A Quasi Method of Characteristics with Applications to Fluid Lines with Frequency Dependent Wall Shear and Heat Transfer

Professor Streeter has given a fine summary of the basic numerical techniques for unsteady flows, presuming that equation One exception, well known to Professor Streeter and included in several of his references, is the simpler case of laminar rather than turbulent friction for low frequency excitation. Only minor variations in the equations are necessary. A much greater departure from equation 4 Numbers in brackets designate Additional References at end of discussion. at intermediate frequencies in turbulent flow. Apparently because of a little-understood resonance of ring vortices, the step response of a tube may contain significant oscillations. Wavelengths of the complicated patterns are about 25 and 50 diameters. (Further information is forthcoming in a thesis by Margolis.) The report also discusses the details of numerical application of the quasi method of characteristics to large amplitude transients, with illustrations. Readers should know that the paper and this discussion represent a highly selected rather than comprehensive review of the important literature on numerical methods for unsteady flow calculations in channels and tubes. T. P. Propson 6 The author has conducted a thorough review of the most popular techniques currrently employed to numerically evaluate the effect of transient flows in liquid piping systems. His discussion of the relative advantages and disadvantages of both the characteristics (explicit) and centered implicit method is excellent; of particular interest to the writer were the author's comments relative to the occurrence of instabilities and inaccuracies occasionally encountered during application of the implicit techniques. Recent unpublished work by the writer has confirmed these problems. When frictional effects are very important, the writer would suggest that equations (64) It may be shown that the error introduced into the integration of the friction term by these finite-difference equations is usually about one-half of that introduced by equations (30) and (31)

A Quasi Method of Characteristics with Applications to Fluid Lines with Frequency Dependent Wall Shear and Heat Transfer

Professor Streeter has given a fine summary of the basic numerical techniques for unsteady flows, presuming that equation One exception, well known to Professor Streeter and included in several of his references, is the simpler case of laminar rather than turbulent friction for low frequency excitation. Only minor variations in the equations are necessary. A much greater departure from equation 4 Numbers in brackets designate Additional References at end of discussion. at intermediate frequencies in turbulent flow. Apparently because of a little-understood resonance of ring vortices, the step response of a tube may contain significant oscillations. Wavelengths of the complicated patterns are about 25 and 50 diameters. (Further information is forthcoming in a thesis by Margolis.) The report also discusses the details of numerical application of the quasi method of characteristics to large amplitude transients, with illustrations. Readers should know that the paper and this discussion represent a highly selected rather than comprehensive review of the important literature on numerical methods for unsteady flow calculations in channels and tubes. T. P. Propson 6 The author has conducted a thorough review of the most popular techniques currrently employed to numerically evaluate the effect of transient flows in liquid piping systems. His discussion of the relative advantages and disadvantages of both the characteristics (explicit) and centered implicit method is excellent; of particular interest to the writer were the author's comments relative to the occurrence of instabilities and inaccuracies occasionally encountered during application of the implicit techniques. Recent unpublished work by the writer has confirmed these problems. When frictional effects are very important, the writer would suggest that equations (64) It may be shown that the error introduced into the integration of the friction term by these finite-difference equations is usually about one-half of that introduced by equations (30) and (31)