On the missing link between pressure drop, viscous dissipation and the turbulent energy spectrum

TL;DR

This paper establishes a direct link between pressure drop, viscous dissipation, and the turbulent energy spectrum, explaining experimental results and proposing a modified Kolmogorov scale influenced by surface roughness.

Contribution

It introduces a novel connection between pressure drop and turbulent energy spectrum, and demonstrates how to estimate pressure drop from spectral data in pipe flows.

Findings

Pressure drop correlates with the turbulent energy spectrum.

A modified Kolmogorov length scale accounts for surface roughness effects.

Viscous dissipation does not significantly increase fluid temperature in pipe flow.

Abstract

We present convincing evidence of a direct connection between the pressure drop, viscous dissipation, and the turbulent energy spectrum. We use this finding to explain Nikuradse's experimental results of pressure drop for turbulent flows in rough pipes, in terms of a modified Kolmogorov length scale that varies with the surface roughness. Furthermore, we use Laufer's measurements of turbulent energy spectra in pipe flow to calculate -- to a good approximation -- the turbulent component of the pressure drop directly from an averaged turbulent energy spectrum. We also show that the incompressibility assumption, leads to the conclusion that viscous dissipation in fully-developed (laminar and turbulent) pipe flow, cannot increase the temperature of the fluid through viscous heating.