Determination of critical distributed roughness height inducing transition on AEDC cone at transonic/supersonic speed in CIRA PT-1 Wind Tunnel

As said, in order to perform the data volume requirement in realistic way, it is necessary to define the order of polynomial dependence between each independent variable and response parameters. In particular, trend polynomial orders of Mach number, transition trip roughness height and position and Reynolds number with respect transitional Reynolds number are defined.
In general, a parabolic dependence between transition Reynolds number and Mach number can be assumed, according to literature data reporter.

Because of insufficient available data in literature referred to cone geometries, it is difficult to determine the relation between trip transition height and transitional Reynolds number. However, according to literature data, reported in the paragraph 1.2.2, considering that laminar to turbulent transition position will coincide definitively with the trip position for all values of transition trip height higher than a critical value, a second order dependence can be assumed.
Assuming valid the equations and using a variable change (i.e. Log (Re ) and Log (Re) ) the relation between Reynolds number and transitional Reynolds number reduces to linear trend. However in order to better understand the influence of the Reynolds number on the transition position, a conservative choice of a second order dependence is done.

According to 1.2.4, as the transition trip position grows, ReXT first decreases up to a critical value and after rises with a not well-defined trend. Assuming (in a conservative way) that this kind of dependence is valid also for 3D geometry, the dependence between transition Reynolds number and transition tripping position can be assumed of the fourth order. In this activity the trip position will be represented nondimensionally by Xt / L .