The frost growth process in low temperature air-coolers of a refrigeration system is described by a complex set of partial differential equations which do not lend themselves to direct analytical solution. Although various forms of lumped and distributed models have been developed, they are often difficult to work with because of their complexity. Recent numerical solution schemes, either for the governing equations themselves or for simplified approximations of them, have been growing in popularity as computing power increases. Such solution schemes can yield excellent results when compared to experiments, but the time required to construct and solve them is great and good computing resources are needed.
Owing to the difficulty in using both approximate and numerical solutions, there is a continuing demand for correlations that are capable of predicting frost layer thickness with reasonable accuracy over a wide range of conditions. Many correlations have been presented, but have not met with good results outside narrow ranges of conditions specific to certain types of experimental apparatuses. It is thus desirable to obtain a more general correlation based on the consideration of the physical behavior during frost growth as opposed to the pure regression fits common to most current correlations. The correlation detailed herein is presented as a potential solution, as care has been given to account for the physical behavior of the frost layer during growth.
A particular functional form is chosen to mimic the solutions to other physical processes that exhibit similar behavior, such as the velocity profile in growing boundary layers and transient heat conduction. Significant parameters during frost growth are included in the form of dimensionless variables and placed in the correlation according to their overall influence on the growth process. Remaining variances in the growth profile, resulting from the impossibility of capturing exact behavior with a correlation, are accounted for by strategic inclusion of experimental coefficients.
The correlation is developed based on transient frost thickness data obtained using high accuracy visual methods for validation. The model is then extended to include data from many different sources, which allows for the coverage of wider ranges of conditions and eliminates design specifics of the apparatus as a factor in prediction. The tradeoff for such generality is a slight reduction in accuracy over the narrower range of experimental conditions used initially. Results show that the correlation is able to match frost growth trends with good accuracy across a wide spectrum of conditions. Results compare favorably with the predictions of other correlations.