Reduced-order modelling of transient flow in transmission lines using distributed lumped parameters

Developed in this paper are mathematical models capturing the one-dimensional underdamped dynamics of confined fluid flow within cylindrical transmission lines. The resulting models are rational transfer functions with coefficients that are explicit functions of the fluid properties and line geometry. Unlike a traditional lumped-parameter approach, the accuracy of the fluid resonant frequencies predicted by the proposed models is precise and not a function of transmission line axial discretisation. Therefore, model order (complexity) is solely a function of the number of desired modes, which in turn influences pressure and flow predictions. The results are applicable to both laminar and turbulent flow. To develop the models, a distributed lumped-parameter approach is employed. Specifically, a quasi-steady state friction approximation is used within the governing partial differential equations. The solution to the linearised ordinary differential equations produces three transcendent transfer functions that are approximated using finite-order rational transfer functions. The parameters of resulting transfer functions are then modified to capture the second-order effects. A fluid power design example using the proposed model is provided to illustrate the utility of these models.