Flow about a fluid sphere at low to moderate Reynolds numbers

1987 ◽  
Vol 177 ◽  
pp. 1-18 ◽  
Author(s):  
D. L. R. Oliver ◽  
J. N. Chung
Keyword(s):  
Reynolds Number ◽  
Equations Of Motion ◽  
Reynolds Numbers ◽  
Solid Sphere ◽  
Fluid Sphere ◽  
State Equations ◽  
Drag Coefficients ◽  
Low Reynolds Number Flows ◽  
Analytical Series ◽  
Reynolds Number Flows

The steady-state equations of motion are solved for a fluid sphere translating in a quiescent medium. A semi-analytical series truncation method is employed in conjunction with a cubic finite-element scheme. The range of Reynolds numbers investigated is from 0.5 to 50. The range of viscosity ratios is from 0 (gas bubble) to 107 (solid sphere). The flow structure and the drag coefficients agree closely with the limited available experimental measurements and also compare favourably with published finite-difference solutions. The strength of the internal circulation was found to increase with increasing Reynolds number. The flow patterns and the drag coefficient show little variation with the interior Reynolds number. Based on the numerical results, predictive equations for drag coefficients are recommended for both moderate- and low-Reynolds-number flows.

Profiles for Low Reynolds Number Flows

1968 ◽  
Vol 183 (1) ◽  
pp. 591-602 ◽  
Author(s):  
G. S. Vasy ◽  
L. J. Kastner ◽  
J. C. McVeigh
Keyword(s):  
Reynolds Number ◽  
Discharge Coefficient ◽  
Low Reynolds Number ◽  
Small Diameter ◽  
Reynolds Numbers ◽  
Number Range ◽  
Low Reynolds Number Flows ◽  
Low Reynolds ◽  
Reynolds Number Flows ◽  
Considerable Range

The characteristics of the orifice meter are well known and have been thoroughly explored by a number of investigators over a considerable range of Reynolds numbers, yet the low Reynolds number range—i.e. below ( Re D = 4000, where ( Re) D is the upstream pipe Reynolds number, has received comparatively little attention, although recent work by two of the authors has supplemented the available data substantially. This work concentrates on very accurate measurements with small diameter orifices, but where less exacting standards of metering accuracy, e.g. ±2-2 1/2 per cent, can be allowed, a closer analysis reveals that there is a choice of orifice profiles which can be used successfully. Consideration is also given to the recommendations of the various standardizing bodies for the allowable tolerances in the diameter of the pipeline in which the orifice meter is situated. These tolerances are often unnecessarily severe and a ‘tolerance number’ depending upon discharge coefficient and the area ratio of orifice to pipe is suggested.

The Development of a Closed Loop High Speed Cascade Wind Tunnel for Aerodynamic and Heat Transfer Testing at Moderate to Low Reynolds Numbers

2013 ◽  
Author(s):  
M. P. Mihelish ◽  
F. E. Ames
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
High Speed ◽  
Closed Loop ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Low Reynolds Number Flows ◽  
Low Reynolds ◽  
Reynolds Number Flows ◽  
Very High

Engine companies typically emphasize research which has been conducted at conditions as close to engine conditions as possible. This focus on engine relevant conditions often causes difficulties in University research laboratories. One particularly difficult testing regime is high speed but low Reynolds number flows. High speed low Reynolds number flows can occur in both low pressure turbines under a normal range of engine operating conditions and in high pressure turbines run at very high altitudes. This paper documents a new steady state closed loop wind tunnel facility which has been developed to study high speed cascade flows at low Reynolds numbers. The initial test configuration has been representative of a first stage vane configuration for a UAV turbofan which flies at a very high altitude. The initial test section was configured in a three full passage four-vane linear cascade arrangement with upper and lower bleed flows. Both heat transfer and aerodynamics loss measurements were acquired and are presented in this paper. Heat transfer measurements were taken at a Reynolds number of 720,000 based on true chord and exit conditions at Mach numbers of 0.7, 0.8, and 0.9. Exit survey measurements were conducted at a chord exit Reynolds number of 720,000 over a similar range in Mach numbers. However, this facility has the capability to run at chord Reynolds numbers of 90,000 or below in the present configuration which uses an approximately three times scale test vane.

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