**1. Introduction**

Ancient buildings are an important part of the world's historical and cultural heritage, which is an important carrier for inheriting national traditional culture and promoting cultural exchanges among nations and cannot be restored once they are damaged [1]. Nowadays, the protection of cultural relics and ancient buildings is gaining more and more attention. "Preserve the original appearance" is the basic principle for the protection of ancient buildings, so higher requirements for the technology of protection and restoration of ancient buildings have been proposed. With the advancement of technology, the conservation and repair of ancient buildings have gradually incorporated modern simulation and digital means from a purely manual approach [2,3] to seek the root mechanism of problem solving.

To better preserve its original appearance and historical value, revitalize the social value of ancient buildings, and enhance the comfort of visitors, many researchers have been conducting various explorations in recent years [4–7], such as ancient building wall repair work and ancient architecture of digital protection, etc. The typical problems of ancient building damage are the degradation of the anti-corrosion paint surface and the moldy wood structure. It was found that the deterioration and mold problems of ancient buildings are influenced by the coupling of multiple factors, such as the thermal and humid environment around the building, air flow, underground soil moisture, and the

**Citation:** Liu, F.; Zhang, X.; Zeng, J.; Li, Y.; Wang, G. The Numerical Study on Indoor Heat and Moisture Transfer Characteristics of an Ancient Palace Building in Beijing. *Processes* **2023**, *11*, 1900. https://doi.org/ 10.3390/pr11071900

Academic Editors: Feng Du, Aitao Zhou, Bo Li and Udo Fritsching

Received: 10 May 2023 Revised: 8 June 2023 Accepted: 20 June 2023 Published: 24 June 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

building envelope, etc. [8–10]. Exploring the patterns of influence of different factors on the deterioration of ancient buildings is an important prerequisite for taking effective conservation measures. At present, numerical simulation methods investigating the effects of airflow, the envelope structure, soil, precipitation, and other factors on the heat and moisture migration of ancient buildings are a low-cost and highly efficient way to grasp the influence law. And the degree of ancient building damage can put forward effective protection schemes for the problems such as dampness. Therefore, it is especially important to carry out more in-depth research and analysis based on numerical simulation methods for ancient buildings and propose reasonable conservation plans.

Currently, some scholars have conducted single-factor or multi-factor coupled analyses in numerical simulation studies. For ordinary residential buildings, Hong et al. [11] used the software CFD to study the indoor wet environment and linearly fitted the factors affecting humidity and concluded that the predicted humidity distribution was in good agreement with the experiment. Teodosiu et al. [12] investigated numerical models for assessing thermal comfort and developed CFD numerical models for airflow modeling and humidity modeling of indoor air, then analyzed and demonstrated the good potential for correctly estimating the indoor environment under stable and uniform thermal conditions. In addition to the relevant research on heat and humidity transfer in residential buildings, existing literature has also investigated building types such as libraries, temples, churches, grottoes, museums, etc. Liu [13] focused on and studied the insulation technology of ancient buildings in the Amu River basin, using AIRPAK software to simulate and analyze the indoor temperature of ancient buildings and explore the effect of active heating measures. Bi et al. [14] conducted an experimental and numerical analysis of the moisture and heat transfer in the cave walls of the Mogao Caves using a comparison of simulation results with experimental temperature and relative humidity values, finding that temperature changes may lead to condensation of moisture in the air, and the application of the one-dimensional model to simulate the cave wall has limitations. Balocco et al. [15] adopted CFD software to carry out a three-dimensional transient simulation of the natural ventilation system of a historical building library in Italy and explored the operation mode of the natural ventilation system inside the building, which confirmed that the ancient building could create a good natural ventilation environment. Li et al. [16] analyzed the hygrothermal environment of the Luohan Hall of Baosheng Temple located in the southeast of China and concluded that the air temperature near the sculpture had different fluctuation modes in different directions, and the relative air humidity fluctuated violently. Cao et al. [17] used the CFD software Fluent to numerically simulate the air movement, temperature, and relative humidity of the micro-environment in the museum and concluded that the large gradient of temperature and humidity distribution was not conducive to the preservation of artifacts. In addition, some scholars have studied numerical simulations for the cultural heritage of wooden structures. Huijbregts et al. [18] conducted a two-dimensional multiarea building simulation on a wooden cabinet in a Dutch castle to study the influence of indoor climate changes on the heat and humidity of the cabinet and concluded that indoor climate conditions were controlled by humidity rather than restricted by the average water content of the room. Napp et al. [19] studied the different indoor climate control schemes of a church in Estonia via field measurement and simulation and concluded that dehumidification measures could be used to prevent mold growth and protect wood parts from cracking.

Summarizing previous research results, it is known that the wet and cold interior of buildings only takes into account the influence of outdoor climatic conditions without exploring the influence of soil moisture and wall moisture on the situation of large indoor humidity. In this paper, soil moisture and wall moisture added to the influence of indoor humidity in ancient buildings.

The object of this study is the world's most complete surviving palace-type ancient building with a construction history of 600 years. The three-dimensional heat and moisture transfer characteristics of palace-style wooden ancient buildings in Beijing are studied. A mathematical model of indoor heat and moisture transfer is established, and the accuracy of the model is verified via comparison with simulated data using actual measurements of indoor relative humidity. The influences of outdoor humidity environment, soil moisture, and wall humidity on the indoor heat and moisture transfer characteristics of ancient buildings are analyzed. And the correlation analysis of these three factors and the main protection measures of ancient buildings are proposed. The research results provide effective theoretical guidance for the conservation of palace-style wooden ancient buildings in Beijing.
