Geometries with periodicity are common in industry applications, such as nuclear reactor cores, heat exchangers, energy storage systems, cooling (or boiling) towers, battery packs, etc. High-resolution Computational Fluid Dynamics (CFD) are currently regarded as a standard tool for numeric analysis of their flow behaviour and heat transfer. The design and optimization generally require numerous parametric simulations, which are time-consuming or even prohibitively expensive. Model Order Reduction (MOR) techniques are proposed as an efficient alternative to CFD modelling. However, implementing MOR for large-scale models still relies on a substantial number of high-dimensional CFD solutions. In this study, Domain Decomposition (DD) is integrated into the frame of MOR for offline and online stages. A global domain is divided into several types of generic subregions. FOM simulations are carried out at the subdomain level, and snapshots are collected for each kind of archetype division. This significantly diminishes the expense of offline training. Reduced Bases (RB) in subdomains are calculated by Proper Orthogonal Decomposition (POD). An intrusive approach based on POD-Galerkin is adopted to construct Reduced Order Models (ROMs) for subdomains with parameterized boundary conditions. The global flow fields are approximated by combining the local ROMs utilizing the Iterative Dirichlet-Neumann method. In addition, non-intrusive local ROMs are built employing the POD Interpolation (PODI) algorithm. The variations in an entire model are assembled using a Boundary Response Map procedure. The methods are adopted to study cross-flow around an array of tubes. The accuracy and acceleration capability of the DD-ROM are analysed and discussed. The research intends to evaluate the feasibility of employing MOR approaches for numerical analysis of large-scale engineering instances.