WUFI

Dear WUFI-team,

I am using WUFI 2D-4 to investigate the risk of frost degradation in brick facades. Specifically, I’d like to estimate the amount of liquid and frozen water in a material cell during freezing periods and use the data to calculate the Freeze-thaw damage risk index as proposed by Zhou (https://www.sciencedirect.com/science/a ... 2317303463)
– Is there a straightforward way in WUFI to get per cell ice vs. liquid water content for each time step of the simulation?
– Can this output be found somewhere within or derived from the (hdf5) result files?

Thank you very much and have a nice summer!
Best regards
Jan Mandinec

Dear Jan,

WUFI takes into account that water contained in small capillaries does not freeze at 0°C but at some lower temperature which depends on the capillary radius. In a given grid element, water in large pores may be frozen while at the same time water in smaller pores is still liquid. WUFI determines this by means of the "freezing limit potential" which is the relative humidity over the pore water in the largest unfrozen pores of capillary-active building materials.

For a plot of the freezing limit potential, see Fig. 20 in Dr. Künzel's thesis

H.M. Künzel: Simultaneous Heat and Moisture Transport in Building Components
https://wufi.de/en/wp-content/uploads/s ... 994_EN.pdf

For example, at a temperature of -4 °C the freezing limit potential is 0.96 (that is, 96 % RH). This means: In the hypothetical case that the material were filled with the equilibrium water content corresponding to 0.96 RH, the capillary tension in the pores would just prevent freezing in all the filled pores. If in the actual time step the water content w is higher than w(0.96), then only the water content exceeding w(0.96) freezes, the rest remains unfrozen.

Say you have in a grid element the temperature -4 °C and the water content w(0.98), then WUFI computes the freezing limit potential via the formula (1 + 0.01*temperature), finds 0.96, concludes that the water content w(0.96) is still liquid and only the water content (w(0.98)-w(0.96)) is frozen. For this time step it then determines the liquid transport properties in such a way that only the liquid portion is considered "transportable", the frozen water content is considered fixed.

Based on the relative humidity in a given grid element, you can use the simple formula above to determine the unfrozen portion of the pore water as in the example given above.

Please note that this is only a simplified treatment of the freezing process. In particular, no water redistribution caused by growing ice crystals or any other mechanism is taken into account. For example, the complex freezing-and-pumping processes occurring in concrete can not be simulated in detail.

Kind regards,
Thomas

Dear Thomas,

thank you for your quick reply, and for pointing me to the "freezing limit potential" curve. This makes the determination of the ice content much clearer.

Just to double-check: does WUFI always uses this formula (1 + 0.01*temperature) to determine the ice content, regardless of the material properties? In the thesis, the curve is derived from the pore radius via Kelvin and the capillary suction stress equations (equations 1 and 2), which suggest material-specific curve. I have also noticed that slope of the simplified formula differs from the curve shown in Fig 20. For example, at -20°C, simplified formula yields w(0.8 ), whereas the figure reads approximately w(0.83).

Could you clarify whether WUFI uses a generalized approximation for all materials, or whether material-specific data is taken into account? If yes how?

Thank you again and best regards
Jan Mandinec

does WUFI always uses this formula (1 + 0.01*temperature) to determine the ice content, regardless of the material properties?

Dear Jan,

WUFI uses this formula for all materials since it is independent of any material properties. It is based on the fact that in thermodynamic equilibrium the vapor pressure over the unfrozen water under capillary tension must be equal to the vapor pressure over the ice.

Without capillary tension, the vapor pressure of unfrozen water at sub-freezing temperatures is higher than the vapor pressure over ice, as shown by any vapor pressure table (the water molecules are more tightly bound in the ice crystals than in the unfrozen water). To reach the mentioned equilibrium, the vapor pressure of the unfrozen water must be lowered and that is effected by the capillary tension (in liquid water under tension the molecules are more tightly bound than in water without tension).

Compute for some sub-zero temperature the vapor pressures both of liquid water without tension and of ice, this will show you how much the vapor pressure of the liquid water must be lowered to reach that of ice, and the Kelvin equation tells you which tension is needed to have this effect. Both equation (1) (dependence of capillary tension on capillary radius) and equation (2) (dependence of vapor pressure or relative humidity on capillary tension) in Dr. Künzel's thesis apply generally and are independent of material properties. What does depend on material properties are the amounts of frozen and unfrozen water, since these are determined by the material-specific moisture storage functions. The freezing criterion in terms of relative humidities is material-independent.

I have also noticed that slope of the simplified formula differs from the curve shown in Fig 20. For example, at -20°C, simplified formula yields w(0.8 ), whereas the figure reads approximately w(0.83).

Yes, the formula (1 + 0.01*temperature) used by WUFI is only an approximation to the curve shown in Fig. 20. If you look closely, that curve is not precisely straight, but it is almost straight, and the formula above seems to be a pretty good approximation. Please keep in mind that freezing is not WUFI's central subject, it is taken into account for completeness as a "side effect". I don't know which possible additional freezing effects there may be in various materials beyond the basic treatment described above. The processes in concrete, for example, are definitely much more complicated, involving "pumping" effects etc.

Regards,
Thomas

Hi
Picking this thread back up.
Is there a way to output from WUFI the ice content in a component?
I'd like to use the Jansenns paper to assess the risk of frost damage
https://www.sciencedirect.com/science/a ... 2324002415

Thank you

David

Dear David,

WUFI does not directly output the ice content since this has not been of major interest so far. However, you can compute the ice content from WUFI's standard output.

For liquid water and frozen water to be in equilibrium, they must have the same vapour pressure. Usually, at temperatures below freezing the vapour pressure of ice is lower than the vapour pressure of (subcooled) liquid water because in the ice crystal lattice the water molecules are bound more tightly than in the liquid water. For example, at -10 °C the vapour pressure over (subcooled) liquid water is 286.2 Pa, whereas the vapour pressure over ice is only 259.7 Pa.

However, if the liquid water is exposed to some tension (negative pressure), its vapour pressure is reduced. The capillary forces in the capillaries of a porous material are doing just that: They create a capillary tension in the liquid water and thus reduce its vapour pressure. If at -10 °C the vapour pressure in some capillary is reduced to 259.7 Pa, this specific capillary has just the right radius r0 to create a capillary tension which reduces the vapor pressure of the liquid water to that of the ice at this specific temperature. The equilibrium value of the relative humidity above the meniscus in this capillary and at this temperature is 259.7/286.2 = 0.907 = 90.7 %. In smaller capillaries the tension is higher and thus too high for equilibrium between liquid and ice, and all the water remains liquid at this temperature. In larger capillaries, the tension is too low for equilibrium at the current temperature, and the water is frozen.

In the steady state, the water contained in a porous material collects in the small pores (which have higher 'suction' power) while the large pores remain empty. If at -10 °C all the filled pores have a smaller radius than the r0 described above, all the water contained in the material will remain liquid. If there is enough water in the material to also fill pores with larger radius than r0, the water in those larger pores will be frozen while the water in the pores smaller than r0 remains liquid.

So in order to determine the amount of ice in the material, we must determine the critical pore radius r0 corresponding to the current temperature of the material and see whether the radius of the largest filled pores is smaller or greater than r0. Alternatively, and equivalently, we can express the critical pore size by the capillary tension created in a pore of this size, or by the relative equilibrium humidity above the meniscus in such a pore.
WUFI uses the latter option. Internally it expresses the amount of moisture by the corresponding relative humidity anyway (instead of the water content; the math is easier). To find the amount of ice (if any) at a given location in the material, look at the temperature and the relative humidity at that spot. For -10 °C, the critical relative humidity below which the water will not freeze is 0.907 (= 90.7 %). If the simulation result says that the current relative humidity is less, (say 80 %) all the water is in pores with radii smaller than r0, and it will be liquid.

If the relative humidity is higher (say 0.95 = 95 %), there is water in pores with radii greater than r0, and that water will be frozen. To find the amount of this frozen water, consult the moisture storage function of the material (tabulated in the material data dialog). In Baumberger sandstone, for example, 95 % RH correspond to the moisture content 57.8 kg/m³. This is the _total_ water content. Liquid water is found in the pores with radius less than r0, and according to the moisture storage function the RH of 90.7 % corresponds to the water content 43.9 kg/m³. The difference 57.8 - 43.9 = 13.9 kg/m³ is frozen water.

Please keep in mind, however, that while the approach described above is taken from standard literature (and apparently in agreement with measurements on soils; Neiss J. 1982), it may be a bit simplistic. For example, it assumes that in contrast to the liquid water which is exposed to the capillary tension, the ice remains at atmospheric pressure, and I am not sure to which degree this is really justified for porous building materials as opposed to porous soils. Also, WUFI treats the freezing as a simple phase change; possible pumping effects (as in frost heaves) and similar effects which may affect the amount of ice are neglected. WUFI takes freezing into account as a "secondary" effect only which somewhat affects the simulation result by releasing some latent heat and by reducing the amount of moveable water. WUFI is not meant to explicitly and exactly simulate the freezing process and the resulting amount and distribution of ice.

The following diagram shows the critical humidity which separates frozen from liquid water:


This curve is almost a straight line, and WUFI computes it using the simplified fomula RH_limit = 1 + (temperature, °C)/100. For example, for a temperature of -10 °C this formula gives RH_limit = 0.90, to be compared with the value 0.907 shown in the table above.

Regards,
Thomas