Reduced-Order Modeling of Fluid Transmission Lines
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Solutions of fluid transients in transmission lines are very difficult to obtain, and they are generally computed using numerical techniques. In addition to their computational difficulties, the numerical methods do not directly translate into models having utility in system design, control design, and system health-monitoring particularly when the lines are parts of a fluid network system. Not surprisingly, these limitations are fully addressed by model- order reduction techniques that yield to low-dimensional linear models, which contain all the essential information. In this dissertation, a procedure for obtaining analytical low-dimensional models quantifying the dynamic behavior of confined single-phase flow in fluid transmission lines experiencing pressure and flow oscillations is formulated and presented. Solutions for the nonlinear Navier-Stokes equations are derived and written in transfer function matrix form using Laplace Transform. Two distributed parameter models for the case of laminar flow are presented. The first model is called the dissipative model and is referred to in the literature as the “exact” model. The second model is obtained using distributed lumped parameters. Since the resulting transfer functions in both models are transcendent, and therefore cannot be used for time-domain analyses, rational transfer function approximation is performed using the infinite product series expansion technique. Both models accurately predict the static and dynamic characteristics of fluid transmission lines using only few terms of the infinite products over a broad frequency range. The two models are then extended to account for turbulent flow using two different approaches. A more accurate model for turbulent flow in smooth-walled pipes is developed using an approximated weighting function. The frequency response functions of the proposed models are compared with those of an existing numerical model showing acceptable coincidence. A major benefit of the proposed models over the existing low-dimensional models is that the coefficients of the rational transfer functions can be directly calculated using analytical equations rather than table or graphs, which introduces flexibility and reduces the difficulties of modeling both laminar and turbulent flow in underdamped fluid transmission lines, while still maintaining model accuracy and complexities.