###### Abstract
In this work, negatively buoyant wall jets with high inflow turbulence were studied in the Richardson number range of 0.13-0.58 and in the Reynolds number range of 4200-8000, and it was found that the dimensionless thermal energy loss decreases with decreasing Reynolds number. [PERSON] et al. [12] focused on studying the jet directions of complex air curtains and evaluated the smoke prevention effect of air curtains from two points of view: smoke and temperature insulation performance. [PERSON] et al. [4] developed a design guide that enables cabinet designers with limited fluid flow expertise to quickly identify the most efficient air curtain design to seal any given cavity from fundamental measurements without the need for intensive computation. [PERSON] et al. [7] and [PERSON] et al. [8], in their investigations, used air guiding strips and cold shelves to achieve the low infiltration of surrounding air and the correct temperature of the testing products with less energy consumption. The results show an energy saving of 16.7 kWh/24 h compared to the unmodified cabinet. The porosity of the back panel impacts the formation of the air curtain. [PERSON] et al. [10] focused on the analysis of the effect of porosity and the location of the perforations on the back panel on the temperature distribution of the products in the vertical open-type refrigerated display cabinet. In many studies, the porous jump model is used to simulate the back panel structure. The porous-jump model is a porous medium and is considered fractal. [PERSON] et al. [13], in their study, present the fractal theory and describe the influence of parameters on diffusion. The other work [14] presents the mathematical model for the transverse permeability of the gas diffusion layer considering the effects of the electrical double layer (EDL). Such mathematical models of fractals ensure the best accuracy and are often found in authors' works but with limited applicability in research objects such as refrigerated cabinets. Turbulent flows are commonly solved using four numerical methods: the finite volume method (FVM), the finite difference method (FDM), the finite element method (FEM), and the boundary element method (BEM) [15]. While in various studies of refrigerated cabinet airflows, the FEM and FVM have been employed for numerical computation, the BEM stands out for its computational efficiency, as it only requires discretizing the domain boundaries rather than the entire domain. Moreover, this method finds extensive application in other scenarios, including determining opening displacements in crack problems [16]. The FDM method, which was used in the [PERSON] and [PERSON] study [17], is no longer used as a standalone approach today. Instead, it is commonly combined with the difference transformation method (DTM) [18]. In summary, the majority of the works cited concentrate on improving the multi-deck display cabinet's performance, encompassing air curtain characteristics, food temperature stability, and the impact of various placement methods. However, only a few studies have explored the correlation between numerical study times, quality, and experimental research. In particular, a previous work [9] introduced a straightforward and rapid 2D numerical analysis of airflows and temperature changes in the OTRDC performed for different shelf configurations and honeycomb inclination angles in order to compare the proposed and unmodified OTRDCs with respect to the internal temperature distribution, air curtain formation time, and temperature variations of M packages placed in different places in the OTRDC [9]. This study builds on previous research and conducts a comparative analysis between numerical and experimental results obtained for OTRDCs equipped with single- and two-layer air curtains. The primary objectives are to improve the quality of the refrigerated cabinet development and to reduce the time required for experimental investigations in testing chambers.