0
Research Papers: Techniques and Procedures

# Mathematical Modeling of Pneumatic Pipes in a Simulation of Heterogeneous Engineering Systems

[+] Author and Article Information
Zbigniew Kamiński

Faculty of Mechanical Engineering,  Bialystok University of Technology, ul. Wiejska 45C, 15-351 Bialystok, Polandz.kaminski@pb.edu.pl

J. Fluids Eng 133(12), 121401 (Dec 23, 2011) (7 pages) doi:10.1115/1.4005261 History: Received March 10, 2011; Revised October 04, 2011; Published December 23, 2011; Online December 23, 2011

## Abstract

Pipes are widely used in hydraulic and pneumatic subsystems for transferring energy or signals. Accurate prediction of pressure transients is very important in the drive and control circuits of complex fluid-line systems. Based on the approximation of Navier-Stokes equations for one-dimensional flow, a mathematical model of the pneumatic pipe with lumped parameters was developed using ordinary differential equations, which can be easily implemented in most computer programs for the simulation of complex heterogeneous engineering systems. Implemented in Matlab-Simulink software, the computer model of the pipe makes it possible to determine the influence of capacitance, inertance, resistance and heat exchange on the dynamic characteristics of the control and power circuits of pneumatic systems. An advantage of the model is that various functions can be selected to describe linear resistances and local resistances are taken into account, particularly at the inlet and outlet. Such resistances largely affect flow resistances in short tubes (up to 10 m) that can be found, e.g., in pneumatic brake systems of road vehicles. Confirmed by Kolmogorov-Smirnov test results, the consistency of the pressure curves obtained in experimental and simulation tests proves the implemented tube model to be useful for the calculations of pneumatic system dynamics.

<>

## Figures

Figure 1

Tube section parameters

Figure 2

Physical model of the pipe

Figure 3

Schematic diagram of the pneumatic power system: 1, 2 – tube, 3 – compressed air source, 4 – cut-off valve, 5, 6, 7 – tank, 8 – divider

Figure 4

Model of the tested pneumatic power system in Matlab-Simulink software

Figure 5

The simulation (continuous lines) and experimental (dotted lines) test results of the pneumatic system shown in Fig. 3 for L1  = 10 m and L2  = 5 m: (a) time curves of pressure and temperature in individual tanks: p1 and T1 in V5 , p2 and T2 in V6 , p3 and T3 in V7 ; (b) time curves of mass flows: m'11 – from tank V5 , m'12 – from tank V6 , m'21 – from tank V6 , m'22 – from tank V7 ; test results: p1  − h = 0, ks2 = 0.1782, R2   = 0.999; p2  − h = 0, ks2 = 0.0693, R2   = 0.987; p3  − h = 0, ks2 = 0.0693, R2   = 0.998

Figure 6

The simulation (continuous lines) and experimental (dotted lines) test results of the pneumatic system shown in Fig. 3 for L1  = 10 m and L2  = 15 m: (a) time curves of pressure and temperature in individual tanks: p1 and T1 in V5 , p2 and T2 in V6 , p3 and T3 in V7 ; (b) time curves of mass flows: m'11 – from tank V5 , m'12 – from tank V6 , m'21 – from tank V6 , m'22 – from tank V7 ; statistical test results: p1 h = 0, ks2 = 0.1089, R2   = 0.999; p2  − h = 0, ks2 = 0.1287, R2   = 0.964; p3  − h = 0, ks2 = 0.1287, R2   = 0.998

## 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 Proceedings Articles
Related eBook Content
Topic Collections