Study On Coupled Heat And Mass Transfer Process And Characteristics Of Earthen Plasters In Mogao Grottoes

Murals and sculptures in Mogao Grottoes have been affected by human activities and environmental changes for a long time.Salt damage is the most typical and ubiquitous deterioration,with symptoms such as efflorescence,crater eruption,hollowing,shedding,and flaking,which have greatly damaged the murals at this site.Salt damage is the most destructive and most difficult disease to control,which poses a great threat to the protection of murals.The transfer of moisture content is one of the main factors causing the occurrence and development of salt damage,the moisture transfer and heat transfer are coupled,and the coupling effect of heat and humidity drives the transfer and enrichment of salt.Many studies of the Mogao Grottoes have focused on the air temperature and humidity inside and outside the cave,but few studies have characterized heat and moisture transfer in the cave walls.The study on heat and mass transfer（HAMT）properties and mechanism of cave walls can provide a theoretical basis and method support for a scientific explanation of mural disease mechanism and preventive protection of mural.This research could be extended to studies of cave site protection along the Silk Road.This paper aims to reveal the coupling mechanism of HAMT and provide the methods in earthen plasters and conglomerates under cave environments.Firstly,this paper proposed a mathematical model of HAMT in the earthen plasters and conglomerates under environmental conditions.Secondly,the microstructure,mineralogical properties,and hygrothermal properties of earthen plasters were studied,and the influence of different reinforced fibers on hygrothermal properties was revealed.Thirdly,the heat and mass model was simulated,and compared with the measured data to verify the property of the model.Then the hygrothermal characteristics in the cave walls were cleared and the damage mechanism under the action of heat and moisture of the two main salts was revealed.Finally,based on sensitivity analysis,the influences of different boundary conditions and material parameters disturbed on the results of the model were identified,thus the influences of model-related factors on thermal and moisture distribution were revealed.The main research contents include the following aspects:（1）To clarify the mechanism of coupled HAMT in cave walls,a 1-D theoretical model of coupled HAMT was established with temperature gradient and steam pressure gradient as the driving potential on the condition of simplifying and assuming the physical process based on the theory of HAMT in porous media.In this model,the capillary pressure to transform the water vapor and liquid water transfer into a unified expression by partial vapor pressure.Based on the classical evaporation-condensation theory,the formula for calculating the wet flow rate and the heat caused by the water phase transition is given.Furthermore,the equations describing the thermal and moisture balance of air in the cave are proposed.Considering the moisture absorption and desorption of the earthen plasters,the calculation method of surface evaporation rate of the paintings is studied,and the calculation formula of moisture absorption and desorption amount is given.（2）To solve the problem of missing parameters of the thermal-moisture coupling model,the hygrothermal properties of two kinds of earthen plasters reinforced by different fibers were tested.The results show that their thermal properties have little difference,but they have significantly different moisture properties.The plaster containing cotton fiber has weak heat transfer performance,strong heat storage performance,and weak water vapor transfer and storage capacity.This ability of sample B can reduce the transfer rate of moisture in the material and slow down the rate of salt transfer to the mural surface with water.（3）MATLAB software programming was used to solve the HAMT model,and the numerical results were compared with the measured data of the west wall in Cave 108.Considering the simplified hypothesis of the model,the two have a good agreement.The results show that the HAMT process in the cave walls is periodically and unsteadily.The temperature change and relative humidity change at each point show a sinusoidal curve,and with the increase of depth,the transmitted wave presents the phenomenon of amplitude attenuation and phase delay,and the heat and moisture flux at each point also change with time.According to the HAMT performance and distribution in the cave wall,it can be divided into ZoneⅠ,ZoneⅡ,ZoneⅢ,ZoneⅣ,and ZoneⅤ.（4）Combined with the previous transfer characteristics and the phase transformation of salt,the damage mechanism of salt（Na Cl and Na₂SO₄）phase change under the action of HAMT was revealed.The results show that the damage mechanism of Na Cl is mainly related to two mechanisms,one is deliquescence,the other is solubility.Deliquescence of Na Cl occurs in the region where RHi of relative humidity is higher than the critical humidity.The damage caused by Na Cl deliquescence in the terrestrial layer is mainly due to the sensitivity of solubility to temperature.The damage of Na₂SO₄ is mainly due to the solution formed by water dissolving salt,which migrates under the action of HAMT.After a long time of accumulation of HAMT,it finally caused structural damage to the earthen plasters.The coupling effect of HAMT played a driving role in the occurrence and development of salt damage.（5）To clarify the influence of different boundary conditions and material parameters disturbed on the results of the HAMT model,the Single-factor Sensitivity Analysis was conducted.The importance of the influence of input parameters into the model on the output results was identified and quantified.The results show that the change of air temperature and relative humidity is the most sensitive factor affecting the hygrothermal distribution in the cave walls,followed by the moisture properties,the thermal properties are less sensitive.When the change of ambient temperature and humidity of air is change,the thermal and moisture distribution shows a great difference.Finally,the temperature and humidity control threshold of the cave is discussed:When the relative humidity of the air in the cave is less than 62%and the air temperature varies from 4℃to 12℃,the phase states of Na₂SO₄ and Na Cl are stable.