Calculation of unsteady processes at solar heating systems

F.Veysi, E.D.Sergievsky

The Moscow Power Engineering Institute (Technical University)

Krasnokazarmennaya, 14, Moscow, 111250, Russia

 

In this work the mathematical model of unsteady thermal conditions of elements of solar heating systems is submitted.

One of basic elements of this system is solar collector. As any solar collector works in a unsteady state of that solar radiation and atmospheric conditions change within day interestingly to analyze its dynamic behavior.

Two dimensional model of the typical solar collector consisting of a transparent cover, an absorbing plate and an air gap between them is considered. The basic equations describing the flow in this model of a solar collector are unsteady type NБvier-StПkes equations and the equation of energy. For completing the model is used a unsteady kindљ k- e љmodel of turbulence.

For check of suitability of this model at calculation of unsteady behavior of solar collectors, the experimental research with use infrared camera has been carried out. In parallel to obtain numerical results of temperature distribution on the surfaces of a plate at unsteady cooling, the system of equations NБvier-StПkes and energy has been solved with use of computer package Phoenics (version 3.3). The good agreement has been received between measured and settlement temperature structures during various time of process of cooling of the plate. The average divergence between results of experiment and numerical model has made 6 % that speaks that the chosen model of turbulence can be used at carrying out of unsteady calculations of solar collectors.

To analyze dynamic characteristics of solar collectors in solar indoor heating systemsљ and to coordinate them from other objects which are included in system it is necessary to calculate thermal behavior of solar collectors under various ambient conditions and at temperature changes on input in a collector within day. Therefore the simplified one-dimensional thermal model which is solved in the environment of program MATLAB/Simulink has been offered. Comparison between one-dimensional and two dimensional model shows, that the one-dimensional model of a solar collector is sufficient for definition of a field of temperatures on an absorbing plate in the air channel and a glass covering. The average divergence between two dimensional and one-dimensional models for temperature structures has made 10 %. As an example calculations for a typical room located in southern regions of Russia have been carried out.

The one-dimensional model can be used as a first step for development of more complex models which include other elements of solar systems, such as the storage tank, heat exchangers and auxiliary heaters, and also in other objects of aviation technology and power systems.