Contribution of large-scale motions to the skin friction in a moderate adverse pressure gradient turbulent boundary layer. (1st June 2018) - Yoon, Min; Hwang, Jinyul; Sung, Hyung Jin
Abstract : Direct numerical simulation of a turbulent boundary layer (TBL) subjected to a moderate adverse pressure gradient (APG, [STIX]x1D6FD=1.45 ) is performed to explore the contribution of large scales to the skin friction, where [STIX]x1D6FD is the Clauser pressure gradient parameter. The Reynolds number based on the momentum thickness develops from Re_[STIX]x1D703≈ 110 to 6000 with an equilibrium region in Re_[STIX]x1D703=4000 –5500. The spanwise wavelength ( [STIX]x1D706_z ) spectra of the streamwise and spanwise velocity fluctuations show that the large-scale energy is significantly enhanced throughout the boundary layer. We quantify the superposition and amplitude modulation effects of these enhanced large scales on the skin friction coefficient ( C_f ) by employing two approaches: (i) spanwise co-spectra of v[STIX]x1D714_z and -w[STIX]x1D714_y ; (ii) conditionally averaged v[STIX]x1D714_z and -w[STIX]x1D714_y . The velocity–vorticity correlations v[STIX]x1D714_z and -w[STIX]x1D714_y are related to the advective transport and the vortex stretching, respectively. Although v[STIX]x1D714_z negatively contributes to C_f, the positive contribution of the large scales ( [STIX]x1D706_z>0.5[STIX]x1D6FF ) is observed in the co-spectra of weighted v[STIX]x1D714_z . For the co-spectra of weighted -w[STIX]x1D714_y, we observe an outer peak at [STIX]x1D706_z≈ 0.75[STIX]x1D6FF and the superposition of the large scales in the buffer region, leading to the enhancement of C_f . The magnitude of v[STIX]x1D714_z and -w[STIX]x1D714_y depends on the large-scale streamwise velocity fluctuations ( u_L ). In particular, the negative- u_L events amplify v[STIX]x1D714_z in the outer region, and -w[STIX]x1D714_y is enhanced by the positive- u_L events. As a result, the skin friction induced by v[STIX]x1D714_z and -w[STIX]x1D714_y increases in the present APG TBL.