scholarly journals Invariance Properties of the Entropy Production, and the Entropic Pairing of Inertial Frames of Reference by Shear-Flow Systems

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1515
Author(s):  
Robert K. Niven
Keyword(s):  
Fluid Flow ◽  
Shear Flow ◽  
Entropy Production ◽  
Absolute Temperature ◽  
Frames Of Reference ◽  
Invariance Property ◽  
Solid Boundary ◽  
Galilean Invariance ◽  
Invariance Properties ◽  
Inertial Frames

This study examines the invariance properties of the thermodynamic entropy production in its global (integral), local (differential), bilinear, and macroscopic formulations, including dimensional scaling, invariance to fixed displacements, rotations or reflections of the coordinates, time antisymmetry, Galilean invariance, and Lie point symmetry. The Lie invariance is shown to be the most general, encompassing the other invariances. In a shear-flow system involving fluid flow relative to a solid boundary at steady state, the Galilean invariance property is then shown to preference a unique pair of inertial frames of reference—here termed an entropic pair—respectively moving with the solid or the mean fluid flow. This challenges the Newtonian viewpoint that all inertial frames of reference are equivalent. Furthermore, the existence of a shear flow subsystem with an entropic pair different to that of the surrounding system, or a subsystem with one or more changing entropic pair(s), requires a source of negentropy—a power source scaled by an absolute temperature—to drive the subsystem. Through the analysis of different shear flow subsystems, we present a series of governing principles to describe their entropic pairing properties and sources of negentropy. These are unaffected by Galilean transformations, and so can be understood to “lie above” the Galilean inertial framework of Newtonian mechanics. The analyses provide a new perspective into the field of entropic mechanics, the study of the relative motions of objects with friction.

scholarly journals Numerical Research of Fluid Flow and Solute Transport in Rough Fractures under Different Normal Stress

Geofluids ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Min Wang ◽  
Qifeng Guo ◽  
Pengfei Shan ◽  
Meifeng Cai ◽  
Fenhua Ren ◽  
...  
Keyword(s):  
Fluid Flow ◽  
Shear Flow ◽  
Solute Transport ◽  
Normal Stress ◽  
Three Dimensional ◽  
Dispersive Transport ◽  
Mean Velocity ◽  
Flow Test ◽  
Hydraulic Aperture ◽  
Mechanical Aperture

The effects of roughness and normal stress on hydraulic properties of fractures are significant during the coupled shear flow test. Knowing the laws of fluid flow and solute transport in fractures is essential to ensure the nature and safety of geological projects. Although many experiments and numerical simulations of coupled shear flow test have been conducted, there is still a lack of research on using the full Navier-Stokes (N-S) equation to solve the real flow characteristics of fluid in three-dimensional rough fractures. The main purpose of this paper is to study the influence of roughness and normal stress on the fluid flow and solute transport through fractures under the constant normal stiffness boundary condition. Based on the corrected successive random addition (SRA) algorithm, fracture surfaces with different roughness expressed by the Hurst coefficient ( H ) were generated. By applying a shear displacement of 5 mm, the sheared fracture models with normal stresses of 1 MPa, 3 MPa, and 5 MPa were obtained, respectively. The hydraulic characteristics of three-dimensional fractures were analyzed by solving the full N-S equation. The particle tracking method was employed to obtain the breakthrough curves based on the calculated flow field. The numerical method was verified with experimental results. It has been found that, for the same normal stress, the smaller the fracture H value is (i.e., more tough the fracture is), the larger the mechanical aperture is. The ratio of hydraulic aperture to mechanical aperture ( e h / e m ) decreases with the increasing of normal stress. The smaller the H value, the effect of the normal stress on the ratio e h / e m is more significant. The variation of transmissivity of fractures with the flow rate exhibits similar manner with that of e h / e m . With the normal stress and H value increasing, the mean velocity of particles becomes higher and more particles move to the outlet boundary. The dispersive transport behavior becomes obvious when normal stress is larger.

Effect of Axis Ratio on Fluid Flow Around an Elliptic Cylinder—A Numerical Study

2013 ◽  
Vol 135 (11) ◽  
Author(s):  
S. Kalyana Raman ◽  
K. Arul Prakash ◽  
S. Vengadesan
Keyword(s):  
Fluid Flow ◽  
Drag Coefficient ◽  
Strouhal Number ◽  
Vortex Shedding ◽  
Numerical Study ◽  
Elliptic Cylinder ◽  
Solid Boundary ◽  
Axis Ratio ◽  
Moderate Reynolds Number ◽  
Wake Formation

The bluff body simulations over canonical forms like circular and square cylinders are very well studied and the correlations for bulk parameters like mean drag coefficient and Strouhal numbers for the same are reported widely. In the case of elliptic cylinder, the literature is very sparse, especially for moderate Reynolds number (Re). Hence, in this work, a detailed study about fluid flow characteristics over an elliptic cylinder placed in a free stream is performed. Simulations are carried out for different Re ranging from 50 to 500 with axis ratio (AR) varied between 0.1 to 1.0 in steps of 0.1. Immersed boundary method is used for the solid boundary condition implementation which avoids the grid generation for each AR and a single Cartesian grid is used for all the simulations. The effect of AR for various Reynolds numbers is also focused on using the in-house code. The influence of AR is phenomenal for all the Re and the values of wake length, drag coefficient, and Strouhal number decrease with decreasing AR for a particular Re. The critical ARs, for vortex shedding and wake formation, are identified for various Re. Detailed correlations for wake length, critical ARs for vortex shedding and wake formation, mean drag coefficient and Strouhal number, in terms of AR, are reported in this work.

A PHENOMENOLOGICAL CONSTITUTIVE MODEL OF NON-CONVENTIONAL ELASTIC RESPONSE

2013 ◽  
Vol 05 (04) ◽  
pp. 1350036 ◽  
Author(s):  
VASSILIS P. PANOSKALTSIS ◽  
DIMITRIS SOLDATOS
Keyword(s):  
Internal Structure ◽  
Elastic Solid ◽  
Absolute Temperature ◽  
Elastic Response ◽  
Dynamical Process ◽  
Covariant Theory ◽  
Local Form ◽  
Spatial Covariance ◽  
Additional Material ◽  
Invariance Properties

In this paper, a general model of elastic (non-dissipative) behavior is developed. This model belongs to a class of models, developed for the description of complex bodies, in which the local state is assumed to be determined not only by the deformation, but also by a family of additional material parameters. The latter, unlike some additional structures used in the mechanics of complex bodies (e.g., directors, order parameters, internal degrees of freedom), are not considered as interactions of microscopic nature; rather they are considered as variables of macroscopic nature that describe the internal structure of the material, while their rates describe the evolution of the internal structure in the course of deformation. Accordingly, these variables are assumed to evolve continuously with time in a manner that guaranties the reversibility of the applied dynamical process. A covariant theory for the continuum in question is derived by means of invariance properties of the global form of the spatial energy balance equation, under the superposition of arbitrary spatial diffeomorphisms. In particular, it is shown that the assumption of spatial covariance of the equation of balance of energy yields the standard conservation and balance laws of classical mechanics but it does not yield the standard Doyle–Ericksen formula. In fact, the "Doyle–Ericksen formula" derived in this work, has some extra terms in it, which are related directly to the internal structure of the material, as the latter is controlled by the additional parameters. In a similar manner, by assuming the absolute temperature as an additional state variable and by employing the invariance properties of the local form of the spatial balance of energy under superimposed spatial diffeomorphisms, which also include a temperature rescaling, a nonisothermal covariant constitutive theory is naturally obtained. A formal comparison of the proposed elastic material with the standard hyperelastic (Green elastic) solid is also presented.

Acceleration and Force

2018 ◽  
Author(s):  
David M. Wittman
Keyword(s):  
Centrifugal Force ◽  
Constant Velocity ◽  
Frames Of Reference ◽  
Second Law ◽  
Know How ◽  
Free Objects ◽  
Inertial Frames ◽  
Acceleration Force ◽  
Newton's Second Law

This chapter develops crucial distinctions between constant‐velocity (also called inertial) frames of reference and accelerating ones. Inertial frames respect Newton’s first law—objects maintain constant velocity unless acted upon by a net force—while accelerating frames violate this law. Therefore, much of our thinking about whether the laws of physics are the same in all frames will really concern *inertial* frames. Newton’s first law gives us a foolproof test for distinguishing accelerating frames from inertial frames; this testworks even if velocitymeasurements are not directly available. We sometimes invent fictitious forces (such as “centrifugal force”) to explain the acceleration of free objects in accelerating frames, but we know how to determine that these are indeed fictitious.We also examine relationships between acceleration, force, andmass (Newton’s second law).We *define*mass as the ratio of force to acceleration, so mass represents a resistance to acceleration, or inertia.

Numerical Simulation of Flow in a Wavy Wall Microchannel Using Immersed Boundary Method

2020 ◽  
Vol 13 (2) ◽  
pp. 118-125
Author(s):  
Mithun Kanchan ◽  
Ranjith Maniyeri
Keyword(s):  
Reynolds Number ◽  
Fluid Flow ◽  
Immersed Boundary Method ◽  
Stokes Equations ◽  
Flow Characteristics ◽  
Immersed Boundary ◽  
Solid Boundary ◽  
Wavy Wall ◽  
Dirac Delta ◽  
Boundary Method

Background: Fluid flow in microchannels is restricted to low Reynolds number regimes and hence inducing chaotic mixing in such devices is a major challenge. Over the years, the Immersed Boundary Method (IBM) has proved its ability in handling complex fluid-structure interaction problems. Objectives: Inspired by recent patents in microchannel mixing devices, we study passive mixing effects by performing two-dimensional numerical simulations of wavy wall in channel flow using IBM. Methods: The continuity and Navier-Stokes equations governing the flow are solved by fractional step based finite volume method on a staggered Cartesian grid system. Fluid variables are described by Eulerian coordinates and solid boundary by Lagrangian coordinates. A four-point Dirac delta function is used to couple both the coordinate variables. A momentum forcing term is added to the governing equation in order to impose the no-slip boundary condition between the wavy wall and fluid interface. Results: Parametric study is carried out to analyze the fluid flow characteristics by varying amplitude and wavelength of wavy wall configurations for different Reynolds number. Conclusion: Configurations of wavy wall microchannels having a higher amplitude and lower wavelengths show optimum results for mixing applications.

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