## 1 Introduction  
The increase in meat consumption among the South Korean population has led to a rise in the number of livestock being raised. With Korea's arable land area being only 1547 thousand hectares, which accounts for just 15% of the total land area, it is challenging to manage the growing volume of livestock manure [1]. The production of livestock manure has been steadily increasing, from 49,868 thousand tons in 2014 to 50,260 thousands in 2017 and reaching 51,886 thousand tons in 2021. The proper management of livestock manure is crucial as its inappropriate disposal into water bodies can lead to severe environmental issues. Methods for treating livestock manure include composting, liquid fertilization, and purification processes, with approximately 75% of the manure generated in Korea being treated through composting [2, 3]. Composing is one of the methods that minimizes environmental impacts while biologically stabilizing organic matter, turning organic waste into a resource. The traditional composting method involves piling compost into cone-shaped heaps and periodically turning them. To enhance efficiency, an additional method involves injecting air through pipes installed at the bottom of the compost pile [4]. In Korea, continuous agitation composting facilities, which fill compost into a trench (U-shaped) structure and stir it daily with a mixer installed at the top, are widely distributed for the efficient processing of livestock manure in confined spaces [5]. However, this method occupies a large area, leading to increased construction costs, and has the disadvantage of making it difficult to capture odors [6]. The odorous substances generated during the composting process can lead to complaints from nearby areas, necessitating the installation of facilities for odor reduction [7]. Recently, enclosed vertical-type composting facilities, which offer higher space utilization and easier odor capture than continuous agitation composting facilities, have been recognized as a superior alternative for the treatment of livestock manure. Enclosed vertical-type composite facilities are cylindrically designed, with blades attached to an internal axis that continuously rotate, stirring the compost. This equipment introduces air through holes located at the bottom or on the rotating blades to supply air to the compost. This technology is widely utilized, and in Korea, approximately 163 farms were equipped with these facilities in 2022 at a total cost of about USD 18.56 million through local government subsidies [8; 9]. Despite active research on enclosed vertical-type composite facilities, there is a lack of study on the internal temperature changes caused by the heat generated during the composite process. This deficiency makes it difficult to effectively monitor the composite process in enclosed vertical-type composite facilities in the field [10; 11]. To address this issue, the development of a numerical analysis model and a computer program that can analyze the internal state is needed. By using a numerical analysis model, it is possible to identify changes in the thermal environment of the compost pile, which can help in devising appropriate operational strategies for enclosed vertical-type composite facilities [12]. Numerical analysis models can be utilized to calculate fluid dynamics and changes, thereby analyzing various environmental conditions within facilities. Such models can be effectively applied in research concerning air flow within livestock buildings, the diffusion of harmful gases, and the improvement of mixing efficiency in biogas facilities. This suggests that it can play a crucial role in enhancing livestock productivity through monitoring and analysis [13; 14; 15]. Few studies have been conducted on composting using computational fluid dynamics (CFD). However, composting process modeling is relatively rare as it presents challenges in incorporating biochemical reactions, internal aeration, and thermal diffusion.