Related Equations Research Articles

CFD investigation of PWR channel shapes effects during rolling motion under normal and accident condition

Thermal-hydraulic parameters of the floating reactor fluctuate constantly, which can endanger the safety features and make challenges for safety systems. The rolling motion has more effect on the thermal-hydraulic of the floating reactor between other six motions. In this study, the effect of fuel shape and heated channel shape on thermal-hydraulic parameters were evaluated along with analysis of the parameter value changes during rolling motion under normal and LOCA accident. Also, simulation of the rolling motion with the oscillating velocity is done. The cylindrical and rectangular fuel shapes, as well as hexagonal and square channel shapes, were compared. For modeling the rolling motion, an UDF program is developed for solving the related equations in CFD code. The results indicated that the rectangular fuel with the square channel has lower changes during rolling motion than the other two models, which can be considered as the main reason for choosing the plate or rectangular fuel types in the new floating reactors.

Effects of cavitation on the hydrodynamic loading and wake vortex evolution of a pre-swirl pump-jet propulsor

The purpose of this study is to investigate the effects of cavitation on the hydrodynamic loading and wake vortex evolution in a pre-swirl pump-jet propulsor, and also the cavitation-vortex interaction mechanism. The cavitating flow is simulated by delayed detached eddy simulation coupled with a homogeneous cavitation model. Based on available experimental validation, the cavitation patterns, hydrodynamic loadings, the tip leakage vortex (TLV) evolutions and trailing edge vortex interactions are orderly investigated under two typical cavitation conditions. Results show that the blade sheet cavitation, TLV cavitation and tip clearance cavitation are regard as the main cavitation types of the rotor, where the sheet cavity on adjacent blades is non-uniformly distributed under the perturbations of the stator wakes and phase effects. The interaction between the thickening sheet cavity and stator wakes causes the shift of dominant frequencies of rotor loading from the rotor blade passing frequency fBPF and its harmonics to stator blade passing frequency fs and its harmonics. The relative vorticity transport equation is used to analyze cavitation-vortex interaction of TLV. The TLV cavitation promotes the vorticity production of TLV at the incipient stage and increases its intensity downstream. The instability of TLV is triggered earlier when cavitation is heavy due to the enhanced mutual interaction between consecutive spirals of the TLVs and their interaction with sheet cavity induced shedding vortices. The trailing edge vortices of stator and rotor mutually interacts with blade sheet cavity, which accelerates the breakdown of trailing vortex system downstream.

Mixed-Sensitivity Control for Drag-Free Spacecraft Based on State Space

This paper investigates a mixed-sensitivity control method for a class of drag-free spacecraft-needed frequency-separation control, which overcomes the coupled problem of a multiple-in multiple-out (MIMO) system with multiple sensitive-axes and disturbances of actuators. Firstly, the relative dynamics equation is established based on the character of displacement error, which is separated by that test-mass (TMs) tracking ideal orbit with high-frequency displacement and cavity of spacecraft tracking TMs with low-frequency displacement. Secondly, the feedback gain matrix is obtained by the LMI/SDP, which is devised by a general system containing a weight function. Finally, the simulation results demonstrate the performance of the proposed method.

Obesity among Medical Students of a Medical College: A Descriptive Cross-sectional Study.

The prevalence of overweight and obesity is increasing these days. The adverse effect of obesity can be seen in different physiological functions. Relative fat mass is a newly identified parameter to estimate whole body fat. This study aimed to find out the prevalence of obesity among medical students of a medical college. A descriptive cross-sectional study was carried out among medical students of a medical college from 1 September 2021 to 30 January 2022. Ethical approval was taken from the Institutional Review Committee (Reference number: FNMC/539/078/79). Simple random sampling was done. Height was measured using a stadiometer and waist circumference was measured using non-stretchable tape. Relative fat mass was calculated using the relative fat mass equation. The data was categorised according to the distribution of fat mass. Point estimate and 95% Confidence Interval were calculated. Out of 180 medical students, 57 (31.67%) (24.87-38.47, 95% Confidence Interval) were obese according to relative fat mass cut-off. The mean fat mass among male and female participants with high relative fat mass was 27.057±1.42 and 35.674±2.63 respectively. The prevalence of obesity was lower than in other studies done in similar settings. body fat; obesity; medical students.

Theoretical analysis of relative diffusion impedance in finite layer: Spiral-shaped Nyquist plots in electrochemical impedance spectroscopy

The spiral shape is ubiquitous in everyday life, and the spiral is also present in electrochemical impedance spectroscopy. By analyzing the diffusion of two ions in the opposite direction in the finite layer, the relative diffusion impedance equation can be obtained and used to simulate a series of different shapes of the Nyquist plots, including spiral shapes. In this paper, the variation law of the spiral Nyquist plot under different conditions is analyzed, and the application of the relative diffusion impedance equation in the area of thin-film solar cells and hydrogen permeation is discussed.

Design and analysis of a wheel-leg compound variable curvature ship hull cleaning robot

Underwater robotic cleaning devices are promising in ship hull maintenance for biofouling removal, but there are still some challenges for commercial application. Due to the complex surface of the ship hull, larger adsorptive force is needed for climbing robots to solve the problem of poor fitting between rigid structure and ship hull, which calls for more driving power. To mitigate the gap, this paper proposed a flexible wheel-leg composite moving mechanism for ship hull cleaning robots. The designed adjustable wheel leg, which is composed of three leg frames on the rotating shaft, eliminates the magnetic wheel's position constraints and expands the movement space. The relation equations of flip angle, pitching angle, turning angle, and hull curvature radius are generated and analyzed based on the robot's posture and steering motion. The mechanical properties of anti-slippage and anti-shedding under different motion states were studied so that the robot's critical point and limit adsorption force could be determined and verified. Simulation results show that the robot has good motion stability.

Study on Diffusion Behavior of Inorganic Materials and Performance of Extinguishing Coal Fire

ABSTRACT The majority of a coal mine’s goaf is semi-closed complex porous medium space, which is a critical place for coal spontaneous combustion disasters. To investigate the flow diffusion pattern of inorganic compounds in fractured coal in the goaf, as well as the capacity to put out coal fires. It examine the viscosity properties of an inorganic material slurry as a function of water/material ratio and time. By building a three-dimensional grouting test platform in the lab, simulating the broken coal body with sand and gravel, designing orthogonal tests to run multiple groups of grouting tests, and analyzing the effects of factors besides grouting pressure, water/material ratio, and air space ratio on the slurry diffusion radius. The effect of grouting pressure on the pattern of slurry diffusion radius of inorganic material and the water/material ratio under the action of grouting pressure is studied. The test of inorganic materials to extinguish coal pile fire is done, and the fire extinguishing and cooling ability is assessed in comparison to mud of the same grade, based on a prior research of inorganic materials to suppress CO formation in coal oxidation warming. According on the findings, the three-dimensional grouting test platform can pass the grouting test of loose sand and gravel bodies at various grouting pressures. The effects of grouting pressure, water/material ratio, and air space ratio on slurry dispersion are discovered to be multivariate power function relationships rather than linear correlations. The related slurry diffusion radius equation is established, and the variables impacting the parameters of the slurry diffusion range are evaluated, with the grouting pressure and water/material ratio having a substantial impact on slurry diffusion. Inorganic materials, as opposed to mud, require less time to extinguish coal pile fires and are less prone to scatter. It can form an oxygen barrier through continually covering the surface of coal. The study’s findings might give a solid foundation for the avoidance of slurry and fire suppression of inorganic materials in the goaf.

Close-range leader–follower flight control technology for near-circular low-orbit satellites

Abstract Based on the characteristics of near-circular orbits and close-range leader–follower flights, the relative dynamics equations of the eccentricity/inclination ( e/i ) vector method are introduced herein. Additionally, the constraint terms in the design of the leader–follower flight formation are found to satisfy the conditions of the line-of-sight angle and inter-satellite distance. The control box algorithm is proposed under the flying task’s constraints, such as the line-of-sight angle and distance between the satellites according to the e/i vector and Gauss perturbation equations. The algorithm comprehensively takes into account the relationship between the relative motion variations in the satellite formation in near-circular orbits as well as their relationship with the velocity increment applied to the satellites. The example simulated in this study not only illustrates the existence of a coupling relationship between the flight-following distance and flight-following line-of-sight angle but also verifies the influence of the relative eccentricity of the two satellites on the leader–follower flight stability. The simulation results show that when the control box algorithm was used to maintain the leader–follower flight, this method was simple, intuitive, and may be feasibly introduced as a flight-following control strategy.

Relative motion relationship and collision mechanism of slipper-retainer assembly of axial piston machines

Under high-speed rotation, the retainer-slipper assembly has serious collision interference, which affects the performance of the key friction pair of the piston pump. And abnormal wear of the retainer and slipper is observed in the faulty piston pump, even with fracture of the retainer and severe wear of the slipper neck. Based on the master-slave principle of the slipper and the retainer, a mathematical model of the relative motion relationship between the slipper-retainer is established. And the collision law between the slipper and the retainer is obtained by combining the relative motion velocity equation of the slipper. The effects of swashplate angle and pump shaft speed on the relative motion trajectory and collision strength of the slipper-retainer assembly are analyzed. The coordinates of all contact points between the slipper and the retainer during one piston cycle are calculated. These results clearly show the friction area of the retainer hole. Researches show that the rotation angle of the power slipper at the transition point is reduced with increasing swashplate angle. The increase of pump shaft speed has no influence on the contact law of the assembly. The collision strength of the assembly increases with the swashplate angle and pump shaft speed. A parametric investigation of the contact and collision between the slipper and the retainer is realized, providing a design method for analyzing the wearing character and mechanical properties of the axial piston pump.

Theory of mean E B shear in a stochastic magnetic field: ambipolarity breaking and radial current

The mean E B shear in a stochastic magnetic field is calculated, using the radial force balance relation and transport equations. This analysis is relevant to the L → H transition with resonant magnetic perturbations, and special focus is placed upon the physics of non-ambipolar transport and radial current. The key physical process is the flow of fluctuating currents along wandering magnetic fields. The increments in poloidal and toroidal rotation, density and ion pressure are calculated. The radial envelope of the magnetic perturbations inside the plasma defines a new scale , which is the characteristic scale of the magnetic fluctuation intensity profile. The net particle outflow due to stochastic magnetic fields is calculated and is determined by the net radial current through the separatrix. Implications for the L → H transition are discussed.

Conservation laws and some new exact solutions for traffic flow model via symmetry analysis

In this paper, we investigate the traffic flow model with congested phase through local and nonlocal symmetry analysis. Firstly, we derive the Lie group of transformations and show that it admits four one-dimensional optimal algebras. Next, by similarity reductions, we construct several exact solutions for each subalgebras as well as analyze the relation of group parameters. Furthermore, we construct a tree representing nonlocally related partial differential equations (PDEs) consisting inverse potential systems (IPS) and potential systems. Then, we prove that the traffic flow model yields one nonlocal symmetry and hence we derive an exact solution for the given system. Moreover, we generate the conservation laws for the governing systems through the nonlinear self-adjoint property. Finally, we study the nonlinear behaviors like weak discontinuity (C1-wave), characteristic shock for the physical model, and the impact of the anticipation factor on their evolutionary behavior graphically.

Stepwise mathematical derivation of the Herschel–Bulkley laminar fluid flow equations—in pipes

Stepwise derivation of flow equations of the Herschel–Bulkley (HB) model is not available in the literature. These equations are crucial for mechanical, chemical and petroleum engineering academia and industries where fundamental works on non-Newtonian fluids may be done to reach future models and estimation methods. Therefore, this work focuses on derivation of laminar flow equations and estimation methods of HB fluids through pipes. In this work, first, stepwise derivation of the HB fluid flow parameters consisting of fluid velocity, flow rate, average velocity and relative velocity equations is presented, followed by a straightforward mathematical model for use in numerical solution. Next, stepwise mathematical derivation of the laminar pressure drop equations by Merlo et al. (An innovative model for drilling fluid hydraulics. Paper presented at the SPE Asia Pacific oil and gas conference, Kuala Lumpur, Malaysia, 1995) and Gjerstad and Time (SPE J 20:1–18, 2014) is presented, and finally practical and user-friendly calculation procedures for different estimation methods are presented. The step-by-step derivation procedures presented in this work contribute to effective learning for engineering students and practitioners in addition to providing a clear example derivation guideline for future researchers to reach other more accurate non-Newtonian hydraulics models and estimation methods.

Elliptical Multi-Orbit Circumnavigation Control of UAVS in Three-Dimensional Space Depending on Angle Information Only

In order to analyze the circumnavigation tracking problem in complex three-dimensional space, in this paper, we propose a UAV group circumnavigation control strategy, in which the UAV circumnavigation orbit is an ellipse whose size can be adjusted arbitrarily; at the same time, the UAV group can be assigned to multiple orbits for tracking. The UAVs only have the angle information of the target, and the position information of the target can be obtained by using the angle information and the proposed three-dimensional estimator, thereby establishing an ideal relative velocity equation. By constructing the error dynamic equation between the actual relative velocity and the ideal relative velocity, the circumnavigation problem in three-dimensional space is transformed into a velocity tracking problem. Since the UAVs are easily disturbed by external factors during flight, the sliding mode control is used to improve the robustness of the system. Finally, the effectiveness of the control law and its robustness to unexpected situations are verified by simulation.

Growth mechanics of the viscoelastic membranes

Living membranes can grow as a response to their environment, and they are also known as viscoelastic materials. However, the growth phenomenon and the viscoelastic behavior of these membranes have been studied separately up to now. The main goal of this paper is to develop a general formulation that can account for growth and viscoelastic behaviors in membranes, simultaneously. Therefore, we propose a formulation for growing quasi-linear viscoelastic membranes. The growth model begins with a multiplicative decomposition of the gradient deformation tensor into elastic and growth tensor, where the growth of the membrane is considered as a single scalar-valued parameter. Furthermore, the quasi-linear viscoelasticity theory is utilized in the elastic configuration as additive decomposition of the second Piola–Kirchhoff stress tensor. To solve the evolution equations for both growth and quasi-linear viscoelastic relations, two implicit second order accuracy integration methods are employed. Moreover, strain-driven and stress-driven growth phenomena are accounted for based on a Total Lagrangian (TL) finite element formulation. The developed formulations can capture growth phenomena and viscoelastic properties of the membranes, individually, and it also enables to model co-existence of growth and viscoelasticity. Eventually, to evaluate the applicability of the developed formulation, several examples are investigated and compared to those available in the literature.

A Hamiltonian Dysthe equation for deep-water gravity waves with constant vorticity

This paper is a study of the water wave problem in a two-dimensional domain of infinite depth in the presence of non-zero constant vorticity. A goal is to describe the effects of uniform shear flow on the modulation of weakly nonlinear quasi-monochromatic surface gravity waves. Starting from the Hamiltonian formulation of this problem and using techniques from Hamiltonian transformation theory, we derive a Hamiltonian Dysthe equation for the time evolution of the wave envelope. Consistent with previous studies, we observe that the uniform shear flow tends to enhance or weaken the modulational instability of Stokes waves depending on its direction and strength. Our method also provides a non-perturbative procedure to reconstruct the surface elevation from the wave envelope, based on the Birkhoff normal form transformation to eliminate all non-resonant triads. This model is tested against direct numerical simulations of the full Euler equations and against a related Dysthe equation derived recently by Curtis, Carter & Kalisch (J. Fluid Mech., vol. 855, 2018, pp. 322–350) in the context of constant vorticity. Very good agreement is found for a range of values of the vorticity.

Stability analysis of spinning liquid-filled cylinders with exponentially varying cross section

In this paper, the stability analysis of a spinning liquid-filled cylinder with exponentially varying cross sections is carried out. Based on the spinning Euler–Bernoulli beam theory, the governing equation for vibration of the spinning cylinder is formulated by using Hamilton's principle. The relative perturbation motion equation of the rotating fluid is derived using the composition theorem of acceleration. Combined with the flow boundary conditions, the fluid forces exerted on the cylinder are obtained. Using the analytical method, the characteristic frequency equation of the system is determined. The stability of the considered system is determined by eigenvalue analysis. The accuracy of the proposed model is validated by comparing it with the existing data in the literature. Finally, a detailed parameter study is conducted to demonstrate the effects of mass ratio, cavity ratio, taper parameter, thickness ratio, and axial position on the vibration and stability of the system. The results show that these parameters play an important role in the instability, natural frequency, and critical spinning speed of the spinning taper cylinder partially filled with liquid.

Temporal instability of confined three-dimensional liquid jet with heat and mass transfer under longitudinal acoustic oscillations

The temporal instability of a confined viscous liquid jet surrounded by high-speed co-flowing viscous gas phase is studied in this work. The effect of the longitudinal acoustic oscillations, which is regarded as gas axial velocity oscillations, is also considered. The heat and mass transfer is characterized by the ratio between conduction heat flux and the evaporation heat flux; then, an explicit dispersion relation equation is obtained. The results suggest that more than one unstable region appears because of the gas velocity oscillations, including Kelvin–Helmholtz (K–H) instability and parametric instability regions. Increasing the forcing frequency enhances the K–H instability, while it has a stabilizing effect on the parametric instability. In addition, the liquid jet tends to be more unstable in non-axisymmetric modes when the gas rotating strength is strong. Although the gas viscosity has a destabilizing effect on the gas–liquid interface, the destabilizing effect is weak due to the low viscosity of the gas phase. According to the linear instability theory, the dominant wavenumber will locate in the most unstable region. Moreover, the parametric instability in non-axisymmetric modes may be observable when the Weber number is large.

Analysis of electromagnetic characteristic in the interior permanent magnet brushless DC motor

The motor vibration is mainly induced by the electromagnetic excitation. In order to improve the running performance of the permanent magnet brushless DC motor (BLDCM) within the rolling rotor compressor, this paper builds the predicted model of the electromagnetic excitation and analyzes the electromagnetic characteristic of the BLDCM. Firstly, the electromagnetic field is divided into four regions in 2D plane, including the magnet, air gap, stator slot, and slot-opening subdomains. Then, the relative equations of the electromagnetic field are constructed, and the vector magnetic potential is solved by the variable separation method. Thus, the magnetic flux density of the air gap is derived by the corresponding vector magnetic potential, which is used to describe the electromagnetic excitation. Based on the built model, the effects of the slot opening and air gap length on the electromagnetic characteristic are analyzed. The analysis results can provide a reference for the improvement of the electromagnetic characteristic of the BLDCM by structure optimization.

Modeling a Wave on Mild Sloping Bottom Topography and Its Dispersion Relation Approximation

Linear wave theory is a simple theory that researchers and engineers often use to study a wave in deep, intermediate, and shallow water regions. Many researchers mostly used it over the horizontal flat seabed, but in actual conditions, sloping seabed always exists, although mild. In this research, we try to model a wave over a mild sloping seabed by linear wave theory and analyze the influence of the seabed’s slope on the solution of the model. The model is constructed from Laplace and Bernoulli equations together with kinematic and dynamic boundary conditions. We used the result of the analytical solution to find the relation between propagation speed, wavelength, and bed slope through the dispersion relation. Because of the difference in fluid dispersive character for each water region, we also determined dispersion relation approximation by modifying the hyperbolic tangent form into hyperbolic sine-cosine and exponential form, then approximated it with Padé approximant. As the final result, exponential form modification with Padé approximant had the best agreement to exact dispersion relation equation then direct hyperbolic tangent form.

A Novel Method for Dynamic Molecular Weight Distribution Determination in Organometallic Catalyzed Olefin Polymerizations

In this study, a mathematical model for the time evolution of molecular weight distribution (MWD) was developed. This temporal model is based on the well-known Ziegler–Natta polymerization mechanism and reaction kinetics by the parametric solving of related differential equations. However, due to the generality of the reactions involved, the model can be extended to the other type of catalysts, such as metallocenes, Phillips, etc. The superiority of this model lies in providing the possibility of a more precise prediction over the active sites and kinetic parameters using a simple mathematical equation, which leads to improved reactor design in large-scale production. The model uses a function to develop a methodology for MWD calculations. In this way, the transient response is limited to the first few minutes of the reaction; however, it is important as it demonstrates the establishment of the final MWD. According to the results, almost for practical conditions with negligible transfer resistances, the time dependency of the MWD has a transient interval, depending on the kinetic constants of polymerization reactions. Increasing the time to infinity results in an increase in MW and a widening in MWD, which confirms the experimental plots well. In short, the main advantage of our proposed model over the previous ones is its ability to predict the MWD even before the completion of the polymerization reaction. The results of the present model match well with those of the well-known Schulz–Flory distribution, which only predicts the final molecular weight distribution, thus confirming that the model is reliable and generalizable.