Some specifics of Blasius problem solutions

Аuthors

Pokrovskiy A. N., Dadashov C. M.^*

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

*e-mail: cingiz_dadashov@mail.ru

Abstract

The presented work performed numerical study of solutions behavior of laminar incompressible boundary layer on a flat plate (Blasiumo problem). It is common knowledge that Blasius proposed a statement of the problem as applied to a flat plate, except for the leading and trailing edges, allowing obtain the plate resistance with an adequate degree of accuracy. In this article, the authors outline four typical types of plates to refine the statement of the problem, and eliminate some inaccuracies being assumed in the previous statements of the problem.

In this paper, the authors conclude that new advanced methods serve the purposes of ensuring an aircraft optimal design and upgrading its performance characteristics. To this effect, it is necessary to improve conventional and develop new methods for aerodynamic characteristics computing with improved accuracy by accounting for viscous effects significantly affecting the aircraft characteristics and dynamics of its motion.

The authors tackle such issues, as a plate’s nose meltback commencing at supersonic flight speeds due to the impossibility of removing of large heat quantity, released in a flow, through the plate nose. In this respect, the authors analyze the succession of the problem statement on triangle strip flow-around by a supersonic airflow, from an idealized infinitely small to really blunted one.

Four approaches to employing various models for the problem solution on resistance of the plates and blunted wedge were examined. Two characteristic plates’ types, namely geometric and physical, are examined.

A method for computing resistance of the plates and blunted wedge, applying programs, was proposed. To compute the plate resistance, the authors show the necessity to compute the friction coefficient with LAYER-2 program, as well as resistance of the cylinder contamination and bottom pressure. C_xpl is computed for both laminar and turbulent layers with account for the friction resistance coefficient C_xfr , coefficient of cylinder blunting resistance C_xbl and bottom pressure coefficient C_xbot :

Сx_pl = Cx_fr + Cx_bl + Cx_bot

In conclusion, it is noted that LAYER-2 program application enabled computing resistance of these plates with improved accuracy, including all components of total resistance:

 

Сw_клина = Cx_зат + Cx_тр + Cx_дон + Cx_клина

.

Keywords:

boundary layer, skin friction coefficient on various flat plates

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