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