Large eddy simulation is performed in heat transfer of turbulent pipe flow with NEK5000 code based on spectral element method to study uncertainty quantification by Grid Convergence Index. The turbulent pipe flow with heat transfer is considered with Reynolds number Re = 19,000 and Prandtl number Pr = 0.71. Three meshes (fine, medium, and coarse) with the fixed interpolation polynomial order, eight and three orders (4th, 6th, and 8th) of interpolation polynomial with the fine mesh are examined. The effects of different grid and interpolation polynomial order are studied to highlight the effectiveness of high-order spectral element. Besides that, to quantify the uncertainty by grid and polynomial order in the numerical results, the Grid Convergence Index using two modified versions from original Roache’s GCI method are estimated based on simulation results. Two modified versions include the modification of Roache’s GCI method described in the ASME V&V 20-2009 guideline and the simplified least square method version GCI.

使用NEK5000代码基于谱元法对管道湍流传热进行大涡模拟，研究网格收敛指数的不确定性量化。考虑带有传热的湍流管流，雷诺数 Re = 19,000，普朗特数 Pr = 0.71。研究了具有固定插值多项式阶数的三个网格（细、中和粗），以及具有细网格的插值多项​​式的八阶和三阶（4th、6th 和 8th）。研究了不同网格和插值多项式阶数的影响，以突出高阶谱元的有效性。除此之外，为了通过数值结果中的网格和多项式阶数来量化不确定性，使用原始 Roache 的 GCI 方法的两个修改版本的网格收敛指数是根据模拟结果估计的。两个修改版本包括 ASME V&V 20-2009 指南中描述的 Roache GCI 方法的修改和简化的最小二乘法版本 GCI。