Boundary shear in rectangular and compound ducts
PhD thesis by Patel, H.S., 1984

Mainly experimental work in a small wind tunnel with rectangular compound section and either smooth of roughened 'floodplains', aimed at obtaining velocity and boundary shear stress data, using air as the medium. This was the first of two PhDs based on the small wind tunnel (see Lai for further work and Rhodes for later work using a much larger wind tunnel). Contains some high quality data on rectangular and compound ducts of varying sizes (see pictures).

Abstract

Experiments have been performed in a rectangular duct for aspect ratios, B/H, varying between 0.1 and 10, and in a compound duct comprising of one rectangular main channel and two symmetrically disposed flood plains, for 0.057 < (H-h)/H < 0.491, B/b =5.2 and b/h = 0.934, in order to obtain boundary shear stress distributions and primary flow isovels. The symbols are defined in Fig. (3.1) which follows page 41.

In the smooth rectangular duct, perturbations were noticed in the bed shear stress distributions and were related to the secondary flow cells, which in turn depend upon the aspect ratio. An empirical equation is presented giving the number of these secondary flow cells for a given aspect ratio, for B/H ≤ 3.0. Equations are also presented giving the percentage of the total shear force carried by the walls, the mean boundary shear stresses, the maximum boundary shear stress and the bed centreline shear stress, in terms of the aspect ratio. Experiments in the rectangular duct were also performed with rough and differentially roughened surfaces. The results are compared with the open channel results at comparable aspect ratios and small differences are shown to exist.

In the compound duct, the boundary shear force results are used to calculate the apparent shear force on vertical, horizontal and inclined interfaces. Their variation with depth is studied to explore the lateral and vertical transfer of momentum. The effect of introducing roughness on the flood plains is also examined. The three-dimensional nature of the flow in the compound duct is demonstrated by the lateral variation of the depth mean velocities, the primary flow isovels and the variation of subsection mean velocities on the flood plains and in the main channel. Various sub division methods for discharge prediction are examined and the methods with horizontal and inclined interfaces are shown to give the best discharge results. The results are also compared with the open channel results and are found to generally accord with them.

Data files

Introduction

Table 2 shows the main experimental programme, using rectangular and compound ducts with different roughness distributions and geometries. Fig. 3.1 defines the notation and Fig. 4.1 shows an outline sketch of the wind tunnel test rig. For further details see the pictures and PhD thesis.

Appendix 2 contains some experimental data from flows in rectangular ducts. The key parameters from experiments 1-11, using a ‘smooth’ rectangular duct with smooth walls and a smooth bed are shown in Tables 2.1-2.5, together with the boundary shear stress data; those from experiments 12-22, using a rectangular duct with rough walls and a rough bed are shown in Tables 2.6-2.10; those from experiments 23-33, using a rectangular duct with smooth walls and a rough bed are shown in Tables 2.11-2.15; those from experiments 34-44, using a rectangular duct with rough walls and a smooth bed are shown in Tables 2.16-2.20. Velocity and resistance data are contained in Tables 2.21-2.31.

The cross-section of the duct was subsequently changed to a compound section, as shown in Fig. 4.1, and two further series of experiments undertaken with either smooth ‘floodplains’ (experiments 51-61) or rough ‘floodplains’ (experiments 62-72). Appendix 3 contains some experimental data from flows in compound ducts. The key parameters from experiments 51-61, using smooth floodplains are shown in Tables 3.1-3.8, together with the boundary shear stress data. The corresponding velocity data are shown in Tables 3.9-3.16. The key parameters from experiments 62-72, using rough floodplains are shown in Tables 3.17-3.23, together with the boundary shear stress data. The corresponding velocity data are shown in Tables 3.24-3.34.

table

Data file links

Rectangular channels:    

Compound channels:

Publications

  • Knight, D.W. and Patel, H.S., 1985, Boundary shear in smooth rectangular ducts, Journal of Hydraulic Engineering, ASCE, Vol. 111, No. 1, 29-47. [J]
  • Knight, D.W. and Lai, C.J., 1985, Turbulent flow in compound channels and ducts, Proc. 2nd Int. Symposium on Refined Flow Modelling and Turbulence Measurements, Iowa, USA, Sept., Hemisphere Publishing Co., I21-1 to I21-10. [C]
  • Knight, D.W. and Patel, H.S., 1985, Boundary shear stress distributions in rectangular duct flow, Proc. 2nd Int. Symposium on Refined Flow Modelling and Turbulence Measurements, Iowa, USA, Sept., Hemisphere Publishing Co., I22-1 to I22-10. [C]