Mechanical and Civil Engineering Seminar
Streamwise homogeneous turbulent boundary layers
PhD Thesis Defense
Boundary layers are everywhere. Understanding them is critical for drag reduction and computing direct numerical simulations (DNS) of them is crucial. However, traditional DNS of flat-plate boundary layers are notoriously computationally expensive, owing to the streamwise inhomogeneity of the boundary layer. This inhomogeneity precludes the use of streamwise periodic boundary conditions for statistically stationary boundary layer simulation. As a result, all growing boundary layer simulations had to use long streamwise domains as well as inflow generation techniques. A couple of methods have been proposed to impose streamwise homogeneity. However, they all suffer from either a lack of stationarity or have difficult implementation. This thesis presents a novel method of boundary layer simulation using a wall-normal rescaling to help impose streamwise homogeneity.
The rescaling method produces a new set of governing equations resembling the original Navier-Stokes equations with additional source terms. The effects of these source terms are quantified through a budget analysis and via additional non-periodic simulations. The key effect of the rescaling source terms is to balance the Reynolds stresses in the outer layer. The governing equations admit statistically streamwise homogeneous and statistically stationary solutions. A sweep of Reynolds number simulations is then conducted in streamwise periodic domains for Reδ∗ = 1460−5650. The global quantities show excellent agreement with established empirical values: the computed shape factor and skin friction coefficient for all cases are within 3% and 1% of empirical values, respectively. Velocity and rms profiles are also well-reproduced. To obtain accurate two-point correlations, a computational domain of length 14δ99 and width 5δ99 is found to be sufficient. Overall, the large computational savings are significant, as the streamwise computational domain alone led to a reduction by a factor of 8.
To study how the rescaling method can improve prediction of turbulent structures, we turn to Resolvent analysis (McKeon & Sharma 2010), an excellent tool that allows one to predict turbulent structure shapes. A new 1D resolvent operator is derived from the rescaled governing equations, and an analysis is conducted into how the additional rescaling terms improve prediction in the outer layer. The analysis of the new resolvent operator reveals that the predicted turbulent structures in the outer layer are displaced closer to the wall. More precisely, the addition of the rescaling source terms moves the outer layer waves towards the wall, while the mean wall-normal velocity displaces the waves towards the free-stream. To verify these predictions, spectral proper orthogonal decomposition (SPOD; Towne et al. 2018), a powerful data-driven tool to ex- tract turbulent structure shapes, was applied to a previously simulated periodic boundary layer data set. The extracted structures show very good agreement between SPOD and the new resolvent operator. The prediction of outer waves is clearly improved via use of the new 1D resolvent operator.
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