Terms Of Inertial Forces Research Articles

Simulation of forced convective power law fluid by using Darcy–Brinkman–Forchheimer flow model field

This study investigates the fully developed heat transfer of steady, incompressible and laminar flow of power law fluid saturated porous medium through the rectangular duct by utilizing Darcy–Brinkman–Forchheimer flow model field. Hydrodynamic flow of power law-based fluid within a rectangular duct with porosity has not been reported in the literature. The consideration of Darcy–Brinkman–Forchheimer flow model makes it very much novel in its own right. The main objective of the present study is to explore the modified Darcy parameter on flow and heat transfer characteristics. Numerical results are obtained for different values of Darcy parameter, Da, inertia coefficient, Fr and power law model, n. We note the significant impact of inertial force on flow and heat transfer in the case of dilatant fluid; however, inertial force term can be ignored in the case of pseudo-plastic fluid due to its lower effect. Furthermore, with the decrease in aspect ratio, the effect of the inertial force can be reduced. It is also noted that, axial velocity significantly enhances with Darcy parameter Da. This behavior of the axial velocity is found to be similar for higher inertia coefficient Fr as well.

Design and validation of a tunable inertial microfluidic system for the efficient enrichment of circulating tumor cells in blood.

The analysis of circulating tumor cells (CTCs) in blood is a powerful noninvasive alternative to conventional tumor biopsy. Inertial‐based separation is a promising high‐throughput, marker‐free sorting strategy for the enrichment and isolation of CTCs. Here, we present and validate a double spiral microfluidic device that efficiently isolates CTCs with a fine‐tunable cut‐off value of 9 μm and a separation range of 2 μm. We designed the device based on computer simulations that introduce a novel, customized inertial force term, and provide practical fabrication guidelines. We validated the device using calibration beads, which allowed us to refine the simulations and redesign the device. Then we validated the redesigned device using blood samples and a murine model of metastatic breast cancer. Finally, as a proof of principle, we tested the device using peripheral blood from a patient with hepatocellular carcinoma, isolating more than 17 CTCs/ml, with purity/removal values of 96.03% and 99.99% of white blood cell and red blood cells, respectively. These results confirm highly efficient CTC isolation with a stringent cut‐off value and better separation results than the state of the art.

Unsteady Approximate Model of Grouting in Fractured Channels Based on Bingham Fluid

It is of great significance for the improvement of grouting technology and engineering practice to master the flow law of grout between parallel plates. However, the traditional calculation model ignores the influence of the inertia term and only considers the stable flow of slurry, so there is a big error in some cases. It is difficult to solve the motion equation of a Bingham fluid considering the inertial force term directly. Combined with the relationship between the steady-state flow equation of a Bingham fluid and a Newtonian fluid, the approximate unsteady-state flow equation of a Bingham fluid suitable for describing slurry flow is constructed. In addition, according to the unsteady flow equation, the relationship between the time and distance of slurry flow in parallel plate fractures can be obtained, and the simplified conditions of the Bingham fluid unsteady flow model are given. Finally, the accuracy of the flow equations and the simplified conditions are verified by experiments and numerical calculations.

Electro-mechanical vibration analysis of functionally graded piezoelectric porous plates in the translation state

To provide reference for aerospace structural design, electro-mechanical vibrations of functionally graded piezoelectric material (FGPM) plates carrying porosities in the translation state are investigated. A modified power law formulation is employed to depict the material properties of the plates in the thickness direction. Three terms of inertial forces are taken into account due to the translation of plates. The geometrical nonlinearity is considered by adopting the von Kármán non-linear relations. Using the d’Alembert's principle, the nonlinear governing equation of the out-of-plane motion of the plates is derived. The equation is further discretized to a system of ordinary differential equations using the Galerkin method, which are subsequently solved via the harmonic balance method. Then, the approximate analytical results are validated by utilizing the adaptive step-size fourth-order Runge-Kutta technique. Additionally, the stability of the steady state responses is examined by means of the perturbation technique. Linear and nonlinear vibration analyses are both carried out and results display some interesting dynamic phenomenon for translational porous FGPM plates. Parametric study shows that the vibration characteristics of the present inhomogeneous structure depend on several key physical parameters.

1-D blood flow modelling in a running human body

In this paper an attempt was made to simulate blood flow in a mobile human arterial network, specifically, in a running human subject. In order to simulate the effect of motion, a previously published immobile 1-D model was modified by including an inertial force term into the momentum equation. To calculate inertial force, gait analysis was performed at different levels of speed. Our results show that motion has a significant effect on the amplitudes of the blood pressure and flow rate but the average values are not effected significantly.

野球打撃動作における身体関節トルクの累積的効果

Motion-dependent term (MDT), which consists of centrifugal force, Coriolis force and gyroscopic effect moment expressed in the equation of motion for a multi-link system, plays significant roles in the generation of bat head speed through not instantaneous effect but cumulative effect of the exerting joint torques in baseball batting. According to our previous studies that calculate dynamics contributions of the whole-body joint torques considering generating factor of the MDT, the forward/backward rotational torque (FBR torque) at torso joint plays a significant role in the generation of bat head speed. These studies, however, show that the lower limb joint torques do not contribute directly to the bat head speed. Therefore, the purpose of this study was to make clear the functional roles of the lower limb joint torques considering the cumulative effect of exerting joint torques. The whole-body with bat was modelled as a system of sixteen-rigid linked segments. The contributions of the lower limb joint torques to the exerting FBR torque at torso joint were quantified through dynamic contribution equation, which relates lower limb joint torques to the torso FBR torque, derived from both dynamics joint force contribution equation of whole-body system and equilibrium balance equation with respect to rotational movement of the lower trunk segment. The results obtained in this study show 1) lower limb joint torque, especially flexion/extension torque at both hip joints, is a large contributor to the generation of the torso FBR torque, and 2) lower trunk inertial force term and other terms are small contributors to the FBR torque. The development of this analytical method would enable us to quantify the contribution of the lower limb joint torques.

The concept of physical surface in nuclear matter

The main point of a physical definition of surface forces in the matter in general, especially in the nuclear matter, is that the curvature of surfaces and its variation should be physically defined. The forces are therefore just the vehicles of introducing physics. The problem of mathematical definition of a surface in term of the curvature parameters thus naturally occurs. The present work addresses this problem in terms of the asymptotic directions of a surface in a point. A physical meaning of these parameters is given, first in terms of inertial forces, then in terms of a differential theory of colors, whereby the space of curvature parameters is identified with the color space. The work concludes with an image of the evolution of a local portion of a surface.

Inertial force term approximations for the use of Global Modal Parameterization for planar mechanisms

Recently a new model reduction technique for flexible multibody systems has been introduced, namely the Global Modal Parameterization (GMP). This method uses a system-level model reduction, in which the reduction is parameterized by the rigid position of the system and a small flexible deformation superposed on this rigid position. Because of the non-linearity, the projection base for reduction is position dependent. This position dependence leads to strongly non-linear inertial terms, with associated increased storage requirements and computational load. This paper gives a short overview of the GMP-method and focuses predominantly on the derivation of the reduced inertial forces. Three different approximations for the inertial terms are presented and numerically validated. It is shown that a substantial reduction in storage requirements, while maintaining accurate results, is possible through these approximations. Copyright © 2010 John Wiley & Sons, Ltd.

Einstein equations and inertial forces in axially symmetric stationary spacetimes

We investigate the relations between the inertial forces and the Einstein equations in axially symmetric stationary spacetimes. For the vacuum stationary axially symmetric spacetimes, we use the Geroch formalism to express the Einstein equations in terms of inertial forces. For the spacetimes with the perfect fluid sources, we use the formalism developed by Hansen and Winicour for establishing the relations. As expected intuitively, the gradients of inertial forces represent the field equations.

Thermomechanical continuum representation of atomistic deformation at arbitrary size scales

A thermomechanical equivalent continuum (TMEC) theory is developed for the deformation of atomistic particle systems at arbitrary size scales and under fully dynamic conditions. This theory allows continuum interpretation of molecular dynamics (MD) model results and derivation of thermomechanical continuum constitutive properties from MD results under conditions of general macroscopically transient thermomechanical deformations, which are not analysed by statistical mechanics. When specialized to the more specific conditions of non-deforming systems in macroscopic equilibrium, this theory yields certain results that are identical to, or consistent with, the results of statistical mechanics. Coupled thermomechanical continuum equations and constitutive behaviour are derived using MD concepts in a time-resolved manner. This theory is a further advancement from the purely mechanical equivalent continuum (EC) theory developed recently. Within the meaning of classical mechanics, the TMEC theory establishes the ultimate atomic origin of coupled thermomechanical deformation phenomena at the continuum level. The analysis is based on the decomposition of atomic particle velocity into a structural deformation part and a thermal oscillation part. On one hand, balance of momentum at the structural level yields fields of stress, body force, traction, mass density and deformation as they appear to a macroscopic observer. On the other hand, balance of momentum for the thermal motions relative to the macroscopically measured structure yields the fields of heat flux and temperature. These quantities are cast in a manner as to conform to the continuum phenomenological equation for heat conduction and generation, yielding scale-sensitive characterizations of specific heat, thermal conductivity and thermal relaxation time. The structural deformation and the thermal conduction processes are coupled because the equations for structural deformation and for heat conduction are two different forms of the same balance of momentum equation at the fully time-resolved atomic level. This coupling occurs through an inertial force term in each equation induced by the other process. For the structural deformation equation, the inertial force term induced by thermal oscillations of atoms gives rise to the phenomenological dependence of deformation on temperature. For the heat equation, the inertial force term induced by structural deformation takes the phenomenological form of a heat source.

Hydrodynamic Forces on Submerged Rigid Bodies -- Steady Flow

Formulae are derived for computing hydrodynamic forces on a submerged rigid body under the assumption that the governing equations for the fluid flow are the steady Navier—Stokes equations. Two new formulae relating the far field behavior of the pressure, the stress vector and either the inertial force term on the rigid body or the velocity behavior in the far field are obtained. Combining these results it is possible to evaluate the hydrodynamic forces solely in terms of the velocity in the far field and a convective inertial force term on the rigid body.

Low-frequency nonlinear equations with inertial force term for toroidal plasmas

Low-frequency nonlinear equations are derived for studying strong turbulence in finite-beta toroidal plasmas. These equations contain the ion inertial force terms originating from the magnetic shear and toroidal geometry.