Liquid water is one of the

Formanski 71 1/07/09 8:57 Page 71 V olume 5 - Number 7 - May 2009 (71-75) Abstract Liquid water is one of the agents responsible for damage of building materials. Therefore determination of its content in porous materials is of primer importance. A new quantitative method, based on IR observation of variation in the surface temperature of a moist sample in the humid environment, is proposed. The mathematical model, on which the method is based, uses the fundamental assumption that the liquid phase appears in Determination of Moisture Content in a Porous Building Material Using Infra-red Based Method Piotr FURMANSKI 1, Tomasz S. WIÂNIEWSKI 2 Institute of Heat Engineering, Warsaw University of Technology, Warsaw, Poland 1) e-mail: pfurm@itc.pw.edu.pl, 2) e-mail: tswis@itc.pw.edu.pl thermodynamic equilibrium with the water vapour in pores of the material. Preliminary measurements on the moist material are carried out on a specially designed experimental stand using infrared camera. It seems that the transient part of the surface temperature response is the most suitable for determination of the water content in the porous material. Keywords: Moisture content, infra-red method. 1. Introduction Presence of moisture in a material usually leads to its degradation. It is also one of the main problems in preservation of ancient buildings and in deterioration of properties of thermal insulations. Most damages in buildings, particularly in old buildings, are a direct or indirect consequence of moisture [1,2,3,6]. The water content in a porous material is defined as the ratio of the mass of moisture inside the sample to the mass of the dry sample. As density of water vapour is almost three orders of magnitude smaller than density of the liquid phase the water content in the sample practically corresponds to its liquid water content. The standard measurement of the moisture content is accomplished by means of the gravimetric method which is a destructive method. Some attempts were already undertaken in the past to use IR thermography for non-destructive evaluation of moisture presence in materials. These attempts were of mainly qualititative nature with no sound mathematical basis. They use dependence of either thermal or radiative properties on the moisture content [1,4]. At low water contents the liquid water occurs in a pendular state and does not form a continuous phase. The limiting value when the liquid water starts to form the continuous phase is known as the critical water content Wcr. Above Wcr the liquid transfer happens in capillaries with the highest evaporation rate; while below it moisture transfer occurs only by vapour transfer, with a sharp decrease in the evaporation rate. Determination of the critical water content can be performed if the sudden increase in evaporation rate is observed [6]. The weathering conditions, such as the cycles of freezing-thawing, wetting-drying and salt crystallization, are more damaging for porous building materials in the presence of water above the critical moisture content. The main objective of this paper is to carry out preliminary experiments on variation in temperature of the moist, porous medium and propose a mathematical model of the energy and moisture transport phenomena in porous sample in a direct contact with the ambient humid air. The model is to be subsequently used to analyze IR assisted non-destructive experimental determination of moisture content in the building material and is aimed to in-situ measurements. 2. Experimental stand and results For the preliminary measurements a simple experimental stand was designed - Figure 1. The sample of common, red brick, with dimensions of the sample: 100 mmx100 mm x40 mm, was surrounded by thermal insulation made from polystyrene. Two thermocouples (chromium-aluminium type) were fixed to the sample. One was located underneath the sample and the other one at its surface exposed to the ambient air - see Figure 1. 71

Formanski 71 1/07/09 8:57 Page 72 The samples were dried for long time in an (a) air dryer to remove moisture and subsequently filled with the known amount of liquid water with the water content corresponding to 5, 10 and 15%, respectively. The samples were then wrapped in a foil and kept in the dryer for three days until its moisture distribution in the samples was uniform. Then each sample was placed in a box compartment filled with the thermal insulation and the upper surface of the sample also covered by a thermal insulation. (b) Figure 2. Variation of temperature in the centre of the sample surface versus time for the sample of moist brick with moisture content W = 15%: a) IR thermogram, b) thermocouple measurements Note: - environmental (air) temperature, - temperature at the bottom of the sample, - surface temperature of the sample. They show a trend that with the increase of water content the rate of the surface temperature drop decreases. It was also found that the maximum surface temperature drop T o T s,min increases with the water content. TABLE 1. Experimental results Water content W [%] 5 10 15 Figure 1. Scheme of the experimental stand and view of the moist sample. Subsequently, the cover was removed and the upper surface of the sample exposed to the ambient air. As temperature T and humidity φ of the ambient air, were different than in the sample heat and moisture transfer with the surrounding occurred. The exposed surface of the samples was observed with the infrared camera Thermocam SC2000 (Flir IR Systems, INC.) operating in the wavelength range from 6 to 12 µm and the radiation temperature of the sample surface recorded. The recorded temperatures of the sample surface are presented in Figure 2a. Variation of temperature versus time was also recorded by the thermocouples. They showed the similar change of the surface temperature as measured by the infrared camera. The ambient temperature do not change more than of 0.5 during the whole measurement time and contributed to the slight increase of the sample temperature in the longer period of time - see Figure 2b. After some cooling time, temperature of the sample surface approached the steady value corresponding to T s,min. This period approximately lasted about 10000 seconds and seemed to not appreciably vary with the water content. A small temperature difference between the sample surface and its interior was also observed - Figure 2b. The recorded temporal variations in the surface temperature were used to calculate the rate of temperature drop. The results are collected in Table 1. Characteristic time of temperature drop Maximum temperature drop 3. Mathematical model τ T o T s,min [s] [ C] In formulating the mathematical model it was assumed that a sample of the moist material is in contact with a humid ambient air at a different temperature. The sample is partially filled with liquid water and partially by water vapour mixed with the air. The vapour and the liquid phase are in thermodynamic equilibrium, i.e., they are in a saturated state. Inside the material conjugated processes of heat transfer by conduction and moisture transfer by diffusion occur [2]. They are accompanied by the condensation or evaporation processes of the moisture, which contribute to heat transfer. The heat and mass transfer in the sample is assumed to be one-dimensional with the lateral surfaces thermally insulated and impermeable for moisture flow. At the front surface, that is in contact with the ambient humid air at temperature T and humidity φ, liquid water evaporates and carries off some heat. The surface also exchanges energy with the surrounding by convection. Due to relatively low rate of vaporization either inside the sample or on its external surface no significant variation of water content across the sample is assumed. Using the above-cited assumptions the energy equation can be written as: 603 2 879 2,7 1375 3,2 (1) 72

Formanski 71 1/07/09 8:57 Page 73 with the corresponding balance of the water vapour: where ρ g stands for density of air and water vapour mixture in the pores and denotes the mass condensation rate. For the case of saturation the mass fraction of vapour in the gaseous phase is equal to its saturation value, i.e. y v = y v,sat, and becomes a unique function of temperature. Then eq.(2) may be multiplied by the latent heat of condensation and added to eq.(1). In this way the heat source in eq.(1) is eliminated: The new symbols introduced in eq.(3) are defined as: with a derivative of the mass fraction of water vapour y v versus temperature where R v - particular gas constant of the water. In a similar manner, for the case of saturation at the external surface facing the ambient air the boundary condition can be expressed as where ρ v is density of vapour at its partial pressure. Noting that where φ is the relative humidity and expanding of the saturation pressure at the surface p v,sat (T s ) in series of the vapour saturation pressure in the ambient air, i.e., p v,sat (T ), allows for eq.(5) to be cast in the form: where the new symbols are defined as: and At the depth of the porous material no heat transfer occurred: (2) (3) (4) (5) (6) (7) at x, while at the initial moment of time the uniform temperature distribution was assumed: T(x,t = 0) = T o (9) A set of equations, i.e., eq.(3), (6), (8) and (9) was analytically solved to give the following expression for temperature of the sample surface: T s (t) = T s,min + (T 0 T s,min )exp(η 2 ) erfc(η) (10) where, - characteristic time of temperature drop, (11) The surface temperature tends to the minimum value at the long times as observed in experiments - see. Figure 2. In eq.(12), the relative humidity at the surface φ s appears. This relative humidity generally depends on the water content in the material and surface temperature and is known as the sorption/desorption isotherm. The sorption isotherm represents the amount of vapour adsorbed at thermodynamic equilibrium conditions as a function of the relative humidity of the moist air. The sorption isotherm strongly depends on temperature, composition and microstructure of the porous material, specific volume area of the porous material and its bulk density. The water content in a porous material can be found from the sorption isotherm for the material φ s (T,W) when the experimentally determined minimum value of the surface temperature, the temperature and relative humidity of the ambient air, as well as the ratio are known eq. (12). A plot of the temporal variation in the surface temperature can also be used in determining W. It then suffices to find the characteristic time τ for and with the known evaluate the thermal effusivity of the porous material. Subsequently, from the known relation between e ef and W the water content can be calculated. 4. Dependence of thermo-physical properties and characteristic time on water content Thermal properties of the moist, porous medium depend, to a significant extent, on water content. Accounting for much greater density and specific heat of the liquid water than air as well as the relation between s g and the water content W, the modified volumetric specific heat of the moist porous material can be expressed as: (13) (8) (11) 73

Formanski 71 1/07/09 8:57 Page 74 (1) In the last, right hand side expression influence of the water content on the specific heat is explicitly separated with the following symbols introduced: The effective thermal conductivity of moist, porous material accounts not only for composition and thermal properties of the constituents of the sample but is also dependent on the internal structure of the medium. The simplest formula for the effective thermal conductivity of the porous material corresponds to constituents located parallel to heat flow. Noting that the thermal conductivity of air is circa twenty times smaller than that of liquid water the modified effective thermal conductivity, defined by eq.(4), can be cast in the following form: where,, (14) In the preliminary experiments a moist sample made of the common, red brick with certain water content was considered. The thermo-physical properties of the dry sample were assumed as follows: ρ d = 1800 kg/m 3, k ef,d = 0,84 W/(m. K), (ρc) ef,d = 1,582 MJ/m 3, ε = 0,3. The liquid water and water vapour properties were adopted as: ρl = 1000 kg/m 3, k l = 0,63 W/(m. K), (ρ c ) l = 4,2 MJ/m 3, D v = 2,49. 10 5 m 2 /s, k v = 0.027 W/m. K) while the air properties to be: k a = 0,0259 W/(m. K), (ρ c ) a = 1,206 MJ/m 3, respectively. The temperature, relative humidity and pressure of the ambient air followed from the experiment with T = 24 C, φ = 0.43 and p = 0.101325 Mpa. The convective heat transfer coefficient on the external surface of the sample was assumed to be h T = 13 W/(m 2. K) and related to the convective mass transfer coefficient by the formula h m = (D v /k v )h T. A simplified formula for the saturation pressure of water vapour as a function of temperature, as cited in [2], was used in the calculations. Due to small variation in temperature across the sample thermo physical properties of the moist material were assumed constant and evaluated at temperature T. Dependence of the characteristic time τ of temperature drop as defined in eq.(11) has been calculated using the presented formulae and shown in Figure 3. The respective experimental data were included in Table 1. Despite simplifying assumptions introduced in the theoretical analysis and small variation in the ambient air temperature during experiments comparison of the experimental data with theoretical results seems promising. Figure 3. Approximate relation between the characteristic time τ and water content W for the considered experimental sample. 74

Formanski 71 1/07/09 8:57 Page 75 Conclusions Presence of liquid water is one of the agents responsible for deterioration of materials such as building materials and thermal insulations. A study on determination of the liquid water content in porous materials was carried out in the paper. Preliminary measurements on the moist material, in the form of common red brick, were also performed on a specially designed experimental stand using infrared camera. A mathematical model of the heat and mass transfer processes in the moist sample was proposed in the paper. The model was used to propose two new methods for determination of the water content in the porous material. One is based on the experimentally found minimum temperature of the material surface while the other on the characteristic time of the drop in this surface temperature. Approximate evaluation of dependence of the characteristic time on the water content for the studied material was carried out and reasonable agreement with the experimental results was found. The adsorption isotherm for the studied material was not known and should be determined in order to verify another method in determining W. Further theoretical and experimental studies will be here valuable especially these, which will allow to carry out the sensitivity analysis of different parameters on a value the water content determined. References [1] Avdelis N.P., Moropoulou A., Theoulakis P.: Detection of water deposits and movement on porous materials by infrared imaging. Infrared Physics & Technology, Vol. 44 (2003), pp.183-190. [2] Furmanski P., Wisniewski T.S., Elzbieta Wyszynska: Detection of moisture in porous materials through infrared methods. Archives of Thermodynamics, Vol. 29 (2008), No.1, pp.19-40. [3] Gayo E., Frutos de J.: Interference filters as an enhancement tool for infrared thermography in humidity studies of building elements, Infrared Physics & Technology, Vol. 38 (1997), pp.251-258. [4] Hüttner R., Schollmeyer E.: The on-line detection of moisture and moist coatings by means of thermal waves, QIRT, Proceedings of Eurotherm Seminar, Vol. 37 (1996), pp.215-219. [5] Milazzo M., Ludwig N., Poldi G.: Moisture detection in walls through measurement of temperature, QIRT, Proceedings of Eurotherm Seminar, Vol. 39 (1998), pp.91-96. [6] Tavukcuoglu A., Grinzato E.: Determination of critical moisture content in porous materials by IR Thermography, QIRT Journal, Vol. 3 (2006), pp.231-245. Nomenclature D v e h T h m k L M v, M a p S g T W ε ρ (ρc) φ Subscripts: a diffusion coefficient of water vapour, m 2 /s thermal effusivity,, J/Km 2 s 1/2 convective heat transfer coefficient, W/(m 2. K) convective mass transfer coefficient, m/s thermal conductivity, W/(m.K) latent heat of condensation, L = 2500 kj/kg molar masses of water and air, M v = 18,015, M a = 28,967 kg/kmol total pressure, p v,sat - saturation pressure of water vapour, Pa volume fraction of gaseous (liquid) phase in pores, kg/m 3 temperature, K ( C) water content, kg of moisture /kg of dry material porosity of material density of porous material, kg/m 3 volumetric specific heat of porous material, J/(m 3. K) relative humidity air 75