Study on Advanced Numerical Algorithms for Fluid Flow and Heat Transfer Problems and Their Applications in Air Convective Heat Transfer Enhancement
Qu Zhiguo
ABSTRACT
Numerical research plays an important role in the simulations for engineering fluid flow and heat transfer problems due to its merits of low cost and being easy to obtain detailed information of different fields. Numerical design of complicated enhanced heat transfer configurations often requires huge computer memory or involves highly-coupled fluid-solid computational region, putting forward new challenge on convergence rate and solution stability and feasibility of the numerical methods. Thus study on high efficient numerical methods is of significant importance. The present thesis focuses on the developments of advanced numerical algorithms and their applications in the simulations of enhanced air convective heat transfer. The major contributions of the present thesis are as follows.
A new segregated algorithm named CLEAR (Coupled and Linked Equations Algorithm Revised) is proposed in this dissertation which deals with the coupling between velocity and pressure in fully implicit nature. The new algorithm completely discards the two basic assumptions of the semi-implicit SIMPLE series algorithms which are widely used in the CFD and CHT community.(Tao W Q, Qu Z G, He Y L. A novel segregated algorithm for incompressible fluid flow and heat transfer problems - CLEAR (Coupled and Linked Equations Algorithm Revised) part I: Mathematical formulation and solution procedure. Numerical Heat Transfer, Part B, 2004.45 (1): 1-17(times cited 4);Tao W Q, Qu Z G, He Y L. A novel segregated algorithm for incompressible fluid flow and heat transfer problems - CLEAR (Coupled and Linked Equations Algorithm Revised) part II: Application examples. Numerical Heat Transfer, Part B, 2004. 45 (1): 19-48. (times cited 3)) The mathematical formulations and implementations of CLEAR algorithm on staggered grid, collocated grid(Qu Z G, Tao W Q, He Y L. Implementation of CLEAR algorithm on collocated grid system and application examples. Numerical Heat Transfer, Par B, 2005, 47(1), 64-96),and non-orthogonal curvilinear coordinates (Two papers are accepted in 2006 and published in the beginning of 2007. Qu Z G, He Y L, Zhao C Y, Tao W Q. Implementation of CLEAR algorithm on non-orthogonal curvilinear coordinates for solution of incompressible flow and heat transfer, Int J Numerical Methods in Fluids. 2007, 53: 1077-1015. (times cited 1);Qu Z. G. Tao W Q., He Y. L. An improved numerical scheme for SIMPLER on non-orthogonal curvilinear coordinates, SIMPLERM. Numerical Heat Transfer, B, 2007, 51 (1):43-66(times cited 7).) (including incompressible and compressible flow) are presented in detail. It is revealed that the CLEAR algorithm can greatly enhance the convergence rate, averagely speaking by a factor of two, with reasonable robustness compared with the SIMPLER algorithm for incompressible fluid flow. For compressible fluid flow, the convergence characteristics of CLEAR are closely related to the Ma number. It can significantly enhance the convergence rate for subsonic flow, transonic and supersonic flow under small under-relaxation factor compared with SIMPLE algorithm, and the CLEAR algorithm convergence rate is almost identical to or lower than that of the SIMPLE algorithm for the transonic and supersonic flow under large under-relaxation factor, however, its robustness is still superior to the latter one.
A method which combines finite element method (FEM) and finite volume method (FVM) and is called unstructured grid method in rectangular coordinates is proposed for the air cooling simulation of electronic devices. It can solve some complicated problems which may not achieve a converged solution by using a conventional method such as the domain extension method. A two dimensional compression storage method in the column direction of a large zonal sparse matrix is proposed for the unstructured grid method in rectangular coordinates.
The heat transfer characteristics of three typical kinds of heat sink are experimentally studied with air forced convection under side-blowing and top-blowing modes. Numerical simulations are conducted for the two heat sinks with better experimental performance and the unstructured grid method in rectangular coordinates is used in the simulation. It is found in the experimental study that the air side heat transfer coefficient and thermal resistance are weakly related to the heating power. For the heat sink without any enhancing techniques, there exists a critical velocity beyond which the thermal resistance of top-blowing mode is higher than that of side-blowing. However, for the heat sink with longitudinal discontinuous fin, side-blowing mode is superior to top-blowing in the whole experimental range. A three dimensional numerical model of full heat sink is set up to numerically investigate the effect of geometry parameters on the thermal resistance. The numerical results show that the heat conduction thermal resistance and the convective thermal resistance are in the same order of magnitude, and hence they should be enhanced simultaneously in order to improve the performance of heat sink effectively.
The field synergy principle is verified to be applicable in the elliptic flow by numerical verification. A unified analysis is made to the three existing enhancing techniques for single phase convective heat transfer. It is found that the field synergy principle is the unified theory in enhancing single phase convective heat transfer.
A three dimensional numerical model is established for the air side heat transfer and fluid flow in the slotted fin and tube heat exchanger and the related numerical simulation is conducted. It is revealed that the heat transfer enhancement essence of slotted fin surface is to improve the synergy between velocity and temperature gradient. A strip location arrangement criterion called “frontal sparser and rear denser” is put forward (Qu Z G, Tao W Q, He Y L. Three-dimensional numerical simulation on laminar heat transfer and fluid flow characteristics of strip fin surface with X-arrangements of strips. ASME Journal of Heat Transfer. 2004, 126(5): 697-707; Cheng Y P, Qu Z G, Numerical design of efficient slotted fin surface based on the field synergy principle. Numerical Heat Transfer, Part A, 2004,45(6):517-538.;Qu Z.G., He Y.L., Tao W.Q. 3D numerical simulation on heat trasnfer performance of slit fin surface and analysis with field synergy principle. Journal of Engineering Thermophysics, 2003,24(5):825-827. Invetion Patent: Tao W. Q. ,Qu Z.G., Chng Y. P. Ehanced fin surface, granted number: ZL.03108079.0)with the idea that that it is more efficient to locate the strips in the downstream part of the fin sheet where the velocity and temperature gradient is in poor synergy than in the upstream part where the velocity and temperature are in good synergy. The slotted fin surface whose strips arrangement satisfied this criterion can improve heat transfer with relatively mild pressure drop penalty(The proposed technique is regarded to be in the interatnional leading level by the evaluation experts group orgnized by National Education Department and has been applied in the intermediate gas cooler of Hangzhou Oxigen Plant to save material and engergy by 20% compared with the old design. This achievement is granted as Shannxi First Class Science and Technolgy Award in 2005.). The concept may be further extended to suggest that the heat transfer enhancement techniques should be adopted in the place where the synergy between the velocity and temperature gradient is worse. This can be served as a general guideline for the design of high efficient enhanced heat transfer surface(This technique is presented in three international conference as kenote lectures. Tao W Q, He Y L, Qu Z G, Cheng Y P. Application of the field synergy principle in developing new type heat transfer enhanced surfaces. Proceedings of 3rd International Symposium on Heat Transfer and Energy Conversion, Guangzhou, China. Jan12-15;W.Q.Tao, Y.L.He, and Z.G.Qu. New design approach for slotted fin surfaces with high performance,Proceeding of Fifth International Symposium on Maultiphase Flow, Heat Mass transfer and Energy Conversion, July, 2005, Xi’an.;Ya-ling He, Wen-quan Tao, Zhi-guo Qu New understanding of convective heat transfer enhancement and its engineering application, Proceeding of 18th National and 7th ISHMET-ASME Heat and Mass Transfer Conference, 2006 , Jan 4-6 , IIT Guwahati India.).
Key words: Numerical methods; heat transfer enhancement; CLEAR,SIMPLER; SIMPLE; staggered grid; collocated grid; non-orthogonal curvilinear coordinates; compressible flow; convergence rate; field synergy principle; slotted fin surface; frontal sparser and rear denser
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