HT_1A: Position paper on material characterization and HAM model benchmarking[1]
Mark Bomberg[2]
Jan Carmeliet[3]
John Grunewald[4]
Andreas Holm[5]
Archiles Karagiozis[6]
Hartwig Kuenzel[7]
Staf Roels[8]
Abstract
Knowledge about the rate of moisture flow in materials is of importance for many practical considerations in construction. To this end, heat, air and moisture (HAM) transport models are increasingly applied to assist in understanding the hygric and thermal behavior of building materials and structures.
Since modeling of building performance is quite a young research subject and the material properties available are often based on classical methods, the applicability of current computer codes is still limited. Thus, there is a real need to introduce new methods for material characterization. This will enhance the future use of computer models dealing with issues such as shrinkage, swelling, hysteresis, bypass flow, dual porosity, mobile and immobile water, salt transport, and numerous related durability applications. To do this, however, we need to develop a solid foundation of material characterization.
Utility of a HAM model depends on three elements: (1) the description of constituent governing physical processes by the model, (2) the description of boundary conditions (climate) and (3) by the use of appropriate material properties (adequately representing both the material and all transport characteristics used in the governing equations). The last aspect of HAM modeling is discussed here. Authors recommend a minimum set of hygric characteristics that provide a unique characterization for each material.
1. Introduction
If an experiment is to evaluate material characteristics for input to HAM models, the material must be characterized to such an extent that another laboratory could select a sample for repeated experiments with an expectation that identical characteristics will be measured. In other words, the problem is how to define a minimum set of material characteristics[9] that will define the hygric performance of the material.
Another issue, addressed elsewhere (Bomberg and Grunewald, 2001) is the need for simultaneous development of both engineering and research HAM models. An engineering model e.g. WUFI/ORNL typically relates moisture flux to the gradient of moisture content and in doing so utilizes secondary moisture characteristics (moisture diffusivity). The research model, on the other hand, uses the gradient of moisture potentials and primary transport coefficients (moisture conductivity).
Use of moisture content as the driving force of liquid flux is not suitable for the research HAM model for the following reasons:
Ø Inability to separate potentials acting on moisture, specifically air entrapment, salinity, temperature (as it relates to liquid and vapour in completely different manner) and therefore there is an inability to address in a fully coupled manner damage phenomena such as freeze-thaw resistance, salt efflorescence, shrinkage, and crack development.
Ø Inability to describe moisture hysteresis (difference between wetting and drying loops), since its effect on moisture content cannot easily be identified in non-equilibrium processes like the transition from suction to redistribution of water
Ø Inability to describe the saturated water flux with moisture content used as the driving force. (Typically, varying degree of air entrapment may cause apparent differences in moisture content.)
Ø There is a difficulty in dealing with transport across material interfaces, since only a ‘real’ potential is continuous across the interface, while moisture content isn’t.
Thus, despite the fact that measuring moisture content is easier, the need to analyze different forces driving moisture (capillarity, osmotic pressures, freezing, envelope stress, air pressure, thermal gradients etc.) when evaluating physical and mechanical effects warrants the use of a research HAM model. Typically, a research HAM model serves as a reference tool and is not likely to become used for design.
Simplified HAM models, typically those based on gradients of vapour concentrations and moisture content as driving forces are more likely to become tools for designers and manufacturers of construction materials. For this to happen, however, one must realize that both correct equations and adequate consideration of material characteristics are necessary. Material characteristics must fulfil two requirements: describe well the moisture response of the material, and be congruent with the HAM model.
In previous discussion (Bomberg and Grunewald, 2001) recommended that a separation between unsaturated and saturated moisture fields be observed. If we accept such a division we do not need to measure the dispersion of air in the unsaturated moisture region. The validity of an engineering model can be expanded to include moisture contents above the capillary region, in one of two ways: (1) with a separate equation describing changes in the air concentration (dissolution and diffusion trough the liquid water) or (2) if changes in the air entrapment are negligible over the considered period of time, than an energy contribution of the entrapped air phase can be added to the capillary suction (capillary potential) of pore water. Unless one of these two modifications is used, the engineering model is limited to the capillary flow region.
Following this approach, the following conditions were postulated as necessary to satisfy mechanical similitude requirements (Bomberg et al (2001).
1. Moisture retention curves determined by different laboratories (i.e., moisture potential determined as a function of moisture content) must be identical.
2. Moisture diffusivity (total vapor and liquid), determined as a function of moisture potential or moisture content must also be identical.
Carmeliet and Roels (2002) analyzed methods of determining the moisture capacity (moisture storage) in porous building materials stating:
“The moisture capacity, which is required to solve the isothermal moisture transport equation, is generally expressed by parametric functions covering both the hygroscopic and over-hygroscopic regime. The modality or number of analytical functions needed to describe the corresponding pore volume distribution is introduced as an important parameter for a proper description of the moisture capacity or capillary pressure curve….” We found that the wetting capillary pressure curve, relevant for many building physics problems of hygroscopic capillary active materials, is preferentially described by bimodal functions or unimodal function with sufficient flexibility towards the hygroscopic zone. The use of fixed values of relative humidity for determining the limit between hygroscopic and over-hygroscopic regime cannot be recommended as useful a-priori information. This limiting moisture content is rather a fitting parameter and is found not to coincide with the knick point moisture content defining the transition from vapor to liquid permeability. The optimal location of the experimental data is highly dependent on the chosen functional model and on the considered material. The goodness of fit only slightly reduces when using a minimal number of optimal data points compared to an extended data set”.
This statement is important in two respects. It highlights that a few experimental points, if properly selected, may be used for material characterization. Obviously a larger number of points may improve the fit of experimentally determined moisture retention curves, but this is not our concern. Our concern is rather the opposite - how few points can one use if these points are selected in critical moisture content regions. In doing so, a compromise must be reached between practical and theoretical aspects of measurements. For instance, one may wish to select equilibrium at 99.4% RH as one of the critical points, yet measurements at this level are difficult. For the sake of the test reliability we select a point between 93 %RH and 95 %RH. Selecting the point in this region is less desirable from a theoretical point of view but is far more practical. Ultimately, a consensus by authors of this paper was reached, as to the minimum set of characteristics needed. One must stress, however, that this minimum set is not selected for defining material characteristics needed for the input to a HAM model, but as a requirement for a common characterization of porous building materials on which such measurements are performed.
2. A minimum set of hygrothermal characteristics
The following list is proposed for acceptance as the minimum requirements for the establishing a platform of material property data:
q Material structure and porosity
1. Density of the material
2. Total porosity of the material (or density of the solid phase)
q Thermal properties
1. Thermal conductivity of a dry material
2. Specific heat of the dry material
q Moisture retention curves
Although Carmeliet and Roels (2002) demonstrated that fixed points should not be recommended, yet, for practical purposes, we can prescribe three values on moisture retention curve as a basis for direct comparisons.
1. Equilibrium moisture content at 80 %RH (75% – 85%)
2. Equilibrium moisture content at >93 %RH (93% - 95%)
3. Capillary moisture content.
If one uses these three experimental points of material characterization for input to a HAM model, one may expect (see Carmeliet and Roels, 2002) reliable results only for a unimodal description of the moisture retention curve.
q Moisture transport characteristics
- Water vapor permeance at an average of 25% RH (dry cup test or equivalent)
- Either the water conductivity (permeability) at the capillary moisture content (see further discussion on measurement techniques) or
(a) 1-D free water absorption process carried on until capillary saturation is reached (this would serve to establish both the A-coefficient and capillary moisture content) and
(b) two 1-D drying tests started with a uniform moisture content that exceeds the capillary moisture content, conducted with either one or two sides open, i.e., either one-sided or two-sided drying experiment.
Note that all information items (a) and (b) are necessary to calculate moisture transport characteristics for the capillary saturated region. This point (see Grunewald in this symposium) should correspond to the characteristic radius in the over-hygroscopic range.
q Additional recommendation
To improve precision of the moisture retention curve we also recommend measuring one more equilibrium point (x-bar pressure) with help of pressure plates. Note that this point is not a requirement for material characterization but a recommendation.
3. methods used to determine this set of characteristics
The following review is brief because of space limitations and is focused on future research needs rather than explanation of traditional testing technology.
3.1. Material structure and porosity
To characterize a material the following properties should be determined:
1. Density (bulk density) and matrix density
2. total open porosity (or vacuum saturation moisture content)
The density r [kg/m3l is defined as the ratio of the oven dry (absolutely dry) mass of the sample to its volume, while the matrix density rmat [kg/m3] is defined as the ratio of the dry mass to the volume of the solid matrix, including closed pores. For wood based materials, instead of oven dry mass and volume determined at an equilibrium moisture content reached at 50% RH and 20 ºC.
The open porosity yo of a porous material sample is defined as the ratio of the open-pore volume to the total volume of the sample. Typical test to obtain vacuum saturation is performed on the oven-dried material. The sample is placed in an airtight container connected to a vacuum pump and air is evacuated in a stepwise manner. To avoid breaking cells one needs at least three hours to evacuate air from the container. Then, de-aired water is supplied to the container, at a low inflow rate. Once the sample is fully immersed, the water supply is cut and the specimen is kept under water for 24 hours. The absolute air pressure in the container shall not exceed 2000 Pa.
3.2. Moisture retention curves
Moisture retention curve (MRC) shows the equilibrium moisture content in relation to the capillary suction, pc, [Pa] at which this equilibrium was measured. Typically, two MRC denote extreme cases of wetting from the absolute dryness (constant mass in exposure to elevated temperature and less than 3% RH) and drying of the vacuum saturated sample. Each moisture retention curve contains two fields: hygroscopic and above-hygroscopic fields of moisture content. The hygroscopic field is described by the sorption isotherms i.e., relation between equilibrium moisture content and the relative humidity at which this moisture equilibrium was measured. The field of capillary moisture (above-hygroscopic) is more difficult to measure and is therefore omitted in this first step to obtaining a common agreement on material characterization.
It has been agreed that to define the wetting loop of the MRC one must determine the equilibrium moisture contents at 80 %RH (75% – 85%) and above 93 %RH (93% - 95%) and capillary moisture content, wcap, [kg/m3]
Capillary moisture content wcap, [kg/m3], is usually measured together with the water absorption coefficient, A, [kg/m2s1/2] during one-dimensional free water intake test. To ensure 1-D character of the water inflow process, the specimen must be sealed on all sides. This can be done using a cling film (note that the film may not touch the water plane) or by applying either a paraffin wax or an epoxy resin. The bottom of the specimen is placed in contact with the water 2 + 1 mm while the top side remains exposed. To minimize water losses from the top surface the whole set may either be placed in a chamber at 95 %RH or the top surface of the specimen can be protected with a flexible material to form an air cushion there. This air cushion will allow air pressure equalization, while reducing water evaporation from that surface.
The A-coefficient is defined as the slope of the first stage of the cumulative inflow curve into an oven dry specimen, in relation to the square root of time. The capillary moisture content is defined as the moisture content of the specimen at the transition from the first to the second stage. The first stage, governed by the capillary nature of the specimen, ends when the water front reaches the upper surface of the specimen. The second stage, typically involving a much lower rate of water ingress is governed by the process of air and water redistribution within the specimen, and involves air dissolution or diffusion through the specimen. These definitions are, however, imprecise. As the proposed method assumes that the moisture front reaches the opposite side of the sample, the height of the sample has to be chosen in such a way that it is only a fraction of the maximum capillary height. Conditions of air pressure on the free surface of the material will depend on the duration of the experiments (and the specimen length, see Descamps, 1997). Furthermore, long experimental times will also increase the thickness of boundary layer at the water ingress face (where the moisture content exceeds the capillary moisture content).
Currently there is an international collaborative research and one expects that HAMSTAD project will define a test protocol for measuring the A-coefficient and capillary moisture content.
3.3. Moisture transport characteristics
Two extreme points on moisture conductivity curve were selected for the purpose of material characterization, namely:
- Water vapor permeance at an average of 25% RH (dry cup test, or equivalent)
- Water conductivity (permeability) at capillary saturation.
The first material characteristic is described in many standards (e.g., pr EN ISO 12572, ASTM E96) and needs no further discussion. The second material characteristic is typically used in soil science and hydrology. To eliminate the effect of air entrapment, water permeability is should be measured with an overpressure exceeding the level of bubbling pressure (the latter denotes a minimum pressure necessary to push a small bubble of air through the water field under conditions of capillary saturation). While this measurement is simple, there is a significant difference between soils and porous building materials, namely the level of overpressure necessary to conduct such a test.
In principle, when using overpressure exceeding the bubbling pressure of the porous material one measures the saturated water conductivity i.e., the Darcy filtration coefficient. How different is the saturated water conductivity from the moisture conductivity at the capillary moisture content? Opinions are divided and the arguments are fundamentally different. Descamps (1997) compares free and bound imbibition and while using identical approach (e.g. Boltzmann transformation or flow gradient method) highlights differences in the moisture diffusivity. Yet, such differences must occur since the transformation from conductivity to diffusivity gives an infinite value at saturation (i.e. diffusivity is not well defined at saturation) and the calculations are not corrected for backpressure created by air entrapment. De Wiest (1969) and Bomberg (1974) referred to other research showing that differences are small when the steady state is established and the flow rate is corrected for apparent density of the air/water mixture. Thus, until more systematic research is done, the issue is unresolved.
Consequently, in the absence of a proven test methodology, an alternative approach may need to be examined. The capillary moisture transport could be calculated from the combination of the water absorption coefficient and 1-D drying tests started with a moisture content that equals or slightly exceeds the capillary moisture content. These two drying tests can be performed on identical specimens exposed to the same environment but with two different drying states, namely with drying from one face only or from both faces.
This approach is also controversial as it is based on the inverse problem. To be able to do such a calculation one must first agree on the relational form for the diffusivity (or permeability) expressed as a function of moisture content. This function will be used for the inverse method. Krus et al (1997), Holm and Krus (1998) used an exponential approximation of moisture diffusivity coefficient as a function of moisture content. For the wetting process, they proposed the following relation between diffusivity at the capillary moisture content Dwcap and the diffusivity at a moisture content in equilibrium with 80 %RH Dw80.
(2)
where: ucap is the capillary moisture content, u80 is the equilibrium moisture content at 80 % RH, Dw(ucap) is the liquid moisture diffusivity at capillary moisture content, Dw(u80) is the liquid moisture diffusivity at equilibrium moisture content at 80 RH and F is a factor allowing recalculation between liquid moisture diffusivity during wetting and that during drying at capillary moisture content. In turn, Krus and Schmidt (1997) related the A-coefficient to diffusivities Dw cap and Dw o at the capillary and hygroscopic moisture contents respectively
(3)
where: Dwo is the diffusivity at the hygroscopic moisture content and uo and K are the correction factors.
The above set of equations is reproduced here to highlight the need for measuring at least two independent moisture transfer processes. The two moisture transfer processes selected here are: the rate of water absorption (A-coefficient measured during free water intake process) and the rate of drying that starts at the capillary moisture content in relation to the moisture content of the specimen. These two sets of measurements, together with information on the moisture retention curve and assumed type of moisture conductivity (or diffusivity) as a function of moisture content will be used for the inverse method.
While one can use any other dependence of moisture conductivity / diffusivity and derive different set of equations to be used for an inverse problem, we presented one approach to explain why two independent measurements are needed for material characterization in absence of moisture conductivity at capillary moisture content.
4. Conclusions
To enhance the future use of HAM models for such issues such as shrinkage, swelling, bypass flow, dual porosity, mobile and immobile water, salt transport, and a variety of durability applications, we need to develop a foundation for material characterization.
This paper presented an introduction to define a minimum set of material characteristics needed for such a foundation. Even for such a limited number of characteristics, one finds that there are no commonly accepted test methods for determination of two critical moisture characteristics
· capillary moisture content,
· moisture conductivity (water permeability) at capillary saturation.
Research on these two test methods is urgently needed.
References
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