Transient Analysis of Mixed Free-Surface-Pressurized Flows With Modified Slot Model: Part 2 — Similarity Law and Eigenvalue Problem

To analyze transient free-surface-pressurized flows with entrapped air in a drainage system, a virtual slot model with ceiling has been introduced. Using this model, calculations for the reduced model and the actual size model are carried out to examine a scale effect on the transient flow. The results show that up-scaling the system causes the increase in compressibility of entrapped air so that the rate of pressure rise decreases. Next, it is confirmed that the partial differential equations for the modified slot model have real eigenvalues and then the initial value problem is well-posed when the velocity difference between air and water is not so large. The increase in the velocity difference yields a system having complex eigenvalue, however the well behaved numerical solutions can be obtained since the friction terms in the differential equations suppress the numerical instability.