Numerical simulation has been an intrinsic part of nuclear engineering research since its inception. In recent years a transition is occurring toward predictive, first-principle-based tools such as computational fluid dynamics. Even with the advent of petascale computing, however, such tools still have significant limitations. In the present work some of these issues, and in particular the presence of massive multiscale separation, are discussed, as well as some of the research conducted to mitigate them. Petascale simulations at high fidelity (large eddy simulation/direct numerical simulation) were conducted with the massively parallel spectral element code Nek5000 on a series of representative problems. These simulations shed light on the requirements of several types of simulation: (1) axial flow around fuel rods, with particular attention to wall effects; (2) natural convection in the primary vessel; and (3) flow in a rod bundle in the presence of spacing devices. The focus of the work presented here is on the lessons learned and the requirements to perform these simulations at exascale. Additional physical insight gained from these simulations is also emphasized.