The aerodynamic resistance to a rotating sphere in the transition régime between free molecule and continuum creep flow

1964 ◽  
Vol 279 (1376) ◽  
pp. 39-49 ◽  
Keyword(s):  
Rarefied Gas ◽  
Aerodynamic Drag ◽  
Aerodynamic Resistance ◽  
Reynolds Numbers ◽  
Approximate Theory ◽  
Drag Torque ◽  
Free Molecule ◽  
Steel Sphere ◽  
Creep Flow ◽  
Wide Range

An experimental and theoretical study has been made of the aerodynamic drag torque on a sphere rotating in a rarefied gas. The drag torque on a magnetically suspended polished steel sphere rotating in air was measured over a wide range of Knudsen numbers from continuum to free molecule flow and for several different Mach numbers up to ca . 1. The drag under free molecule conditions was found to be consistent with the assumption of perfectly diffuse reflexion of molecules at the surface of the rotor. An approximate theory is derived which is analogous to Millikan’s solution to the problem of plane Couette flow and is valid for low Mach and Reynolds numbers. Theory and experiment are found to agree to within 10 % in the range investigated, for Reynolds numbers less than ca . 20.

The aerodynamic resistance to a sphere rotating at high Mach numbers in the rarefied transition régime

1966 ◽  
Vol 293 (1433) ◽  
pp. 156-168 ◽  
Keyword(s):  
Experimental Study ◽  
Aerodynamic Resistance ◽  
Pressure Gauge ◽  
Transition Regime ◽  
Drag Torque ◽  
Free Molecule ◽  
Rotating Sphere ◽  
Mach Numbers ◽  
High Mach ◽  
Molecule Flow

An experimental study has been made of the gaseous drag torque on an isolated sphere rotating at high Mach numbers. The sphere was suspended electromagnetically and spun by induction. The drag torque has been measured through the transition régime from continuum to free molecule flow at Mach numbers (based on equatorial speed) of up to about five. These high Mach numbers were achieved in heavy vapours (diiodomethane, germanium tetrabromide and stannic bromide) with sonic speed as little as a quarter of that in air. To measure the pressure in the vapour a second (smaller) rotating sphere was used as a pressure gauge. The results agree well with those previously obtained and show an unexpected Mach number dependence in the transition régime.

Calculation of the primary trajectories of seeds and other particles in strong winds

1983 ◽  
Vol 219 (1215) ◽  
pp. 217-217
Keyword(s):  
Equations Of Motion ◽  
Aerodynamic Resistance ◽  
Reynolds Numbers ◽  
Spherical Particles ◽  
Spores And Pollen ◽  
General Terms ◽  
Wide Range ◽  
Strong Winds ◽  
Dispersal Distances ◽  
Enormous Number

The movement of variously dense spherical particles representing a variety of seeds, fruits, spores and pollen, and released from rest into arbitrary winds and a gravitational field is discussed in general terms that account in detail for changes in the quasi-static aerodynamic resistance to motion experienced by such particles during aerial flight. A hybrid analytical-empirical law is established which describes this resistance fairly accurately for particle Reynolds numbers in the range 0—60 000 and that allows for the numerical integration of the equations of motion so as to cover a very wide range of flight conditions. This makes possible the provision of a set of four-parameter universal range tables from which the dispersal distances for an enormous number of practical cases may be estimated. One particular case of particle movement in a region of pseudo-thermal convection is also discussed and this shows how a marked degree of deposition concentration may be induced in some circumstances by such a flow. Botanists and ecologists concerned with seed and particle dispersal in the environment may find the universal range tables of particular interest and use. This is because the tables obviate the need for the integration of the equations of motion when dealing with individual cases and permit an estimation of range purely on the basis of the specified quantities of particle size, density and altitude of release, atmospheric wind speed, density and viscosity, and the acceleration due to gravity.

Extra Drag Force on a Circular Cylinder Due to the Presence of Solid Particles in Subsonic Compressible Flow

1991 ◽  
Author(s):  
Stanley B. Mellsen
Keyword(s):  
Compressible Flow ◽  
Incompressible Flow ◽  
Aerodynamic Drag ◽  
Collection Efficiency ◽  
Reynolds Numbers ◽  
Solid Particles ◽  
Circular Cylinders ◽  
Critical Mach Number ◽  
Wide Range ◽  
Inertia Parameters

Abstract The effect of particles, such as dust in air on aerodynamic drag of circular cylinders was calculated for compressible flow at critical Mach number and for incompressible flow. The effect of compressibility was found negligible for particles larger than about 10 μm, for which the air can be considered a continuum. Drag coefficient and collection efficiency are provided for a wide range of inertia parameters and Reynolds numbers for both compressible and incompressible flow.

Experimental investigation of the aerodynamic drag of roof-mounted insulators for trains

2019 ◽  
Vol 234 (8) ◽  
pp. 834-846
Author(s):  
Jonathan Tschepe ◽  
Jörg-Torsten Maaß ◽  
Christian Navid Nayeri ◽  
Christian Oliver Paschereit
Keyword(s):  
Boundary Conditions ◽  
Energy Demand ◽  
High Speed ◽  
Aerodynamic Drag ◽  
Aerodynamic Resistance ◽  
Reynolds Numbers ◽  
Experimental Investigations ◽  
Flexible Material ◽  
High Speed Trains ◽  
The Impact

This paper presents the results of experimental investigations on the aerodynamic drag of roof-mounted insulators for use on low- and high-speed trains. Wind tunnel investigations at different Reynolds numbers in the subcritical, critical, and supercritical flow regime were performed, in addition to investigations using wall-mounted cylinders. Furthermore, the impact of insulator sheds made of flexible material was analyzed. For a better understanding of the aerodynamic behavior of the insulators when mounted on trains, different boundary conditions representing realistic configurations as found on the roof of trains were simulated. From the measured drag, the energy demand to overcome the aerodynamic resistance of different types of insulators was calculated. Depending on the above mentioned boundary conditions, a noticeable contribution of the insulators to the entire train's aerodynamic drag could be observed. With flexible insulator sheds, a further increased air resistance was observed with the onset of fluttering. Similar to the cylinder, the aerodynamic behavior of the insulators depends on the respective Reynolds number.

On the drag of a flat plate at zero incidence in almost-free-molecule flow

1959 ◽  
Vol 5 (3) ◽  
pp. 481-490 ◽  
Author(s):  
V. C. Liu
Keyword(s):  
Flat Plate ◽  
Skin Friction ◽  
Flow Regime ◽  
Rarefied Gas ◽  
Approximate Theory ◽  
Free Molecule ◽  
Transition Flow ◽  
Rigid Spheres ◽  
Governing Parameter ◽  
Transition Flow Regime

A physical theory is proposed for the skin friction on a flat plate at zero incidence in the transition flow regime, i.e. in the flow of a moderately rarefied gas. The ratio of the molecular mean free path to the characteristic size of the plate is assumed of order unity or larger. A general formula for the perturbation to the well-known friction of the free-molecule theory is given. This perturbation is attributed to the intermolecular collisions which are neglected on the basis of the free-molecule hypothesis. The expected rate of collisions are calculated for rigid spheres, using the classical kinetic theory.Although this is intended as an approximate theory, the theoretical results check surprisingly well with the limited experimental data that are available. The present theory shows that the ratio of the Reynolds number to the Mach number squared is the governing parameter for determining the intermolecular collision effect on skin friction in the transition flow regime.

scholarly journals Mine aerology of dust aerosols under conditions of hydro-vortex coagulation

2020 ◽  
pp. 155-165
Author(s):  
Nikolay Petrovich KOSAREV ◽  
◽  
Vladimir Nikolaevich MAKAROV ◽  
Aleksandr Vladimirovich UGOL'NIKOV ◽  
Nikolay Vladimirovich MAKAROV ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Aerodynamic Drag ◽  
Coal Dust ◽  
Aerodynamic Resistance ◽  
Experimental Studies ◽  
Similarity Criteria ◽  
Dust Suppression ◽  
Dust Aerosols ◽  
Wide Range ◽  
Mine Workings

Dust suppression is the most popular method for depositing dust from the air to blast isolation. Improving the isolation system for probable coal dust explosions is an integral part of the problem of dust explosion protection of mining enterprises, the solution of which is one of the most important tasks in the field of occupational safety and health. Purpose: study of physics of the process and the construction of a mathematical model of the movement of aerosols in mine workings in a wide range of changes in the inertial kinematic parameters of the air flow. Research methods. Based on the Boussinesq equation, the Fourier rule and the similarity theorem of complex systems, the analogy of vorticity dispersion and kinematic viscosity, a mathematical model of the movement of dust aerosols under hydro-vortex coagulation conditions is constructed. Some similarity criteria are obtained that ensure the identity of experimental studies and real aerological processes in mines, as well as criterion equations for calculating the coefficient of aerodynamic drag and the time of unsteady inertial motion. Results. Equations are obtained that make it possible to identify aerodynamic processes of aerosol motion under hydro-cyclonic dust suppression through the criteria of Reynolds, Euler and Archimedes, corresponding to the overStokes and Stokes flow regimes. The possibility of reducing the aerodynamic resistance to 20% during hydro-vortex coagulation has been confirmed, which makes it possible to increase the energy efficiency of dust suppression by up to 15% and to increase the turbulization coefficient by at least 20%, thereby reducing the likelihood of a hazardous concentration of dust aerosols. Application. The use of the proposed mathematical model will make it possible to better calculate local aerological processes in mine workings and, as a consequence, to increase the efficiency of turbulization and dust suppression process control at mining enterprises.

Calculation of the primary trajectories of seeds and other particles in strong winds

1983 ◽  
Vol 389 (1796) ◽  
pp. 15-66 ◽  
Keyword(s):  
Equations Of Motion ◽  
Aerodynamic Resistance ◽  
Reynolds Numbers ◽  
Spherical Particles ◽  
Spores And Pollen ◽  
General Terms ◽  
Wide Range ◽  
Strong Winds ◽  
Dispersal Distances ◽  
Enormous Number

The movement of variously dense spherical particles representing a variety of seeds, fruits, spores and pollen, released from rest into arbitrary winds and a gravitational field is discussed in general terms that account in detail for changes in the quasi-static aerodynamic resistance to motion experienced by such particles during aerial flight. A hybrid analytical-empirical law is established that describes this resistance fairly accurately for particle Reynolds numbers in the range 0-60000 and that allows for the numerical integration of the equations of motion so as to cover a very wide range of flight conditions. This makes possible the provision of a set of four-parameter universal range tables from which the dispersal distances for an enormous number of practical cases may be estimated. One particular case of particle movement in a region of pseudo-thermal convection is also discussed and this shows how a marked degree of deposition concentration may be induced in some circumstances by such a flow.

Drag coefficients of air rifle pellets with wide range of geometries

2021 ◽  
pp. 095440622199119
Author(s):  
Nicos Ladommatos
Keyword(s):  
Drag Coefficient ◽  
Aerodynamic Drag ◽  
Reynolds Numbers ◽  
Air Velocity ◽  
Drag Coefficients ◽  
Small Influence ◽  
Wide Range ◽  
Coefficient Increase ◽  
Air Rifle ◽  
Mach And Reynolds Numbers

Air rifle and air pistol target shooting are included in major intentional and national sports competitions and are also highly popular sport pastimes. Published scientific studies of pellet drag are very rare, in contrast to a large number of scientific studies published on aerodynamic drag of sports balls and other sports projectiles. Measurements are presented of the drag coefficients for 31 air rifle pellets of mainly 4.5 mm (0.177 in) calibre having a wide range of geometries. The drag coefficient measurements were made with a low-turbulence open wind tunnel at flow velocity of 200 m/s (Mach and Reynolds numbers 0.57 and 56,000 for 4.5 mm pellets). The detailed geometry of some pellets was altered systematically in order to improve understanding of how pellet geometry affects drag coefficient. The drag coefficient for the 31 pellets varied widely from 0.36 to 0.78, and it was influenced substantially by the curvature of the flow separating from the pellet head rim. Large curvatures delayed flow re-attachment onto the pellet tail, thereby lowering pellet base pressure and increasing the value of drag coefficient. Pellets with hemi-spherical or ogive-shaped noses generally had lower values of drag coefficient than pellets with other nose shapes. The presence of the pellet tail was beneficial by providing a surface onto which the flow detaching from the pellet rim could re-attach. However, for minimisation of drag coefficient, the pellet tail had to be of a certain optimum length which depended on the shape of the pellet nose. Small differences in pellet geometry had significant influence on the value of drag coefficient. Increase in air velocity from 120 to 200 m/s had small influence on the value of drag coefficient for three common sports pellets having flat, conical and dome-shaped noses.

Turbulent three-dimensional dielectric electrohydrodynamic convection between two plates

2012 ◽  
Vol 696 ◽  
pp. 228-262 ◽  
Author(s):  
A. Kourmatzis ◽  
J. S. Shrimpton
Keyword(s):  
Spatial Data ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Energy Budgets ◽  
Turbulent Regime ◽  
Scalar Flux ◽  
Wide Range ◽  
Scalar Variance

AbstractThe fundamental mechanisms responsible for the creation of electrohydrodynamically driven roll structures in free electroconvection between two plates are analysed with reference to traditional Rayleigh–Bénard convection (RBC). Previously available knowledge limited to two dimensions is extended to three-dimensions, and a wide range of electric Reynolds numbers is analysed, extending into a fully inherently three-dimensional turbulent regime. Results reveal that structures appearing in three-dimensional electrohydrodynamics (EHD) are similar to those observed for RBC, and while two-dimensional EHD results bear some similarities with the three-dimensional results there are distinct differences. Analysis of two-point correlations and integral length scales show that full three-dimensional electroconvection is more chaotic than in two dimensions and this is also noted by qualitatively observing the roll structures that arise for both low (${\mathit{Re}}_{E} = 1$) and high electric Reynolds numbers (up to ${\mathit{Re}}_{E} = 120$). Furthermore, calculations of mean profiles and second-order moments along with energy budgets and spectra have examined the validity of neglecting the fluctuating electric field ${ E}_{i}^{\ensuremath{\prime} } $ in the Reynolds-averaged EHD equations and provide insight into the generation and transport mechanisms of turbulent EHD. Spectral and spatial data clearly indicate how fluctuating energy is transferred from electrical to hydrodynamic forms, on moving through the domain away from the charging electrode. It is shown that ${ E}_{i}^{\ensuremath{\prime} } $ is not negligible close to the walls and terms acting as sources and sinks in the turbulent kinetic energy, turbulent scalar flux and turbulent scalar variance equations are examined. Profiles of hydrodynamic terms in the budgets resemble those in the literature for RBC; however there are terms specific to EHD that are significant, indicating that the transfer of energy in EHD is also attributed to further electrodynamic terms and a strong coupling exists between the charge flux and variance, due to the ionic drift term.

Sign in / Sign up

Export Citation Format

Share Document