Experimental fitting of the re-scaled balje maps for low-reynolds radial turbomachinery

With the increasing popularity enjoyed by ultra-micro scale turbomachinery, designers are often faced with severe challenges due to the substantial phenomenological difference between the low-Reynolds fluid-dynamics in rotating or strongly curved flows and the established knowledge acquired through decades of theoretical and experimental studies on medium and large-scale machines. The problem is complicated by the absence of an extended and reliable database that might be used for preliminary design and provide indications for scale-up or scale-down. As a result, custom-designed experimental campaigns are necessary that make the development of any new machine exceedingly costly. The situation has seen some improvement in recent years, after the publication of a sufficient number of experimental results and numerical simulations that pave the way towards a development of semi-empirical correlations. The purpose of this work is to present and discuss a preliminary and simple method to extend the currently available design maps into the small scale range (Re < 105) by introducing in the Balje charts an efficiency correction that depends on the specific speed ns. The method results in a Stodola-like formula which originates a lower-than-standard Cordier curve on the classical Balje charts. A validation with some experimental results is also presented and discussed. Though the agreement is more than satisfactory, it must be stressed that the method provides only approximate results, and thus it must be considered as an evolving temporary solution, that needs to be updated as long as larger series of (numerical or physical) experimental results become available.