Incomplete similarity of a plane turbulent wall jet on smooth and transitionally rough surfaces

Abstract

This study assesses the hypothesis of incomplete similarity for a plane turbulent wall jet on smooth and transitionally rough surfaces. Typically, a wall jet is considered to consist of two regions: an inner layer and an outer layer. The degree to which these two regions reach equilibrium with each other and interact to produce the property of self-similarity remains an open question. In this study, the analysis of the outer and inner regions indicates that each region is characterised by a half-width which exhibits its own distinct dependence on the streamwise distance x from the slot, and a single self-similar structure for both regions does not exist. More specifically, the inner and outer layers of the wall jet exhibit different scaling laws, which results in two selfsimilar mean velocity profiles, both of which retain a dependence on the slot height H. As such, incomplete similarity of the wall jet on smooth and transitionally rough surfaces is confirmed by this study. In addition, comparison of the experimental results for the transitionally rough surface with the smooth wall case indicates that the surface roughness modifies the development of the mean velocity profile in both the inner and outer regions, although the effect on the outer region is relatively small and close to the experimental uncertainty.

Direct numerical simulation of a wall jet: flow physics

“…Eriksson et al (1998) and Rostamy et al (2011a) showed that the measured mean streamwise velocity and all Reynolds stresses scale with the parameters defined by George et al (2000). Tang et al (2015) showed that inner layer mean velocity profiles collapse with the similarity parameters defined by Barenblatt et al (2005). Efforts have also been made to identify the inner layer region with the standard log-law, which is given for boundary layers as u + = A ln(y + ) + B with u + = u uτ , y + = yuτ ν , A = 2.44 and B = 5.0.…”

“…Figure 7(a) shows the decay of maximum mean streamwise velocity U max of the wall jet as a function of streamwise distance from the jet exit plane on a log-log scale. The current DNS is compared with the power-law given by Tang et al (2015) and Barenblatt et al (2005). The power-law is generally defined as;…”

“…To the best of authors' knowledge, this Reynolds number is the highest and the domain range the longest for any reported DNS of a wall jet. This particular Reynolds number is selected in order to compare the DNS results with the experiments of Rostamy et al (2011a,b); Tang et al (2015) and numerical simulations of Banyassady & Piomelli (2014. The highly resolved unsteady flow field is used to present large scale coherent structures in the transition and fully developed regions in the inner and outer layers.…”

Axisymmetric wall jet development in confined jet impingement

“…48 Typical growth rates for both planar and radial wall jets are β T ≈ 0.8-1. 10,[41][42][43][44]46 However, the evolution of the velocity scales (i.e., the decay rate of u m ) is dependent on the wall jet geometry; the radial wall jet decelerates faster due to spreading in the azimuthal direction. Typical decay rates for planar wall jets range from α ≈ 0.6 to 0.5, 10,46 which is much lower than the typical values for radial wall jets of α ≈ 1.1.…”

“…The growth rates ( β) of Y 1/2 for top and wall layers resulting from the fit of Equation (2) to the data shown in Fig. 10 are listed in Table III Values for β i from the literature 10,[41][42][43][44]46 are also tabulated in Table III and plotted together in Fig. 11 for comparison.…”