Direct numerical simulations (DNS) of turbulent flows have increasing importance because they not only provide fundamental understanding of turbulent flows but also complement and extend experimental results. DNS of high Reynolds numbers, however, require huge computing cost so high-performance computing has been strongly pursued. In this study, we examine the feasibility of cost-efficient DNS on Intel Xeon Phi many-core processors that are currently adopted by 10% of the 100 largest supercomputers in the world as listed in the Top500 site. For this purpose, we port and optimize our in-house turbulent flow solver named as DNS-TBL (direct numerical simulation-turbulent boundary layer) on Xeon Phi Knights Landing (KNL) many-core processors and conduct benchmark tests on KNL and conventional multicore processors. The key architectural features of KNL processors and strategies to exploit them for performance enhancement are discussed. The optimized code is validated by conducting numerical simulations of zero-pressure gradient turbulent boundary layers at high Reynolds numbers and by comparing simulated turbulent statistics to those reported in previous studies. With the details of optimization strategies and validation processes, this work can serve as a practical guideline for acceleration of large-scale and precise DNS with many-core computing.