Effects of targeted wall geometries on response of turbulent pipe flow at high Reynolds number

Highlights: • The first study that documents the effects of targeted wall shapes on recovery of turbulent pipe flow. • Insights into how the response and recovery differs based on particular Fourier modes of the wall shape. • One can control the turbulent pipe flow response between first and second order through the implementation of different wall shapes. • Targeted wall shapes induce flow manipulation on boundary layer structures (LSM and VLSM), the recovery from which are observed here on the core flow. The three-dimensional turbulent pipe flow response to targeted wall conditions was numerically examined at a high Reynolds number of $1.58\times 10^5$. The perturbed wall was designed based on azimuthal Fourier modes of $m=3$ (Case I) and $m=15$ (Case II), as well as their superposition at $m\in \left(3+15\right)$ (Case III). The mean flow and turbulent fields were investigated and compared, which depicted long-lasting changes in flow properties. A rapid decay of turbulence levels immediately past the perturbation was observed for all cases. However, Case I showed a faster overall recovery rate compared to the higher Fourier Mode cases. While the flow recovered by $19D$ in Case I, the higher Fourier Mode wall shapes (Cases II and III) showed a longer recovery length at $45D$. The flow response also differed between these wall shapes. While Case I depicted a monotonic response, the other two wall shapes exhibited a non-monotonic second-order response characteristic along with a delayed recovery trend. The second-order response of turbulence was also evident in the Reynolds stress variations for cases with a higher Fourier mode wall shapes. The overshoot of Reynolds stresses, accompanied by their rapid decay rate downstream of the modified wall shape, was observed to follow known second-order turbulent response in pipe flow. Dominant flow structures were further identified in the downstream wake of each insert which provided a qualitative description of potential mechanisms behind the observed recovery trends.