Scaling of wall turbulence Part III: Applications in CFD models and drag control
We report several examples of applying the obtained scaling results to improve turbulent CFD predictions (She et al, JFM 2018) as well as drag reductions (Yao, Chen & Hussain, JFM 2019) of wall flows. First, an algebraic model for compressible turbulent boundary layers (CTBL) is developed – predicting mean profiles of velocity, temperature and density – valid from incompressible to hypersonic flow regimes (Mach number Ma from 0 to 6). The accuracy of our new model is notably superior to popular current models such as Baldwin-Lomax and Spalart-Allmaras models, due to an improved eddy viscosity function compared to competing models. Second, we introduce the modification of the popular k-
equation, which achieves better predictions of both mean velocity profile and the turbulence intensity (
) of pipe flows (Chen et al PRE 2016, JoT 2016). These results suggest the path for developing advanced CFD models by incorporating the multi-layer structures. Finally, we present a new method for skin friction reduction in wall flows. We show that the lack of drag reduction at high Re (
= 550) observed by Canton et al. (PRF 2016) is remedied by the proper choice of the large-scale control flow, i.e. a pair of near-wall spanwise opposed wall-jet forcing (SOJF), whose height follows our predicted scaling of Reynolds shear stress peak. The flow control definitely suppresses the wall shear stress at a series of Reynolds numbers, namely, 18%, 14%, and 10% drag reductions at = 180, 395, and 550, respectively.