Details:AirLayers

Air Layers

WUFI can also include air layers in the building component. It does not simulate the air convection (which would not make much sense in one dimension anyway), but it allows for the air layer as a resistance to heat and moisture flows.

In addition to heat conduction, in air layers heat can also be transferred by convection and radiation. In addition to water vapor diffusion, in air layers water vapor can also be transferred by convection. Since WUFI is primarily intended for solid materials, it only allows for heat conduction and water vapor diffusion (plus liquid transport, which is not relevant here). However, the additional transport phenomena can be included by adjusting the heat conductivity and the diffusion resistance so that the correct heat and vapor flows result from the calculation.

The method is based on the following considerations which are valid for non-ventilated air layers. (No general treatment is possible for ventilated air layers; they may even exhibit the same conditions as the exterior air. Building components outward from the air layer may then be disregarded except for their shielding of rain and radiation.)

The relative contributions of heat conduction, convection and radiation are dependent on the thickness and orientation of the air layer, the nature of the two surfaces and the temperature. Fortunately, the dependence on the temperature may be neglected in building physics. Furthermore, it suffices to distinguish between metallic and non-metallic surfaces. So if we restrict ourselves to, say, vertical air layers with non-metallic surfaces, we can simply determine (e.g. from measurements) a heat resistance Rnon-met which depends only on the air layer thickness and which comprises all transport phenomena.

Now, for WUFI the effective heat conductivity λ^* has to be chosen so that for an air layer with a given thickness the heat resistance Rnon-met as determined above results. Note: the thickness with wich the air layer is included in the assembly for calculation need not (but can) be identical with the real thickness, since the real thickness has already been allowed for in the specific choice of Rnon-met.

The heat resistance of an air layer with the desired thickness, orientation (vertical, horizontal) and surfaces (metallic, non-metallic) may be looked up in a relevant table. Let's choose non-metallic surfaces here, since in building components non-metallic surfaces are predominant, and call this value Rnon-met. We also choose an arbitrary thickness Dx^*, which shall be the thickness of the air layer as inserted in WUFI's component assembly. Then
 
 R_non-met = Dx^* / l^*,
 
therefore
 
 l^* = Dx^* / R_non-met.
 

Since water vapor diffusion and convective water vapor transport are based on analogous mechanisms as heat conductivity and convective heat transport, the coefficients describing vapor transport can be derived from the coefficients for heat transport, using similarity relations. For vapor flow, we have formally:
 
 -g_v = D_c / µ^* · Dc / Dx^* = Dc / S
 

gv	[kg/m²s]	:	water vapor diffusion flux density
Dc	[m²/s]	:	concentration-related diffusion coefficient
µ*	[-]	:	effective water vapor diffusion resistance factor
c	[kg/m³]	:	water vapor concentration
Dx*	[m]	:	effective layer thickness
S	[m³/s²Pa]	:	water vapor diffusion resistance,

 
therefore
 
 
 µ^* = D_c · S / Dx^*
 
But we have
 
 D_c = 0.083 · (T/273)^1.81 ≈ 0.09   [1],
 
and, because of similarity relations,
 
 S ≈ R_met / 3.5   [2],
 
where we have to use the heat resistance Rmet of air layers between metallic surfaces (i.e., without radiation exchange), since we want to estimate the vapor diffusion resistance and there is no transport mechanism analogous to radiation involved, in contrast to the above case of heat transport.

Finally, we have the freedom to choose an arbitrary thickness Dx^* with which the layer is included in the component assembly for calculation, since the real thickness was already allowed for in the choice of the specific value for Rmet.
 
 &micro^* = 0.09 · R_met / (3.5 · Dx^*) = 0.026 · R_met / Dx^*
 

For vertical air layers, Rnon-met and Rmet may be taken from this table (interpolated after [3]):

	thickness		Rnon-met		Rmet
	[cm]		[m²K/W]		[m²K/W]
	0		0		0
	1		0.140		0.280
	2		0.160		0.430
	3		0.171		0.526
	4		0.178		0.590
	5		0.180		0.620
	6		0.178		0.627
	7		0.176		0.623
	8		0.174		0.613
	9		0.172		0.598
	10		0.170		0.580
	11		0.168		0.557
	12		0.166		0.530
	13		0.164		0.501
	14		0.162		0.468
	15		0.160		0.430

The other basic material parameters may be determined according to the following:

• if Dx^* was chosen not equal to the real thickness, multiplication of the 'bulk density' 1.29 kg/m³ by (real thickness)/Dx^* results in the correct heat capacity;
• the 'porosity' should be chosen very high (e.g. 0.999 m³/m³);
• the specific heat capacity by mass of the air layer is 1 kJ/kgK, even if Dx^* is chosen not equal to the real thickness.

For the graphical display of the component assembly, it will be advisable to choose Dx^* equal to the real thickness. Note however that if you want to repeat the calculation with an air layer of a different thickness, it is not sufficient to simply adapt the layer thickness in the component assembly. Instead, l^* and µ^* have to be newly determined from scratch.
 

Regarding the 'moisture storage function' of air layers, see the reference: Moisture Storage Function.

The definition of the diffusion resistance factor (µ-value) is discussed in the reference: Water Vapor Diffusion.

Literature:

[1] Schirmer, R.: Die Diffusionszahl von Wasserdampf-Luft-Gemischen und die Verdampfungsgeschwindigkeit,
Beiheft VDI-Zeitschrift, Verfahrenstechnik (1938), H. 6, p. 170-177.
 
[2] Illig, W.: Die Größe der Wasserdampfübergangszahl bei Diffusionsvorgängen in Wänden von Wohnungen, Stallungen und Kühlräumen,
Gesundheitsingenieur 73 (1952), H. 7/8, p. 124-127.
 
[3]Gösele, K., Schüle, W.: Schall·Wärme·Feuchte. Bauverlag 1989.