Turbulent mixing through gaps is an important intersubchannel phenomena in fuel rod bundle in reactor core, which leads to momentum and energy transfer with no net mass transfer between adjacent subchannels in the fuel assembly. In the present applications, turbulent mixing coefficient is usually referred to describe turbulent effect, which commonly set to a constant or utilize Reynolds number dependent fitting correlation based on experimental data. However, high-quality turbulent fluctuating measurement in liquid metal reactor could be a challenge while CFD approach tend to perform well in predicting turbulent flow phenomena in this situation due to providing much more detailed data. In this paper, a high-scalable high-performance spectral element method CFD code NEK5000 combining high passed filtered LES model has been employed to simulate turbulent flow through parallel wall channel and square channel with a cylindrical rod for single-phase flow. In the parallel wall channel, mesh sensitivity analysis and model validation have been accomplished by comparing the simulation data with DNS references utilizing key parameters such as velocity profile and stresses in the near wall region. Meanwhile, for the square channel with a cylindrical rod, instantaneous lateral velocity monitored in the gap center has been compared with each other in different Reynolds number (Re=10300 and Re=20500) and geometric condition cases as well as with the experimental data for calculation validation. From the simulation approach, both of the absolute oscillation amplitude and the oscillation frequency increases with the increase of Reynolds number while the augment of pitch diameter ratio relaxes the oscillation intension. Finally, the simulation results of turbulent mixing coefficient dependent on Reynolds number have been validated with both experimental and theoretic references to show the effectiveness of Nek5000 LES methodology. The root mean square (RMS) value of lateral fluctuating velocity has been adopted to reflect the effective mixing capability, predicting the turbulent mixing phenomena with a reasonable degree of accuracy from the specific calculation strategy..