Numerical Simulation Of Rayleigh-Bénard Convection With Non-uniform Heating From Below

Thermal convection is a ubiquitous physical phenomenon, and Rayleigh-Benard (RB)convection system is a classical fluid mechanics model abstracted from many phenomenon of thermal convection to study the thermal convection problems. In many cases of nature and engineering, the external driving force of thermal convection is not uniform. Non-uniform external driving force will bring convection system many new dynamic characteristics. More and more researchers begin to study the effect of non-uniform heating on flow field characteristics and heat transfer efficiency of RB convection system which aim is to brings us new understanding of the RB convection problem and to direct the engineer practice.In this thesis, large eddy simulation method and Hilbert-Huang transform analysis method are adopted, both the conditions of uniform Heating and non-uniform Heating from below are calculated and analyzed. The effects of non-uniform heating on the heat transfer efficiency and the flow field characteristics of RB convection system are also discussed. The main results are as follows:(1)Both in the condition of uniform heating and non-uniform heating, the surface average Nu number of RB convection increases as the Ra number increases. At low Ra number, the Nu number of three group under non-uniform heating condition significantly increase; when the Ra number exceeds a certain critical value, the Nu number show a downward trend; when the Ra number exceeds a certain range, Nu number under the condition of non-uniform heating is smaller than Nu number under uniform heating. Therefore, in a certain range of Ra number, we can change the bottom heating mode to achieve the purpose of improving or reducing the heat transfer efficiency of the system.(2)In the condition of non-uniform heating, the structure characteristics of the flow field under the condition of non-uniform heating are completely different from that conditon under uniform heating. It specifically appeared as the follows: non-uniform heating leads to the vertical stratification into horizontal stratification in temperature field, and the two larger scale circulations become a larger scale circulation in velocity field. So we conclude that strengthening of horizontal flow under non uniform heating condition inhibit the the transmission of heat to some extent.(3)The time series data of RB convection was analyzed preliminarily by Hilbert-Huang transform method. It is found that the RB signal is a typical non-stationary, multi-scale structure signal. There is a strong intermittency in the small scale modes of the RB convection.Except for minority modes which obey the Gauss distribution, it is deviated from the Gauss distribution in most modes. It can be found that the frequency is mainly concentrated in the low frequency part from the Hilbert spectrum, and the Hilbert marginal spectrum is more realistic than Fourier spectrum to reflect the relationship between frequency and energy in RB convection.