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Effect of streamwise spacing on periodic and random unsteadiness in a bundle of short cylinders confined in a channel

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Abstract

While flow across long tube bundles is considered classical data, pin-fin arrays made up of short tubes have become a growing topic of interest for use in cooling gas turbine airfoils. Data from the literature indicate that decreasing streamwise spacing increases heat transfer in pin-fin arrays; however, the specific mechanism that causes increased heat transfer coefficients remains unknown. The present work makes use of time-resolved PIV to quantify the effects of streamwise spacing on the turbulent near wake throughout various pin-fin array spacings. Specifically, proper orthogonal decomposition was used to separate the (quasi-) periodic motion from vortex shedding and the random motion from turbulent eddies. Reynolds number flow conditions of 3.0 × 103 and 2.0 × 104, based on pin-fin diameter and velocity at the minimum flow area, were considered. Streamwise spacing was varied from 3.46 pin diameters to 1.73 pin diameters while the pin-fin height-to-diameter ratio was unity and the spanwise spacing was held constant at two diameters. Results indicated that (quasi-) periodic motions were attenuated at closer streamwise spacings while the level of random motions was not strongly dependent on pin-fin spacing. This trend was observed at both Reynolds number conditions considered. Because closer spacings exhibit higher heat transfer levels, the present results imply that periodic motions may not contribute to heat transfer, although further experimentation is required.

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Abbreviations

d P :

Tracer particle diameter

D :

Pin-fin diameter

D h :

Duct hydraulic diameter

DR:

Dynamic range

E n :

Percent energy contained in POD mode n

H:

Channel height, pin-fin height

L c :

Wake closure position

n :

POD mode number

POD:

Proper orthogonal decomposition

Re D :

Reynolds number, \( Re_{D} = U_{\hbox{Max} } D\nu^{ - 1} \)

RMS:

Root-mean-square

s max :

Maximum measured particle displacement

S L :

Longitudinal/streamwise pin–fin spacing (X-direction)

S T :

Transverse pin-fin spacing (Y-direction)

Stk:

Stokes number, \( {\text{Stk}} = \left( {{{d_{P} \rho_{P} } \mathord{\left/ {\vphantom {{d_{P} \rho_{P} } {18\mu }}} \right. \kern-0pt} {18\mu }}} \right)\left( {{{U_{\hbox{Max} } } \mathord{\left/ {\vphantom {{U_{\hbox{Max} } } D}} \right. \kern-0pt} D}} \right) \)

T :

Time

U max :

Time-mean velocity through minimum array flow area

\( \overline{U} \) :

Local time-mean streamwise velocity

u′:

Local fluctuating streamwise velocity, RMS velocity

v′:

Local fluctuating transverse velocity, RMS velocity

\( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {x} \) :

Position vector

X :

Longitudinal/streamwise direction

Y :

Transverse direction

Z :

Wall-normal direction

ρP :

Tracer particle density

θ:

Circumferential location

λ:

POD scalar temporal functions

ϕ:

POD vector spatial functions

σs :

Minimum measurable particle displacement

ν:

Kinematic viscosity

μ:

Dynamic viscosity

\( \tilde{\omega }_{Z} \) :

Instantaneous Z-vorticity

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Acknowledgments

The authors would like to acknowledge the Science, Math, and Research for Transformation (SMART) fellowship program and the Department of Defense (DoD) for sponsoring this work.

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Authors and Affiliations

  1. Mechanical and Nuclear Engineering Department, The Pennsylvania State University, University Park, PA, USA

    Jason K. Ostanek & Karen A. Thole

  2. Naval Surface Warfare Center, Philadelphia, PA, USA

    Jason K. Ostanek

Authors
  1. Jason K. Ostanek
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  2. Karen A. Thole
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Correspondence to Jason K. Ostanek.

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Ostanek, J.K., Thole, K.A. Effect of streamwise spacing on periodic and random unsteadiness in a bundle of short cylinders confined in a channel. Exp Fluids 53, 1779–1796 (2012). https://doi.org/10.1007/s00348-012-1394-1

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  • DOI: https://doi.org/10.1007/s00348-012-1394-1

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