Dimensional analysis of a transverse gust encounter

Abstract

A dimensional analysis of transverse gusts was performed using the Buckingham Π theorem in an effort to standardize their characterization. This analysis identified three key terms that characterized transverse gusts: gust strength, gust width, and gust development rate. The strength and width terms currently exist in gust literature with varying amounts of general use and are commonly defined as the gust ratio, GR=v/U∞, and encounter width, We=w/c, respectively. Gust development rate is a new parameter to fully characterize and compare different velocity profiles and is similar to characterization metrics used in other unsteady flow research. For a single persistent or discrete gust the existing term is dimensionless pitch rate, Ω⁎=α˙c/2U∞, and for sinusoidal gusts the term is reduced frequency, k=πfc/U∞. These existing terms are therefore used as the dimensionless gust development rate. A short analysis of these terms demonstrates how all other desired information about a gust profile can be determined from these parameters. The set of dimensionless parameters allows for a more complete classifications of gusts based on strength and development rate. The parameters are applied to a selection of recent gust studies to show how the addition of a gust development rate term can help to identify areas of the gust field that are understudied.