Research Papers

A Lumped-Parameter Modeling Methodology for One-Dimensional Hyperbolic Partial Differential Equations Describing Nonlinear Wave Propagation in Fluids

[+] Author and Article Information
Stephanie Stockar

Department of Mechanical
and Aerospace Engineering,
Center for Automotive Research,
The Ohio State University,
Columbus, OH 43212
e-mail: stockar.1@osu.edu

Marcello Canova, Giorgio Rizzoni

Department of Mechanical
and Aerospace Engineering,
Center for Automotive Research,
The Ohio State University,
Columbus, OH 43212

Yann Guezennec

Department of Mechanical
and Aerospace Engineering,
Center for Automotive Research,
The Ohio State University,
Columbus, OH 43212

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received February 4, 2013; final manuscript received June 24, 2014; published online August 28, 2014. Assoc. Editor: Yang Shi.

J. Dyn. Sys., Meas., Control 137(1), 011002 (Aug 28, 2014) (11 pages) Paper No: DS-13-1059; doi: 10.1115/1.4027924 History: Received February 04, 2013; Revised June 24, 2014

Modeling the transient response of compressible fluid systems using dynamic systems theory is relevant to various engineering fields, such as gas pipelines, compressors, or internal combustion engines. Many applications, for instance, real-time simulation tools, system optimization, estimation and control would greatly benefit from the availability of predictive models with high fidelity and low calibration requirements. This paper presents a novel approach for the solution of the nonlinear partial differential equations (PDEs) describing unsteady flows in compressible fluid systems. A systematic methodology is developed to operate model-order reduction of distributed-parameter systems described by hyperbolic PDEs. The result is a low-order dynamic system, in the form of ordinary differential equations (ODEs), which enables one to apply feedback control or observer design techniques. The paper combines an integral representation of the conservation laws with a projection based onto a set of eigenfunctions, which capture and solve the spatially dependent nature of the system separately from its time evolution. The resulting model, being directly derived from the conservation laws, leads to high prediction accuracy and virtually no calibration requirements. The methodology is demonstrated in this paper with reference to classic linear and nonlinear problems for compressible fluids, and validated against analytical solutions.

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Grahic Jump Location
Fig. 1

Schematic representation of one-dimensional control volume

Grahic Jump Location
Fig. 2

Schematic representation of a staggered grid

Grahic Jump Location
Fig. 5

Sensitivity of the frequency resolution to number of lumps and SBF order

Grahic Jump Location
Fig. 7

Effect of the mesh size on the accuracy and prediction ability of the model (quadratic SBF)

Grahic Jump Location
Fig. 4

Comparison between analytical and ROM solution

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Fig. 6

Distribution of the flow variables in the shock tube

Grahic Jump Location
Fig. 3

Schematic of straight pipe with the orifice termination



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