| The engineering background of natural convection heat transfer in a horizontalannulus with an internal slotted circle is natural cooling of enclosed isolated-phasebuses used in power plants. The local overheated of enclosed isolated-phase busesinduced by thermal effective can affect the normal running of machine seriously. So itis necessary to make some effective measure for heat dissipating. The theoreticalmodel for those above is natural convection heat transfer in a horizontal annulus withan internal slotted circle. The other reason for focusing on those problems is abundantand complex phenomenon induced by non-linear characteristics. In the scope of somecertain parameters, some non-linear phenomenon such as self-sustained oscillation,bifurcation, and chaos will appear during the investigation of natural convection heattransfer in a horizontal annulus with an internal slotted circle. Study on thosewonderful and complex dynamic characters is necessary and worth for thedevelopment of heat transfer theory and cognition of natural law.Firstly, two-dimensional model is applied for natural convection heat transfer ina horizontal annulus with an internal slotted circle. The based regulars of flow andheat transfer are discussed and compared with some existed experimental results.Secondly, the laser interferometer experiment platform had been constructed to studythe natural convection heat transfer of cylindrical envelope with different internalstructure and analysis the non-linear phenomenon. Thirdly, three-dimensional modelis applied for natural convection heat transfer in a horizontal annulus with an internalslotted circle. Two-dimensional, three-dimensional, and experimental results arecompared and analyzed for investigating three-dimensional flow and heat transfer andnon-linear characteristics. Finally, compact finite difference schemes are developedfor predicting non-linear characteristics accurately. Based on those objects above, themain content in this paper is as follows:1) Natural convection heat transfer in cylindrical envelope with an internalconcentric cylinder with slots is solved by two dimensional SIMPLE algorithms withQUICK scheme. The based flow and temperature field is obtained, includingsymmetric and non-symmetric two-vortex flow pattern and temperature with theshape of T, four vortex flow pattern and temperature with the shape of double T.Typical non-linear phenomenon is obtained by two-dimensional model, includingstatic bifurcation, self-sustained oscillation, and the route from steady to chaos.2) Experimental and two-dimensional numerical methods are applied for solving natural convection heat transfer in cylindrical envelope with an internal slottedconcentric cylinder with different site. The results indicate that for vertical slottedstructure, temperature field of both experiment and numerical solution is steady, andtwo different temperature fields are obtained under the same boundary conditions.The phenomenon of static bifurcation is verified by both experimental and numericalmethod; for level slotted structure, experimental boundary conditions are steady andsymmetric, but the non-symmetric unsteady experimental temperature fields areobtained, the oscillated phenomenon is obvious on the top of internal slottedconcentric cylinder, the amplitude of oscillation increases with the increasingRayleigh numbers, the numerical solution of two-dimensional model is steady, and itcan not reflect the oscillation phenomenon in experimental temperature.3) Three-dimensional mathematical model was established, and it is applied forsolving natural convection heat transfer in cylindrical envelope with an internalslotted concentric cylinder. The numerical results of Wang’s experimental parametersindicate that when the Rayleigh number is lower, the system is steady, three and twodimensional numerical solutions are consistent with experimental solutions. When theRayleigh number is higher, the system is unsteady with steady and symmetricboundary condition. Those oscillated solution shows three characteristics of flow andheat transfer. The discrepancy between two-dimensional numerical and experimentalresults increases gradually with the increasing Ra numbers, but the three-dimensionalnumerical results is continent with experimental results.4) For cylindrical envelope with an internal vertical slotted concentric cylinder, theflow and heat transfer of this system is steady and two-dimensional. There exists acritical Rayleigh number Racor slotted degree Sc. When the value of parameters ishigher than the critical value, the flow and heat transfer is oscillating with time andthree-dimensional with steady and symmetric boundary conditions.5) Three-dimensional model is applied for solving natural convection heat transferin cylindrical envelope with an internal level slotted concentric cylinder in this paper.The results indicate that the temperature is steady, and two different temperature fieldsare obtained under the same boundary conditions. Both three-dimensional anddimensional numerical solution can reflect experimental temperature field.Three-dimensional numerical method can predict the experimental temperature fieldand static bifurcation phenomenon.6) Three-dimensional model is applied for solving natural convection heat transfer in cylindrical envelope with an internal vertical slotted concentric cylinder in thispaper. When Rayleigh number is equal to6.46×104, three-dimensional numericaltemperature field is oscillating with time, and it can predict experimental temperaturefield. The oscillated temperature lines are obvious on the top of internal slottedconcentric cylinder, the amplitude of oscillation increases with the increasingRayleigh numbers. Three-dimensional numerical method can reflect the oscillatedtemperature, which can not be obtained by two-dimensional numerical scheme. Theoscillated system induced by non-linear characteristic can be verified by experimentaland numerical method.7) Compact correction methods are developed firstly for solving two typical partialdifference equations. The compact method based on SIMPLE is developed bydeferred correction method, and it can obtain the high order accurate solutions. Theproblem of natural convection heat transfer of cavity heated from below is calculatedby this method. Numerical results show that the compact scheme has higher accuracythan classical scheme and predict static bifurcation phenomenon.8) Compact finite difference scheme based on SIMPLE algorithm by author isapplied for solving natural convection heat transfer in cylindrical envelope with aninternal slotted concentric cylinder. The numerical results indicate that with theincreasing Rayleigh numbers, the system evolve from steady, periodic oscillating, tochaos. Different numerical method can predict the route from steady to chaos and beconsistent with SIMPLE algorithm with QUICK scheme.. |
PDF Full Text Request