Page 20

FPREF 13..14

144 2 Mass transfer For p control volumes, the result is a system of p equations with p unknowns: K´a ‰ Š p;p Pa ‰ Š p ˆ K´ a;i;j;kPa;i;j;k p (2.26) where K´a ‰ Š p;p is a p rows, p columns permeance matrix, [Pa]p a column matrix of p unknown air pressures, and K´a ;i;j;kPa;i;j;k p a column matrix of p known air a ´pressures or air flows. Once the air pressures are known, then the flows follow from: Ga;ˆ i;j;k K;i;j;k Pa;i‡ j Pa;i (2.27) a For anisotropic ´materials the same algorithm applies on condition that the lines linking the centres of the control volumes coincide with the main directions of the permeability tensor, allowing use of the related … K† x;y;z values. Under non-isothermal conditions, thermal stack links the air with the heat balances. Most of the time, the solution requires iteration between both. 2.2.5 Airflow across assemblies with air-open layers, leaky joints, leaks and cavities The flow equations were introduced above. For operable windows and doors, the exponent b is typically set at 2/3: Ga ˆ a L ΔPa 2 =3 with L the length of the casement in m and a the air permeance per metre run of casement, with units kg/(m.s.Pa2/3). Most assemblies combine air-open layers, open porous materials, joints and cavities. In such cases, writing the conservation law as a partial differential equation fails. One approach consists of transforming the assembly into an equivalent hydraulic circuit, with a combination of well-chosen points xa connected by air permeances (Figure 2.9). Per point, the sum of the airflows from the neighbouring points must be zero. As each flow equals KΔPa, insertion in the conservation law gives: X iˆl;m;n jˆ1 Kxa ;i‡jPa;i‡j Pa;l;m;n X iˆl;m;n jˆ1 Kxa ;i‡j ˆ 0 (2.28) Hydraulic resistance Sum of the four flows zero Transparent circles for the boundary conditions Fig. 2.9 Equivalent hydraulic circuit


FPREF 13..14
To see the actual publication please follow the link above