Mass transfer submodel
Engine cycle modeling - Spark-ignition engines

Valve mass flow rates are calculated on the basis of quasi-stationary, adiabatic and compressible flow assumptions. Depending on the direction of flow, upstream conditions will be considered as generating conditions (i.e. where fluid velocity is neglected). Flow is calculated at the throat (narrowest passage between seat and valve). This analogy is only justified if a flow coefficient C _dj is introduced to distinguish between the geometric cross-section and the effective cross-section (figure 22 ): $\begin{array}{l}\frac{\text{d}{m}_j}{\text{ d}t}=\frac{\text{d}{m}_j}{\text{ d}t}\left(P_{\text{amont }},T_{\text{amont }},r_{\text{amont }},{\gamma }_{\text{amont }},P_{\text{aval }}\right)\\ =A_j{C}_{\text{d}j}{P}_{\text{amont }}\sqrt{\frac{2{\gamma }_{\text{amont }}}{\left({\gamma }_{\text{amont }}-1\right)r_{\text{amont }}{T}_{\text{amont }}}\left(X^{\frac{2}{{\gamma }_{\text{amont }}}}-X^{\frac{{\gamma }_{\text{amont }}+1}{{\gamma }_{\text{amont }}}}\right)}\end{array}$