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Abstract
This work studied the effects of roughness on the transport of passive scalars, narrowing the gap in knowledge between scalar and momentum transport. Numerical simulations were used to investigate a wide spectrum of statistical quantities, identifying the underlying physical mechanisms, examining the similarities and differences between scalar and momentum behavior, and determining important quantities commonly used in turbulence modeling and engineering applications. The Reynolds number based on the friction velocity ranged from Reτ = 1, 050 to 7, 500, with a corresponding equivalent sand-grain roughness heightk +s between 70 and 485; the Prandtl number Pr range is between 0.2 and 2.0.
The rough-wall scalar log-layer intercept is modified by both Reτ and Pr. The scalar roughness function ∆Θ+ appears to have a “fully-rough” behavior, tending to a limiting value that depends on Pr and (at high Pr) on the geometry. Comparison with previous studies indicates the possibility that ∆Θ+ may be independent of the geometry below a critical value of Pr.
The relative importance of the dispersive fluxes increases with Reτ and Pr; they can be smaller, comparable to, or larger than the dispersive stress depending on Pr. They become insensitive to Reτ , and may become only a function of the geometry for high Prandtl numbers. The Form-Induced (FI) flux is consistently smaller than the total FI drag.
The FI production dominates the scalar variance budget in the Roughness SubLayer (RSL); it is much more significant than the TKE FI production. Both FI production and diffusion are relatively insensitive to Reτ while the shear production and dissipation are strongly reduced as Reτ increases.
The scalar dissipation budget is far more complex than the scalar variance budget; roughness reduces this complexity due to significant reduction in the magnitude of of key terms. The production-of-dissipation is primarily due to the turbulent production P T εθ component, which was shown to be about twice as large as the other contributions for Pr = 1.0. P T εθ is enhanced by roughness because of improved the alignment between the fluctuating scalar gradient and the principal compressive direction of the strain-rate tensor.
