0
Research Papers

Comparative Study of Bond Graph Models for Hydraulic Transmission Lines With Transient Flow Dynamics

[+] Author and Article Information
Limin Yang1

 Centre for Ships and Ocean Structures, Norwegian University of Science and Technology, Otto Nielsens vei 10, NO-7491 Trondheim, Norwaylimin.yang@ntnu.no

Jørgen Hals

 Centre for Ships and Ocean Structures, Norwegian University of Science and Technology, Otto Nielsens vei 10, NO-7491 Trondheim, Norwayjorgen.hals@marintek.sintef.no

Torgeir Moan

 Centre for Ships and Ocean Structures, Norwegian University of Science and Technology, Otto Nielsens vei 10, NO-7491 Trondheim, Norwaytorgeir.moan@ntnu.no

1

Corresponding author.

J. Dyn. Sys., Meas., Control 134(3), 031005 (Mar 27, 2012) (13 pages) doi:10.1115/1.4005505 History: Received January 20, 2011; Revised September 30, 2011; Published March 27, 2012; Online March 27, 2012

The partial differential equation describing one-dimensional flow in a hydraulic pipeline with linear resistance can be approximated and solved numerically using different modal approaches. Modal models can be obtained either by using rational transfer functions (RTF) in the Laplace domain solution or by using separation of variables (SOV) techniques. The pipeline models have four possible input–output configurations: pressure inputs at both ends, flow rate inputs at both ends, and the two cases of mixed inputs. In this paper, modal bond graph representations for pipeline sections are reviewed, and new bond graphs are proposed for combinations of solution method and input–output configurations not yet presented in the literature. This includes bond graph representations for the two mixed input cases developed using the SOV technique, and bond graphs for the other two cases, pressure inputs or flow rate inputs, constructed on the basis of RTF solutions. Through numerical simulations of hydraulic single lines, the obtained models are compared to alternative models already established in the literature. It is shown that the modal models developed by the RTF and SOV methods have the same accuracy when the same number of modes is used. For both of these approaches, correction methods to maintain a high accuracy when truncating high-order modes are described, and also adapted to the bond graph form. Finally, simulation results for various line configurations are illustrated.

Copyright © 2012 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 2

Schematic illustration of a fluid transmission line

Grahic Jump Location
Figure 3

Overview of solution methods used to establish bond graph representations of hydraulic transmission lines by considering different causality inputs. The dashed-line frame indicates that for these cases also the mathematical derivation, not only the bond graph representation, is new.

Grahic Jump Location
Figure 4

Bond graph representation found by using separation of variables when pressure inputs are considered [10]. Here, “I,” “C,” “R,” “0,” “1,” and “TF” are standard bond graph elements (see e.g. [15]). The two-port “C”-field “CEQ ” represents an equivalent compliance that corrects for the truncated high frequency modes.

Grahic Jump Location
Figure 5

Bond graph representation found by using separation of variables when flow rate inputs are considered [10]. The “I”-field “IEQ ” is introduced in order to correct for the truncated high frequency modes

Grahic Jump Location
Figure 1

Chart showing different methods for solving the transmission line problem in the time domain

Grahic Jump Location
Figure 6

The bond graph representation of the jth mode for the pipeline with [Pup , Qdown ] as inputs. The coefficient of each element shown in the figure is given in Eqs. 24,26.

Grahic Jump Location
Figure 7

The residual bond graph representation for correcting the error caused by the truncated high frequency modes. In this graph, the fields “CEQ ” and “IEQ ” represent the two-port equivalent capacitive and inertial terms for all high frequencies.

Grahic Jump Location
Figure 8

The bond graph representation of the jth mode for the pipeline with Qup and Pdown as inputs. The coefficient of each element shown in the figure is given in Eqs. 24,26.

Grahic Jump Location
Figure 9

A bond graph representation of the ith mode for the pipeline with [Pup , Qdown ] as inputs derived by use of the rational transfer function approximation method [12]

Grahic Jump Location
Figure 10

The bond graph representation of the ith mode for the pipeline with Pup and Pdown as inputs by using modal approximation method

Grahic Jump Location
Figure 11

Simplified modal bond graph of Fig. 1 for the ith mode

Grahic Jump Location
Figure 12

Modal bond graph for the case when i = 0

Grahic Jump Location
Figure 16

The bond graph representation of the jth mode for eliminating the Gibbs phenomenon with Pup and Qdown as inputs

Grahic Jump Location
Figure 17

Typical pipe line system in pressure transient analysis

Grahic Jump Location
Figure 18

Downstream pressure response due to an upstream ramped pressure input in the pipe system of Fig. 1

Grahic Jump Location
Figure 15

Bond graph for the mode i = 0

Grahic Jump Location
Figure 19

Downstream pressure response due to an upstream ramped pressure input in the pipe system of Fig. 1 by using SOV model. The influence of the truncated high-frequency modes was considered for all the simulation models.

Grahic Jump Location
Figure 20

Modal bond graph by Lebrun [10] for solving the problem of a pipeline with one end blocked as shown in Fig. 1

Grahic Jump Location
Figure 21

Same case as Fig. 1, but using Lebrun’s bond graph model

Grahic Jump Location
Figure 13

The bond graph representation of the ith mode for the pipeline with Qup and Qdown as inputs by using modal approximation method

Grahic Jump Location
Figure 14

Simplified of modal bond graph of Fig. 1 for the ith mode

Grahic Jump Location
Figure 22

Same case as Figs. 1, 1, and 2. Comparison of the three different methods with ten modes included.

Grahic Jump Location
Figure 23

Downstream pressure response due to upstream unit step pressure input in the pipe system of Fig. 1. Two bond graph models, as shown in Figs.  616, were used in the simulation.

Grahic Jump Location
Figure 24

A configuration for testing the dynamic of pipeline with pressures as inputs

Grahic Jump Location
Figure 25

The numerical results of the inlet flow rate by considering the configuration of Fig. 2

Grahic Jump Location
Figure 26

A configuration for the pipeline giving flow–flow boundary conditions

Grahic Jump Location
Figure 27

Top: The pressure pulsations at the upstream side of the pipeline. Bottom: Difference between the two models. The testing configuration of Fig. 2 is employed.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In