Validation of Results of Analytical Calculation of Steady State Heat Transfer in Nuclear Fuel Element using ANSYS APDL

Transcription

1 International esearch Journal o Engineering and echnology (IJE) e-issn: Volume: 05 Issue: 0 Jan-08 p-issn: Validation o esults o Analytical Calculation o Steady State Heat ranser in Nuear Fuel Element using ANSYS APDL J. C. Odii, E. B Agyekum, B. K. Aornu 3, M. N. S. Ansah 4,,3,4 National esearch omsk Polytechnic University, ussia, omsk, Lenin Avenue, 30, *** Abstract - his research studied the analytical solution o the steady state analysis o heat conduction in a cylindrical Nuear uel element. he uel element used or this modelling was Uranium Oxide uel, the adding material was Zircaloy-. he model was a simple one, considering the act that we exuded the eect o the gas gap in between the uel pellet and the adding material, we also exuded the eect o axial heating, this made us to assume an ininite length uel element. Ater the analytical solution was obtained, a graph o temperature against the radial distance was plotted and compared the result with the one obtained using ANSYS APDL, the results were the same, hence our model was validated. he behavior o each o the contour along the radial direction depicts the our (4) boundary conditions and thereore validates the results o the Analytical solution. During the validation, it was observed that the boundary conditions taken, in reality actually aected the thermal lux and thermal gradient at the axial direction. From the Simulation results, there was an observation that the thermal gradient and thermal lux along the axial direction were airly constant, except or some dents at edges due to the little lashes o heat during heat transer along the radial direction. his is normal, as there is no perect heat transer medium. With this and other results obtained rom the Simulation, the research can say that the aim o validating Steady State Heat ranser o Nuear Fuel Element was accomplished. Key Words: Analytical, steady, ANSYS, APDL, heat, conduction, simulation, adding, nuear uel, element, calculations transer, temperature, heat lux, thermal gradient. uel element material, this is because o the important role played by heat transer coeicient in removing heat rom nuear reactors. Formulation o Analytical result Fourier s equation o heat conduction in cylindrical coordinate without the axial and azimuthal terms k Q c p () t Where is the density, is the heat capacity at constant pressure, is the thermal conductivity and is the volumetric heat density in theuel pellet. Equation () is the transient equation o the uel rod conduction. I the conduction equation is time independent, then we have heat equation that is in steady state with internal heating ( ), hence we the poisson equation o heat conduction or the pellet and laplace equation o heat or the adding material. d d d d k d d d d Q 0 0 () (3).INODUCION Heat removal rom nuear reactors involves the removal o heat rom the cylindrical uel elements, this occurs in the radial direction, through the principles o heat resistances by conduction. he thermal properties o uel materials plays an important role in heat removal in nuear reactors. Properties such as thermal conductivity, speciic heat capacity and density depends on temperature. Hence materials with very bad thermal coductivity will deinitely be a bad nuear Where are the heat conductivity and temperature o the uel pellet and temperature o the adding. By taking boundary conditions, we can solve the steady state case, analytically. d d 0 0 (4) 08, IJE Impact Factor value: 6.7 ISO 900:008 Certiied Journal Page 050

2 International esearch Journal o Engineering and echnology (IJE) e-issn: Volume: 05 Issue: 0 Jan-08 p-issn: Solving equation () (5) (6) (7) he boundary conditions (4), (5), (6) and (7), shows that (a) temperature is constant at the innermost part o the uel pellet, hence temperature gradient is zero, (b) at the layer between the pellet outer diameter and the adding inner diameter, the heat lux is constant or the linear heat density is constant, (c) at the outer boundary between the adding and the ant, the thermal lux depends on the temperature dierence o the adding and the ant, and the heat transer coeicient o the ant. (8) (9) Applying boundary condition o equation (4), we have: A 0 d k d k d d We thereore have: d Q A d k k d k d k h d d d Q d ( ) Applying boundary condition in (6) we have: Integrating (0), we have: Using the boundary condition (7) Q k A Q Q h ln k k k A3 Q ln h Q Q A3 ln h k Q Q ln h k d d Q k Q k A Q k ln A 3 Q A Q ln A Q Q Q Q 4 ln ln k h k Q k 4 4 (3) (4) (5) (6) (7) (8) (9) (0) () Solving (3) d d Q k (0) We can obtain the uel pellet temperature distribution thus: Q Q h Q k ln Q () d d d d 0 d A d () Applying boundary condition in (5) we have: Q k A k k () 08, IJE Impact Factor value: 6.7 ISO 900:008 Certiied Journal Page 05

3 International esearch Journal o Engineering and echnology (IJE) e-issn: Volume: 05 Issue: 0 Jan-08 p-issn: Fuel geometrical and thermal parameters used or this validation exercise are as ollows: system. hereore, the research can say that while PCMAHCAD helped we to solve the Analytical solution, ANSYS APDL assisted with the numerical simulation result. able : able o parameters Using PC-MAHCAD worksheet we plotted the analytical results 0.08m. Analytical esults A graph o the temperature as a unction o radius was plotted to observe how it changes within the uel rod both in the pellet and the adding, especially at the point where the pellet and the adding overlap. In this work, our uel rod is assumed to have ininite length, this is the essence o the boundary condition imposed to ease the analytical calculation. he resulting graph below showed a good behavior o the model, which will be validated using ANSYS APDL. he PC-MAHCAD toolbox was used to compute and plot the analytical solution it is user riendly computing environment with a lot o symbolic solution which provides an accurate analysis o result. As can be seen rom the graph below, the plotting is quite simple with simple labeling 08, IJE Impact Factor value: 6.7 Chart -: emperature versus radius at steady state or Analytical solution Numerical Simulation results or the steady state heat transer using ANSYS APDL are as ollows: ISO 900:008 Certiied Journal Page 05

4 International esearch Journal o Engineering and echnology (IJE) e-issn: Volume: 05 Issue: 0 Jan-08 p-issn: Chart -: adial emperature distribution contour Chart 5: adial thermal lux distribution graph Chart 3: adial emperature Distribution Graph Chart 6: adial hermal gradient distribution contour Chart 4: adial thermal lux distribution contour Chart 7: adial hermal gradient distribution graph 08, IJE Impact Factor value: 6.7 ISO 900:008 Certiied Journal Page 053

5 International esearch Journal o Engineering and echnology (IJE) e-issn: Volume: 05 Issue: 0 Jan-08 p-issn: Chart : Axial thermal gradient distribution graph Chart 8: Axial thermal lux distribution contour. Conusion: he contour distributions and the corresponding graphical representations obtained rom the Numerical simulation, corresponds to the boundary conditions taken in the analytical solution. he behavior o each o the contour along the radial direction depicts the our (4) boundary conditions and thereore validates the results o the Analytical solution. During the validation, it was observed that the boundary conditions taken in reality actually aected the thermal lux and thermal gradient at the axial direction. From the Simulation results, the research observed that the thermal gradient and thermal lux along the axial direction were airly constant, except or some dents at edges due to the little lashes o heat during heat transer along the radial direction. his is normal, as there is no perect heat transer medium. With this and other results obtained rom the Simulation, the research can conude that the aim o validating Steady State Heat ranser o Nuear Fuel Element was accomplished. Chart 9: Axial thermal lux distribution graph eerences. Kayla Kruper, steady state heat transer in ad nuear uel rod in COMSOL, ensselaer Polytechnic Institute, 04. ozhgar Othman, steady state and transient analysis o heat conduction in Nuear uel elements,masters Degree project, stockholmsweden, Phillipp Hangi, investigating BW stability with a new linear requency-domain method and detailed 3D Neutronics Chart 0: Axial thermal gradient distribution contour 08, IJE Impact Factor value: 6.7 ISO 900:008 Certiied Journal Page 054

6 International esearch Journal o Engineering and echnology (IJE) e-issn: Volume: 05 Issue: 0 Jan-08 p-issn: Lahey and F.J Moody, the thermal hydraulics o a Boiling water Nuear eactor 5. Neil odreas, Mujid Kazimi and Franci, Nuear system Elements o thermal-hydraulic design 6. D.D Lanning et al, FAPCON-3: Modiication to uel rods materials properties and perormance Modes or high-burnup application, James Duderstadt, Louis Hamilton, Nuear eactor analysis 8. Nikolay Ivanov Kolev, Nuear thermal hydraulics,, Springer international, Bahman Zohuri and Nima Fathi, thermalhydraulic analysis o nuear reactor,springer international, ANSYS Mechanical APDL Veriication manual, elease 5.0 November, 03. Chris Hartmann, Anji Seberino and oger Yeh, Programming with Mathcad Prime, PC, 0 08, IJE Impact Factor value: 6.7 ISO 900:008 Certiied Journal Page 055