Transitional and turbulent boundary layer with heat transfer

We report on our direct numerical simulation of an incompressible, nominally zero-pressure-gradient flat-plate boundary layer from momentum thickness Reynolds number 80-1950. Heat transfer between the constant-temperature solid surface and the free-stream is also simulated with molecular Prandtl number Pr = 1. Skin-friction coefficient and other boundary layer parameters follow the Blasius solutions prior to the onset of turbulent spots. Throughout the entire flat-plate, the ratio of Stanton number and skin-friction St/ C(f) deviates from the exact Reynolds analogy value of 0.5 by less than 1.5%. Mean velocity and Reynolds stresses agree with experimental data over an extended turbulent region downstream of transition. Normalized rms wall-pressure fluctuation increases gradually with the streamwise growth of the turbulent boundary layer. Wall shear stress fluctuation, tau('+)(w)(rms), on the other hand, remains constant at approximately 0.44 over the range, 800 < Re(theta) < 1900. Turbulent Prandtl number Pr(t) peaks at around 1.9 at the wall, and decreases monotonically toward the boundary layer edge with no near-wall secondary peak, in good agreement with previous boundary layer heat transfer experiments. In the transitional region, turbulent spots are tightly packed with numerous hairpin vortices. With the advection and merging of turbulent spots, these young isolated hairpin forests develop into the downstream turbulent region. Isosurfaces of temperature up to Re(theta) = 1900 are found to display well-resolved signatures of hairpin vortices, which indicates the persistence of the hairpin forests. (c) 2010 American Institute of Physics. [doi:10.1063/1.3475816]