Interstitial condensation risk assessment

1. Introduction

Damage caused by moisture is a significant factor contributing to the degradation and diminished thermal performance of building components. Consequently, the development of tools to forecast and manage moisture accumulation in building envelopes has been a crucial aspect of building science [1-5]. Currently, a spectrum of hygrothermal engineering tools exists, ranging from basic 1D steady-state heat and vapor transport models, such as the widely recognized as dew-point or GLASER method, to fully coupled 2D and even 3D transient Heat Air and Moisture (HAM) models [6-7], from which WUFI [2] and DELPHIN [4] are commercially available. However, there is a trade-off between ease of use and accuracy. In cases where hygric inertia, air transport, or 2D/3D effects are significant, predictions based on the standard 1D Glaser method (as outlined in EN ISO 13788 [8]) may deviate from reality. To achieve more realistic outcomes, the adoption of advanced hygrothermal models that consider these effects becomes imperative [2,4]. While advanced hygrothermal simulations yield highly detailed results when properly employed, they are often perceived as overly complex for everyday engineering tasks during the early design stage.

Addressing this gap, the present article introduces a practical 3D heat and vapor model designed to assess the risk of interstitial condensation in building enclosures. Essentially, this model represents a three-dimensional adaptation of the Glaser method and extends the capabilities of the existing 3D steady-state thermal modeling tool TRISCO from Physibel [9]. The modeling methodology is succinctly outlined and validated against a two-dimensional problem with constant boundary conditions proposed by Simões et al. in 2002 [10] and a one-dimensional (monthly) validation from EN ISO 13788.

The second part of the article delves into the applicability of the proposed methodology. This section serves as a guide to understanding the conditions under which the model can be safely utilized and when a more detailed analysis is preferable. The article concludes with a practical case study demonstrating the model's applicability by informing design decisions for the energy-efficient retrofit of a curtain wall system.

2. Modelling approach

2.1. Governing Equations

The combined steady-state heat and vapour transport is modelled with following (simplified) conservation equations for energy (1) and moisture mass (2) :
div (λ.grad θ)=Ф (1)
div (δ.grad p_v )=G_c (2)

Herein, λ is the thermal conductivity (W/(mK)), θ temperature (K), Ф an energy source/sink term (W/m³), δ the vapour permeability (kg/(m.s.Pa)), p_v vapour pressure (Pa) and G_c a condensation/evaporation term (kg/m³). Often the vapour permeability 𝛿 of a material is expressed as the vapour permeability of air divided by the materials vapour resistance factor (𝛿_a/µ). In what follows 𝛿_a is taken equal to 2.10^-10 kg/(m.s.Pa).

Equation (1) and (2) are coupled through the vapour pressure which is limited by the temperature dependent saturation vapour pressure (p_v,sat) expressed by:

p_v,sat=610,5 exp((17,269.θ)/(237,3.θ)) for θ≥0°C p_v,sat=610,5 exp((21,875.θ)/(265,5+θ)) for θ<0°C (3)

2.2. Numerical solution method

The Finite Difference Method (FDM) is used to solve the above set of partial differential equations (PDE). The computational domain is subdivided in a number of finite volumes (orthogonal mesh) resulting in discrete balance equations for all elements. The equations express an energy and moisture balance for the control volume around each system node. All heat/vapour flows in the energy/moisture balance are expressed as linear functions of neighboring node temperatures/vapour pressures. Both the discrete temperature and vapour pressure field are solved by an iterative solver (see TRISCO manual [9] for parameters). If no condensation occurs, equation (1) and equation (2) are uncoupled allowing to readily solve both equations separately. However, when condensation occurs a coupling strategy emerges. The followed strategy is outlined in figure 1 below. For the description we introduce the terms 'wetted zones' and ‘potential wetted zones’. The ‘wetted zones’ correspond to zones where the P_v nodes are fixed to their P_v,sat. At the start of a calculation this can only be at nodes where an initial moisture excess is introduced. In the wetted zones all P_v nodes are fixed to P_v,sat during the calculation of the moisture balance. The ‘potential wetted zones’ on the other hand are the nodes outside ‘the wetted zone’ for which after solving the moisture balance the calculated vapour pressure P_v exceeds the saturation vapour pressure P_v,sat. An iteration starts when the ‘potential wetted zone’ is not empty after solving the moisture balance. Hereby the wetted zone grows by transferring in each iteration step a percentage of nodes from the ‘potential wetted zone’ to the ‘wetted zone’ (the nodes with the highest difference between P_v and P_v,sat are selected). This percentage is a user-defined calculation parameter. Further, the user has the option to limit the ‘wetted zones’ to material interfaces (cfr. EN ISO 13788). Suggestions for the choice of the calculation parameters will be discussed in the validation exercise (paragraph 3.1). The iteration process is finished when the ‘potential wetted zone’ is empty which then corresponds to the solution. When the calculation covers several consecutive months, the calculated (accumulated) condensation will serve as a moisture excess for the following month. When drying occurs, a time step can be split to the shortest drying time of any wet node. After the time that the wet node(s) is (are) dry, the corresponding vapour pressures become an unknown and the system is solved again.

3. Model validation

The newly developed 3D heat and vapour transport model has been validated against two sets of validation examples: 1) 2D steady-state and 2) 1D transient (monthly). The first validation case, proposed by Simões et al. 2002 [10], considers the calculation of interstitial condensation within a two-dimensional homogeneous layer under steady-state conditions. This validation case will be used to further explain the modelling approach and to illustrate the impact of the user-defined calculation parameters in the iterative calculation process.
The second validation case is exercise D from EN ISO 13788:2012 which corresponds to the drying out of a 1D wetted flat roof over an 8-year period (with monthly time steps). The complete set of validation cases from EN ISO 13788:2012 can be downloaded from the Physibel Knowledge Base (www.physibel.be/en/knowledge).

3.1. 2D-validation homogeneous layer with interstitial condensation within layer

Simões et al. 2002 [10] proposes 2 validation cases on the problem of two-dimensional interstitial condensation. The first case corresponds to a rectangular homogenous layer. The second case considers a T-shaped homogenous layer. Unfortunately, Simões et al. 2002 [10] limits the discussion of the latter validation case to a qualitative approach making it difficult to use. Therefore only the first validation case will be used here.

The validation case corresponds to a two-dimensional rectangular wall (0.3 m by 0.6 m), made of cellular autoclaved concrete, exposed to steady-state heat and vapour diffusion at the long sides. The thermal conductivity λ of the homogenous wall is 0.16 W(m.K) and the vapour resistance factor µ is set to 8 (-). The following boundary conditions are exposed along the long sides:

• Indoor: T_i = 18°C and RH_i = 90%, with surface heat transfer coefficient h_i of 8.33 W/(m².K) (the environmental vapour pressure is imposed to the surface nodes)
• Outdoor: T_e = 0°C and RH_e = 85%, with surface heat transfer coefficient h_e = 25 W/(m².K) (the environmental vapour pressure is imposed to the surface nodes)

The validation case is modelled in TRISCO with a two-dimensional with the same rectangular mesh (2 cm x 1 cm) as used by Simões et al. 2002 [10]. But actually, the proposed validation case concerns a one-dimensional problem allowing to analytically determine the condensation rate/zone based on the Glaser method (e.g. according to EN ISO 13788). The left graph in Figure 2 illustrates the initial calculated vapour pressure and saturation vapour pressure. This shows that from 0.07 m to 0.26 m the vapour pressure is higher than the saturation vapour pressure which is physically impossible. The means that after solving the moisture balance this zone of 0.19 m will be a ‘potential wetted zone’. The difference between the initially calculated vapour pressure and saturation vapour pressure is illustrated on the right graph in figure 2 (black curve).
The percentage of nodes that can be transferred during each iteration step from the ‘potential wetted zone’ to the ‘wetted zone’ is considered as a parameter: a)100%, b) 50%, 10%, 5% and 1%. For the current example, the wetted zone is not restricted to material interfaces but can occur in all calculation nodes within a material layers.
The resulting difference between vapour pressure and saturation vapour pressure is shown on the right graph in Figure 2.
When 100% of the nodes within the ‘potential wetted zone’ are transferred to the ‘wetted zone’ the iteration basically reduces to one step. As a consequence, within the ‘wetted zone’ the vapour pressure field follows the saturation vapour pressure profile. This is a convex function for the vapour pressure (left graph in Figure 2) resulting in condensation in the nodes in this area. However, at the border of the potential condensation zone the profile has a concave discontinuity which corresponds mathematically to local evaporation. This is illustrated in Figure 3 below where the wetted zone in blue (19 cm) is containing nodes with evaporation at the borders (red).
In the second simulation 50% of nodes of the ‘potential wetted zone’ are transferred to the ‘wetted zone’ during each iteration step (green curve in Figure 2). This results in a smooth transition and a ‘wetted zone’ of 9 cm. The simulations are also repeated for a transferring percentage of 10%, 5% and 1%. The results are not show on the graph as they fall on the results transferring 50% of the nodes in the iteration process.

Table 1 compares the simulation results with results of Simões et al. 2002 [10]. This table indicates that potentially transferring 100% of the nodes results in an incorrect solution (existence of evaporation). When lowering the parameter to 50% a better result is found. Though, the existence of evaporation nodes indicates that the result is still incorrect and a lower percentage is required. When transferring 10% of the nodes no evaporation is found and the size of the wetted zone is equal to the size mentioned by Simões et al. 2002. Using a transferring percentage of 10% of course increases the number of iteration and thus the simulation time. Table 1 shows that further lowering the transferring percentage will further increase the simulation time (without changing the result). It can be concluded that for this simulation the optimal parameter for the transferring percentage is around 10%. As a general guideline it can be stated that the transferring percentage should be sufficiently low to avoid physically incorrect evaporation zones, but not unnecessary low to avoid long simulation times.

_{Table 1. Simulation results: Influence of node transferring percentage to wetted zone on predicted condensation, size of condensation zone and simulation time.}

3.2. 1D-validation: drying of a wetted layer (EN ISO 13788)

This validation exercise, outlined in Annex D of EN ISO 13788, assumes a flat roof in which the roof insulation is wetted by precipitation during construction before the installation of the weatherproof membrane. To do this, the insulation layer is divided into two and it is assumed that there is excess moisture content of 1 kg/m² at interface I2. The roof built-up is show below in Figure 4. For the monthly climate conditions and material properties we refer to EN ISO 13788.

The calculation covers several consecutive months. As indicated in Figure 1 the remaining moisture will serve as a moisture excess for the following month. The calculation stops when the initial moisture content is dried out.

The results in Figure 5 indicate that the roof is dried out after a period of 83 months which is in line with the results from EN ISO 13788.

4. Model applicability

The objective of this section is outlining the applicability of the proposed model in comparison to more complex (dynamic) hygrothermal models. As introduced earlier, existing hygrothermal engineering tools span from straightforward 1D steady-state heat and vapor transport models (such as the GLASER method) to fully-coupled 2D and even 3D transient HAM models. A guideline presented by Straube and Burnett [11] can assist in selecting the appropriate tool. They distinguish between three distinct needs for hygrothermal modeling: 1) design, 2) assessment, and 3) study. The first two needs are typically addressed by design professionals such as architects and engineers, while researchers and students delve into the detailed study of enclosure performance. In all three categories, hygrothermal simulation should furnish the modeler with sufficient and pertinent information necessary for decision-making. Additionally, Straube and Burnett [11] propose a framework to guide the selection of a suitable modeling approach based on the following aspects:

1. Geometry of enclosure
2. Boundary conditions
3. Material properties
4. Physics
5. Performance thresholds

In the selection process of a suitable modelling tool these aspects need to be critically reviewed from two sides: a) is it essential to obtain appropriate information for the final decision making and b) is the required input data and model available.
In the light of these aspects the following paragraph will review the proposed modelling methodology.

4.1. Geometry of enclosure

The proposed model allows the user to create either 1D, 2D or 3D geometries. To illustrate the importance of considering 2D and 3D effects the validation case of paragraph 3.1 is here extended with its 2D and 3D variants. The results, expressed in Figure 6 as interstitial condensation per square meter inner surface, indicate that 2D and 3D effects can highly impact the results and thus the assessment.

The proposed model is implemented in TRISCO containing a user-friendly interface to build up a any (orthogonal shaped) 3D component.

4.2. Boundary conditions

The model is steady-state but has the option to run consecutive simulations with monthly averaged boundary conditions. This allows to assess the annual accumulated moisture due to interstitial condensation (or drying time in case the simulation starts with an initial moisture excess).
The model is limited to circumstances where this quasi-stationary monthly averaged approach is justified. It is not intended to be used for problems where (hygro)thermal inertia is important.

4.3. Material properties

The model assumes constant material properties. This basically limits its use to materials for which the vapour permeability is not influenced by relative humidity, such as mineral wool, glass, metals, EPDM, PVC,…. In case the building enclosure studied contains materials for which the vapour permeability is influenced by its relative humidity (wood, cellulose insulation,…) and hygric buffering is substantial, it is advised to move to more advanced models. Such models however, requires that sufficiently accurate material functions are available.

4.4. Physics

The proposed model considers the combined heat and vapour transport, but is not intended to investigate problems where moisture buffering and/or capillary moisture transport is important (wind-driven rain on masonry, capillary active insulation materials, rising damp,…).
Further, it is also important to stress that the proposed model assumes the building enclosure to be perfectly air tight. When any type of air transport is relevant (e.g. wind-washing, natural convection in or around insulation layers, forced convection through leaks,…) the model cannot be safely used. This is a general limitation for all available HAM-tools for the purpose of design and assessment. Even if a simulation tool would be capable to incorporate air transfer, it can be questioned if sufficient input data is available (in terms of size and distribution of air leaks).

4.5. Performance thresholds

The proposed model explicitly calculates the level of (accumulated) interstitial condensation which can serve as a direct performance threshold in the evaluation of the building enclosure. Alternatively, an initial moisture excess can be defined at an interface for which the drying out period can be calculated. In addition, the proposed method calculates the monthly temperature field and relative humidity field which can be used to assess the risk for mould formation.

5. Case study: retrofit curtain wall

The presented model is applied in this section to evaluate the risk for surface and interstitial condensation for the energy-efficient retrofit of a curtain wall system. The high-rise building of instance dates from the late ’90 and has poor thermal performance. One of the possible design options is renewing only the glass and add interior insulation in front of the original opaque parts. The original opaque part in between the mullions contains of a mineral wool layer (9 cm) covered on both sides with a steel plate (8 mm) and is protected from the outside with a highly ventilated cavity. The idea is to add at the inside of this opaque element a layer of 10 cm of mineral wool and to finish the window tablet at the same height as the original transom (see Figure 7).

The introduced curtain wall system is modelled with and without the additional interior insulation to verify the impact on the risk for surface and interstitial condensation. The relevant materials properties are summarised in Figure 8c below. The simulation is conducted assuming interior climate conditions of 20°C and 40% and an exterior climate of -5°C and 80%. Figure 8 gives an overview of the results.

The results illustrate that the risk for condensation does increase by adding interior insulation. For example, with interior insulation the temperature at the level transom drops resulting in surface condensation (red zone with 100% relative humidity in Figure 8e). Figure 8f illustrates further that a limited amount of interstitial condensation can be expected behind the interior insulation and window tablet. In this figure the interior insulation and window tablet are clipped to illustrate the location of the expected condensation. The amount of condensation is however limited to about 20 gram/month for the simulated conditions. In summary it can be stated that the simulations reveal that the main risks of adding interior insulation to the existing curtain wall system of instance is linked to surface conditions on the transoms rather than to interstitial condensation.

6. Conclusions

The article presented a three-dimensional quasi-stationary heat and vapour model to estimate the risk for interstitial condensation in building enclosures. The model, which is in fact a three-dimensional implementation of the Glaser method, should be approached as a practical assessment tool rather than accurate moisture transfer prediction tool. The aim of the tool is assess the risk for annual moisture built up and/or drying under the same limitations as the well-known Glaser method (EN ISO 13788). This means that for constructions were (hygroscopic) moisture buffering, capillary moisture transport and/or air transport is relevant the proposed method cannot be safely used. However, for building enclosures where these physical phenomena are not relevant, the model can be an interesting decision making tool. This has been illustrated in this article by the study on an energy-efficient renovation of a curtain wall.

[1] H. Janssen, The influence of soil moisture transfer on building heat loss via the ground. PhD thesis, Catholic University of Leuven, Departement of Civil Engineering, July 2002.

[2] H. M. Künzel, “Simultaneous Heat and Moisture Transport in Building Components: One- and two-dimensional calculation using simple parameters,” tech. rep., Fraunhofer IRB Verlag Stuttgart, 1995.

[3] C. Rode Pedersen, Combined heat and moisture transfer in building constructions. PhD thesis, Technical Uni-versity of Denmark, Lyngby, 1990

[4] A. Nicolai, Modelling and numerical simulation of salt transport and phase transitions in unsaturated porous building materials. PhD thesis, Syracuse University, Departement of Mechanical Engineering,

[5] A. Janssens, Reliable Control of Interstitial Condensation in Lightweight Roof Systems: Calculation and As-sessemnt Methods. PhD thesis, Katholieke Universiteit Leuven, 1998.

[6] C. E. Hagentoft, A. S. Kalagasidis, B. Adl-Zarrabi, S. Roels, J. Carmeliet, H. Hens, J. Grunewald, M. Funk, R. Becker, D. Shamir, O. Adan, H. Brocken, K. Kumaran, and R. Djebbar, Assessment Method of Numerical Prediction Models for Combined Heat, Air and Moisture Transfer in Building Components: Benchmarks for One-dimensional Cases, Journal of Thermal Envelope and Building Science, vol. 27, pp. 327–352, Apr. 2004.

[7] C.-E. Hagentoft, “HAMSTAD: WP2: Benchmark package,” tech. rep., University of Technology, Chalmers, 2002.

[8] EN ISO 13788 (2012) Hygrothermal performance of building components and building elements — Internal surface temperature to avoid critical surface humidity and interstitial condensation — Calculation methods

[9] TRISCO manual, https://www.physibel.be

[10] N. Simões, F.G. Branco A.Tadeu, Definition of two-dimensional condensation via BEM, using the Glaser method approach, Engineering Analysis with Boundary Elements 26(6):527-536, 2002

[11] J.F Straube and E.F.P Burnett, Chapter 5, ASTM Manual 40-Moisture Analysis and Condensation Control in Building Envelopes, American Society of Testing and Materials, Philadelphia, 2001