Turbulent pipe flow manipulation with targeted wall shapes: improving the efficiency of geothermal energy systems*

The response and recovery of turbulent pipe flow to wall perturbations with amplitudes (a_m) of 0.05, 0.1, and 0.15, and lengths (L) of 2D, 4D, and 6D (where D represents the diameter of the pipe), are investigated numerically using Large Eddy Simulations. The Reynolds number is fixed at 25,000. The wall perturbations follow distinct three-dimensional azimuthal Fourier modes (m) corresponding to m=3, 15 and 3+15, which associates with a second-order pattern of flow recovery. The preliminary results show that the perturbed wall characterized by a_m=0.15 and L=2D, coincides with a high magnitude of rotation in localized regions along the circumference, leading to a prolonged flow recovery. Additionally, in comparison to the cases at a_m=0.05 and 0.1, the wall geometry corresponding to the maximum amplitude exhibits a higher axial velocity gradient near the wall that persist for at least 5D downstream from the wall perturbations, confirming its slower flow recovery. Such prolonged flow recovery also coincides with a decrease in skin friction which has implications on the drag reduction during pipe flow. In view of this, evaluation of an optimized pipe-insert geometry is currently underway, that can serve the geothermal industry by lowering drag and achieving efficient energy extraction.