MODELS FOR CALCULATING ANGULAR RADIATION COEFFICIENTS AND PROBLEMS OF ACCOUNTING ALL VISIBLE ELEMENTS OF SURFACES

Abstract

During studies of systems for transmitting and receiving energy of radiant origin (thermal, light), there is always a stage of calculation and evaluation of the particles of such energy. Calculations are related to the characteristics of objects that radiate, receive and reflect rays. Of course, it is necessary that these calculations give a minimum error as a result. If purely analytical methods are used, then they will give accurate results, but will depend on the complexity of the descriptions of the objects (radiating, receiving or reflecting energy). Replacing analytical calculation methods with geometric ones facilitates the situation regarding the description of objects, the possibility of adjusting the geometric shape of objects (inverse problem), step-by-step observation of the modeling process, visualization of results. But here you have to put up with approximations and neglecting some parts of the surfaces, which should be avoided. Projection methods, in particular, the method of radial-parallel projection, are the basis of the geometric determination of the angular coefficients characterizing the parts of radiation energy. The value of the angular coefficients is affected by the distance and location of two geometric elements, as well as the presence of opaque elements between them – obstacles to the passing of energy. These coefficients are geometric invariants. Research is related to determining the rationality of using projections on different surfaces – a sphere, a cube, a cylinder (respectively, in the method of a sphere of unit radius, the method of a half-cube, the method of coaxial cylinders). When estimating the parts of radiant energy falling on the surface of the receiver at the point for which calculations are being made, all parts of this energy from all the cells into which the radiating surface is divided should be taken into account, i.e. not only the elements of the radiating surface located at the «zenith» of the point should be taken into account calculations, as well as elements of the radiating surface located «near the horizon» (at a small angle to the plane tangent to the receiver surface at the calculation point). In this sense, the method based on projection onto cylindrical surfaces will be more effective.

Keywords: geometric modeling, methods and models of radiant energy exchange, projection, angular radiation coefficients, surfaces.