A Wall Function for Calculating the Skin Friction With Surface Roughness

Abstract

Wall functions are used in CFD to provide skin friction values and hence the boundary conditions for flow variables along solid surfaces. In this paper the effect of surface roughness on skin friction is incorporated in a wall function approach which uses Spalding’s formula. The use of Spalding’s formula extends the method to a wider range of wall distance than the logarithmic friction law. For CFD applications the results are then re-formulated for explicit calculation throught the use of an additional variable — the ratio of the surface roughness height to the distance from the solid surface. For a given computational grid this information is readily available in a CFD calculation. This methodology is applied to a linear compressor cascade that has been experimentally measured for different roughness values. The comparison of the simulation followed the same trends as the experiment, but with less overall effect.

Effects of surface roughness on deviation angle and performance losses in wet steam turbines

“…13 and 15 (a) and 16 (a) contribution of the viscous losses is less than other loss mechanisms for the smooth blade (k s ¼ 5 mm), but according to Fig. 15 (c), 16 (c) and 19 contribution of the viscous losses has increased significantly for the fully rough case k s ¼ 800 mm.…”

“…Good results were obtained using the Cebeci model coupled with Mayle's [15] transition model. Then, Shabbir and Turner [16] modified Spalding's formula to predict skin friction of rough surfaces and validated their code by comparing the results with measured rough cascade data by Bammert and Milsch [17].…”

A Numerical Study of Water Injection on Transonic Compressor Rotor Performance

“…For details about wall functions please see the paper by Shabbir and Turner [64]. As mentioned before, the vast majority of entropy generation occurs in these two layers, the laminar sub-layer and the buffer layer.…”

Roughness Coefficient of a Highly Calcinated Penstock

“…On the other hand, manufacturers use directly measurable quantities Ra, Rq and Rz to represent the surface texture of their products. Equations available in literature [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31] that try to relate these parameters vary greatly and there is no consensus on a single relation on these parameters. Equations proposed by [19][20][21][22][23][24] mostly use sand grains, emery papers or machined surfaces to produce the empirical equations using Ra, while suggested equations for groove height or liquid crystal surfaces, Rq [26][27] is mostly used for surfaces with sprayed particles as an alternative.…”

“…Regardless, a table is prepared from available literature to calculate and check surface roughness values (ε) using all three parameters Ra, Rq, Rz. Values of surface roughness (ε) are calculated using these three parameters as given in Table 9 [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31].…”