[en] Highlights: • The large scale internal heated water pool natural convection simulation is validated by using ANSYS FLUENT 18.2. • The numerical study of geometric size effect on the internal heated water pool natural convection behavior is conducted. • The Nu-Ra' correlations for the internal heated water pool are proposed based on the current simulation results. -- Abstract: The internal heated melt pool natural convection behavior is one of the important phenomena in the nuclear reactor severe accident investigation aspect. Based on the previous research, the Nusselt number is the function of the internal Rayleigh number, and the geometric size could affect the internal Rayleigh number in the order of 5. According to the previous experimental and simulation results, the relationship of Nusselt number and internal Rayleigh number varies with different tests and conditions, and the local heat transfer coefficient is also varied with the vessel polar angle. Therefore, it is important to investigate how geometric size could affect the internal heated melt pool natural convection behavior. In the present work, the validation of numerical simulation method is conducted through comparison with the COPRA water test experimental data. Then the geometric size effect on the internal heated water pool natural convection behavior is investigated by using ANSYS FLUENT 18.2 and the wall modeled large eddy simulation (WMLES) turbulence model is applied in the current simulation. The water pool temperature distribution, water pool velocity distribution, and local heat flux along the curved wall are obtained in this study. The mechanism of geometric size effect on the internal heated water pool natural convection behavior is investigated. Besides, both the upward and downward Nusselt number with internal Rayleigh number correlations are proposed based on the current simulation results. Based on the current simulation, the cases with 0.1 m, 0.3 m and 0.5 m water pool radius show the similar natural circulation behavior in the temperature distribution and heat flux distribution aspects, and the cases with 1.0 m, 1.5 m, 2.0 m and 2.5 m water pool radius show another type of natural circulation behavior. However, the cases with 0.1 m, 0.3 m, 0.5 m and 1.0 m water pool radius show the similar Nusselt number with internal Rayleigh number correlations, and the cases with 1.5 m, 2.0 m and 2.5 m water pool radius show another type of Nusselt number with internal Rayleigh number correlations. The present study could provide useful references for the severe accident management, and further improve the understanding of how geometric size could affect the internal heated water pool natural convection behavior.