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Geomaterials such as vuggy carbonates are known to exhibit multiple spatial scales. A common manifestation of spatial scales is the presence of (at least) two different scales of pores with different hydromechanical properties. Moreover, these pore-networks are connected through fissures and conduits. Although some models are available in the literature to describe flows in such media, they lack a strong theoretical basis. This paper aims to fill this gap in knowledge by providing the theoretical foundation for the flow of incompressible single-phase fluids in rigid porous media that exhibit double porosity/permeability. We first obtain a mathematical model by combining the theory of interacting continua and the maximization of rate of dissipation (MRD) hypothesis, and thereby provide a firm thermodynamic underpinning. The governing equations of the model are a system of elliptic partial differential equations (PDEs) under a steady-state response and a system of parabolic PDEs under a transient response. We then present, along with mathematical proofs, several important mathematical properties that the solutions to the model satisfy. We also present several canonical problems with analytical solutions which are used to gain insights into the velocity and pressure profiles, and the mass transfer across the two pore-networks. In particular, we highlight how the solutions under the double porosity/permeability differ from the corresponding ones under Darcy equations. [ABSTRACT FROM AUTHOR]

When interacting with a virtual object (VO) through a haptic device, it is crucial to feedback a contact force to the human operator (HO) that displays the VO physical properties with high fidelity. The core challenge, here, is to expand the renderable range of these properties, including larger stiffness and smaller inertia, at the available sampling rate. To address this challenge, a framework entitled high-fidelity contact rendering (HFCR) has been developed in this paper. The framework consists of three main strategies: an energy-based rendering of the contact force, smooth transition (ST) between contact modes, and remaining leak dissipation (LD). The essence of these strategies is to make the VO emulate its continuous-time counterpart. This is achieved via physically meaningful modifications in the constitutive relations to suppress artificial energy leaks. The strategies are first developed for the one-dimensional (ID) canonical VO; then, generalization to the multivariable case is discussed. Renderability has been analyzed exploring different stability criteria within a unified approach. This leads to stability charts and identification of renderable range of properties in the presence and absence of the HO. The framework has been validated through simulation and various experiments. Results verify its promising aspects for various scenarios including sustained contact and sudden collision events with or without the HO. [ABSTRACT FROM AUTHOR]

Hydrodynamic phase field models for multiphase fluids formulated using volume fractions of incompressible fluid components do not normally conserve mass. In this paper, we formulate phase field theories for mixtures of multiple incompressible fluids, using volume fractions, to ensure conservation of mass and momentum for the fluid mixture as well as the total volume for each fluid phase. In this formulation, the mass-average velocity is nonsolenoidal when the densities of incompressible fluid components in the mixture are not equal, making it a bona fide compressible model subject to an internal constraint. Derivation of mass conservation and energy dissipation in phase field models based on both Allen-Cahn dynamics and Cahn-Hilliard dynamics are presented. One salient feature of the phase field models is that the hydrostatic pressure is coupled with the transport of the volume fractions making the momentum transport and the volume fraction transport fully coupled in light of the mass conservation. Near equilibrium dynamics are explored using a linear analysis. In the case of binary fluid mixtures, one potential growth mode is identified in all the models for a class of free energy, which has been adopted for multiphase fluids. The growth is either absent for all waves or of a longwave feature. [ABSTRACT FROM AUTHOR]

Fluid compressibility has a major influence on the efficiency of switch-mode hydraulic circuits due to the release of energy stored in fluid compression during each switching cycle and the increased flow rate through the high-speed valve during transition events. Multiple models existing in the literature for fluid bulk modulus, the inverse of the com-pressibility, are reviewed and compared with regards to their applicability to a switch-mode circuit. In this work, a computational model is constructed of the primary energy losses in a generic switch-mode hydraulic circuit with emphasis on losses created by fluid compressibility. The model is used in a computational experiment where the system pres-sure, switched volume, and fraction of air entrained in the hydraulic fluid are varied through multiple levels. The computational experiments resulted in switch-mode circuit volumetric efficiencies that ranged from 51% to 95%. The dominant energy loss is due to throttling through the ports of the high-speed valve during valve transition events. The throttling losses increase with the fraction of entrained air and the volume of fluid experi-encing pressure fluctuations, with a smaller overall influence seen as a result of the sys-tem pressure. The results of the computational experiment indicate that to achieve high efficiency in switch-mode hydraulic circuits, it is critical to minimize both the entrained air in the hydraulic fluid and the fluid volume beh\'een the high-speed valve and the pump, motor, or actuator. These computational results are compared with experimental results in Part II of this two part paper series. [ABSTRACT FROM AUTHOR]

This paper presents a numerical solution of the hyperbolic heat conduction equation in a thermal barrier coating (TBC) structure under an imposed heat flux on the exterior of the TBC. The non-Fourier heat conduction equation is used to model the heat conduction in the TBC system that predicts the heat flux and the temperature distribution. This study presents a more realistic approach to evaluate in-service peiformance of thin layers of TBCs typically found in hot sections of land based and aircraft gas turbine engines. In such ultrafast heat conduction systems, the orders of magnitude of the time and space dimensions are extremely short which renders the traditional Fourier conduction law, with its implicit assumption of infinite speed of thermal propagation, inaccurate. There is, therefore, the need for an advanced modeling approach for the thermal transport phe-nomenon taking place in microscale systems. A hyperbolic heat conduction model can be used to predict accurately the transient temperature distribution of thermal barrier structures of turbine blades. The hyperbolic heat conduction equations are solved numerically using a new numerical scheme codenamed the mean value finite volume method (MVFVM). The numerical method yields minimal numerical dissipation and dispersion errors and captures the discontinuities such as the thermal wave front in the solution with reliable accuracy. Compared with some traditional numerical methods, the MVFVM method provides the ability to model the behavior of the single phase lag thermal wave following its reflection from domain boundary surfaces. In addition, parametric studies of properties of the substrate on the temperature and the heat flux distributions in the TBC revealed that relaxation time of the substrate material, unlike the thermal dijfusivity and thermal conductivity has very little effect on the transient thermal response in the TBC. The study further showed that for thin film structures subject to short time durations of heat flux, the hyperbolic model yields more realistic results than the parabolic model. [ABSTRACT FROM AUTHOR]

This paper reviews models of helical cable behavior with an emphasis on recent models that study internal cable damping. Cable models are categorized into three major classes consisting of thin rod models, semicontinuous models, and beam models. Research on cable vibration damping resulting from internal factors is investigated and related, with conclusions supported by multiple bodies of work highlighted and inconsistencies that may require further study noted. Internal damping mechanisms due to interwire friction, variable bending stiffness, and internal and viscoelastic dissipation are explored with specific damping terms presented for the various models. Damping through inclusion of friction forces, viscoelastic shear effects, or bending stiffness as a function of cable curvature and wire properties must be included to produce a realistic cable model. [ABSTRACT FROM AUTHOR]