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Developing and fully developed turbulent flow in ribbed channels

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Abstract

Wall-mounted roughness features, such as ribs, are often placed along the walls of a channel to increase the convective surface area and to augment heat transfer and mixing by increasing turbulence. Depending on the relative roughness size and orientation, the ribs also have varying degrees of increased pressure losses. Designs that use ribs to promote heat transfer encompass the full range of having only a few streamwise ribs, which do not allow fully developed flow conditions, to multiple streamwise ribs, which do allow the flow to become fully developed. The majority of previous studies have focused on perturbing the geometry of the rib with little attention to the spatially and temporally varying flow characteristics and their dependence on the Reynolds number. A staggered rib-roughened channel study was performed using time-resolved digital particle image velocimetry (TRDPIV). Both the developing (entry region) and a fully developed region were interrogated for three Reynolds numbers of 2,500, 10,000, and 20,000. The results indicate that the flow was more sensitive to Reynolds number at the inlet than within the fully developed region. Despite having a similar mean-averaged flowfield structure over the full Reynolds number range investigated, the population and distribution of coherent structures and turbulent dissipation within the fully developed region were also found to be Reynolds number dependent. Exploring the time-accurate flow characteristics revealed that in addition to vortices shed from the rib shear layer, the region of the rib wake was governed by a periodic process of bursting of the wake vortices resulting in the intermittent ejection of the inter-rib recirculation region into the core flow. This periodic process was the driving mechanism resulting in mixing and heat transfer augmentation. A quadrant-splitting burst analysis was also performed to determine the characteristic frequency and duration of inter-rib bursting as well as the wake shedding frequency, both of which were determined to be Reynolds number dependent.

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Abbreviations

BFR:

Back-flow region

C :

Vortex circulation

CL:

Channel centerline

CS:

Coherent structure

D h :

Hydraulic diameter

DEV:

Fully developed channel region

e :

Rib height

h :

Channel height

IN:

Inlet channel region

ML:

Mixing layer

n ID :

Number of identified burst events per bin

n total :

Total number of burst events for the test case

p :

Rib pitch

Q1 − Q4:

Quadrant number

Re :

Flow Reynolds number, \( Re = {{U \cdot D_{h} } \mathord{\left/ {\vphantom {{U \cdot D_{h} } \nu }} \right. \kern-\nulldelimiterspace} \nu } \)

RMS:

Quadratic mean, root mean square

RR#:

Recirculating region

t :

Time

Δt :

Burst duration

t*:

Nondimensionalized time, \( t^{*} = {t \mathord{\left/ {\vphantom {t {\tau_{f} }}} \right. \kern-\nulldelimiterspace} {\tau_{f} }} \)

ΔT :

Inter-burst time

ΔT*:

Nondimensionalized time, \( \Updelta T^{*} = {{\Updelta T \cdot U} \mathord{\left/ {\vphantom {{\Updelta T \cdot U} e}} \right. \kern-\nulldelimiterspace} e} \)

TKE:

Turbulent kinetic energy, \( {\text{TKE}} = u^{\prime 2} + \nu^{\prime 2} \)

u :

Streamwise velocity component

u′:

Fluctuating streamwise velocity, \( u^{\prime } = u - U \)

U :

Bulk streamwise velocity

v :

Wall-normal (spanwise) velocity component

v′:

Fluctuating wall-normal velocity, \( v^{\prime } = v - U \)

w :

Channel width

x :

Channel streamwise direction

y :

Channel wall-normal (spanwise) direction

σ:

Population standard deviation

ε:

Turbulent dissipation rate

ω:

Vorticity

ν:

Kinematic viscosity

τ f :

Characteristic fluid scale, \( \tau_{f} = {{D_{h} } \mathord{\left/ {\vphantom {{D_{h} } U}} \right. \kern-\nulldelimiterspace} U} \)

Ψ:

Stream function

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Acknowledgments

The generous support of Pratt & Whitney and technical program managers Dr. Atul Kohli, Mr. Jeff Prausa and Dr. Bill Cousins are acknowledged.

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Authors and Affiliations

  1. Mechanical Engineering Department, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, 24061, USA

    Nicholas D. Cardwell & Pavlos P. Vlachos

  2. Mechanical and Nuclear Engineering Department, Pennsylvania State University, University Park, PA, 16802, USA

    Karen A. Thole

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  1. Nicholas D. Cardwell
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  2. Pavlos P. Vlachos
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  3. Karen A. Thole
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Correspondence to Pavlos P. Vlachos.

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Cardwell, N.D., Vlachos, P.P. & Thole, K.A. Developing and fully developed turbulent flow in ribbed channels. Exp Fluids 50, 1357–1371 (2011). https://doi.org/10.1007/s00348-010-0993-y

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