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Time-resolved stereo PIV measurements of the horseshoe vortex system at multiple locations in a low-aspect-ratio pin–fin array

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Abstract

Pin–fin arrays are a type of cooling feature found in heat exchangers, with elements (generally cylindrical or square) that span between two endwalls. Flow around the pin–fins generates highly turbulent mixing that increases convective heat transfer from the pins to the cooling flow. At the junction of a pin–fin and the endwall, a complex flow known as the horseshoe vortex (HSV) system is present. Although the HSV is a well-studied phenomenon, its behavior is not understood in the highly turbulent flow of a pin–fin array. Furthermore, the presence of close confining endwalls for low-aspect-ratio (short) pin–fins may have an impact on HSV dynamics. The present study utilized time-resolved stereo particle image velocimetry to examine the fluid dynamics of the HSV system in rows 1, 3, and 5 of a low-aspect-ratio pin–fin array, for a range of Reynolds numbers. In the first row, instantaneous flowfields indicated a clearly defined HSV at the leading edge, with dynamics similar to previous studies of bluff-body junction flows. The time-averaged HSV system moved closer to the pin with increasing Reynolds number, with more concentrated vorticity and turbulent kinetic energy (TKE). For downstream rows, there was a significant increase in the amount of mid-channel vorticity, with levels on the same order as the value in the core of the HSV. The time-averaged HSV system in downstream rows showed minimal variation with respect to either Reynolds number or row location. Regions of maximum streamwise and wall-normal turbulent fluctuations around the HSV were a result of its quasiperiodic oscillation between so-called backflow and zero-flow modes, which were present even in downstream rows despite the extremely high mid-channel turbulence. In the downstream rows, normalized TKE across the entire field of view decreased with increased Reynolds number, likely due to dissipation rates proportionally outpacing increases in mean channel velocity and Reynolds number. The flowfield results from this study corroborate prior findings from heat transfer measurements that indicate a fully developed condition is established at around the fifth row in an array.

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Abbreviations

D :

Pin–fin diameter

dt :

Time between S-PIV image-pair exposures

f :

S-PIV sampling frequency

H :

Pin–fin height, H = D

HSV:

Horseshoe vortex

\(\overline{{n^{{\prime }} n^{{\prime }} }}\) :

Variance of component of velocity, n (where n is u, v, or w)

S-PIV:

Stereo particle image velocimetry

Re D :

Reynolds number based on D and U m , \(Re_{D} = \frac{{D*U_{m} }}{\nu}\)

S L :

Streamwise array spacing, S L = 3.46 * D

S w :

Spanwise array spacing, S w = 2 * D

Δt + :

Sampling timestep in inner coordinates, \(\varDelta t^{ + } = \frac{{{\raise0.7ex\hbox{$u_{\tau }^{2}$} \!\mathord{\left/ {\vphantom {1 f}}\right.\kern-0pt} \!\lower0.7ex\hbox{$f$}} }}{\nu}\)

Tu:

Turbulence level, \({\text{Tu}} = \left.\left( {\sqrt {\frac{2}{3}{\text{TKE}} } } \right)\right/U_{m}\)

TKE:

Turbulent kinetic energy, \({\text{TKE}} = \frac{1}{2}\sqrt {\overline{{u^{\prime } u^{\prime } }} + \overline{{v^{\prime } v^{\prime } }} + \overline{{w^{\prime } w^{\prime } }} }\)

u :

Streamwise component of velocity

u τ :

Friction velocity

u + :

Streamwise component of velocity in inner coordinates, \(u^{ + } = \frac{u}{{u_{\tau } }}\)

U m :

Channel mean velocity upstream of array

U max :

Maximum average velocity in the channel, U max = 2 * U m

v :

Endwall normal component of velocity

|V| :

Velocity magnitude

w :

Spanwise component of velocity

X :

Streamwise direction

y + :

Wall-normal direction in inner coordinates, \(y^{ + } = \frac{{yu_{\tau } }}{\nu}\)

Y :

Endwall normal direction

Z :

Spanwise direction

ν :

Kinematic viscosity

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  1. Corey D. Anderson

    Present address: United Technologies–Pratt & Whitney, East Hartford, CT, USA

Authors and Affiliations

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

    Corey D. Anderson & Stephen P. Lynch

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Correspondence to Stephen P. Lynch.

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Anderson, C.D., Lynch, S.P. Time-resolved stereo PIV measurements of the horseshoe vortex system at multiple locations in a low-aspect-ratio pin–fin array. Exp Fluids 57, 5 (2016). https://doi.org/10.1007/s00348-015-2091-7

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  • DOI: https://doi.org/10.1007/s00348-015-2091-7

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