Numerical study of thermal streak spacing in turbulent boundary layer with constant heat-flux boundary condition

Direct numerical simulation (DNS) of the fully developed thermal field in a flume was performed. Constant heat flux boundary condition was imposed on the heated bottom in a way, which allowed tracing of the temperature fluctuations on the wall. Free surface boundary conditions for momentum and adiabatic boundary condition for temperature were applied on the free surface. III-posedness of the energy equation with such boundary conditions was removed with an additional constrain: average non-dimensional wall temperature was fixed to zero. DNS was performed at constant friction Reynolds number Re=171 and Prandtl numbers 1 and 5.4. The type of the boundary condition did not affect the profile of the mean temperature. The main difference between two types of boundary conditions is in the temperature RMS fluctuations, which retain a nonzero value on the wall for constant heat flux boundary condition, and zero for constant non-dimensional temperature. Certain changes are visible also in the behavior of skewness, flatness, and other turbulent statistics in the near-wall region. An important issue is the difference between the thermal streak spacing on the isoflux wall and the velocity streak spacing near the wall. While the thermal streaks closely follow the velocity streaks for isotemperature wall boundary condition, the temperature streaks near the isoflux wall do not coincide with the velocity low speed streaks. The DNS shows that thermal streak spacing near the wall depends on Prandtl number. Thermal streak spacing is larger than the velocity streak spacing and is approaching to the well known value of the velocity streak spacing (90-100 wall units) at Prandtl number Pr=5.4.