Abstract
Previous experimental studies on turbulent square duct flow have focused mainly on high Reynolds numbers for which a turbulence-induced eight-vortex secondary flow pattern exists in the cross-sectional plane. More recently, direct numerical simulations (DNS) have revealed that the flow field at Reynolds numbers close to transition can be very different; the flow in this ‘marginally turbulent’ regime alternating between two states characterised by four vortices. In this study, we experimentally investigate the onset criteria for transition to turbulence in square ducts. In so doing, we highlight the potential importance of Coriolis effects on this process for low-Ekman-number flows. We also present experimental data on the mean flow properties and turbulence statistics in both marginally and fully turbulent flow at relatively low Reynolds numbers using laser Doppler velocimetry. Results for both flow categories show good agreement with DNS. The switching of the flow field between two flow states at marginally turbulent Reynolds numbers is confirmed by bimodal probability density functions of streamwise velocity at certain distances from the wall as well as joint probability density functions of streamwise and wall normal velocities which feature two peaks highlighting the two states.
Highlights
Following the findings of Nikuradse (1926) on the existence of secondary currents in square duct turbulent flow, further experimental studies (Hoagland 1960; Brundrett & Baines 1964; Launder & Ying 1972; Melling & Whitelaw 1976) have been conducted to obtain a better understanding of the phenomenon, which came to be known as ‘Prandtl’s secondary flow of the second kind’
One of the earliest direct numerical simulations (DNS) of square duct turbulent flow was conducted by Gavrilakis
Given the previous results of Draad & Nieuwstadt (1998) and the excellent agreement between experiment and simulation here for two different Ekman numbers, we conclude that Coriolis forces can be significant in fully developed laminar square duct flow, especially for water
Summary
Following the findings of Nikuradse (1926) on the existence of secondary currents in square duct turbulent flow, further experimental studies (Hoagland 1960; Brundrett & Baines 1964; Launder & Ying 1972; Melling & Whitelaw 1976) have been conducted to obtain a better understanding of the phenomenon, which came to be known as ‘Prandtl’s secondary flow of the second kind’. The working section (as shown in figure 2a) consists of eight square duct modules made of stainless steel, each of length 1.2 m and cross-sectional dimensions of 80 mm × 80 mm (2h × 2h), followed by a transparent section 150 mm in length, constructed from Perspex and another stainless steel module, 1.2 m long, bringing the total length to 10.95 m With this arrangement, there is a distance of about 240h before the transparent section, where laser Doppler velocimetry (LDV) measurements were taken, which is enough for both fully developed laminar and turbulent flow at the Reynolds numbers studied. Given the previous results of Draad & Nieuwstadt (1998) and the excellent agreement between experiment and simulation here for two different Ekman numbers, we conclude that Coriolis forces can be significant in fully developed laminar square duct flow, especially for water. This is distinct from the temporal switching observed in the axially minimal flow unit in the DNS of Uhlmann et al (2007)
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