On additional “multi-scale” similarity criteria for experimental work-out of aerospace engineering products

Aeronautical and Space-Rocket Engineering


DOI: 10.34759/vst-2023-1-91-97

Аuthors

Khatuntseva O. N.*, Shuvalova A. M.**

*e-mail: olga.khatuntseva@rsce.ru
**e-mail: nuts97@inbox.ru

Abstract

Despite the rapid development of mathematical modeling methods, the stage of experimental work-out in the design and creation of aerospace vehicles still plays a particularly important role. On the one hand, it allows exploring the most difficult modes for mathematical modeling, and on the other hand, it allows validating numerical methods. The products functioning under conditions of a possible turbulent mode creates certain difficulties for the correct con-duct of experiments on aerodynamic models t with a view to further correct transfer of the obtained data to a full-scale object.

In earlier studies of one of the authors, the issues related to the possibility of accounting for additional entropy production due to the stochastic perturbations excitation while a turbulent flow mode implementation were considered in details. This allowed modifying the Navier-Stokes (NSE) equations by posing them in an expanded phase space. In this case, the left part of the NSE, i.e. the full derivative in time, is being supplemented by a term characterizing the change in velocity when an additional «stochastic» variable changes. Inclusion of an additional term characterized by entropy production (which is always non-negative) in the equations allows, in particular, to account for the irreversibility of physical processes in time in cases where this production is non-zero. Based on this approach, both «laminar» and «turbulent» solutions for the Hagen-Poiseuille problem [8], the plane Couette problem [7] and the plane Poiseuille problem [6] were analytically obtained for large values of the Reynolds number.

This article shows that the «modified» Navier-Stokes equations allow obtaining extra similarity criteria, which, in fact, are analogs of the well-known similarity criteria ob-tained for «classical» NSE, but wielding a multiscale character: starting from the scales of a viscous boundary layer and ending with a macroscale flow.

Multiscale similarity criteria can be useful for more complete and accurate ex-perimental and numerical modeling of liquid and gas flow, in particular, when creating new products of aerospace equipment operated under conditions of possible turbulent mode. This approach will allow selecting the «right» size of the surface roughness and appropriate technological approaches when creating aerodynamic models for experimental research.

The article considered the issues of creating aerodynamic models with a controlled surface roughness size for conducting multiscale hydro- and aerodynamic experiments. It is noted that the most promising methods for such models creating can be technologies based on the SLS printing [13-17].

Keywords:

full-scale and numerical aerodynamic experiments, aerodynamic model, turbulent flow, similarity criteria, technologies based on SLS printing

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