Experiments on turbulent flows in rough pipes: spectral scaling laws and the spectral link

Motivated by a recently proposed theory that entails the existence of a “spectral link” between the turbulent energy spectra and the attendant turbulent mean velocity profile in a pipe flow, we establish new scaling laws for the turbulent energy spectra of pipe flows. These new scaling laws— an inner scaling law and an outer scaling law—differ from the scaling laws that were predicated on Townsend’s attached–eddy hypothesis in that they are proper analogues (or spectral counterparts) of the classical scaling properties of the turbulent mean velocity profile. To test the new scaling laws, we have recourse to (1) published computational data from direct numerical simulations and (2) new experimental data from unprecedented measurements, carried out in our laboratory, of the streamwise component of the turbulent energy spectrum on numerous locations along the radii of three rough-walled pipes, for flows spanning a decade in Reynolds number. We show that the new scaling laws are consistent with the turbulent energy spectra of both smooth– and rough– walled flows. In addition, we use the new experimental data to probe the spatial distribution of the streamwise turbulent kinetic energy u2 , the longitudinal integral length scale L11 , and the Kolmogorov length scale η in turbulent rough–walled pipe flows. We document in our rough– pipe flows a striking phenomenon recently discovered in smooth–pipe flows: the occurrence of an outer peak in u+2 (y + ), whose magnitude is an increasing function of the Reynolds number, but the Reynolds number where the outer peak emerges is an order of magnitude smaller than the corresponding Reynolds number in smooth pipes. Last, we carry out a comparative study of the three canonical wall–bounded turbulent flows: pipe flow, channel flow, and boundary layer flow. We are able to trace the similarities and disparities among the turbulent mean velocity profiles of the three canonical flows to corresponding similarities and disparities among the attendant turbulent energy spectra—new evidence of the existence of a spectral link between the turbulent mean-velocity profile and the turbulent energy spectra.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Theoretical & Applied Mechans

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2012

Author dc:creator

• Zuniga Zamalloa, Carlo

Contributors dc:contributor

• Gioia, Gustavo
• Chrakraborty, Pinaki
• Christensen, Kenneth T.
• Freund, Jonathan B.

• turbulence
• rough pipe
• energy spectra
• hotwire
• friction factor

Statement dc:rights

• Copyright 2012 Carlo Zuniga Zamalloa

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/34359

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/34359