Mathematical basis, Natural ventilation
Simulation of natural ventilation in the module for BSim requires input at various locations of the model.
Natural ventilation can be activated at thermal zone level.
In the calculations BSim considers only Windoors/opening to the exterior.
The model to use can be automatically selected by BSim.
Natural ventilation is implemented as a special form of Venting in a module for BSim.
Calculation methods for natural ventilation
\[ q_v = \left| \pm q_{Vv}^2 \pm q_{\text{VT}}^2 \right|^{\frac{1}{2}} = \left| \frac{c_v}{|c_v|} \left( c_v v_{10} \right)^2 + \frac{\Delta T}{|\Delta T|} \left( c_T |\Delta T|^{\frac{1}{2}} \right)^2 \right|^{\frac{1}{2}} \tag{1} \]
Single Sided One Level
One pair of openings in one face, in the same vertical level.
Thermal buoyancy and wind:
\[
c_V = 0{,}03A
\]
\[ c_T = 0{,}05 h^{1/2} A \]
Single Sided Horizontal
One pair of openings in a non vertical face.
Thermal buoyancy:
\[ c_T = 0{,}06A \left( \frac{gA^{1/2}}{T_i} \right)^{1/2} \quad \text{for } h/A^{1/2} < 0{,}1 \]
\[ c_T = 0{,}18A \left( \frac{gh}{T_i} \right)^{1/2} \quad \text{for } 0{,}1 < h/A^{1/2} < 0{,}7 \]
Wind:
\[ c_V = 0 \]
Single Sided Dif Level
Several pairs of openings in one face in different vertical levels.
Uniform temperature distribution in the thermal zone.
Thermal buoyancy:
\[
c_T = \sum_{j=1}^{n_0} C_{d,j} A_j \left( \frac{2(H_0 - H_j)g}{T_i} \right)^{1/2}
\]
\[ \sum_{j=1}^{n} C_{d,j} A_j |H_0 - H_j|^{1/2} \frac{H_0 - H_j}{|H_0 - H_j|} = 0 \]
Wind:
\[ c_V = 0{,}03A \]
Cross
Openings in two faces in the same vertical level (cross ventilation)
Thermal buoyancy:
\[ c_T = 0 \]
Wind:
\[ c_v = \sum_{j=1}^{n_v} C_{d,j} A_j \left( C_{p,j} - \frac{2p_i}{\rho_u (k h^{\alpha} v_{10})^2} \right)^{1/2} k h^{\alpha} \]
\[ \sum_{j=1}^{n} C_{d,j} A_j \left( \frac{ |2\Delta p_j| }{ \rho } \right)^{1/2} \frac{ \Delta p_j }{ |\Delta p_j| } = 0 \]
\[ \Delta p_j = p_{v,j} - p_i = \frac{1}{2} C_{p,j} \rho_u v_{\text{ref}}^2 - p_i \neq 0 \]
Combined Two Level
Openings in several levels in two non parallel faces.
Thermal buoyancy:
\[
c_T = \sum_{j=1}^{n_0} C_{d,j} A_j \left( \frac{2(H_0 - H_j)g}{T_i} \right)^{1/2}
\]
\[ \sum_{j=1}^{n} C_{d,j} A_j |H_0 - H_j|^{1/2} \frac{H_0 - H_j}{|H_0 - H_j|} = 0 \]
Wind:
\[ c_v = \sum_{j=1}^{n_v} C_{d,j} A_j \left( C_{p,j} - \frac{2p_i}{\rho_u (k h^{\alpha} v_{10})^2} \right)^{1/2} k h^{\alpha} \]
\[ \sum_{j=1}^{n} C_{d,j} A_j \left( \frac{2|\Delta p_j|}{\rho} \right)^{1/2} \frac{\Delta p_j}{|\Delta p_j|} = 0 \]
\[ \Delta p_j = P_{v,j} - p_i = \frac{1}{2} C_{p,j} \rho_u v_{\text{ref}}^2 - p_i \neq 0 \]
Combined
Openings in more levels in more than two faces (combined buoyancy- and cross ventilation). \[ q_v = \sum_{j=1}^{n_1} C_{d,j} A_j \left( \frac{2\Delta p_j}{\rho} \right)^{1/2} \]
\[ \Delta p_j = p_j - p_i = \left( \frac{1}{2} \rho_u C_{p_j} \cdot v_{\text{ref}}^2 + \rho_u g (H_{0,\text{ref}} - H_j) \frac{\Delta T}{T_i} \right) - p_i \neq 0 \]
