Wave drag of planar periodic relief structures

Fluid, gas and plasma mechanics


Volkov V. A.*, Semenov V. V.**, Sidhu J S. S.***

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: vladimir_volkov45@mail.ru
**e-mail: vasily_semenov@mail.ru
***e-mail: sarjitsidhu@usm.my


For smooth and piecewise smooth planar relief structures with any periodic profile, within the framework of linear theoryan exact formula, linking the total wave drag coefficient of the aforementioned finite relief structures and their infinite counterparts were obtained. The specified exact formula contains a defect function, which arguments are two similarity parameters: the fractional part of the wave number and the phase value at the leading edge. The defect function is defined only for periodic relief structures, having infinite analogues. Those, where the defect function identically equals zero are called special, and all the rest are usual. The defect function of usual periodic relief structures becomes zero for integer values of the wave number. It can differ from zero only for fractional values of the wave number. The drag wave force of special relief structures is directly proportional to their length. For all the other planar relief structures, this rule may not be applied. The uniqueness of the special planar relief structures is stems from the fact that they have a saw-tooth profile, in which all the vertices of the teeth have the same obtuse angle, which bisector is parallel to the axis.

The presence of the abovementioned properties in the special relief structures make them promising candidates for the role of standards used during calibration tests of various installations. If the calibrated planar attachments have special relief structures, then the following advantages will be achieved. Firstly, the technology of special planar relief structures manufacturing is the simplest and virtually insensitive to defects of its practical realization. Secondly, using the same reference attachment with special planar relief structures, and successively cutting off from it by parallel forming bands, makes it possible to perform a precision calibration for a specified range of wave drag. The use of reference planar attachments with special relief structures can increase the accuracy of various installations, and, at the same time, reduce the amount and cost of testing carried out during calibrations.


planar relief, velocity, Mach number, pressure, density, sine wave, wave drag, relief defect


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