On a Novel Approximate Solution to the Inhomogeneous Euler–Bernoulli Equation with an Application to Aeroelastics

This paper focuses on the development of an explicit finite difference numerical method for approximating the solution of the inhomogeneous fourth-order Euler–Bernoulli beam bending equation with velocity-dependent damping and second moment of area, mass and elastic modulus distribution varying with distance along the beam. We verify the method by comparing its predictions with an exact analytical solution of the homogeneous equation, we use the generalised Richardson extrapolation to show that the method is grid convergent and we extend the application of the Lax–Richtmyer stability criteria to higher-order schemes to ensure that it is numerically stable. Finally, we present three sets of computational experiments. The first set simulates the behaviour of the un-loaded beam and is validated against the analytic solution. The second set simulates the time-dependent dynamic behaviour of a damped beam of varying stiffness and mass distributions under arbitrary externally applied loading in an aeroelastic analysis setting by approximating the inhomogeneous equation using the finite difference method derived here. We compare the third set of simulations of the steady-state deflection with the results of static beam bending experiments conducted at Cranfield University. Overall, we developed an accurate, stable and convergent numerical framework for solving the inhomogeneous Euler–Bernoulli equation over a wide range of boundary conditions. Aircraft manufacturers are starting to consider configurations with increased wing aspect ratios and reduced structural weight which lead to more slender and flexible designs. Aeroelastic analysis now plays a central role in the design process. Efficient computational tools for the prediction of the deformation of wings under external loads are in demand and this has motivated the work carried out in this paper.

Characteristics of Air Resistance in Aerostatic Bearings

The definition of air resistance is nonuniform when analyzing the bearing capacity, stiffness, and stability of an orifice throttling aerostatic restrictor. In this study, a capillary tube similar to the inlet section of an aerostatic restrictor is used as the research object, and the Bernoulli equation under adiabatic conditions is established. Through an experiment, the pressure and temperature of the capillary tube inlet and outlet and the flow through the capillary tube are measured. Based on the air resistance definition, the empirical formula of the coefficient k is obtained, and the theoretical air resistance of the capillary path is calculated. The relative error between the theoretical air resistance and experimental air resistance is kept within 10%. The comparison results verify the accuracy of the air resistance theory and provide a basis for the subsequent establishment of a universal definition of air resistance. Subsequently, air resistance can be used to design aerostatic bearings and help improve their characteristics.

Electric Vehicles That Extract Heat from the Air Without Charging: Entropy Law Does Not Prohibit This

Electromobiles protect the biosphere in places of human residence. Globally, they destroy it, as the electrical energy they consumed is extracted using "dirty" energy carriers. This article suggests learning the electromobiles to generate electrical energy in eco-friendly way, extracting heat from the air. Specifically, we suggest to equip the electromobiles with the Or lov and etc. installation, which schematically is a converging tube where the air flow is by itself accelerated and, according to the Bernoulli equation, is cooled; and its narrow end contains the electrical energy generating turbine. The problem is that the Orlovand etc. installation is prohibited by the entropy increase law due to the flow entropy decrease during its operation. However, it is important that actually in this case the Clausius entropy, i.e. thermal entropy, decreases. The thermal and total entropy increase laws are different laws that separately require verification. Planck, Fermi et al. indicatedthe cases of total conversion of heat into other forms of energy accompanied by thermal en- tropy decrease. These cases, proving invalidity of the thermal entropy increase law, admit transition to electromobiles with air heat trac- tion. As well as transition of water transport to ship's electric engines with water heat traction.

A Dissipation Function–Based Method for Calculating the Energy Loss of Intracranial Aneurysms

At present, the energy loss (EL) mechanism of intracranial aneurysm (IA) rupture is explored based on the global EL calculated by Bernoulli equation, but the details of EL are still unclear. This study aimed to explore the temporal and spatial characteristics of EL of IAs and reveal its mechanism. A novel method for calculating the EL of IAs based on dissipation function (DF) was proposed. DF was derived from the differential form of the energy equation and reflected the irreversible conversion from mechanical energy to internal energy caused by the friction between the fluid micelles. Eight sidewall IAs located at the posterior communicating segment of the internal carotid artery were collected; the three-dimensional (3D) geometric models of IAs were established employing image segmentation and 3D reconstruction. Computational fluid dynamics was applied to obtain hemodynamic parameters of IAs. The temporal and spatial characteristics of EL of IAs were achieved utilizing our proposed method. The simulation results indicated that EL occurred mainly in the boundary layer and the region adjacent to high-velocity inflow jet, EL increased rapidly during cardiac systole and reached its maximum at end-systolic phase and then decreased gradually during diastole until the end of cardiac cycle. The proposed method achieved some improvements over the traditional Bernoulli equation–based method by acquiring the temporal and spatial characteristics of EL, and it could provide insights into the EL of IAs and contribute to further rupture mechanism investigation.

Solutions of Bernoulli Equations in the Fractional Setting

We present a general series representation formula for the local solution of the Bernoulli equation with Caputo fractional derivatives. We then focus on a generalization of the fractional logistic equation and present some related numerical simulations.

Study on the smoke propagation characteristics of metro tunnel fire under the effects of piston wind

Metro trains running in tunnels cause piston wind, and when a metro train stops in a tunnel due to a fire, the effect of the piston wind on smoke propagation characteristics cannot be ignored. In this paper, a theoretical model based on the unsteady flow theory of the Bernoulli equation was established to describe the change in piston wind speed under fire conditions. The characteristics of the smoke propagation in tunnel fires under the effect of the piston wind were analysed by means of numerical simulation. The result indicates that the piston wind has a significant effect on the characteristics of smoke distribution. In a longitudinally ventilated tunnel, whether the direction of piston wind is the same as that of longitudinal ventilation could seriously affect the control of fire smoke. When the direction is the same, the piston wind could enhance the smoke control effect of the longitudinal ventilation. Otherwise, the smoke control effect could be significantly diminished, and the smoke control by the critical wind speed of longitudinal ventilation would fail. The findings could contribute to a better understanding of the characteristics of tunnel fire to control smoke spread under the influence of piston wind.