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Turbulent flow in channels in terms of turbulent shear and normal stresses
Author(s) -
Churchill Stuart W.,
Chan Christina
Publication year - 1995
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690411202
Subject(s) - turbulence , concentric , mechanics , shear stress , shear (geology) , shear velocity , mathematics , turbulence modeling , geometry , physics , geology , petrology
The local time‐averaged velocity, the mixed‐mean velocity, and the friction factor for fully turbulent flow between parallel plates and in round tubes and concentric circular annuli can be expressed in terms of integrals of the turbulent shear stress, The pressure distribution across a channel can similarly be expressed in terms of an integral of normal stresses. These formulations, which are simple and exact, can be integrated numerically using experimental data, compyted values, or correlating equations for turbulent stresses. Their greatest merit, however, may arise from the insight they provide with respect to the contributions of the fluctuating components of the velocity. For example, for concentric circular annuli such a formulation identifies a difference between the locations of the maximum in the velocity and the zero in the total shear stress. This difference, which has been overlooked in most experimental and semitheoretical investigations, introduces an error of unknown but possibly significant magnitude into all of the results. It also precludes the application of the mixing‐length, eddy viscosity and k ‐ ϵ models.