Proceedings e report - Firenze University Press

DIMENSIONAL CHANGES DUE TO FLOWS OF HEAT AND MOISTURE IN WOOD AND WOOD-BASED MATERIALS
direction. The drastic change of dy at position 16 mm indicates a crack. The right part of Fig.5 shows a
comparison of DICT and strain gauge data which correlate quite well [4].
1.3. Other experimental details
Since the measurement generates point clouds which are subjected to errors, sophisticated algorithms
are needed in order to reconstruct the surface form the measurement. Dimensional changes can of
course be calculated by comparing the object's data for different climatic situation.
In order to measure the object's response to climatic variations one can just utilize natural variations,
or one can simulate them in climate chambers. Double climate chambers are a very convenient way to
study the results of differential climates. WKI has a double climate chamber which can accommodate
wall elements as big as 8 metres long and 2.3 metres high.
2. Numerical simulations
Experimental studies of dimensional changes are time consuming and expensive. Furthermore,
experiments with objects of the cultural heritage are often not possible since the objects are unique,
and possible damages cannot be accepted. For these reasons, numerical simulations are very important
in the study of climate effects. They can also reveal insight into stresses and strain in the interior of the
object, which are difficult to measure. Many authors have worked on the differential equations
describing the flow of heat in moisture in materials, especially with respect to their application in civil
engineering. Wood and wood based panels are often used as walls for buildings, and their insulation
properties against heat and moisture are consequently important. Furthermore, heat and moisture
exchange affects dimensional stability. Cracks and warping can be the consequence of improper
design.
The more advanced equations are based on the principles of conservation of enthalpy and mass and
consider effects such as phase transitions and the coupling of heat flow and moisture flow [5].
Numerical simulations of heat flow concentrate on heat conduction and vapour flow (associated with a
phase transition) because the other mechanisms (thermal radiation and flow of air or liquids) are not
relevant in practice or too difficult to calculate. These two effects are described by the following
equations:
q = −λ∇θ
(1)
and
Sh
= −hv∇
gv
(2)
where q [W/m 2 ] is heat flow density, λ [W/mK]the thermal conductivity, θ [K] the temperature, Sh
[W/m 3 ] the heat generation associated with a phase transition from vapour to liquid or vice versa, hv
[J/kg] the latent heat of water and gv [kg/m 2 s] the vapour flow density.
Possible mechanisms for the transport of liquid water are capillary transport, surface diffusion,
percolation, hydraulic flow, electric fields, and osmosis, among which the first is by far the most
important. Using the Kelvin formula which relates capillary pressure to the relative moisture of air ϕ
one obtains
gw = −Dϕ∇
ϕ
(3).
In this equation Dϕ [kg/m·s] is the transport coefficient.
Finally, the transport of water vapour has to be considered which is possible by gas diffusion,
molecular transport, diffusion by solution in other materials (e. g., polymers), and convection.
Convection is normally not considered because it is not often relevant and difficult to calculate. The
other three mechanisms are summarized by
g = −δ
∇ϕ
p
(4)
v p sat
where δp [kg/m·s·Pa] is the vapour permeability and psat [Pa] the saturation pressure of vapour.
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