Prediction of mass and momentum transport in turbulent plane wall jets over smooth and transitionally rough surfaces

Abstract

This paper is concerned with the prediction of mass and momentum transport in turbulent wall jets developing over smooth and transitionally rough plane walls. The ability to accurately predict the resulting wall shear stresses and vertical profiles of the Reynolds stresses in these flows is prerequisite to the accurate prediction of bed scour, sediment re-suspension and transport by turbulent diffusion. The computations were performed by solving the Reynolds-averaged forms of the equations describing conservation of mass, momentum and concentration. The unknown correlations that arise from the averaging process (the Reynolds stresses in the case of the momentum equation, and the turbulent mass fluxes in the case of concentration) were obtained from the solution of modeled differential equations that describe their conservation. Since these models are somewhat more complex than those typically used in practice, their benefits are demonstrated by comparisons with results obtained from simpler, eddy-viscosity based closures. Comparisons with experimental data show that results of acceptable accuracy can be obtained only by using the appropriate combination of models for the turbulent fluxes of mass and momentum that properly account for the reduction of the Reynolds stresses due to wall damping effects, and for the modification of the mass transfer rates due to interactions with the mean rates of strain.

Appendix: Numerical accuracy

Grid-independence tests were performed with the number of cross-stream nodes varied by a factor of 3 viz. 30, 60 and 90. The differences between the results obtained with the finest and the coarsest grids was of the order of 1 % (e.g. the jet’s spreading rate, a sensitive parameter whose value is detemined by the details of the turbulence field, was predicted with the 30 nodes simulations to be 0.079 and with the 90 nodes simulations to be 0.078). The reasons for such small dependence of the computed results on the grid arise from the fact that the flow is uni-directional and is thus largely free of the interpolation errors that arise when the flow streamlines are not aligned with the grid lines. Indeed the computational grid is designed so as to adapt to the physical extent of the flow and in this way remain aligned with the streamlines, and with all the cross-stream nodes always located within the flow.

Quantification of the degree of correspondence between the predictions and the measurements of Eriksson et al. [24] is presented in Table 4 for the maximum values of the Reynolds stresses at three streamwise locations, and in Fig. 11 for the cross-stream profiles of streamwise velocity. Undoubtly some of the observed differences arise from shortcomings in the models but it should also be noted that the experimental results themselves are subject to uncertainties. In this regard, it is interesting to note that all the models yield differences that are positive in sign which may suggest that the measurements underestimate the actual values to some extent. Figure 11 also shows that the percentage differences decrease markedly with distance from the nozzle exit. This is to be expected considering that the starting profiles for the computations had to be assumed due to the absence of measurements there.

See Table 4 and Fig. 11.

Table 4 Percentage difference beween predicted and measured maximum Reynolds stresses

Fig. 11

Cross-stream variation of relative differences beween predicted and measured mean velocity. Data of Eriksson et al. [24]