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Spatially Averaged Log-Law for Flows over Rough Bed in Zero- and Non-Zero-Pressure Gradient Boundary Layers

Czernuszenko W.

Archives of Hydro-Engineering and Environmental Mechanics

2011

Vol. 58, nr 1-4

65-86

Theoretical bases for building a logarithmic law for non-uniform flows over a large relative roughness are presented. In order to define the equivalent velocity distribution and to smooth out 3D flow irregularities, a special spatial averaging operation is defined. Basic equations are spatially averaged and double-averaged momentum equations for primary component velocity are derived for uniform flow over a gravel bed as well as for non-uniform flows. A new hypothesis is proposed, and some assumptions are introduced to solve these momentum equations. This results in a new version of the logarithmic velocity distribution (log law). To define this distribution, a full reconstruction of Nikuradse's graph for flows over an irregular gravel riverbed is considered. It is based on very precise measurements of velocity and other hydraulic parameters. In the case of non-uniform flows, the logarithmic velocity profile appears also in accelerating flows in a gravel bed channel, but the friction velocity should be re-defined according to Eq. (24). The same applies to decelerating flow with a positive pressure gradient, but only if the gravitational force exceeds the pressure gradient. For accelerating flows, the additive constant BP depends on the pressure gradient, and its values grow with a growing pressure gradient.

Validation and sensitivity analysis of the mathematical model of a cross - flow heat exchanger with non - uniform flow of agents

Bury T., Składzień J., Piątek R.

Systems : journal of transdisciplinary systems science

2008

Vol. 13, spec. iss. 1/2

19--27

The paper deals with experimental and numerical thermodynamic analysis of a cross-flow heat exchanger with non-uniform flow of mediums through the exchanger. The main aim of the work is validation of a computer code for analyses of the considered type exchangers. The validation procedure was realized by means of comparison of the experimental and numerical results. Next, the sensitivity analysis of the code was also accomplished. Selected results of analyses carried out and the most important conclusions are presented in the paper.