CFD Simulations and Reduced Order Modeling of a Refrigerator Compartment Including Radiation Effects 54 Abstract—Considering the engineering problem of natural convection in domestic refrigerator applications, this study aims to simulate the fluid flow and temperature distribution in a single commercial refrigerator compartment by using the experimentally determined temperature values as the specified constant wall temperature boundary conditions. The free convection in refrigerator applications is evaluated as a 3-D, turbulent, transient and coupled non-linear flow problem. Radiation heat transfer mode is also included in the analysis. According to the results, taking radiation effects into consideration does not change the temperature distribution inside the refrigerator significantly; however the heat rates are affected drastically. The flow inside the compartment is further analyzed with a reduced order modeling method called Proper Orthogonal Decomposition (POD) and the energy contents of several spatial and temporal modes that exist in the flow are examined. The results show that approximately 95 % of all the flow energy can be represented by only using one spatial mode. Keywords—refrigerator compartment, CFD, POD, radiation effects I. INTRODUCTION aintaining a preset low temperature by spending the least amount of electricity is the most important characteristic of a refrigerator for evaluating its performance. Optimizing its design for performance requires a well understanding of the natural convection inside it. Natural convection in enclosures has been extensively studied both experimentally and numerically. General reviews were focused on the importance of scaling analysis and experiments to determine the flow details. [1-3] The studies performed by Corcione [4], Markatos and Pericleous [5], Davis [6] and Hyun and Lee [7] are examples for 2D studies in the literature. Experimental benchmark studies of low-level turbulence natural convection in an air filled vertical cavity were conducted by Tian and Karayiannis [8], Ampofo and Karayiannis [9], Ampofo [10, 11] and Penot and N’Dame [12]. A work different from the studies mentioned so far was a preliminary attempt to study transient natural convection phenomena in a two-dimensional cavity heated symmetrically from both sides with a uniform heat flux [13]. There are also several other studies related to the 2D simulations of cavities in literature [14, 15, 16, 17, 18, 19]. Although 2D cavity model for a refrigerated space is good enough when the dimensional conditions are satisfied [12], the results may deviate from the experiments at the corners. On the other hand, 3D modeling gives more realistic and accurate results. One of the commonly used benchmark numerical solutions for natural convection in a cubical cavity was obtained by Wakashima and Sayitoh [20]. Transition to time- periodicity of a natural convection flow in a 3D differentially heated cavity was studied by Janssen et al. [21]. Fusegi et al. [22] also worked on 3D natural convection of air in cubical enclosures. There are also experimental studies in literature related to the subject. [23- 27]. Other 3D analyses focused on temperature and velocity distribution determination across the enclosures caused by the heat source are also available in literature [28, 29]. There are various studies related to natural convection in enclosures; however refrigerator applications are limited. For refrigerators, simulation includes steady-state simulation and dynamic simulation. For steady-state simulation, the thermal capacity of foam insulation is neglected. For dynamic simulation, not only the refrigeration system, but also the refrigerated space (cabinet) is considered to be dynamic, so the simulation is complicated. Dynamic simulation of natural convection bypass two-circuit cycle refrigerator for both the component and system basis is performed by Ding et al. [30, 31]. Similarly, Salat et al. [32] investigated the turbulent convection in a large air filled cavity by the help of direct numerical simulation (DNS) and Large Eddy Simulation (LES) methods. In a different study, the velocity and temperature distributions in commercial refrigerated open display cabinets are examined by applying finite element method. [33]. Laguerre and Flick [34] analyzed heat transfer by natural convection in domestic unventilated refrigerators. Based on [34], Laguerre et al. performed an experimental study of heat CFD Simulations and Reduced Order Modeling of a Refrigerator Compartment Including Radiation Effects O. Bayer 1 , R. Oskay 2 , A. Paksoy 3 , S. Aradag 4 1 Middle East Technical University, Ankara/Turkey, byrzgr@gmail.com 2 Middle East Technical University, Ankara/Turkey, roskay@metu.edu.tr 3 TOBB University of Economics and Technology, Ankara/Turkey, apaksoy@etu.edu.tr 4 TOBB University of Economics and Technology, Ankara/Turkey, saradag@etu.edu.tr M