Вот, собственно, когда он был изобретен
The crossflow fan appears to have been invented by Mortier in the 1890's and is described in his U.S. Pat. No. 507,445 which was granted in 1893. An improvement on the crossflow fan is disclosed in Datwyler's U.K. Pat. No. 988,712. In that improved fan, the vortex is free to move circumferentially around the fan and the vortex thus is able to adjust its position to prevailing flow conditions. For a discussion on the crossflow fan, see the monograph titled "A Study Of The Cross Flow Fan" by A. M. Porter and E. Markland in the Journal of Mechanical Engineering Science, Vol. 12, No. 6, 1970.
А вот это по поводу методик расчета

More than one century has passed since Mortier's first cross-flow fan patent in 1891, but the design is still based on empirical considerations and on the re-adaptation of previously developed configurations. The complexity of the flow field inside the machine is the main reason for the lack of an established design procedure, because the characteristics of the eccentric vortex that forms within the impeller are deeply influenced by the geometry of the impeller and also of the casing. In this paper, the objectives that should be pursued in the design procedure are discussed and defined, and guidelines for cross-flow fan design are determined through the analysis of an experimental database of fan performance and efficiencies, which is obtained by the systematic variation of the most important geometric parameters of the casing in combination with different impellers.
Я извиняюсь, что не перевел. Просто нету времени. Да и надо ли, и так, вроде все понятно.
А вот
тут можно за деньги или после регистрации (фиг их буржуев разберет, нет, чтобы нахаляву выложить)

получить информацию по критериям подобия для проектирования этого типа вентиляторов. Свежачок, так сказать.