Drag Force, Drag Torque, and Magnus Force Coefficients of Rotating Spherical Particle Moving in Fluid

2012 ◽  
Vol 30 (1) ◽  
pp. 55-67 ◽  
Author(s):  
N. Lukerchenko ◽  
Yu. Kvurt ◽  
I. Keita ◽  
Z. Chara ◽  
P. Vlasak
2016 ◽  
Vol 20 (1) ◽  
pp. 65-76
Author(s):  
Tanase Tanase

Abstract The present paper is a theoretical study aiming for to assess the influence of the different factors such as deviation from the spherical form of a particle, specific mass load of the pneumatic conveying pipe and the report between the particle diameter and the pipe diameter, over the floating speed of a particle. For a non-spherical particle, the Magnus force is affecting the floating speed of the given particle by increasing or decreasing it. The equation deducted within the present study, describes the movement of a particle or a fluid swirl under the resultant force with emphasis on the evaluation of the nature and magnitude of the Magnus force. The same Magnus Force explains the movement of the swirls in fluids, as for the wind swirls (hurricane) or water swirls. The next part of the study relate the report between the particle diameter and the pipe diameter as well as the specific loads of the pipe, to the same floating speed. A differentiation in denominating the floating speed is proposed as well as that for the non-spherical particle the floating speed should be a domain, rather than a single value.


2021 ◽  
Vol 11 (24) ◽  
pp. 11740
Author(s):  
Yong Chul Kim

Traditionally, circular cross-section towers have been used as supporting systems of wind turbines, but weaknesses have become apparent with recent upsizing of wind turbines. Thus, polygonal cross-section towers have been proposed and used in Europe. In this study, the effects of polygonal cross-sections on the aeroelastic and aerodynamic characteristics of wind turbines were examined through a series of wind tunnel tests. Aeroelastic tests showed that a square cross-section tower showed instability vibrations, and polygonal cross-section towers showed limited vibrations for tower-only cases. However, for wind turbines with various polygonal cross-section towers, no instability vibrations were observed, and displacements increased proportionally to the square of mean wind speed. Furthermore, pressure measurements showed that local force coefficients changed largely depending on wind direction and azimuth angle. Local drag force coefficients decreased with increasing number of tower sides, approaching those of the tower-only case, and local lift force coefficients showed larger absolute values than those of the tower-only case. The maximum mean and fluctuating drag force and the maximum fluctuating lift coefficients at each height decreased with increasing number of tower sides.


Author(s):  
Luis San Andrés ◽  
Keun Ryu ◽  
Paul Diemer

Green technologies are a mandate in a world concerned with saving resources and protecting the environment. Oil-free turbocharger (TC) systems for passenger and commercial vehicles dispense with the lubricant in the internal combustion engine (ICE), hence eliminating not just oil coking, but also suppressing nonlinear behavior, instability and excessive noise; all factors to poor reliability and premature mechanical failure. The work hereby presented is a stepping stone in a concerted effort toward developing a computational design tool integrating both radial and thrust foil gas bearings for oil-free automotive TCs. The paper presents the physical analysis and numerical model for prediction of the static and dynamic forced performance of gas thrust foil bearings (GTFBs). A laminar flow, thin film flow model governs the generation of hydrodynamic pressure and a finite element plate model determines the elastic deformation of a top foil and its support bump strip layers. For a specified load, the analysis predicts the minimum gas film thickness, deformation and pressure fields, the drag torque and power loss, and the axial stiffness and damping force coefficients, respectively. Open source archival test data on load capacity and drag torque serves to benchmark some of the model predictions. Next, predictions are obtained for a GTFB configuration designed for an oil-free TC operating at increasing gas temperatures, axial loads, and shaft rotational speeds. The largest drag torque occurs at the highest temperature since the gas viscosity is also highest, whereas the largest load determines operation with a minute film thickness that sets a limit for the manufacturing tolerance. While airborne, the drag friction factor for the bearing is small, ranging from 0.009 to 0.015, thus demonstrating the advantage of an air bearing technology over engine oil-lubricated bearings. The synchronous speed axial stiffness increases with operating speed (and load), whereas the axial damping coefficient remains nearly invariant. The operating gas temperature plays an insignificant role on the variation of the force coefficients with frequency, whereas the operating speed and the ensuing applied thrust load determine the largest changes. The model predicts, as an excitation frequency (ω) increases, a GTFB axial stiffness (Kz) that hardens and a damping coefficient (Cz) that quickly vanishes. The most important finding is that CzΩ/Kz ≈ γ = the material loss factor for the bearing. Hence, the success of foil bearing technology relies on the selection of a metal underspring structure that offers the largest mechanical energy dissipation characteristics.


2013 ◽  
Vol 721 ◽  
pp. 155-179 ◽  
Author(s):  
Holger Homann ◽  
Jérémie Bec ◽  
Rainer Grauer

AbstractThe impact of turbulent fluctuations on the forces exerted by a fluid on a towed spherical particle is investigated by means of high-resolution direct numerical simulations. The measurements are carried out using a novel scheme to integrate the two-way coupling between the particle and the incompressible surrounding fluid flow maintained in a high-Reynolds-number turbulent regime. The main idea consists of combining a Fourier pseudo-spectral method for the fluid with an immersed-boundary technique to impose the no-slip boundary condition on the surface of the particle. This scheme is shown to converge as the power $3/ 2$ of the spatial resolution. This behaviour is explained by the ${L}_{2} $ convergence of the Fourier representation of a velocity field displaying discontinuities of its derivative. Benchmarking of the code is performed by measuring the drag and lift coefficients and the torque-free rotation rate of a spherical particle in various configurations of an upstream-laminar carrier flow. Such studies show a good agreement with experimental and numerical measurements from other groups. A study of the turbulent wake downstream of the sphere is also reported. The mean velocity deficit is shown to behave as the inverse of the distance from the particle, as predicted from classical similarity analysis. This law is reinterpreted in terms of the principle of ‘permanence of large eddies’ that relates infrared asymptotic self-similarity to the law of decay of energy in homogeneous turbulence. The developed method is then used to attack the problem of an upstream flow that is in a developed turbulent regime. It is shown that the average drag force increases as a function of the turbulent intensity and the particle Reynolds number. This increase is significantly larger than predicted by standard drag correlations based on laminar upstream flows. It is found that the relevant parameter is the ratio of the viscous boundary layer thickness to the dissipation scale of the ambient turbulent flow. The drag enhancement can be motivated by the modification of the mean velocity and pressure profile around the sphere by small-scale turbulent fluctuations. It is demonstrated that the variance of the drag force fluctuations can be modelled by means of standard drag correlations. Temporal correlations of the drag and lift forces are also presented.


2004 ◽  
Vol 10 (1) ◽  
pp. 48-55 ◽  
Author(s):  
P. Mallikarjuna ◽  
Ch. Suresh Babu ◽  
T. Murali ◽  
M. R. Satish Kumar

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