Fourier Pipes: Turbulent Pipe Flow Manipulation Using Targeted Wall-Shapes

Abstract This study introduces a novel technology to enhance geothermal energy extraction through flow manipulation inside the well casing. These novel pipe-inserts are placed at regular distances inside the casing and are characterized by smooth manufactured wall perturbations following distinct Fourier modes. The effects of insert thickness and length were studied by varying amplitude (0.05D, 0.1D, 0.15D) and length (2D, 4D, and 6D), respectively. The controlled perturbations allowed for flow deceleration near the wall and induced local mixing in the flow. The results demonstrated a linear increase in mean centerline velocity magnitude with increasing thickness and length of pipe-inserts. Turbulence intensity along the wake centerline increased with thickness, indicating greater mixing, while recovery behavior remained mostly consistent. Increasing the insert thickness enhanced pressure gradient along the pipe, which resulted in over a 35% rise in maximum pressure-drop at the insert. An increase in insert length lowered pressure-drop magnitude by at least 5.29%. This suggested that longer inserts could optimize energy transportation by minimizing pressure losses. The longest insert (6D) also lowered the maximum skin friction by 3.14%. These findings provided valuable insights for future design optimization aimed at energy efficient fluid extraction and transportation, which could enhance various geothermal energy applications and related systems.