Direct Numerical Simulation of turbulent flow in pipes with an arbitrary roughness topography using a combined momentum–mass source immersed boundary method

• We use an immersed boundary method to simulate flow over arbitrary wall topographies.
• The method includes both momentum and mass sources, in conjunction with a fast solver.
• Laminar as well as turbulent flow are accurately reproduced by the method.
• The turbulent outer layer is unaffected by the complexity of the wall topography.
• The pressure-drag and wall shear-stress match results for undulated channel flow.

In this work, we consider a combined momentum–mass source immersed boundary method that can be used to easily simulate flows in domains with arbitrary wall topographies, taking advantage of existing standard fast solvers for straight walls. This method is incorporated into a standard second-order finite-volume code with a Fast Fourier Transform solver, previously used for direct numerical simulations of flow in pipes with a straight wall, making it possible to study the influence of a large range of roughness topographies on the flow. The method is validated for both laminar and turbulent flow over walls with sinusoidal undulations. The implementation of the immersed boundary method preserves the second-order accuracy of the original code, and first-order methods are presented to calculate the shear-stress and the pressure-drag at the wall. Results for turbulent flow over walls represented by a single wave-number, as well as by a superposition of many wave-numbers, show that the flow in the outer layer is not affected by the nature of the wall topography, provided that the variation in the diameter is not too large. Furthermore, it is found that the relative contributions of the pressure and the shear to the total drag on the wall behave similarly to undulated channel flow, when considered as a function of an effective slope parameter.