On scaling pipe flows with sinusoidal transversely corrugated walls: analysis of data from the laminar to the low-Reynolds-number turbulent regime

Abstract

Direct numerical simulation was used to study laminar and turbulent flows in circular pipes with smoothly corrugated walls. The corrugation wavelength was kept constant at 0.419D, where D is the mean diameter of the wavy-wall pipe and the corrugation height was varied from zero to 0.08D. Flow rates were varied in steps between low values that generate laminar flow and higher values where the flow is in the post-transitional turbulent regime. Simulations in the turbulent regime were also carried out at a constant Reynolds number, Re τ = 314, for all corrugation heights. It was found that even in the laminar regime, larger-amplitude corrugations produce flow separation. This leads to the proportion of pressure drop attributable to pressure drag being approximately 50 %, and rising to approximately 85 % in transitional rough-wall flow. The near-wall structure of turbulent flow is seen to be heavily influenced by the effects of flow separation and reattachment. Farther from the wall, the statistical profiles examined exhibit behaviours characteristic of smooth-wall flows or distributed roughness rough-wall flows. These observations support Townsend's wall-similarity hypothesis. The organized nature of the present roughness allows the mean pressure drop to be written as a function of the corrugation height. When this is exploited in an analysis of the mean dynamical equation, the scaling problem is explicitly revealed to result from the combined influences of roughness and Reynolds number. The present results support the recent analysis and observations of Mehdi et al. (J. Fluid Mech., vol. 731, 2013, pp. 682-712), indicating that the length scale given by the distance from the wall at which the mean viscous force loses leading order is important to describing these combined influences, as well as providing a dynamically self-consistent connection to the scaling structure of smooth-wall pipe flow.

Shared dynamical features of smooth- and rough-wall boundary-layer turbulence

“…MKW13 show that when consistently normalized using u τ and y m the mean vorticity profiles from smooth and rough flows merge near y m . The recent analysis of pipe flow DNS by Saha et al (2015) provides additional corroboration. The geometric simplicity of their sinusoidal roughness allowed the mean pressure gradient in corrugated-wall pipe flow to be expressed as an explicit function of the roughness height.…”

“…The y + range and |Ω + z | values over which this power-law dependence exists, however, varies considerably depending upon the surface condition. The rough-wall extension of the present theory postulates that this starting position is a function of both roughness and Reynolds number (Mehdi et al 2013;Saha et al 2015). Accordingly, the theory prescribes that the mean vorticity profiles can be brought into alignment beginning near the onset of the inertial domain by scaling the data as in figure 13(b).…”

Heat transfer and thermal efficiency enhancement using twisted tapes in sinusoidal wavy tubes with nanofluids: a numerical study

“…A wavy tube with a sinusoidal wavy wall can be assumed as a smoothed version of a corrugated pipe to reduce the pressure loss due to its grooves. Several practical applications of corrugated and wavy tubes are reported in industrial heat exchangers, including chemical reactors, paint manufacturing, the food industries, marine and pharmaceuticals (Abbasian Arani and Memarzadeh, 2022; Saha et al , 2015; Li et al , 2023a). Fluid flow inside corrugated and wavy pipes is characterized by complex interactions between free shear layers, separated vortices and driving wall-bounded shear flow, which may increase the rate of heat transfer.…”