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

Abstract

The three-dimensional turbulent pipe flow response to targeted wall conditions was numerically examined at a high Reynolds number of 1.58×105. 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∈3+15 (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.