Calculation of energy spatial distribution for complicated emitter

Аuthors

Nikolaenko V. S., Filippov G. S.^1*, Yashchenko B. Y.²

1. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia
2. Lavochkin Research and Production Association, NPO Lavochkin, 24, Leningradskay str., Khimki, Moscow region, 141400, Russia

*e-mail: Filippov.Gleb@gmail.com

Abstract

The new technique is developed for carrying out calculations of an indicatrix of an infrared radiation of the aircraft propulsion system (PS). It is based on a Monte-Carlo method. It is a numerical method of solution of mathematical tasks by means of model operation of random values.

Creation of Mathematical Model

The engine represents the composite geometrical figure therefore in calculation a number of simplifications is accepted:

1. The surface of a nozzle is set by the geometrical elements.
2. Values of temperature and degree of blackness of separate elements of a nozzle surface were accepted by constants.
3. The radiation let out and absorbed by a stream of combustion gases is not considered. Availability of gas in a nozzle is not considered.
4. In input dates for calculation some elements of a nozzle ( stabilizers, swirlers, etc.) were not considered.

Each geometrical surface is divided breaks into a number of the elementary surfaces with area dS_{m, n} . For each elementary surface temperature dT_{m, n} and blackness degree ⍺_{m, n} are set. The beam direction for a microcell of the radiating surface is set in a random way. The beam leaves the center of this microcell. It is considered that all radiant energy of a microcell is distributed in the specified random direction.
Then beam crossing with all geometrical surfaces in the main frame (the equations of a beam and the equation of surface of revolutions are solved in unison) is considered (fig.).
The surface is reflecting at realization of conditions of an identical orientation, crossing in limits (|Z_max| >|Z_m,n|> |Z_min|). If the surface is reflecting, in a point of their crossing the new casual direction of a reflected beam is defined. If the closest surface is a summation hemisphere, the beam leaves the nozzle, and the coordinates of it intersection with the conditional summation hemisphere are defined.
Energy of a reflected beam decreases depending on a surface reflectivity. Coordinates of a cross point of a beam with a summation hemisphere and energy of a beam are recording. The summation hemisphere is divided into sections. Energies of the beams falling on each section are summering. Thus, the radiation indicatrix is calculated.

The relative positioning of PS and frame: 1 crossing of a beam with a surface; 2 cross points of the line of a beam with surfaces; 3 point with coordinates of Xc m,n,Ycm,n, Zcm,n ; 4 point with coordinates of X02m,n, Y02m,n, Z02m,n (in a local frame) or Xcnm,n, Ycnm,n, Zcnm,n (in the main frame); 5 vector ⍴_{m n} of the casual direction of a beam; 6 surfaces of the partial platform of dS_m,n; 7 vector of a normal of Dn_m,n to a surface of the partial platform of dS_m,n

Keywords:

mathematical modeling, indicatrix, radiation, radiator, reflector

References

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