Calculation of Temperature Rise in Dry-type Air-core Reactors Using Strong Coupling of Fluid-Temperature Field

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1 Reseach Jounal of Applied Sciences, Engineeing and Technology 5(10: , 013 ISSN: ; e-issn: Maxwell Scientific Oganization, 013 Submitted: Septembe 15, 01 Accepted: Octobe 4, 01 Published: Mach 5, 013 Calculation of Tempeatue Rise in Dy-type Ai-coe Reactos Using Stong Coupling of Fluid-Tempeatue Field 1 Yujiao Zhang, 1 Xiongfeng Huang, Gang Hu, 3 Tao Huang and 3 Jiangjun Ruan 1 College of Electical Engineeing and New Enegy, College of Compute and Infomation Technology, China Thee Goges Univesity, Yichang 44300, China 3 Depatment of Electical Engineeing, Wuhan Univesity, Wuhan 43007, China Abstact: The ventilation system design of dy-type ai-coe eacto is a complex task that must detemine the themal loads to achieve the maximum insulation mateial exploitation. In this study, the tempeatue ise in eacto is due to Joule s losses and heat dissipation by ai convection, convection and adiation. The Joule s losses calculated by coupled magnetic field-cicuit analysis ae used as the input fo the themal field by finite-element analysis, which is diectly coupled with fluid analysis. Finally, the tempeatue distibutions of eacto can be calculated. Theefoe, the themal pefomance analysis of ai-coe eacto could be conducted in the ealy design stage to guaantee the insulation mateial equiements. Keywods: Coupled magnetic field-cicuit, dy-type ai-coe eacto, finite-element analysis, fluid field, themal field, tempeatue ise INTRODUCTION In powe system, dy-type ai-coe eacto is employed to limit cuent, steady voltage and compensate eactive powe. In pactical applications, ai-coe eacto duing opeation is pone to faults, including patial dischage, oveheating and bunout (Liu et al., 003. In the case of dy-type eactos with fully encapsulated windings, the insulation between tuns is usually a solid dielectic mateial. In selecting appopiate mateials to be utilized as tuns insulation on the conductos, it is necessay to evaluate dielectic popeties, mechanical popeties and aging chaacteistics unde opeating conditions. Pefomance at tempeatue is one of the main evaluating citeia fo mateials, so the tempeatue ise is one of the main aging mechanisms that have to be consideed, especially fo the oveall system (IEEE Std., Accuate calculation of the tempeatue distibution is pivotal to the optimal design, which is a multiphysical coupled pocess that involves electomagnetic losses as well as fluid dynamic and themal behavio. In taditional eseach, the aveage tempeatue ise of eacto was calculated by empiical fomula (Wu et al., Howeve, even if aveage tempeatue ise satisfies design equiement, the hottest-spot tempeatue in eacto might exceed the maximum tempeatue limits of insulation mateials. Moeove, themal field was simulated by finite-element method (FEM afte calculating the heat tansfe coefficient by using Nusselt numbe (Liu, 1991; Wu et al., 00; Ho et al., 006, 007. Nevetheless, the fluid dynamic behavio cannot be accuately descibed not by simulating fluid field. The calculation esults wee vey diffeent with the measuement esults, so the heat tansfe coefficient must be epeatedly modified. Theefoe, a coupled analysis of fluid field and themal field is mandatoy to compute the tempeatue ise in the design stage (Zhang et al., 01a. In this study, we calculated tempeatue distibutions by using the coupled magnetic field-cicuit method and coupled fluid-dynamical and themal finite-element analysis in a type of dy-type ai-coe eacto, as shown in Fig. 1. Though the big ventilation duct, cooling ai taken in fom the exteio to the inteio of eacto by fan is sent to exothemic pats such as the windings. On the top of eacto, thee ae two layes of ainpoof shield fo potecting the eacto against ain. A -D computational model can be established to analyze the multi-physics simulation due to the axial symmety. The Joule s losses calculated by the coupled field-cicuit analysis ae used as the input fo the themal field analysis, which is deeply dependent on accuate ai fluid field analysis. THEORY AND FORMULATION Coupled magnetic field-cicuit calculation: The dytype ai-coe eacto contains paallel seveal encapsulated windings and each of them contains Coesponding Autho: Yujiao Zhang, College of Electical Engineeing and New Enegy, China Thee Goges Univesity, Yichang 44300, China 941

2 Res. J. Appl. Sci. Eng. Technol., 5(10: , 013 Fo the encapsulated windings, the main heat dissipation mode is heat conduction. Fo the suface between encapsulated windings and suounding ai, the main heat dissipation mode is heat foced convection and themal adiation. Finally, ou concen is the tempeatue distibutions of each encapsulated winding. Heat conduction: Fo the encapsulated windings, the steady state heat conduction equation fo solid is given as Zhang et al. (01b: 1 T T ( k + ( k = Q (5 Fig. 1: This type of eactos in substation paallel seveal layes of small-diamete aluminum conductos. The ac voltage, whose fequency is 50 Hz, is applied to the conducto in each laye. In cylindical coodinate system, the magnetic field equation can be given as Liu et al. (003: 1 A 1 A ( + ( = µ 0J (1 The teminal voltage of the conductos in the i th laye is given as: u dψ dt i = ir i i + ( k = The coefficient of heat conductivity Q = The heat geneation of unit volume in aluminum conductos Heat convection: The foced convection of ai satisfies the Navie-Stokes Equations, which consist of thee goups of equations. Fo two-dimensional incompessible steady fluid, the Navie-Stokes Equations in cylindical coodinate system can be simplified as following (Wu et al., 00: Continuity equation: ( υ 1 υz + = 0 Momentum consevation equations: (6 Ψ ii = NN ii SS AAAAAAAA = NN ii AA ll gggggg (3 Ψ i = The flux linkage of conductos in the i th laye N i = The numbe of tuns Fom Eq. (1-3, the voltage equation can be descibed with magnetic vecto potential (A. These equations can be solved by FEM. Afte obtaining the value of A, the cuent can be calculated. Then, Joule s losses can be calculated by Eq. (4. Q = ρj (4 ρ = Resistivity of aluminum J = Cuent density Stong coupling of fluid-tempeatue field calculation: Fo the system of the eacto shown in Fig. 1, thee ae thee heat dissipation modes, involving heat conduction, heat convection and themal adiation. 94 υ υ ρυ ( + υz = p 1 ( υ υ + µ + υz υz ρυ ( + υz = p 1 υz υ z + µ + Enegy equation is given as: T T ρ υ υ c( + z = k T + Q ρ = The density of ai μ = The viscosity coefficient p = Pessue c = The specific heat (7 (8 (9

3 Res. J. Appl. Sci. Eng. Technol., 5(10: , 013 T = The fluid tempeatue and υ and υ z ae the velocity in the - and z- diections, espectively Because of the lage Reynolds numbe (>300, the fluid gets tubulent. The standad k-ε tubulence model was used in the tubulence calculation (Zhang et al., 01a. ( ( ρk ρ kut µ t k + = µ + + Gk ρε t xi xj σ k xj ( ρε ( ρεu t xj x k k i + = xi µ t ε C1 ε ε µ + + G k C ε ρ σ ε j u v w µ t Gk = x y u v u w v w y x x y G k = The tubulent geneation ate μ t = ρc u (k /ε = The viscosity coefficient (10 (11 (1 As the constants in the equations, C 1ε = 1.44, C ε = 1.9, C μ = 0.09, σ k = 1.0, σ ε = 1.3. Radiation: Fo a system of two sufaces (suface i and j adiating to each othe, the heat tansfe ate between sufaces i and j is expessed as Wu et al. (00: Q = σε FAT T ( ij i ij i ( i j σ = Stefan-Boltzmann constant ε i = The effective emissivity of suface i F ij = The adiation view facto between suface i and j A i = The aea of suface i and T i T j = The absolute tempeatue of suface i and j CALCULATION AND ANALYSIS Stucto of eacto: Accoding to the eacto shown in Fig. 1, the model of oveall eacto and the vetical pat of ventilation duct is axisymmetic, so a -D model is established, as shown in Fig.. Thee ae ten encapsulated windings and each of them has thei own diffeent size. Moeove, on both sides of each encapsulated winding ae wound with fou layes of DMD (Dacon Myla Dacon and thee layes of glass fibe dipped by epoxy. Each laye of aluminum conducto is wound with fou layes of polyeste film. It means that thee ae eight layes of polyeste film between two layes of aluminum conducto. Finite-element model and bounday conditions: On the basis of model shown in Fig., the finite-element Fig. : The calculation model of eacto 943

4 Res. J. Appl. Sci. Eng. Technol., 5(10: , 013 Fig. 3: Patial FE model Table 1: Main geomety and mateial popeties of the model Themal Mateial conductivity Width (W/(m K (mm Aluminum conducto 17.7 Diffeent diamete in each laye DMD Polyeste film Glass fibe dipped by epoxy model is established, as shown in Fig. 3. The total elements and nodes ae 371,550 and 68,051. Table 1 descibes the main geometical and mateial popeties of the analyzed model. The themal field and fluid field ae coupled diectly accoding to Navie-Stokes equations. Fistly, coupled magnetic field-cicuit calculation is caied out, then, the Joule heat is obtained. Secondly, the Joule heat is coupled into the themal field as heat geneation ate, in addition to some othe pope fluid and themal bounday conditions, the themal field and fluid field is simultaneously calculated. Pope bounday conditions should be set as followings. Set non-slip bounday condition (υ x = 0, υ y = 0 on the suface of eacto Set suounding tempeatue (hee 0 C in accodance with nomal tempeatue Fig. 4: The hottest tempeatue of the encapsulated winding Set efeence pessue to zeo at the node in ai outlet Set axisymmetic bounday condition (υ x = 0 at the node on axis Set adiative heat tansfe bounday conditions fo the sufaces of shielding and encapsulated windings. Set Stefan-Boltzman constant to 5.67e-8 and tempeatue offset to 73. Hee all the emissivity is set to 0.9. CALCULATION RESULTS AND ANALYSIS Afte coupled magnetic field-cicuit analysis, the Joule s losses can be calculated. Table gives the losses of evey aluminum conducto in each encapsulated winding. In foced ai cooling eacto, the cooling ai blows fom bottom to top and flows though the ai passages between two encapsulated windings. Fom Fig. 4, the tempeatue distibution in one encapsulated winding is non unifom because the heat conductivity of insulation mateial is much smalle than that of aluminum conducto. Fom Fig. 5, we can find that the flow velocity of ai in passage between encapsulated windings, which ae nea the outside and inside wall, is faste. Theefoe, the hottest point is on the encapsulated winding in middle of model, as shown in Fig. 6. Table : The heat geneation ate of evey aluminum conducto in each encapsulated winding (W/m 3 Laye of aluminum conducto No

5 Res. J. Appl. Sci. Eng. Technol., 5(10: , 013 insulation mateials and the stuctues of divese components in eacto, such as ainpoof shield which may influence on the ai flow among the encapsulated windings. ACKNOWLEDGMENT This study is suppoted by National Natual Science Foundation of China (No REFERENCES Fig. 5: Ai velocity distibution and patial vecto velocity Fig. 6: The tempeatue distibutions in eacto The ainpoof shield has an impotant influence on the ai velocity among the encapsulated windings. Thus, the ai cooling should be consideed in the design of ainpoof shield. The unifom tempeatue ise distibution might be achieved by impovement of the geometical stuctue of ainpoof shield. CONCLUSION In this study, the tempeatue ise of a foced ai cooling dy-type ai-coe eacto is calculated by finite element method fo coupled magnetic-themal-fluid field. The cuent distibution among the encapsulated windings is analyzed by using coupled magnetic fieldcicuit method. The tempeatue ise distibution of eacto is tightly elated with cuent Joule s losses in each encapsulated windings, the themal paametes of Ho, S.L., Y. Li, X. Lin, H.C. Wong and K.W.E. Cheng, 006. A 3-D study of eddy cuent field and tempeatue ises in a compact bus duct system. IEEE T. Magn., 4(4: Ho, S.L., Y. Li, X. Lin, E. Lo, K.W.E. Cheng, et al., 007. Calculations of eddy cuent, fluid and themal fields in an ai insulated bus duct system. IEEE T. Magn., 43(4: IEEE Std., C IEEE Standad Requiements, Teminology and Test Code fo Dy-Type Ai-Coe Seies-Connected Reactos. Tansfomes Committee of the IEEE Powe Engineeing Society, DOI: / IEEESTD Liu, J., Adaptive Finite Element Method and Tempeatue Field Calculation fo Reacto. Xi an Jiaotong Univesity, Xi an, China. Liu, Z., Y. Geng, J. Wang and D.W.A. Chen, 003. Design and analysis of new type ai-coe eacto based on coupled fluid-themal field calculation. Diangong Jishu Xuebao T. China Electotech. Soc., 18(6: Wu, S., D. Wu and S. Yan, A study of design and calculation method fo dy-type eacto with ai coe. Tansfome, 34(3: 18-. Wu, A., D. Chen, J. Wang, B. Cai and Y. Geng, 00. Evaluation of themal pefomance fo ai-insulated busba tunking system by coupled magneto-fluidthemal fields. Poceeding of Intenational Confeence on Powe System Technology, 4: , DOI: /ICPST Zhang, Y., J. Ruan, T. Huang, X. Yang, H. Zhu, et al., 01a. Calculation of tempeatue ise in ai-cooled induction motos though 3-D coupled electomagnetic fluid-dynamical and themal finite-element analysis. IEEE T. Magn., 48(: Zhang, Y., X. Huang, T. Huang, J. Ruan and X. Wu, 01b. Ventilation stuctue impovement of aicooled induction moto using multiphysics simulations. Telkomnika, 10(3: