used, in which the results on the effect of shell stiffness on the frequency spectrum of the medium volume are obtained. When solving practical problems of pipeline systems vibration, the use of the finite element method in a coupled formulation is an effective tool that allows us to consider all physical processes taking into account their mutual influence on each other.

Assessment of the Influence of Water Saturation and Capillary Pressure Gradients on Size Formation of Two-Phase Filtration Zone in Compressed Low-Permeable Reservoir

The paper examines the influence of capillary pressure and water saturation ratio gradients on the size of the two-phase filtration zone during flooding of a low-permeable reservoir. Variations of water saturation ratio s in the zone of two-phase filtration are associated with the pressure variation of water injected into the reservoir; moreover the law of variation of water saturation ratio s(r, t) must correspond to the variation of injection pressure, i.e. it must be described by the same functions, as the functions of water pressure variation, but be subject to its own boundary conditions. The paper considers five options of s(r, t) dependency on time and coordinates.
 In order to estimate the influence of formation and fluid compressibility, the authors examine Rapoport – Lis model for incompressible media with a violated lower limit for Darcy’s law application and a time-dependent radius of oil displacement by water. When the lower limit for Darcy’s law application is violated, the radius of the displacement front depends on the value of capillary pressure gradient and the assignment of s function. 
 It is shown that displacement front radii contain coefficients that carry information about physical properties of the reservoir and the displacement fluid. A comparison of two-phase filtration radii for incompressible and compressible reservoirs is performed.
 The influence of capillary pressure gradient and functional dependencies of water saturation ratio on oil displacement in low-permeable reservoirs is assessed.
 It is identified that capillary pressure gradient has practically no effect on the size of the two-phase filtration zone and the share of water in the arbitrary point of the formation, whereas the variation of water saturation ratio and reservoir compressibility exert a significant influence thereupon.

MHD model of an incompressible polymeric fluid. Linear instability of the resting state

We study the linear stability of a resting state for a generalization of the basic rheological Pokrovski-Vinogradov model for flows of solutions and melts of an incompressible viscoelastic polymeric medium to the nonisothermal case under the influence of magnetic field. We prove that the corresponding linearized problem describing magnetohydrodynamic flows of polymers in an infinite plane channel has the following property: for certain values of the conduction current which is given on the electrodes, i.e. on the channel boundaries, the problem has solutions whose amplitude grows exponentially (in the class of functions periodic along the channel).

Some Approximate Solutions of the Dynamic Problem of Axisymmetric Shock Deformation of a Previously Unstressed Incompressible Elastic Medium

Approximate theoretical solutions are presented for the boundary value problem of the shock load on the boundary of a circular cylindrical cavity in the space occupied by an incompressible elastic medium undeformed previously. We assume that the shock load causes the movement of the medium particles along helical trajectories. Data on the types and velocities of shock waves are based on the analysis of the dynamic conditions for the compatibility of discontinuities; and these conditions are supplemented by the relations along the characteristic directions. We show that the leading front of the dynamic process in an undeformed previously medium is a plane-polarized shock wave which is simultaneously included in one of the families of characteristics. This property results in the constancy of shear direction on the plane-polarized shock wave. This condition makes it possible to significantly simplify the obtaining of approximate theoretical solutions for the near-front neighborhood of the shock wave. The two approximate solutions of the problem are presented. One of them bases on solving a system of evolutionary equations that was obtained using the matched asymptotic expansions method; and the second solution, on a version of the ray method.

Variational Formulation of Linear Equations of Coupled Thermohydrodynamics and Heat Conductivity

We consider the coupled processes of thermohydrodynamics and heat conduction and construct a variational model of such coupled problems using four-dimensional space-time continuum where time is an equal coordinate along with spatial coordinates. In this consideration 3D subspace of generalized four-dimensional pseudo-continuum is associated with three-dimension deformed media. In the general case we consider irreversible processes and use the variational principle of possible displacements and the variational Sedov’s principle to construct variation model. It is assumed that the 4D pseudo-continuum considered below is transversely isotropic in the direction of the unit vector of time. Thus, an asymmetric 4D stress tensor preserves the symmetry properties with respect to spatial tangential stresses in 3D subspaces. It is shown that the proposed version of the model allows us to formulate the full range of consistent thermomechanical and thermodynamic physical relations, and the system of governing equations includes, as special cases, the equations of thermoelasticity, thermohydrodynamics, the linear Navier–Stokes equations for compressible and incompressible media, the equations of heat balance with the laws of thermal conductivity of Fourier, Maxwell–Cattaneo.

Transversely isotropic magnetoactive elastomers: theory and experiments

The current contribution is concerned with the development of novel constitutive equations for anisotropic magnetoactive elastomers (MAEs). A hyperelastic material model for an incompressible magnetoelastic medium representing transversely isotropic MAEs has been developed to investigate their response behavior in the presence of the applied magnetic field while undergoing finite deformation. Transversely isotropic MAE samples in circular cylindrical geometry with 15% iron particle volume fraction are then fabricated and experimentally tested to measure their permeability and torque–twist response. The experimental results have then been effectively utilized to identify the constant material parameters in the proposed material model. Finally, the accuracy and validity of the proposed constitutive equations are demonstrated through the comparison of the simulation and experimental results.

Nonstationary Axisymmetric Elastic Processes in an Incompressible Medium with Preliminary Finite Irreversible Deformations

The kinematic equations of the multiplicative model of large elastoplastic deformations are generalized for hardening materials with different principal directions of the stress and plastic strain rate tensors. By taking into account the intermediate configuration, an algorithm is proposed for analyzing dynamic elastic processes in a medium with preliminary irreversible deformations. The use of the algorithm is illustrated by the example of cylindrical elastic shock waves in an incompressible elastoplastic medium.

Simple One-Dimensional Waves in an Incompressible Anisotropic Elastoplastic Medium with Hardening

We study simple one-dimensional waves (Riemann waves) in an incompressible anisotropic elastoplastic medium with hardening. The motion is parallel to the planes of constant phase. We show that there exist two types of such waves: fast and slow waves, whose velocities are different everywhere except for some points in the plane of stress components. The medium is assumed to be nonlinear and defined by its elastic properties as well as by conditions for the formation of plastic deformations. We find the velocities of the characteristics that carry the Riemann waves, and analyze the evolution of the Riemann waves and the overturning conditions for these waves.