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

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

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1964.0088 ◽

1964 ◽

Vol 279 (1376) ◽

pp. 39-49 ◽

Cited By ~ 3

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.

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The aerodynamic resistance to a sphere rotating at high speed

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1963.0010 ◽

1963 ◽

Vol 271 (1345) ◽

pp. 143-153 ◽

Cited By ~ 22

Keyword(s):

Boundary Layer ◽

High Speed ◽

Aerodynamic Resistance ◽

Point Of View ◽

Magnetic Suspension ◽

Gas Flows ◽

Drag Torque ◽

Rotating Sphere ◽

Theoretical Predictions

An attempt has been made to adapt the technique of magnetic suspension of steel rotors to the study of high-speed aerodynamic problems. Surface speeds up to ca. 800 m/s are possible. The advantages and shortcomings of the technique from the aerodynamic point of view are discussed together with the different regimes of flow at present attainable with the apparatus. The particular case of a rotating sphere in the boundary-layer regime is considered and some results obtained with this technique are presented. Observations with smoke and with schlieren photographs show that the gas flows from the poles to the equator where it is thrown off as a narrow plane radial jet. These results are in accord with Howarth’s theoretical predictions. The measured drag torque on the sphere is however somewhat higher than the predicted value and possible reasons for this are considered. The work is now being extended to other regimes of flow.

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Transition regime sphere drag near the free molecule limit

AIAA Journal ◽

10.2514/3.6380 ◽

1971 ◽

Vol 9 (7) ◽

pp. 1434-1435 ◽

Cited By ~ 8

Author(s):

WINFRED M. PHILLIPS ◽

A. R. KUHLTHAU

Keyword(s):

Transition Regime ◽

Free Molecule ◽

Sphere Drag

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Transport Path in Hydrogenated Microcrystalline Silicon

MRS Proceedings ◽

10.1557/proc-715-a25.3 ◽

2002 ◽

Vol 715 ◽

Cited By ~ 1

Author(s):

N. Wyrsch ◽

C. Droz ◽

L. Feitknecht ◽

J. Spitznagel ◽

A. Shah

Keyword(s):

Raman Spectroscopy ◽

Volume Fraction ◽

Conductivity Measurement ◽

Dark Conductivity ◽

Transition Regime ◽

Conductivity Data ◽

Crystalline Volume Fraction ◽

Microcrystalline Silicon ◽

Crystalline Fraction ◽

Transport Path

AbstractUndoped microcrystalline silicon samples deposited in the transition regime between amorphous and microcrystalline growth have been investigated by dark conductivity measurement and Raman spectroscopy. From the latter, a semi-quantitative crystalline volume fraction Xc of the sample was deduced and correlated with dark conductivity data in order to reveal possible percolation controlled transport. No threshold was observed around the critical crystalline fraction value Xc of 33%, as reported previously, but a threshold in conductivity data was found at Xc≈50%. This threshold is interpreted here speculatively as being the result of postoxidation, and not constituting an actual percolation threshold.

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