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# Article

## DNS of a spatially developing turbulent boundary layer with passive scalar transport

Authors: Li, Q., Schlatter, P., Brandt, L.B., Henningson, D.S.H. Article Accepted Int. J. Heat and Fluid Flow 30(5)   916-929 2009

### Abstract

A direct numerical simulation (DNS) of a spatially developing turbulent boundary layer over a flat plate under zero pressure gradient (ZPG) has been carried out. The evolution of several passive scalars with both isoscalar and isoflux wall boundary condition are computed during the simulation. The Navier-Stokes equations as well as the scalar transport equation are solved using a fully spectral method. The highest Reynolds number based on the free-stream velocity $U_\infty$ and momentum thickness $\theta$ is $Re_\theta=830$, and the molecular Prandtl numbers are ranging from 0.2 to 2. To the authors' knowledge, this Reynolds number is by far the highest with such a variety of scalars. A large number of turbulence statistics for both flow and scalar fields are obtained and compared when possible to existing experimental and numerical simulations at comparable Reynolds number. The main focus of the present paper is on the statistical behaviour of the scalars in the outer region of the boundary layer, distinctly different from the channel-flow simulations. Agreements as well as discrepancies are discussed while the influence of the molecular Prandtl number and wall boundary conditions are also highlighted. A $Pr$ scaling for various quantities is proposed in outer scalings. In addition, spanwise two-point correlation and instantaneous fields are employed to investigate the near-wall streak spacing and the coherence between the velocity and the scalar fields. Probability density functions (PDF) and joint probability density functions (JPDF) are shown to identify the intermittency both near the wall and in the outer region of the boundary layer. The present simulation data will be available online for the research community.