Flow past an oblate ellipsoid of revolution aligned along the major axis

1970 ◽  
Vol 5 (2) ◽  
pp. 319-323
Author(s):  
A. I. Shvets
Keyword(s):  
Major Axis ◽  
Oblate Ellipsoid ◽  
Flow Past ◽  
Ellipsoid Of Revolution

Reachable domain of spacecraft with a single normal impulse

2019 ◽  
Vol 91 (7) ◽  
pp. 977-986 ◽  
Author(s):  
Junhua Zhang ◽  
Jianping Yuan ◽  
Wei Wang ◽  
Jiao Wang
Keyword(s):  
Major Axis ◽  
Emergency Evacuation ◽  
Semi Major Axis ◽  
Content Type ◽  
Orbital Transfers ◽  
Ellipsoid Of Revolution ◽  
Rendezvous And Docking ◽  
Practical Implications ◽  
Initial Orbit

Purpose The purpose of this paper is to obtain the reachable domain (RD) for spacecraft with a single normal impulse while considering both time and impulse constraints. Design/methodology/approach The problem of RD is addressed in an analytical approach by analyzing for either the initial maneuver point or the impulse magnitude being arbitrary. The trajectories are considered lying in the intersection of a plane and an ellipsoid of revolution, whose family can be determined analytically. Moreover, the impulse and time constraints are considered while formulating the problem. The upper bound of impulse magnitude, “high consumption areas” and the change of semi-major axis and eccentricity are discussed. Findings The equations of RD with a single normal impulse are analytically obtained. The equations of three scenarios are obtained. If normal impulse is too large, the RD cannot be obtained. The change of the semi-major axis and eccentricity with large normal impulse is more obvious. For long-term missions, the change of semi-major axis and eccentricity leaded by multiple normal impulses should be considered. Practical implications The RD gives the pre-defined region (all positions accessible) for a spacecraft under a given initial orbit and a normal impulse with certain magnitude. Originality/value The RD for spacecraft with normal impulse can be used for non-coplanar orbital transfers, emergency evacuation after failure of rendezvous and docking and collision avoidance.

Viscous shear flow past small bluff bodies attached to a plane wall

1975 ◽  
Vol 69 (4) ◽  
pp. 803-823 ◽  
Author(s):  
Masaru Kiya ◽  
Mikio Arie
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Shear Flow ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Major Axis ◽  
Plane Wall ◽  
Local Boundary ◽  
Flow Past ◽  
Viscous Shear

Numerical solutions of the Navier-Stokes equations are presented for two-dimensional viscous flow past semicircular and semielliptical projections attached to a plane wall on which a laminar boundary layer has developed. Since the major axis is in the direction normal to the wall and is chosen to be twenty times as long as the minor axis in the present case, the flow around the semielliptical projection will approximately correspond to that around a normal flat plate. It is assumed that the height of each obstacle is so small in comparison with the local boundary-layer thickness that the approaching flow can be approximated by a uniform shear flow. Numerical solutions are obtained for the range 0·1-100 of the Reynolds number, which is defined in terms of the undisturbed approaching velocity at the top of the obstacle and its height. The geometrical shapes of the front and rear standing vortices, the drag coefficients and the pressure and shear-stress distributions are presented as functions of the Reynolds number. The computed results are discussed in connexion with the data already obtained in the other theoretical solutions and an experimental observation.

Low Reynolds numbers flow past an ellipsoid of revolution of large aspect ratio

1965 ◽  
Vol 23 (4) ◽  
pp. 657-671 ◽  
Author(s):  
Yun-Yuan Shi
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Three Dimensional ◽  
Major Axis ◽  
Reynolds Numbers ◽  
The Body ◽  
Large Aspect Ratio ◽  
Low Reynolds Numbers ◽  
Ellipsoid Of Revolution ◽  
Limiting Case

The results of Proudman & Pearson (1957) and Kaplun & Lagerstrom (1957) for a sphere and a cylinder are generalized to study an ellipsoid of revolution of large aspect ratio with its axis of revolution perpendicular to the uniform flow at infinity. The limiting case, where the Reynolds number based on the minor axis of the ellipsoid is small while the other Reynolds number based on the major axis is fixed, is studied. The following points are deduced: (1) although the body is three-dimensional the expansion is in inverse power of the logarithm of the Reynolds number as the case of a two-dimensional circular cylinder; (2) the existence of the ends and the variation of the diameter along the axis of revolution have no effect on the drag to the first order; (3) a formula for drag is obtained to higher order.

1. On the Figures of Equilibrium of a Rotating Mass of Fluid

1882 ◽  
Vol 11 ◽  
pp. 610-613 ◽  
Author(s):  
William Thomson
Keyword(s):  
Natural Philosophy ◽  
Oblate Ellipsoid ◽  
Single Ring ◽  
Figures Of Equilibrium ◽  
Ellipsoid Of Revolution ◽  
Definite Limit

(a) The oblate ellipsoid of revolution is proved in Thomson and Tait's Natural Philosophy (first edition, § 776, and the Table of § 772) to be stable, if the condition of being an ellipsoid of revolution be imposed. It is obviously not stable for very great eccentricities without this double condition of being both a figure of revolution and ellipsoidal.(b) If the condition of being a figure of revolution is imposed, without the condition of being an ellipsoid, there is, for large enough moment of momentum, an annular figure of equilibrium which is stable, and an ellipsoidal figure which is unstable. It is probable, that for moment of momentum greater than one definite limit and less than another, there is just one annular figure of equilibrium, consisting of a single ring.

I. On the conduction of heat in ellipsoids of revolution

1879 ◽  
Vol 29 (196-199) ◽  
pp. 98-102
Keyword(s):  
Major Axis ◽  
Mathematical Treatment ◽  
Ellipsoid Of Revolution ◽  
Slight Alteration

The object of the present paper is to investigate the expressions which present themselves in the mathematical treatment of the problem of the conduction of heat in an ellipsoid of revolution. The results obtained constitute a generalisation of the corresponding solution for the sphere, and are found, in the first instance, for an ellipsoid whose major axis is the axis of revolution, but a slight alteration will render them applicable also to a planetary ellipsoid.

scholarly journals Hydromechanics of low-Reynolds-number flow. Part 4. Translation of spheroids

1976 ◽  
Vol 75 (4) ◽  
pp. 677-689 ◽  
Author(s):  
Allen T. Chwang ◽  
Theodore Y. Wu
Keyword(s):  
Major Axis ◽  
Reynolds Numbers ◽  
Prolate Spheroid ◽  
Stream Velocity ◽  
Semi Major Axis ◽  
Reynolds Number Flow ◽  
Flow Past ◽  
Flow Part ◽  
Number Flow ◽  
Low Reynolds

The problem of a uniform transverse flow past a prolate spheroid of arbitrary aspect ratio at low Reynolds numbers has been analysed by the method of matched asymptotic expansions. The solution is found to depend on two Reynolds numbers, one based on the semi-minor axis b, Rb = Ub/v, and the other on the semi-major axis a, Ra = Ua/v (U being the free-stream velocity at infinity, which is perpendicular to the major axis of the spheroid, and v the kinematic viscosity of the fluid). A drag formula is obtained for small values of Rb and arbitrary values of Ra. When Ra is also small, the present drag formula reduces to the Oberbeck (1876) result for Stokes flow past a spheroid, and it gives the Oseen (1910) drag for an infinitely long cylinder when Ra tends to infinity. This result thus provides a clear physical picture and explanation of the ‘Stokes paradox’ known in viscous flow theory.

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