Research Papers

Frost Layer Growth Based on High-Resolution Image Analysis

[+] Author and Article Information
D. Janssen

Department of Mechanical Engineering,
University of Minnesota,
111 Church Street SE,
Minneapolis, MN 55455
e-mail: janssenda@gmail.com

W. F. Mohs

Department of Mechanical Engineering,
University of Minnesota,
111 Church Street SE,
Minneapolis, MN 55455
e-mail: william.mohs@skope.co.nz

F. A. Kulacki

Life Fellow ASME
Department of Mechanical Engineering,
University of Minnesota,
111 Church Street SE,
Minneapolis, MN 55455
e-mail: kulacki@me.umn.edu

1Present address: SKOPE Ltd., 66 Princess Street, Christchurch 8140, New Zealand.

2Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF THERMAL SCIENCE AND ENGINEERING APPLICATIONS. Manuscript received April 16, 2015; final manuscript received November 23, 2015; published online February 17, 2016. Assoc. Editor: Pedro Mago.

J. Thermal Sci. Eng. Appl 8(2), 021018 (Feb 17, 2016) (12 pages) Paper No: TSEA-15-1117; doi: 10.1115/1.4032536 History: Received April 16, 2015; Revised November 23, 2015

We report the results of experiments using high-resolution imaging and digital analysis of transient frost growth to obtain quantitative information on frost thickness. The measurement technique provides faster data acquisition and much higher accuracy than traditional approaches. An empirical model of frost growth that captures the fast and slow growth periods is developed based on this data. The key physical and correlating parameter is the ratio of sensible heat transfer-to-total heat transfer, and the growth rate varies inversely with this ratio. The resulting correlation faithfully captures measured growth rates across a wide spectrum of frosting conditions and gives better predictive capability than that of existing correlations. The present model eliminates the need for specifics of the experimental apparatus and test surface as factors in prediction, as well as the necessity of measuring the frost–air interface temperature.

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Grahic Jump Location
Fig. 1

Apparatus and instrumentation. The in-plane camera is not shown.

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Fig. 2

Test surface assembly

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Fig. 3

In-plane image of frost growth: (a) t = 0 s, (b) t = 40 min, and (c) t = 240 min. Resolution is 135 px/mm. Baseline is in white, and average frost thickness is dotted.

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Fig. 4

Variation possible when choosing frost thickness measurement locations. Peaks (gray line) at 1.01 mm, arithmetic average height (dotted line) at 0.62 mm, and valleys (black line) at 0.41 mm. Resolution is 1 mm at 135 px/mm.

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Fig. 5

Frost profiles for different test conditions. (a) Ambient air temperature is −0.6 °C, ambient dew point temperature is −7.8 °C, and test surface temperature is −9.6 °C. (b) Ambient air temperature is 0 °C, ambient dew point temperature is −7.7 °C, and test surface temperature is −19.2 °C. Images are sequenced at a 20-min interval.

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Fig. 6

(a) Typical frost profile (135 px/mm); (b) with digital edge construction; and (c) after conversion to physical units with the average value (0.73 mm)

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Fig. 7

Typical frost growth versus time and approximate analytical representations. Frost growth curve is a normalized version of the correlation of Cremers and Mehra [6].

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Fig. 8

Exponential system behavior, Eq. (2)

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Fig. 9

Variation of the K(θ) for the trial function δ = K(θ)tθ. When θ ∼ 0.4, the transition to a more stable, lower growth rate is seen.

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Fig. 10

Polynomials A and B determined by regression for the data runs of Table 1: (a) accelerated growth, θ < 0.4; (b) slow growth, θ > 0.4

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Fig. 11

Linear regression fits for full dataset. Solid lines are 1:1.

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Fig. 12

Comparison of predicted and measured thickness for the slow growth period, θ < 0.4

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Fig. 13

Comparison of accuracy between Eq. (3) and other thickness correlations (runs 1–4). Data points are averages over present data runs.

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Fig. 14

Equation (9) and measurements of Cheng and Shiu [31]. Solid line indicates predicted values (Eq. (3)).

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Fig. 15

Comparison of predictions to data of Lee and Ro [29]. Solid lines are predicted values.

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Fig. 16

Equation (3) with data of Fossa and Tanda [30]. Solid line indicates predicted values.



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