## 1 Introduction  
With the improvement of living standards, many aquatic products, such as squids, tunas, sea bases, puffer fishes and turbots are increasingly demanded by the consumers due to the advantages of low-fat content and high-quality proteins [1, 2, 3, 4, 5]. In order to maintain the high quality of aquatic products during the long term, it is necessary to store fresh aquatic products in a suitably low-temperature environment, e.g., at 272.25, 268.15, 263.15 or 255.15 K [6, 7, 8]. The best solution is a cold chain defined by IIR and ASHRAE as the series of actions and equipment applied to maintain a product within a specified low-temperature range from harvest/production to consumption. Thus, uninterrupted temperature-controlled transport and storage systems for refrigerated products form part of the cold chain [9, 10]. Refrigerated warehouses are key facilities used along the cold chain to maintain the quality and safety of aquatic products during frozen storage [11].  
Optimization of stacking modes is one of the research focuses to improve the food quality in refrigerated warehouses. In recent years, computational fluid dynamic (CFD) is widely used in the field of the cold chain, due to the high resolution of flow distribution in time and space, accurate determination of temperature distribution and powerful visualization capabilities [12; 13; 14]. [PERSON] et al. [15] investigated the cooling rate of the citrus fruit in refrigerated containers and found that reducing the airflow bypass between pallets could increase the cooling rate of agricultural products. [PERSON] et al. [16] studied the temperature distribution in refrigerated trucks with aquatic products placed under the refrigeration unit. The heights of aquatic products under the refrigeration unit were 0, 0.533, 1.066 and 1.6 m. It was found out that the most uniform temperature distribution occurred when lacking any products under the refrigeration unit. [PERSON] et al. [17] put forward a baffle structure of refrigerated containers, which could reduce the cooling time at least 22.9%. Based on the numerical simulation, [PERSON] et al. [18] discovered that the \"gaps on both sides and middle\" stacking mode could achieve the most uniform temperature distribution. The freezing completion effect in aquatic products has been assessed by the decrease of the highest temperature of aquatic products for the residence time. Thus, [PERSON] et al. [19] simulated a refrigerated warehouse with stacked packages and found that larger air velocity and refrigerating units with lower locations could promote the freezing completion effect and the temperature uniformity in the warehouse. [PERSON] et al. [20] examined a refrigerated warehouse for vegetables and developed a heat transfer model by user-defined functions. [PERSON] et al. [21] simulated a refrigerated warehouse and found that the uniformity of flow distribution can be improved by increasing gaps between goods.  
Research of diverse stacking modes usually focuses on the freezing completion effect in food, the uniformity of flow and temperature distributions, etc. The pyramidal stacking mode (PSM) has been proposed [22], but not analyzed. Therefore, the present study investigated and reports numerical simulation results for four PSMs and their corresponding neat stacking modes (NSMs) possessing the same top views. The freezing completion effect in aquatic products, the temperature uniformity of products and of flow distribution, and the efficiency of air circulation in a refrigerated room, are analyzed. The objective is to assess the application of PSMs, and to identify the best performing stacking modes under the concerned experimental conditions.