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This study evaluates how Reynolds-averaged Navier-Stokes (RANS) models perform in simulating the characteristics of mean three-dimensional perturbed flows in pipes with targeted wall-shapes. The principal objective of this investigation is to evaluate which of the well-established RANS models can best predict the flow response and recovery characteristics in perturbed pipes at moderate and high Reynolds numbers (1×104-1.58×105). First, the flow profiles at various axial locations are compared between simulations and experiments. This is followed by assessing the well-known mean pipeflow scaling relation in the far downstream region, where the flow obtains a fully-developed state. The consistency of computationally predicted results and their similarities with experiments suggested that the Standard k-ε model can accurately capture the pipeflow characteristics in response to introduced perturbation with smooth sinusoidal axial variations. [ABSTRACT FROM AUTHOR]

The response and recovery of turbulent pipe flow to three-dimensional perturbed wall changes were examined numerically in a wide range of Reynolds numbers between R e = 5 × 10 3 and 1.58 × 10 5 . The perturbations were based on distinct azimuthal Fourier modes corresponding to m = 3, 15, and 3 + 15. The long-lasting response of the flow was examined by characterizing both the mean and turbulent field in the wake of pipe inserts for each Re. The variation of the recovery with increasing Reynolds number revealed an asymptotic behavior for R e ≥ 7.5 × 10 4 , which scaled with Re4 for both mean velocity and turbulence kinetic energy. Two peaks were observed for the mean velocity along the wake centerline, where the location of peaks followed a power-law trend in the form of L p / D ∝ R e 4 / 3 , where D is the pipe diameter. A fast decay of turbulence past the wall change further suggested that maximum Reynolds shear stress in the downstream wake decays as (x / D) − 1 / 3 for all Re. The flow also exhibited long-lasting responses that obstructed its relaxation at 20D downstream of the perturbation, even for low Re of 5 × 10 3 . Overall, the recovery exhibited a second-order response. [ABSTRACT FROM AUTHOR]

The three-dimensional turbulent pipe flow response to targeted wall conditions was numerically examined at a high Reynolds number of 1. 58 × 1 0 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 ∈ 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 19 D in Case I, the higher Fourier Mode wall shapes (Cases II and III) showed a longer recovery length at 45 D. 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. • 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. [ABSTRACT FROM AUTHOR]