Applications of Matched Asymptotic Expansion Methods to Acoustics. II. The Open‐Ended Duct

1972 ◽  
Vol 52 (5B) ◽  
pp. 1406-1410 ◽  
Author(s):  
M. B. Lesser ◽  
J. A. Lewis
Keyword(s):  
Asymptotic Expansion ◽  
Matched Asymptotic Expansion

A micromechanical investigation of interfacial transport processes. I. Interfacial conservation equations

1993 ◽  
Vol 345 (1675) ◽  
pp. 165-207 ◽  
Keyword(s):  
Mass Transfer ◽  
Asymptotic Expansion ◽  
Control Volume ◽  
Transport Processes ◽  
Matched Asymptotic Expansion ◽  
Immiscible Fluid ◽  
Conservation Equations ◽  
Interfacial Transport ◽  
Fluid Systems ◽  
Expansion Scheme

Macroscale interfacial conservation equations are derived for transport processes occurring in immiscible fluid—fluid systems possessing moving and deforming interfaces via a rigorous matched asymptotic expansion scheme from the more exact, continuous (‘diffuse’) microscale equations underlying them . A surface-fixed coordinate system is developed for the parameterization of the interface, alleviating approximations which result when either a material or a space-fixed control volume is used to investigate systems undergoing interphase mass transfer.

The Accuracy of Short Bearing Theory in Presence of Cavitation

1990 ◽  
Vol 112 (4) ◽  
pp. 650-654 ◽  
Author(s):  
A. T. Prata ◽  
R. T. S. Ferreira
Keyword(s):  
Asymptotic Expansion ◽  
Numerical Integration ◽  
Reynolds Equation ◽  
Matched Asymptotic Expansion ◽  
Aspect Ratios ◽  
Very High

The accuracy of the short bearing approximation in presence of cavitation is tested for bearing aspect ratios (length/diameter) ranging from 0.1 to 1, and for eccentricity to clearance ratios from 0 to 1. Results for short bearings are obtained via the method of matched asymptotic expansion of [3]. These results are compared to those for finite bearings, which are calculated by numerical integration of the Reynolds equation utilizing boundary fitted coordinates that accommodate to the cavitation boundary. Except for very high eccentricities, the short bearing theory was shown to be accurate in predicting the load, within ten percent, for bearing aspect ratios up to 0.5. For large aspect ratios the short bearing theory overpredicts the load.

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