On the median volume diameter approximation for droplet collision efficiency

Karen Finstad, Edward Lozowski, Lasse Makkonen

Research output: Contribution to journalArticleScientificpeer-review

44 Citations (Scopus)

Abstract

In this note, we examine a shortcut for calculating the overall collision efficiency of a droplet spectrum, known as the “median volume diameter” (mvd) approximation. By calculating the overall collision efficiency of a circular cylinder for a variety of natural droplet spectra, first precisely using a spectrum weighting approach, and then as approximated using the mvd, as well as several other representative droplet sizes, we show by comparison that the mvd approximation is a good one, with an average absolute error of about 0.02. While trying to give some mathematical justification for why the mvd approximation works, we show that it can be derived from a single-point numerical integration formula, and that extension of this formula to 2, 3 or 4 points should give correspondingly better approximations. Detailed comparisons confirm that use of the 2-point formula reduces the average error by one-half, while the 3- and 4-point formulae can reduce it even more, depending on the type of spectrum.
Original languageEnglish
Pages (from-to)4008-4012
JournalJournal of the Atmospheric Sciences
Volume45
Issue number24
DOIs
Publication statusPublished - 1988
MoE publication typeA1 Journal article-refereed

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On the median volume diameter approximation for droplet collision efficiency. / Finstad, Karen; Lozowski, Edward; Makkonen, Lasse.

In: Journal of the Atmospheric Sciences, Vol. 45, No. 24, 1988, p. 4008-4012.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - On the median volume diameter approximation for droplet collision efficiency

AU - Finstad, Karen

AU - Lozowski, Edward

AU - Makkonen, Lasse

PY - 1988

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AB - In this note, we examine a shortcut for calculating the overall collision efficiency of a droplet spectrum, known as the “median volume diameter” (mvd) approximation. By calculating the overall collision efficiency of a circular cylinder for a variety of natural droplet spectra, first precisely using a spectrum weighting approach, and then as approximated using the mvd, as well as several other representative droplet sizes, we show by comparison that the mvd approximation is a good one, with an average absolute error of about 0.02. While trying to give some mathematical justification for why the mvd approximation works, we show that it can be derived from a single-point numerical integration formula, and that extension of this formula to 2, 3 or 4 points should give correspondingly better approximations. Detailed comparisons confirm that use of the 2-point formula reduces the average error by one-half, while the 3- and 4-point formulae can reduce it even more, depending on the type of spectrum.

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DO - 10.1175/1520-0469(1988)045<4008:OTMVDA>2.0.CO;2

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