The role of turbulence in determining the heat-transfer characteristics of impinging jets

The pioneering predictor of fluvial bed-load transport rate proposed by Meyer-Peter and Muller in 1948 is still extensively used in basic research and engineering applications. A review of the basis for its formulation reveals, however, that an unnecessary bed roughness correction was applied to cases of plane-bed morphodynamic equilibrium. Its inclusion followed a flow resistance parameterization in terms of the Nikuradse roughness height, which has been shown (well after the publication of their work) to be inappropriate for the characterization of mobile bed rough conditions in rivers. Removing the unnecessary correction and incorporating an improved correction of the boundary shear stress due to sidewall effects allow elucidation of the most parsimonious form of the bed-load relation of Meyer-Peter and Muller that is dictated by their own data set. The new predictor is presented in terms of two alternative power law forms. These amended forms show that, in the case of lower-regime plane-bed equilibrium transport of uniform bed sediment, the new estimates of volume bed-load transport rates are less than or equal to half the values that would be obtained with the original relation of Meyer-Peter and Muller in the absence of the unnecessary bed roughness correction. The meticulous database and clear analysis of the original work of Meyer-Peter and Muller greatly aided the present writers in their reanalysis, which liberally uses the hindsight offered by 58 years of subsequent research.

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Reanalysis and Correction of Bed-Load Relation of Meyer-Peter and Müller Using Their Own Database

The displacement height appears in the logarithmic velocity profile for rough-wall boundary layers as a reference height for the vertical co-ordinate. It is shown that this height should be regarded as the level at which the mean drag on the surface appears to act. The equations of motion then show that this also coincides with the average displacement thickness for the shear stress.A simple analytical model, experimental results and dimensional analysis are all used to indicate how the displacement height depends upon the detailed geometry of the roughness elements.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112081002279

On the displacement height in the logarithmic velocity profile

In 1965, Rouse critically reviewed hydraulic resistance in open channels on the basis of fluid mechanics. He pointed out the effects of cross-sectional shape, boundary nonuniformity, and flow unsteadiness, in addition to viscosity and wall roughness that are commonly considered. This paper extends that study by discussing the differences between momentum and energy resistances, between point, cross-sectional and reach resistance coefficients, as well as compound/composite channel resistance. Certain resistance phenomena can be explained with the inner and outer laws of boundary layer theory. The issue of linear-separation approach versus nonlinear approach to alluvial channel resistances also is discussed. This review indicates the need for extensive further research on the subject.

/pdf/open-channel-flow-resistance-3t7c3yob4q.pdf

Open Channel Flow Resistance

The axial and radial velocity components w and u, and the concentration c of a Rhodamine 6G dye were measured simultaneously in a turbulent buoyant jet, using laser-Doppler anemometry combined with a recently developed laser-induced-fluorescence concentration measurement technique. These non-intrusive techniques enable measurements in a region of plume motion where conventional probe-based techniques have had difficulties. The results of the study show that the asymptotic decay laws for velocity and concentration of a tracer transported by the flow are verified experimentally in both jets and plumes. The momentum and volume fluxes and the mean dilution factor are determined in dimensionless form as a function of the normalized distance from the flow source. Contradictory results from earlier experimental plume investigations concerning the decay laws of w and c and the plume width ratio b_c/b_w are discussed. The turbulence properties and the transition from momentum-driven jets to buoyancy-driven plumes are presented. The turbulence is found to scale with the mean flow as predicted by dimensional analysis and self-similarity. Buoyancy-produced turbulence is found to transport twice as much tracer as jet turbulence. Although velocity statistics in jets and plumes are found to be highly self-similar there is a strong disparity in the distribution of tracer concentration in the two flows. This occurs in the time-average mean flows as well as the r.m.s. turbulent quantities. Instantaneous concentration fluctuations are found to exceed time averages by as much as a factor of 3. The experimental results should provide a reasonable basis for validation of computer models of axisymmetric plumes.

/pdf/investigations-of-round-vertical-turbulent-buoyant-jets-fts3lg6qh5.pdf

Investigations of round vertical turbulent buoyant jets

Diffusion of submerged jets

As the direct result of turbulence generated at the borders of a submerged jet, the fluid within the jet will undergo both lateral diffusion and deceleration, and at the same time fluid from the su...

Diffusion of Submerged Jets

Two methods are used in design of stable channels, one is regime theory of India and other is limiting-tractive-force theory; description of four types of canals which can be designed by modified form of regime theory; use of tractive-force theory for design in coarse noncohesive range; estimation of design slope in any case by regime theory; method of combining strong points of two theories.

Maurice L. Albertson

Papers

Diffusion of submerged jets

Diffusion of Submerged Jets

Uniform Water Conveyance Channels in Alluvial Material

Uniform Water Conveyance Channels in Alluvial Material

Fluid mechanics for engineers