Aerodynamic Calculation of Rough Surface in Rarefied Gas Flow Applying the Solution of Inverse Problem
Creators: name:  O. AKSENOVA 
name:   I. KHALIDOV 
Publisher: name: Proceedings of  the 9th European Conference for Aerospace Sciences. Lille, France, 27 June - 1 July, 2022
Year: 2022
Subjects: FLIGHT PHYSICS
COMPUTATIONAL FLUID DDYNAMICS

description: The most effective method to determine the parameters of surface roughness in rarefied gas flow is the solution of the inverse problem, because applied in practical calculations profile diagrams show only the roughness of the largest scale. However, the main input into the influence of surface roughness on aerodynamic values takes the roughness of smaller scale [1][3], usually negligible on the profile diagram. So the best way to find the roughness parameters is to calculate them from aerodynamic measurements, solving the inverse problem. Based on this solution algorithm allows us applying the results of our previous investigations concerning the problem of accounting surface roughness in aerodynamic calculation [1][3]. Surface roughness is simulated on micro-level by Gaussian or poly-Gaussian random field [1][3], [4]. The possibility of precise approximation of real micro-reliefs by these models of random fields is confirmed in different technology processes. In particular, rough surfaces are simulated which have been modeled as well by ionic bombardment of the steel using nitrogen ions, as by chemical etching of the steel by alcohol solution of nitric acid. In both cases very good agreement with experimental measurements is confirmed [4]. The scattering kernel on the smooth surface is supposed to be raydiffuse or described by CercignaniLampis model. This approach gives the opportunity to solve the inverse problem if original experimental measurements of aerodynamic values (scattering function, momentum or energy exchange coefficients) on the same surface with different roughness parameters are known. The lack of rarefied gas experiments with measured surface roughness parameters limits the number of test examples for our algorithm. However, several computations based on experimental data from [5][8] and from other papers allows us to make following conclusion. The value of the main roughness parameter obtained from the solution of inverse problem is substantially higher (at least 2550%) than similar value of the same parameter measured from the profile diagrams. Therefore, the effect of surface roughness in aerodynamic values of rough surface in rarefied gas flow is always significantly underestimated. The main reason is the low precision of roughness parameter measurements from the profile diagrams, and the second is that aerodynamic shadowing effect usually is not been taken into account. References [1] O. A. Aksenova and I. A. Khalidov, Inverse Problem of Finding Surface Roughness Parameters in Rarefied Gas Flow, in Rarefied Gas Dynamics, AIP Conference Proceedings 2132(1), 170005 (2019), pp. 17000511700058; doi: https://doi.org/10.1063/1.5119658 [2] O. A. Aksenova and I. A. Khalidov, Surface Roughness in Rarefied Gas Aerodynamics: Statistical and Fractal Models, (St.-Petersburg, St.-Petersburg University Publishers, 2004, in Russian), pp. 1120. [3] O. A. Aksenova and I. A. Khalidov, Analytic Model of the Effect of Poly-Gaussian Roughness on Rarefied Gas Flow near the Surface, in Rarefied Gas Dynamics, AIP Conference Proceedings 1786, 100007 (2016), pp. 10000711000078; doi: http://dx.doi.org/10.1063/1.4967618 [4] M. Litvak and V. Malyugin, Journal of Technical Physics 82, No.4, pp. 99107 (2012, in Russian). [5] A. I. Erofeev, O. G. Friedlander et al., The Influence of Roughness of the Surface on the Interchange of Momentum between Gas Flow and Solid Surface, in Rarefied Gas Dynamics, AIP Conference Proceedings 1501, edited by M. Mareschal, (Melville, NY, 2012), pp. 11681174. [6] A.I. Erofeev, A.P. Nikiforov, S.B. Nesterov, R.A. Nezhmetdinova, in TSAGI Journal, 47, 4, pp. 1227 (2016). [7] G. Markelov, , S. Stefanov, Statistical simulation of gas flows through short rough microchannels in Rarefied Gas Dynamics, AIP Conference Proceedings 1404, (Melville, NY, 2011). [8] N. E. Gimelshein, T. C. Lilly, S. F. Gimelshein, A. D. Ketsdever and I. J. Wysong, Surface Roughness Effects in Low Reynolds Number Nozzle Flows, in Rarefied Gas Dynamics, edited by M. S. Ivanov and A. K. Rebrov, (Novosibirsk: Siberian Branch of RAS, 2007), pp. 695702.