Principle Of Conservation Of Momentum Research Articles

Two-dimensional simulation of debris flows over mobile bed: Enhancing the TRENT2D model by using a well-balanced Generalized Roe-type solver

The mathematical description of debris flows over mobile-bed is performed by using a two-phase shallow-water approach. The system of partial differential equations that follows by using the mass and momentum conservation principles is hyperbolic and characterized by a nonconservative nature. This feature, as well as the highly nonlinear relationship between the conserved and the primitive variables, is particularly challenging in the framework of finite-volume, explicit Godunov-type numerical approaches. This paper presents our effort to enhance the capabilities of the TRENT2D model (acronym for Transport in Rapidly Evolutive, Natural Torrent, see Armanini et al., Computers and Geosciences, 2009). Firstly, from a mathematical point of view, the eigenstructure of the original system has been analysed in detail in order to obtain useful information for improving the numerical scheme. Moreover, some previously neglected physical mechanisms, leading to a diffusive behavior, have been investigated and a new term has been added in order to account for them. On the other hand, from a numerical point of view, the original Riemann solver (LHLL), which satisfies only the C-property, has been substituted with a more accurate well-balanced Generalized Roe solver and the discretization of the diffusive terms has been introduced in the numerical scheme. The application of the two versions of TRENT2D to a set of test cases, both theoretical and real, allows to appreciate the improvement of the new version of the model.

Bivelocity hydrodynamics. Diffuse mass flux vs. diffuse volume flux

An intimate physical connection exists between a fluid’s mass and its volume, with the density ρ serving as a proportionality factor relating these two extensive thermodynamic properties when the fluid is homogeneous. This linkage has led to the erroneous belief among many researchers that a fluid’s diffusive (dissipative) mass flux and its diffusive volume flux counterpart, both occurring in inhomogeneous fluids undergoing transport are, in fact, synonymous. However, the existence of a truly dissipative mass flux (that is, a mass flux that is physically dissipative) has recently and convincingly been shown to be a physical impossibility [H.C. Öttinger, H. Struchtrup, M. Liu, On the impossibility of a dissipative contribution to the mass flux in hydrodynamics, Phys. Rev. E 80 (2009) 056303], owing, among other things, to its violation of the principle of angular momentum conservation. Unfortunately, as a consequence of the erroneous belief in the equality of the diffuse volume and mass fluxes (sans an algebraic sign), this has led many researchers to wrongly conclude that a diffuse volume flux is equally impossible. As a consequence, owing to the fundamental role played by the diffuse volume flux in the theory of bivelocity hydrodynamics [H. Brenner, Beyond Navier–Stokes, Int. J. Eng. Sci. 54 (2012) 67–98], many researchers have been led to falsely dismiss, without due consideration, the possibility of bivelocity hydrodynamics constituting a potentially viable physical theory, which it is believed to be. The present paper corrects this misconception by using a simple concrete example involving an isothermal rotating rigid-body fluid motion to clearly confirm that whereas a diffuse mass flux is indeed impossible, this fact does not exclude the possible existence of a diffuse volume flux and, concomitantly, the possibility that bivelocity hydrodynamics is indeed a potentially viable branch of fluid mechanics.

Dike-break induced flows: a simplified model

A simplified model for the prediction of the steady-state outflow through a breach in an inland dike is presented. It consists in the application of the mass and momentum conservation principles to a macroscopic control volume. A proper definition of the shape of the control volume enables to take the main characteristics of the flow into account and thus to compensate for the extreme simplification of the spatial representation of the model. At the breach, a relation derived from the shallow-water equations is used to determine the direction of the flow. Developments have been guided by numerical simulations and results have been compared to experimental data. Both the accuracy and the domain of validity of the simplified model are found satisfactory.

Gravity, massive particles, photons and Shapiro delay

An impact model of gravity designed to emulate Newton’s law of gravitation is applied to particles with relative motions at slow and relativistic speeds. Based on this model, a gravitational interaction mode is then conceived between photons and massive particles. This implies a deflection perpendicular to the propagation direction of a photon twice as large as expected from the mass-energy relation of photons—in accordance with observations and the General Theory of Relativity. The longitudinal interaction is compatible with the energy and momentum conservation principles applied to massless entities, and the results are consistent with the observed Shapiro delay.

Startup flow of gelled crudes in pipelines

The startup flow of thixotropic yield stress fluids in tubes is studied numerically. In the situation of interest, the structured fluid is displaced by another fluid, under the application of a constant entrance pressure. The fluid is assumed to obey a recently proposed model for thixotropic yield-stress fluids that relies on a structure parameter. The momentum conservation principle is employed in a simplified form that arises by assuming quasi-steady flow, i.e. the shear stress radial distribution is assumed to be linear as it is in steady flow. Inertial effects are also included in the analysis. A numerical procedure was developed to integrate the differential equations that arise, and the average velocity as well as the radial distribution of the structure parameter are obtained for different combinations of the rheological and flow parameters, allowing the determination of the necessary conditions for a successful startup. Among other features, the approach is capable of predicting the “avalanche effect [5],” i.e. situations of no flow for long time periods and then the sudden onset of motion.

Mathematical Modeling for Convection-Enhanced Drug Delivery

Convection-enhanced delivery (CED) techniques for cancer therapeutics have now been widely used. Consequentially, the measurement of efficiency of CED becomes more and more important. It is difficult to quantify CED efficiency and extent by using clinical and experimental methods alone. With the development of computer science, more and more researches introduce mathematical modeling method to assess CED efficiency and extent. Based on mass and momentum conservation and transport physical principles, this paper introduces a mathematical model for convection-enhanced intratumoral drug delivery in porous tumor tissue, and presents 2D numerical solution algorithm for this CED model, which is easy to be expanded to 3D cases. By showing results with different variables, this paper analyzes dominating factors’ impact on drug distribution and shows the rationality of our CED model. This work is helpful for predicting the drug distribution in tumor and opens up new opportunities for using computer science to help clinical tumor treatment plan.

A Method for Simulation of a Cryogenic Liquid Propellant Engine

The purpose of this paper is developing a method for simulation of a cryogenic staged combustion-closed cycle engine. Since, aerospace systems are usually complicated and important; the simulation task becomes extremely important. If the propulsion system of space vehicle is not successfully simulated, then designers must rely on huge tests which are time and money consuming and also dangerous. The mathematical model of the engine includes a set of equations which describe all the system's elements operation. These equations correspond to mass, momentum and energy conservation principles and are simplified to make easy the process of calculations. A Fortran 90 code is developed for this simulation. Comparison of the simulation code with the actual values, demonstrates that the model can accurately predict the behavior of the real engine

Flexural Behavior of Concrete-Filled Circular Steel Tubes under High-Strain Rate Impact Loading

Nine simply supported circular steel concrete-filled tubes (CFTs), two circular steel posttensioned concrete-filled tubes (PTCFTs), and one circular steel fiber–reinforced concrete-filled tube (FRCFT) have been tested in an instrumented drop-weight impact facility. The weight and the height of the drop-weight were varied to cause failure in some test specimens. The failure modes and local damages in those specimens have been investigated extensively. Failure in the steel tubes was commonly tensile facture or rupture along the circumference. Concrete core in the impact area commonly crushed under compression and cracked under tension. The use of prestressing strands and steel fibers significantly restrained the concrete tension cracks in the PTCFT and FRCFT specimens, respectively. The experimental results are analyzed in the context of principles of energy and momentum conservation.

Forced convection heat transfer of polymer melt flow inside channels with contraction/expansion sections

Polymer melt flow inside channels with contraction/expansion sections is commonly found in numerous forming applications. Due to high polymer viscosity, this flow presents laminar behaviour, high pressure drop and relevant viscous heating effect. The analysis presented in this work comprises the numerical simulation of a set of equations (mass, linear momentum and energy conservation principles) that models this class of flow. The generalized Newtonian formulation is employed, being the apparent polymer viscosity computed as a function of temperature and shear strain rate. The governing equations are discretized using the finite difference method with central formulae (for both diffusion and convection terms). The work is focused on the assessment of the local and global Nusselt numbers based upon a parametric study of the effects of the contraction/expansion aspect ratio and entrance flow velocity. The main findings indicate that, similarly to Newtonian flows, the Nusselt number presents a good correlation with Reynolds, Prandtl and Eckert numbers.

Comparative study of finite difference approaches in simulation of magnetohydrodynamic turbulence at low magnetic Reynolds number

Two approaches to finite difference approximation of turbulent flows of electrically conducting incompressible fluids in the presence of a steady magnetic field are analyzed. One is based on high-order approximations and upwind-biased discretization of the nonlinear term. Another is consistently of the second order and nearly fully conservative in regard of mass, momentum, kinetic energy, and electric charge conservation principles. The analysis is conducted using comparison with high-accuracy spectral direct numerical simulations of channel flows with wall-normal and spanwise magnetic fields. Focus of the analysis is on the quality of finite difference approximation in the situation when the magnetic field leads to significant transformation of the flow structure. In the case of turbulent flows at moderate magnetic fields, the conservative scheme approach offers better stability and equal or higher accuracy than the approach based on the upwind discretization. The conservation property is expected to become increasingly important and even indispensable at stronger magnetic fields.

Magnetic resonance velocity imaging derived pressure differential using control volume analysis

BackgroundDiagnosis and treatment of hydrocephalus is hindered by a lack of systemic understanding of the interrelationships between pressures and flow of cerebrospinal fluid in the brain. Control volume analysis provides a fluid physics approach to quantify and relate pressure and flow information. The objective of this study was to use control volume analysis and magnetic resonance velocity imaging to non-invasively estimate pressure differentials in vitro.MethodA flow phantom was constructed and water was the experimental fluid. The phantom was connected to a high-resolution differential pressure sensor and a computer controlled pump producing sinusoidal flow. Magnetic resonance velocity measurements were taken and subsequently analyzed to derive pressure differential waveforms using momentum conservation principles. Independent sensor measurements were obtained for comparison.ResultsUsing magnetic resonance data the momentum balance in the phantom was computed. The measured differential pressure force had amplitude of 14.4 dynes (pressure gradient amplitude 0.30 Pa/cm). A 12.5% normalized root mean square deviation between derived and directly measured pressure differential was obtained. These experiments demonstrate one example of the potential utility of control volume analysis and the concepts involved in its application.ConclusionsThis study validates a non-invasive measurement technique for relating velocity measurements to pressure differential. These methods may be applied to clinical measurements to estimate pressure differentials in vivo which could not be obtained with current clinical sensors.

On the propulsive force developed by asymmetric capacitors in a vacuum

The present work provides a detailed analysis of already published reports on the observation of an anomalous force in a vacuum associated with vacuum sparks in asymmetric capacitors charged with “constant” high voltages. Known experimental details of these experiments are put forward and propulsion performance is compared with the only known propulsion system known to exist in a vacuum associated with sparks: the vacuum arc thruster (VAT). VAT's are known for decades and work on principles of momentum conservation. They vaporize particles from the electrodes themselves through a high spark current in one direction in order to develop a thrust in the opposite direction. However, the known performance trend for these thrusters does not account for the vacuum spark force values published by NASA. Furthermore, they have not observed the electrode erosion usually associated with VAT operation, even after extended testing. Therefore it is possible that a new propulsion mechanism might be at work, but that should be verified and confirmed experimentally in the future in order to resolve the question.

Pointing control of spacecraft using two SGCMGs via LPV control theory

In this paper, we consider a pointing control of a spacecraft using two single-gimbal control moment gyros (SGCMGs). Our pointing control problem is to make the line-of-sight of a camera or an antenna that is fixed on a body axis aim along a desired direction. To solve this problem, we first state the control objective for the pointing control through the angular momentum conservation principle. Then, we develop a gain-scheduled (GS) controller via linear parameter-varying (LPV) control theory. Finally, the feasibility of the proposed control method is shown by a numerical simulation.

Optimized Configuration for the Upper Body with a Bisecting Hip Mechanism in Passive Dynamic Walking

Biped passive dynamic walking is a promising idea towards the goal of humanoid robotics further after the proposal of the upper body in these years. In this paper, we deduce the dynamic robot model with the upper body based on bisecting hip, in which the section of the swing phase is performed by Lagrange method, while the section of the collision phase is completed in terms of the principle of angular momentum conservation. The analysis of the global stability and the local stability are combined with each other, based on which the configurations of parameters with different mass and size of the upper body are discussed. Finally the optimized configuration of the model is obtained after the simulation in Adams environment. Results verify that the model with an upper body exhibits an extraordinary stability and robustness under circumstances of either a single disturbance or random disturbances.

Transient simulation of household refrigerators: A semi-empirical quasi-steady approach

This paper outlines a simulation model for the cycling behavior of household refrigerators and, therefore, for predicting their energy consumption. The modeling methodology follows a quasi-steady approach, where the refrigeration system and also the refrigerated compartments are modeled following steady-state and transient approaches, respectively. The mass, energy and momentum conservation principles were used to put forward the equation set, whereas experimental data were collected and used to reduce the model closing parameters such as the thermal conductances and capacitances. The experiments were carried out using a controlled temperature and humidity environmental chamber. The model predictions were compared to experimental data, when it was found that the energy consumption is well predicted by the model with a maximum deviation of ±2%. A sensitivity analysis was also carried out to identify opportunities for energy savings.

Electronic transport in polycrystalline graphene

Most materials in available macroscopic quantities are polycrystalline. Graphene, a recently discovered two-dimensional form of carbon with strong potential for replacing silicon in future electronics, is no exception. There is growing evidence of the polycrystalline nature of graphene samples obtained using various techniques. Grain boundaries, intrinsic topological defects of polycrystalline materials, are expected to dramatically alter the electronic transport in graphene. Here, we develop a theory of charge carrier transmission through grain boundaries composed of a periodic array of dislocations in graphene based on the momentum conservation principle. Depending on the grain boundary structure we find two distinct transport behaviours - either high transparency, or perfect reflection of charge carriers over remarkably large energy ranges. First-principles quantum transport calculations are used to verify and further investigate this striking behaviour. Our study sheds light on the transport properties of large-area graphene samples. Furthermore, purposeful engineering of periodic grain boundaries with tunable transport gaps would allow for controlling charge currents without the need of introducing bulk band gaps in otherwise semimetallic graphene. The proposed approach can be regarded as a means towards building practical graphene electronics.

Research as a guide for improving student learning: An example from momentum conservation

This paper describes an investigation of student ability to apply the principle of momentum conservation in one dimension. As part of the investigation, we conducted interviews with students who had completed introductory calculus-based mechanics. We found that some of them attributed special significance to a certain limiting case: An (elastic) collision between a light incident object and an initially stationary massive target. They used their correct prediction of the observable outcome of such a collision to support an incorrect view of momentum. A tutorial designed to help students understand this special case improved their performance on examination questions on more general collisions. The process of developing curriculum based on students’ spontaneous, productive reasoning is illustrated.

A new model for life estimation of creep

This paper deals with a new model for life estimation of creep derived from the law of energy conservation and the momentum conservation principle. By mathematical technique, the expressions of these two rules are transformed into a simple function, which can describe the relationship between the internal energy and creep life. This model supposes that the internal energy change of a specimen is a constant from the initial state to the failure one under certain conditions. Moreover, owing to its simple expression, it is very easy to use this model to predict the creep life. To check the validity of the new model proposed in this paper, the published data of 2.25Cr–1Mo, 1Cr–0.5Mo, 18Cr–12Ni–Mo and 1Cr–1Mo–0.25 V steels have been studied and analyzed. A well agreement is noted between the model and the results.

New concept of compressive load transmitting member applicable to large space structures

Large space structures require limitations in weight and assembly effort in order to be realistically constructed and operated. Components for transmitting tensile and compressive loads are the most fundamental, wires and membranes being ones that are most efficient for tensile load transmission, whereas the development of light-weight component for compressive load transmission is still expected. New concept of compression carrying component is proposed, based on the simple principle of momentum conservation. This new concept utilizes the momentum of medium that reciprocates between the load transmitting points. Various media for this new component are examined from the points of utility, handling and load carrying capacity. Proposed innovative component may be readily realized by adopting photon or ion particles, if the required level of load is small.

Spatial autoregressive structure of meander evolution revisited

Meandering rivers are intrinsically dynamic geomorphic systems that exhibit progressive change in their planforms as they migrate across their floodplains. Recent research in river meandering has focused on the development of linear mathematical models of meander migration. These models, which are based on momentum and mass conservation principles, aim to capture the basic physical mechanisms governing flow-sediment interactions in meandering rivers. A common attribute of the models is that bank erosion is represented as a linear function of near-bank velocity and near-bank velocity is expressed as a spatial convolution of channel curvature. Thus, in all of these process-based models, planform curvature, as mediated through its influence on near-bank velocity, has a strong effect on channel migration. Mathematical details of the curvature–migration relation depend on the number of curvature related convolution terms in the model; the number of such terms increases with increasing model order. Although first- through fourth-order linear models have been developed, few studies have examined rigorously the relation between planform curvature and migration in natural rivers to determine if even the simplest model-based curvature–migration relations correspond to relations derived from empirical data. This paper evaluates empirically the spatial structure of the relation between upstream planform curvature and local channel migration for bends along the Beatton River, British Columbia, Canada. In particular, we compare empirically derived curvature–migration relations to the exponential-decay form of this relation embodied in first-order linear mathematical models of meander migration. For this purpose, we use a refined empirical methodology and recently developed analytical techniques that overcome limitations of a similar analysis of the Beatton River bends conducted by Furbish (1991). The refined methodology examines the influence of upstream lags of planform curvature on migration rates. The new analytical techniques provide data on channel curvature and migration rate at a much finer spatial interval than in the analysis of Furbish (1991). The validity of the approach for revealing the exponential-decay structure of the curvature–migration relation is confirmed by applying it to a synthetic data set generated using a first-order mathematical model. In contrast to the findings of Furbish (1991), our results for the Beatton River bends show that the structure of the spatially distributed upstream curvature effect is more complex than pure exponential decay. The findings suggest that oscillatory components of the relation between curvature and migration rate are important in the planform dynamics of individual complex bends. These findings are consistent with results of recent empirical analysis of the curvature–migration relation based on discrete signal processing and with the structure of the curvature–migration relation in high-order mathematical models of meander migration.