An effective numerical method is presented to compute transients in piping systems in which frequency-dependent parameters influence the response. Frequency-dependent friction is utilized as the parameter-of-concern herein, however, the procedure can accommodate other factors such as frequency-dependent wavespeed equally well. The method, a variation in the impulse response method, is developed from the frequency response analysis and incorporates the fast Fourier transform. Examples are included showing the application of the method in computing both classic waterhammer and transients in pipes with frequency-dependent friction. Computed results agree very well with those from the standard method of characteristics and with physical experiments.
The classic formula for waterhammer wavespeed is extended to calculate the complex-valued, frequency-dependent wavespeed in a viscoelastic pipe, which takes into account the effect of viscoelasticity of pipe wall material on wave propagation. With the complex wavespeed, the standard impedance or transfer matrix is directly used to analyze resonating conditions in systems including viscoelastic pipes, and the impulse response method presented previously by the authors is applied to compute nonperiodic transients. Numerical results are compared with experimental data and good agreement is observed.
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