In pool-type research reactors, the fuel core is placed in a large open pool of water, and it is consistently cooled by natural circulation. To meet the increasing demands of reactor-based research, i.e., neutron irradiation and isotope production, many institutes have been considering upgrading the designed power levels of their research reactors to maximize their utility. However, increasing operating power levels without replacing the major components of the reactor system is challenging because two important analyses must be extensively performed: (1) neutron transport analysis for nuclear fission and decay heat generation and (2) thermohydraulic analysis for heat removal in the core. In this paper, we investigate thermohydraulic limits on the maximum power of the Purdue University research reactor (PUR-1) using computational fluid dynamics (CFD) simulations which are coupled with the results from Monte Carlo neutron transport simulations. We design a PUR-1 fuel assembly, which is designated as the hottest one for CFD simulations, that includes a narrow, rectangular, and upward coolant channel. Here we demonstrate that the thermohydraulic limit for PUR-1 core power is 350 kW without changing the coolant system. Given a conservative safety margin, however, the estimated maximum power level is decreased to 170 kW. In the end, the results of two additional cooling systems—guide pipe and lowered coolant temperature—are presented to demonstrate the potential of advanced cooling capacity. They would enable reactors to operate at higher core power levels.