Mathematical Modelling of Tank Wagon Vibrations Considering Partially Filling of the Tank with Liquid Cargo

Mathematical modelling of processes of motion makes it possible to assess the dynamic characteristics of a wagon at the stage of its design. However, it is necessary to consider the type of cargo transported, the movement of which affects the values of these features.The paper considers a mathematical model of an eight-axle railway tank wagon developed using the Lagrange’s equation of the second kind. The considered mathematical model suggests an approach based on the consideration of the influence of the energy of a liquid cargo in a steady state of motion. This influence was considered by evaluating the kinetic and potential energies of vibrations of the transported liquid cargo.Differential equations of vibration compiled for the model under consideration represent the liquid cargo as a solid. The approach for considering the effect of liquid cargo during vibrations of a tank wagon assumes that the total volume of the displaced liquid approximately corresponds to the volume of the layer of the fluid determined by displacement of bouncing, or in the case of galloping, with an angular displacement of one end section of the tank wagon, the second section rises by the same value, in other words, we observe the system of communicating vessels. Based on these assumptions, energy additions are obtained that consider movement of a liquid cargo under steady-state modes of motion.According to the proposed approach, preliminary calculations were performed, and the results obtained were assessed. The results obtained showed satisfactory convergence with the calculations carried out using other approaches to modelling of the processes of movement of railway tank wagons.

On the spacing of meandering jets in the strong-stair limit

Based on an assumption of strongly inhomogeneous potential vorticity mixing in quasi-geostrophic $\beta$ -plane turbulence, a relation is obtained between the mean spacing of latitudinally meandering zonal jets and the total kinetic energy of the flow. The relation applies to cases where the Rossby deformation length is much smaller than the Rhines scale, in which kinetic energy is concentrated within the jet cores. The relation can be theoretically achieved in the case of perfect mixing between regularly spaced jets with simple meanders, and of negligible kinetic energy in flow structures other than in jets. Incomplete mixing or unevenly spaced jets will result in jets being more widely separated than the estimate, while significant kinetic energy outside the jets will result in jets closer than the estimate. An additional relation, valid under the same assumptions, is obtained between the total kinetic and potential energies. In flows with large-scale dissipation, the two relations provide a means to predict the jet spacing based only on knowledge of the energy input rate of the forcing and dissipation rate, regardless of whether the latter takes the form of frictional or thermal damping. Comparison with direct numerical integrations of the forced system shows broad support for the relations, but differences between the actual and predicted jet spacings arise both from the complex structure of jet meanders and the non-negligible kinetic energy contained in the turbulent background and in coherent vortices lying between the jets.

On the energy of nonlinear water waves

This article presents results concerning the excess kinetic and potential energies for exact nonlinear water waves. In particular, it is proven, for periodic travelling irrotational water waves, that the excess kinetic energy density is always negative, whereas the excess potential energy density is always positive, in the steady reference frame. A characterization of the total excess energy density as a weighted mean of the kinetic energy along the wave surface profile is also presented.

Modeling and Control of a Single Rotor Composed of Two Fixed Wing Airplanes

This paper proposes a simple flying rotor prototype composed of two small airplanes attached to each other with a rigid rod so that they can rotate around themselves. The prototype is intended to perform hover flights with more autonomy than existing classic helicopters or quad-rotors. Given that the two airplanes can fly apart from each other, the induced flow which normally appears in rotorcrafts will be significantly reduced. The issue that is addressed in the paper is how this flying rotor prototype can be modeled and controlled. A model of the prototype is obtained by computing the kinetic and potential energies and applying the Euler Lagrange equations. Furthermore, in order to simplify the equations, it has been considered that the yaw angular displacement evolves much faster than the other variables. Furthermore a study is presented to virtually create a swashplate which is a central mechanism in helicopters. Such virtual swashplate is created by introducing a sinusoidal control on the airplanes’ elevators. The torque amplitude will be proportional to the sinusoidal amplitude and the direction will be determined by the phase of the sinusoidal. A simple nonlinear control algorithm is proposed and its performance is tested in numerical simulations.

The Eventuality of Equating Energy and Mass - Laws and Theories

Einstein's famous equation, , revolutionized the theory of physics and introduced new perspectives to the study of energy and mass. However, a close consideration of its principles raises essential concerns on the equitability of mass and energy as well as other phenomena like the speed of light. The unavoidable scientific claim of this paper is that the total energy of matter depends on its internal and external energies, which are accounted for by kinetic and potential energies. In the current work, thought experiments reveal important additions to this idea regarding the apparent effects of external energy on the nature of matter and particles. This paper employs detailed thought experiments and theoretical discussions to identify and address several notable inconsistencies related to the energy and mass equation based on previous works in physics. The relative external energy of an object will be influenced by the position of the observer. The outcomes of the experiments presented herein also provide key insights into the constancy of the internal energy of all matter and particles. Generally, this paper provides an important basis for analyzing the theory underlying the physics of energy and mass, addressing questionable ideas that are common but poorly substantiated and providing a new understanding of the nature of mass and energy that lays the foundations for further research in this area by projecting the difference between them.

Validation and application of the lattice Boltzmann algorithm for a turbulent immiscible Rayleigh–Taylor system

We develop a multicomponent lattice Boltzmann (LB) model for the two-dimensional Rayleigh–Taylor turbulence with a Shan–Chen pseudopotential implemented on GPUs. In the immiscible case, this method is able to accurately overcome the inherent numerical complexity caused by the complicated structure of the interface that appears in the fully developed turbulent regime. The accuracy of the LB model is tested both for early and late stages of instability. For the developed turbulent motion, we analyse the balance between different terms describing variations of the kinetic and potential energies. Then we analyse the role of the interface in the energy balance and also the effects of the vorticity induced by the interface in the energy dissipation. Statistical properties are compared for miscible and immiscible flows. Our results can also be considered as a first validation step to extend the application of LB model to three-dimensional immiscible Rayleigh-Taylor turbulence. This article is part of the theme issue ‘Progress in mesoscale methods for fluid dynamics simulation’.

Reciprocal Interaction between Waves and Turbulence within the Nocturnal Boundary-Layer

<p>The presence of waves in the nocturnal boundary layer has proven to generate complex interaction with turbulence. On complex terrain environments, where turbulence is observed in a weak but continuous state of activity, waves can be a vehicle of additional production/loss of turbulence energy. The common approach based on the Reynolds decomposition is unable to disaggregate turbulence and wave motion, thus revealing impaired to explicit the terms of this additional interaction. In the current investigation, we adopt a triple-decomposition approach to separate mean, wave, and turbulence motions within near-surface boundary-layer flows, with the aim of unveiling the role of wave motion as source and/or sink of turbulence kinetic and potential energies in the respective explicit budgets. This investigation reveals that the waves contribute to the kinetic energy budget where the production is not shear-dominated and the budget equation does not reduce to a shear-dissipation balance (e.g., as it occurs close to a surface). Away from the surface, the buoyancy effects associated with the wave motion become a significant factor in generating a three-terms balance (shear-buoyancy-dissipation). Similar effects can be found in the potential energy budget, as the waves affect for instance the production associated with the vertical heat flux. On this basis, we develop a simple interpretation paradigm to distinguish two layers, namely near-ground and far-ground sublayer, estimating where the turbulence kinetic energy can significantly feed or be fed by the wave. To prove this paradigm and evaluate the explicit contributions of the wave motion on the turbulence kinetic and potential energies, we investigate a nocturnal valley flow observed under weak synoptic forcing in the Dugway Valley (Utah) during the MATERHORN Program. From this dataset, the explicit kinetic and potential energy budgets are calculated, relying on a variance-covariance analysis to further comprehend the balance of energy production/loss in each sublayer. With this investigation, we propose a simple interpretation scheme to capture and interpret the extent of the complex interaction between waves and turbulence in nocturnal stable boundary layers.</p>

Position Control of a Pneumatic Actuator Under Varying External Force

In this paper a high accuracy position control strategy for a pneumatic actuation system subjected to a varying external force is proposed. A novel approach for the mathematical modeling of the pneumatic actuator, based on energy methods, is presented. The Lagrangian is derived from combining the kinetic and potential energies, leading to formulation of the Euler-Lagrange equation of motion. The nonlinear backstepping method is applied to derive the control law, and the derivative of the potential energy is used as the controlled parameter. Experimental results show that tracking a sine wave of 0.1m magnitude produces a maximum error of ±0.008m while the actuator is subjected to a time varying external force with a magnitude ranging from 570N to 1150N.

Thermalization in a Quantum Harmonic Oscillator with Random Disorder

We propose a possible scheme to study the thermalization in a quantum harmonic oscillator with random disorder. Our numerical simulation shows that through the effect of random disorder, the system can undergo a transition from an initial nonequilibrium state to a equilibrium state. Unlike the classical damped harmonic oscillator where total energy is dissipated, total energy of the disordered quantum harmonic oscillator is conserved. In particular, at equilibrium the initial mechanical energy is transformed to the thermodynamic energy in which kinetic and potential energies are evenly distributed. Shannon entropy in different bases are shown to yield consistent results during the thermalization.