Research Papers: Forced Convection

Heat Transfer of Springs in Oblique Crossflows

[+] Author and Article Information
Daniel B. Biggs

Department of Aerospace Engineering,
University of Michigan,
Ann Arbor, MI 48109
e-mail: dbbiggs@umich.edu

Christopher B. Churchill

Astro Aerospace,
Carpinteria, CA 93013
e-mail: chris.churchill@gmail.com

John A. Shaw

Department of Aerospace Engineering,
University of Michigan,
Ann Arbor, MI 48109
e-mail: jashaw@umich.edu

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received January 4, 2017; final manuscript received August 29, 2017; published online January 10, 2018. Assoc. Editor: Danesh K. Tafti.

J. Heat Transfer 140(4), 041702 (Jan 10, 2018) (13 pages) Paper No: HT-17-1002; doi: 10.1115/1.4038338 History: Received January 04, 2017; Revised August 29, 2017

An experimental program is presented of heated tension springs in an external crossflow over a range of laminar Reynolds numbers, spring stretch ratios, and angles of attack. Extensive measurements of the forced convection heat transfer of helical wire within a wind tunnel reveal an interesting nonmonotonic dependence on angle of attack. Computational fluid dynamics (CFD) simulations, showing good agreement with the experimental data, are used to explore the behavior and gain a better understanding of the observed trends. A dimensionless correlation is developed that well captures the experimental and CFD data and can be used as an efficient computational tool in broader applications.

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Fig. 1

Experimental setup in the wind tunnel (a) photograph of wind tunnel setup, (b) schematic of setup (side view), and (c) schematic of spring in crossflow (top view)

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Fig. 2

Normalized electrical resistance–temperature calibration for steel springs

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Fig. 3

Example wind tunnel data for spring at airspeed Ua=4m/s, angle of attack α=0deg, and stretch ratio λ = 4: (a) applied voltage and electrical current and (b) electrical resistance and temperature rise

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Fig. 4

Calculated wire temperature profile accounting for end conduction

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Fig. 5

(a) Plot of Nusselt number (Nu) versus angle of attack (α) for experiments on straight wire (solid circles) and correlation Eq. (9) (solid lines), showing the expected monotonic decrease of Nu with angle of attack (α); (b) Data for all wire diameters versus the normal component of Reynolds number (Ren) exhibit a square root dependence, agreeing with selected correlations (bold line is Eq. (9)): (a) wire diameter d = 0.305 mm and (b) all wire data, excluding data at α=90deg

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Fig. 6

Experimentally measured convective heat transfer (Nu) of springs versus angle of attack (α) at nine stretch ratios (λ): (a) λ = 4.0, (b) λ = 5.7, (c) λ = 7.7, (d) λ = 9.5, (e) λ = 11.8, (f) λ = 13.8, (g) λ = 15.8, (h) λ = 17.8, and (i) λ = 20.0

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Fig. 7

Projected frontal area model and example comparison to experimental data: (a) projected frontal areas for λ = 4.0, (b) area knockdown factor, and (c) λ = 11.8

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Fig. 8

Comparison of frontal area model (thin line) and experimental data (bold line) taken over fine increments (Δα=0.5deg) on a spring specimen at λ = 8 and Re=147: (a) top view schematic and (b) experiment data and frontal area model

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Fig. 9

CFD mesh at λ = 4: (a) control volume mesh and (b) spring mesh

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Fig. 10

CFD convergence study for a spring at stretch ratio λ=4.23 and airspeed Ua=16m/s: (a) total fluid box size, (b) mesh density, and (c) number of coils

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Fig. 11

Example CFD coil-averaged Nu's for a spring at stretch ratio λ = 4: (a) α=20deg, (b) α=50deg, and (c) α=70deg

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Fig. 12

Comparison of average Nusselt numbers between experiments and CFD simulations: (a) λ=4.0, (b) λ=7.7, (c) λ=11.8, and (d) λ=15.8

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Fig. 13

CFD simulations of spring heat transfer at Re=300

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Fig. 14

CFD results for ε=0.10 (λ = 4) and Re=300 (Ua=16 m/s) showing local distributions of h and |u|: (a) h distributions (top view), (b) h distributions viewed along flow, and (c) velocity field in the spring cut-plane

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Fig. 15

CFD results (square points) for λ = 4 and Re=300 in fine increments (Δα=2deg) compared to 2D channel index c (vertical gray lines)

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Fig. 16

Function b in the spring heat transfer correlation, corresponding to Nu at Re=300

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Fig. 17

Function m in the spring heat transfer correlation

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Fig. 18

Average Nu CFD data (open squares) and empirical correlation curves versus angle of attack for springs at four Reynolds numbers and ten stretch ratios): (a) λ = 4.0, (b) λ = 6.85, (c) λ = 9.70, (d) λ = 12.6, (e) λ = 15.4, (f) λ = 18.3, (g)λ = 21.1, (h) λ = 24.0, (i) λ = 26.8, and (j) λ = 29.7

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Fig. 19

Comparison of LH and RH springs: (a) LH spring, (b) RH spring, (c) LH spring (close up), and (d) RH spring (close up)



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