This paper examines modelling the laminar dynamic fluid responses within hydraulic transmission lines that have a tapered shape from the inlet to outlet. There are excellent models available for fast simulation of pressure and flow dynamics within uniform lines, however the established models for tapered lines have some notable inaccuracies and simulation complexities. The transmission line method (TLM) structure is applied in this paper since it can be computed quickly and has shown to accurately model the effects of frequency-dependent friction. This paper presents a method of optimizing the TLM weighting functions, minimizing the error between the TLM transmission matrix terms and a numerical exact solution. Optimizations have shown that using the TLM to model tapered lines has improved accuracy over the existing models when compared in the frequency domain. Two-dimensional interpolation of a look-up table is possible allowing for quick selection of the optimized parameters. This model can be used in numerous applications where line dynamic effects must be accounted for, especially with digital hydraulic switched inertance converters.
Keywords: Transmission line method, TLM, tapered fluid lines, optimization, modelling, simulation.