DNS study on "diameter effect" of drag reduction in viscoelastic-fluid flow

It is well known that the small amount of polymers or surfactant additives to flowing liquid give rise to drag reduction (DR) in turbulent flow [1]. However this mechanism has not been satisfactorily clarified. One of many interesting aspects is the so-called ‘diameter effect’, which has been observed experimentally [2, 3]. For instance, the discrepancy between results obtained by different pipe diameters represents the diameter effect (see Fig. 1): this effect is seen as additional dependence of the skin friction coefficient, Cf, on the pipe diameter (or channel width) as well as Reynolds number, Re. Although several experimental studies were published about the diameter effect, the relationship between the DR rate and rheological parameters (such as Weissenberg number, We) is still not clear. Therefore we have performed a series of direct numerical simulations (DNS) on a viscoelastic-fluid flow in a channel and discussed the diameter effect with focusing on effects of Re and We on the DR induced by polymers or surfactant additives.