This paper describes a method of modelling time-varying flow in hydraulic pipelines which may be incorporated into time domain simulations of hydraulic systems operating with variable time steps. A previously reported finite element method is extended. New approximations to frequency-dependent friction for laminar and turbulent flow are presented. These are applicable to this finite element method as well as the method of characteristics and finite difference methods. Simulation results are compared against theory and excellent agreement is found.

Tension Leg Platforms (TLPs) are predominately used for deep water oil and gas production. The use of tendons creates a small amplitude, high cyclic response in the vertical plane (heave, roll and pitch). Under these conditions fatigue cracking becomes an important consideration. The amplitude of the vertical motion is minimised by ensuring the natural frequency of the TLP lies above the energetic part of the wave spectrum. However, due to non-linear wave loading effects, it is possible for waves to create an output at their sum-frequency, which may consequently equal the natural frequency of the platform. This phenomenon is more commonly known as ‘springing’. The Volterra method [1] is a technique used to model the behaviour of TLPs under these conditions. This approach quantifies the linear and non-linear (quadratic, cubic, etc) responses separately using transfer functions, which are determined from the input and output of the system. In this paper an orthogonalised Volterra series for use with both Gaussian and non-Gaussian input data is presented. The data used in the Volterra modelling was collected from tests conducted on a model TLP. The wave height and platform motion were measured at wave frequencies around one, a half and a third of the model’s heave natural frequencies. Both regular and irregular wave tests were performed to varying wave heights and frequencies. Using the Volterra method, the transfer functions were calculated up to the third order. Difficulties encountered due to the use of discrete data were identified and where possible their effects minimized. The results demonstrate clear evidence of springing, with dynamic amplification present at sum-frequencies close to the natural frequency of the platform for the non-linear responses.

Transfer functions are useful tools in observing the behaviour of non-linear systems. Transfer functions convert an input signal into an output signal, and for non-linear systems can be calculated separately for each order of response using the Volterra series. The Volterra series quantifies the linear and non-linear responses separately for systems with either Gaussian or non-Gaussian inputs, and is particularly useful when calculating transfer functions from experimental data, as the calculations can be performed using a discrete frequency domain format. The application of the Volterra series to discrete experimental data requires careful consideration of various factors that impact ANZIAM J. 46 (E) ppC572-C587, 2005C573 on the successful calculation of transfer functions. The single largest problem faced when using discrete experimental data is the difficultly presented when determining the optimal sample length of the data adopted during the calculation process. Equal lengths of sample data are extracted from each individual record to calculate averaged input and output spectra. When using experimental data of finite record length, a trade off between the number of sample lengths obtained from each record and the frequency interval of the resulting transfer functions occurs. Here we explore those factors that lead to the selection of an optimal sample length. We begin with an overview of the Volterra series approach, and how experimental data can be used to calculate transfer functions. The factors that influence the selection of the optimal sample length are described and methods outlined that ensure the most meaningful results are obtained. We demonstrate these methods using the results from an experimental procedure performed on a model Tension Leg Platform.