Theoretical study on stability of fluid network based on sensitivity

In fluid networks, flow fluctuation is an important indicator for fluid network stability. However, changes of flow are affected by a variety of factors, and flow resistance change is one of the common influencing factors. Changes in branch flow resistance can cause changes in the flow in that branch and others, which will affect the stability of the entire fluid network. In order to quantitatively analyze the effect of branch flow resistance changes on flow fluctuation, this study introduced the concept of building a sensitivity-based mathematical model and calculated the sensitivity of each branch to construct a sensitivity matrix, and then, based on the uniqueness of the correspondence between the system state and the sensitivity matrix, sensitivity was used to quantitatively describe the system state. In the sensitivity matrix, the column element indicates the sensitivity of the flow resistance change in one branch to the flow change in other branches; the row element indicates the sensitivity of the branch flow change to the flow resistance change in other branches. This study proposed an algorithm which can quickly and accurately calculate the sensitivity value, and it gave a detailed solution to the problem of over-iteration and ill-conditioned solution in the sensitivity solution process. It was verified by an example that the method can accurately describe the influence of the flow resistance change from a branch in a fluid network on the flow in itself and other branches. The fluid network stability theory based on sensitivity has certain guiding significance for the design and optimization of fluid networks.