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With the increasing thermal challenges of electronic equipment, topology optimization of heat sinks has aroused great research interest in recent years. However, most related researches deal with heat transfer problems of the laminar flow. Only several papers deal with heat transfer problems of the turbulent flow which exhibits better heat dissipation capacity. This paper intends to demonstrate the topology optimization of turbulent forced convective heat sinks with a computational-cheap multi-layer thermofluid model. Based on the assumption of a hydrodynamically fully developed turbulent flow, a single-layer flow model is derived from the 3D turbulent flow model. Viscous effects in the out-of-plane direction are modeled as the additional terms in the derived momentum and transportation equations. Similarly, based on the assumption of adaptive temperature profiles in the out-of-plane direction, heat fluxes between adjacent layers are modeled and a multi-layer heat transfer model is constructed. Further, the porosity field is introduced to describe the channel's topology and the corresponding topology optimization scheme is presented. Topology optimizations of a heat sink for coil-cooling are carried out to reduce the average temperature rise of the heat source under a maximum volume fraction constraint. The accuracy of the multi-layer model is evaluated via 3D thermofluid simulation of optimized and reference designs. Topology-optimized heat sinks exhibit better thermal performance and provide up to a 32.39% reduction of the average temperature rise, compared with the reference designs. Additionally, a comparative study is also provided between designs optimized in heat transfer problems under laminar and turbulent flows. [ABSTRACT FROM AUTHOR]