Delimitación del Problema

To check the importance of long wave radiation in the heat and moisture balance of the vitrine, a new test case will be simulated with and without the longwave radiation model. This new test case considers the case where the vitrine is directly hit by solar (shortwave) radiation. The intensity of the incident radiation corre- sponds with the beam radiation on a south oriented surface for a day in July for the climate of Uccle, Belgium as shown in Fig. 5.10.

0 1 2 3 4 5 6 7 8 0 12 24 36 48 60 72 84 96 108 120 a) I (W/m 2 ) time (h) 0 1 2 3 4 5 6 7 8 50 51 52 53 54 55 56 57 58 59 60 b) RH (%) time (h)

Figure 5.10: Incident radiation on the vitrine

To evaluate the importance of the longwave radiation model the average rel- ative humidity and the relative humidity at the bottom of the cavity behind the painting are compared for the simulation with and without the longwave radiation model. The outcome of this comparison is given in Fig. 5.11.

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Fig. 5.11(a) shows that modelling the vitrine without the effect of longwave radiation results in a serious overestimation of the risk of moisture related damage: without longwave radiation condensation would occur behind the painting, while in reality radiation heats up the cold backside of the vitrine hence lowering the local relative humidity (Fig. 5.11(b)) and the risk of condensation. So it is of crucial importance that in case of very low air velocities (here cm/s) longwave radiation is taken into account in the simulations as done in section 5.3.1.

5.4

Conclusion

In this chapter the new CFD - HAM model was applied to a ‘real-life’ problem where the assessment of moisture related damage is of the highest importance: a microclimate vitrine for paintings. The simulation study predicts phenomena also observed in practice, which demonstrates the practical use of the model. It was found that the presence of the microclimate vitrine succeeds in stabilizing the rel- ative humidity inside the painting and that an increase in temperature inside the vitrine can result in an increasing relative humidity in the enclosed air. Different authors explained this by the buffering effect of the hygroscopic materials inside the vitrine. The simulation showed that this is only part of the explanation: the presence of temperature gradients in the vitrine due to non-uniform boundary con- ditions is the second necessary condition for this phenomenon to occur. It was also found that relative humidity fluctuations due to incident radiation were less effectively buffered than fluctuations due to varying ambient temperature. Adding silica gel to the vitrine proved to have an added negative effect on the hygric re- sponse of the painting in case of incident radiation. The impact of the paint layer on the relative humidity at the painted surface proved to be modest, yet its effect on the moisture response inside the panel was significant. It was found that the paint layer acts as an extra protection for the material behind the paint. On the other hand its presence reduces the stabilizing effect of the vitrine in case of in- cident radiation. Summarizing, it can be stated that the microclimate vitrine is an excellent protection from fluctuations in ambient temperature, yet direct radiation on the vitrine should be avoided as much as possible.

CASESTUDY 157 0 1 2 3 4 5 6 7 8 0 12 24 36 48 60 72 84 96 108 120 a) I (W/m 2 ) time (h) 0 1 2 3 4 5 6 7 8 0 10 20 30 40 50 60 70 80 90 100 b) RH (%) time (h)

(a) without radiation model

0 1 2 3 4 5 6 7 8 0 10 20 30 40 50 60 70 80 90 100 RH (%) time (h)

(b) with radiation model

Figure 5.11: Relative humidity at the bottom of the back cavity of the painting (red line) and average relative humidity in the vitrine (blue dashed line)

6

Conclusions and Perspectives

6.1

General Conclusion

In this work the possibility was studied to take the effect of distributions and local microclimates in indoor air into account in the simulation of the hygrothermal response of individual objects for an improved assessment of the risk of moisture related damage. The first part of this study is dedicated to the use of local transfer coefficients in combination with nodal air models for the prediction of the local air - material interaction. As the moisture content of porous materials is affected by both heat and water vapour transport, data on both local heat and water vapour transfer coefficients is required in this approach.

Since different definitions are available for the mass transfer coefficient (thus also for the water vapour transfer coefficient), it was first investigated which limi- tations are associated with the different definitions and which of these definitions is best suited for the applications considered in this work. It was found that the use of vapour density as driving force for the mass transfer coefficient was only justi- fied in case of isothermal and isobaric situations, while the use of vapour pressures resulted in mass transfer coefficients which are not independent of the ambient pressure. However, if the species mass fraction was used as driving force, the val- ues found for the mass transfer coefficients were independent of temperature and ambient pressure. The use of the latter definition is thus recommended.

CFD simulations were performed to check whether local mass transfer coeffi- cients could be determined out of the heat transfer coefficients by using the heat

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and mass analogy for the case of indoor air flow. The simulations showed that when average indoor conditions are used as a free stream reference, as imposed by nodal models, the non-analogous boundary conditions for heat and mass transfer met in practice, cause the loss of the analogy for local transfer coefficients. Yet the prediction of the average mass transfer coefficient with the analogy still yields reasonable accuracy as the local differences in boundary conditions are levelled out.

The importance of the use of the correct mass transfer coefficients for the pre- diction of the hygric response of porous materials in the hygroscopic range was checked. It was found that the influence of the mass transfer coefficient is very limited in case of uniform free stream conditions (as for instance in a windtunnel experiment). However, in case of air flow in an enclosure, like rooms in a build- ing, the mass transfer coefficient associated with the average indoor conditions as free stream reference will have an important effect on the hygric response due to the strong variations in the air volume. In this case the mass transfer coefficient rather expresses the influence of indoor air distributions than the influence of the boundary layer. Taking the correct indoor air distribution into account is thus of crucial importance.

To conclude the study on transfer coefficients the time dependent behaviour of the mass transfer coefficients in an enclosure was investigated. It was found that for a transient moisture response with steady-state air velocity the local mass transfer coefficients strongly varied in time. This phenomenon causes the need for a dynamic coupling between the calculation of the transfer coefficients and the prediction of the hygrothermal material response, or, more general, between the air flow calculation and the hygrothermal material model.

In the second part of this thesis a dynamically coupled 3D CFD - HAM model was developed by integrating a HAM material model in a commercial CFD solver (Fluent 6.2). This new model is capable of simulating the local hygrothermal interaction between porous objects and the indoor climate as it allows for the cal- culation of coupled heat and water vapour transfer in air and porous materials. In the porous material moisture transfer by vapour diffusion, liquid moisture storage, hysteresis and latent heat release was taken into account.

The newly developed model was employed to study the hygrothermal response of a painting in a microclimate vitrine. Thanks to the simulation of the 3D tem- perature and relative humidity distributions in the vitrine physical insights and explanations were offered concerning non-intuitive phenomena such as the rise of the relative humidity inside the vitrine with rising temperature.

The model is thus capable of predicting the effect of air distributions on the hygrothermal behaviour of porous objects in practical cases and is hence a valuable tool for the study and prevention of moisture related damage in valuable objects.

CONCLUSIONS ANDPERSPECTIVES 161