Reduced Order Modeling of Natural Gas Transient Flow in Pipelines
A reduced order modeling approach for natural
gas transient flow in pipelines is presented. The Euler
equations are considered as the governing equations and
solved numerically using the implicit Steger-Warming flux
vector splitting method. Next, the linearized form of the
equations is derived and the corresponding eigensystem is
obtained. Then, a few dominant flow eigenmodes are used to
construct an efficient reduced-order model. A well-known test
case is presented to demonstrate the accuracy and the
computational efficiency of the proposed method. The results
obtained are in good agreement with those of the direct
numerical method and field data. Moreover, it is shown that
the present reduced-order model is more efficient than the
conventional numerical techniques for transient flow analysis
of natural gas in pipelines.
[1] E. Tentis, D. Margaris, D. Papanikas, "Transient gas flow simulation
using an Adaptive Method of Lines", C. R. Mecanique, Vol. 331, 2003,
pp. 481-487.
[2] W. Yow, "Analysis and Control of Transient Flow in Natural Gas Piping
Systems", Ph.D. Thesis, The University of Michigan, 1971.
[3] H. H. Rachford and T.A. Dupont , "A Fast Highly Accurate Means of
modeling Transient Flow in Gas Pipelines by Variational Methods",
Society of Petroleum Engineers Journal, 1974, pp. 356-362.
[4] E. B. Wylie, M. A. Stoner and V. L. Streeter, "Network System
Transient Calculations by Implicit Methods" Society of Petroleum
Engineers Journal, Dec., 1971, pp. 356-362.
[5] J. Zhou and M. A. Adewumi, "Simulation of Transient Flow in Natural
Gas Pipelines", 27th Annual Meeting Pipeline Simulation Interest Group
(PSIG), Albuquerque, New Mexico, Oct. 18-20, 1995.
[6] E. H. Dowell, "Eigenmode Analysis in Unsteady Aerodynamics:
Reduced-Order Models", AIAA Journl, Vol. 34, No. 8, August 1996, pp.
1578-1583.
[7] M. C. Romanowski and E. H Dowell, "Using Eigenmodes to Forms an
Efficient Euler Based Unsteady Aerodynamics Analysis" Proceeding of
the Special Symposium on Aeroelasticity and Fluid/Structure Interaction
Problems, ASME International Mechanical Engineering Congress and
Exposition, Chicago Illions, AD-Vol. 44, 1994, pp. 147-160.
[8] K. C. Hall, R. Florea and P. J. Lanzkorn, "A Reduced Order Model of
Unsteady Flows in Turbomachinary", American Society of Mechanical
Engineers, ASME Paper 94-GT-291, June 1994.
[9] K. C. Hall, "Eigenanalysis of Unsteady Flows About Airfoils, Cascade
and Wings", AIAA Journal, Vol. 32, No. 12, 1994, pp. 2426-2432.
[10] E. H. Dowell and M. C. Romanowski, "Eigenmode Analysis in
Unsteady Aerodynamics: Reduced-Order Models", Appl .Mech. Rev.,
Vol. 50, No. 6, 1997, pp. 371-385.
[11] V. Esfahanian and M. Behbahani-Nejad, "Reduced Order Modeling of
Unsteady flows about Complex Configurations Using the Boundary
Element Method" , J. Fluid Eng-T ASME, Vol. 124, 2002, pp. 988-993.
[12] H. Shahverdi, A. S. Nobari, M. Behbahani-Nejad, H. Haddadpour, "An
efficient reduced-order modelling approach based on fluid eigenmodes
and boundary element method", Journal of Fluids and Structures, Vol.
23, 2006, pp. 143-153.
[13] K. C. Hall, R. Florea and P. J. Lanzkorn, "A Reduced Order Model of
Unsteady Flows in Turbomachinary", AIAA Journal Vol. 117, No. 3,
1995, pp. 375-383.
[14] R. Florea, K. C. Hall and G. A. Cizmas, "Reduced Order Modeling of
Unsteady Viscous Flow in a Compressor Cascade", AIAA Journal, Vol.
36, No. 6, 1998, pp. 1039-1048.
[15] A. K. Hoffman, S. T. Chiang, "Computational Fluid Dynamics For
Engineers", Wichita, Kansas, 2000.
[16] T. D. Taylor, N. E. Wood, J. E. Power, "A Computer Simulation of Gas
Flow in Long Pipelines", Soc. Pet. Eng, Trans, AIME, Vol. 225, 1962,
pp. 297-302.
[17] M. Behbahani-Nejad, H. Hadadpour, V. Esfahanian, "Reduced-Order
Modeling of Unsteady Flows without Static Correction Requirement", J.
of Aircraft, Vol. 42, No. 4, 2005.
[1] E. Tentis, D. Margaris, D. Papanikas, "Transient gas flow simulation
using an Adaptive Method of Lines", C. R. Mecanique, Vol. 331, 2003,
pp. 481-487.
[2] W. Yow, "Analysis and Control of Transient Flow in Natural Gas Piping
Systems", Ph.D. Thesis, The University of Michigan, 1971.
[3] H. H. Rachford and T.A. Dupont , "A Fast Highly Accurate Means of
modeling Transient Flow in Gas Pipelines by Variational Methods",
Society of Petroleum Engineers Journal, 1974, pp. 356-362.
[4] E. B. Wylie, M. A. Stoner and V. L. Streeter, "Network System
Transient Calculations by Implicit Methods" Society of Petroleum
Engineers Journal, Dec., 1971, pp. 356-362.
[5] J. Zhou and M. A. Adewumi, "Simulation of Transient Flow in Natural
Gas Pipelines", 27th Annual Meeting Pipeline Simulation Interest Group
(PSIG), Albuquerque, New Mexico, Oct. 18-20, 1995.
[6] E. H. Dowell, "Eigenmode Analysis in Unsteady Aerodynamics:
Reduced-Order Models", AIAA Journl, Vol. 34, No. 8, August 1996, pp.
1578-1583.
[7] M. C. Romanowski and E. H Dowell, "Using Eigenmodes to Forms an
Efficient Euler Based Unsteady Aerodynamics Analysis" Proceeding of
the Special Symposium on Aeroelasticity and Fluid/Structure Interaction
Problems, ASME International Mechanical Engineering Congress and
Exposition, Chicago Illions, AD-Vol. 44, 1994, pp. 147-160.
[8] K. C. Hall, R. Florea and P. J. Lanzkorn, "A Reduced Order Model of
Unsteady Flows in Turbomachinary", American Society of Mechanical
Engineers, ASME Paper 94-GT-291, June 1994.
[9] K. C. Hall, "Eigenanalysis of Unsteady Flows About Airfoils, Cascade
and Wings", AIAA Journal, Vol. 32, No. 12, 1994, pp. 2426-2432.
[10] E. H. Dowell and M. C. Romanowski, "Eigenmode Analysis in
Unsteady Aerodynamics: Reduced-Order Models", Appl .Mech. Rev.,
Vol. 50, No. 6, 1997, pp. 371-385.
[11] V. Esfahanian and M. Behbahani-Nejad, "Reduced Order Modeling of
Unsteady flows about Complex Configurations Using the Boundary
Element Method" , J. Fluid Eng-T ASME, Vol. 124, 2002, pp. 988-993.
[12] H. Shahverdi, A. S. Nobari, M. Behbahani-Nejad, H. Haddadpour, "An
efficient reduced-order modelling approach based on fluid eigenmodes
and boundary element method", Journal of Fluids and Structures, Vol.
23, 2006, pp. 143-153.
[13] K. C. Hall, R. Florea and P. J. Lanzkorn, "A Reduced Order Model of
Unsteady Flows in Turbomachinary", AIAA Journal Vol. 117, No. 3,
1995, pp. 375-383.
[14] R. Florea, K. C. Hall and G. A. Cizmas, "Reduced Order Modeling of
Unsteady Viscous Flow in a Compressor Cascade", AIAA Journal, Vol.
36, No. 6, 1998, pp. 1039-1048.
[15] A. K. Hoffman, S. T. Chiang, "Computational Fluid Dynamics For
Engineers", Wichita, Kansas, 2000.
[16] T. D. Taylor, N. E. Wood, J. E. Power, "A Computer Simulation of Gas
Flow in Long Pipelines", Soc. Pet. Eng, Trans, AIME, Vol. 225, 1962,
pp. 297-302.
[17] M. Behbahani-Nejad, H. Hadadpour, V. Esfahanian, "Reduced-Order
Modeling of Unsteady Flows without Static Correction Requirement", J.
of Aircraft, Vol. 42, No. 4, 2005.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:60558", author = "M. Behbahani-Nejad and Y. Shekari", title = "Reduced Order Modeling of Natural Gas Transient Flow in Pipelines", abstract = "A reduced order modeling approach for natural
gas transient flow in pipelines is presented. The Euler
equations are considered as the governing equations and
solved numerically using the implicit Steger-Warming flux
vector splitting method. Next, the linearized form of the
equations is derived and the corresponding eigensystem is
obtained. Then, a few dominant flow eigenmodes are used to
construct an efficient reduced-order model. A well-known test
case is presented to demonstrate the accuracy and the
computational efficiency of the proposed method. The results
obtained are in good agreement with those of the direct
numerical method and field data. Moreover, it is shown that
the present reduced-order model is more efficient than the
conventional numerical techniques for transient flow analysis
of natural gas in pipelines.", keywords = "Eigenmode, Natural Gas, Reduced Order Modeling,
Transient Flow.", volume = "2", number = "7", pages = "932-5", }