This content is not included in your SAE MOBILUS subscription, or you are not logged in.
A 1D Real-Time Engine Manifold Gas Dynamics Model Using Orthogonal Collocation Coupled with the Method of Characteristics
ISSN: 0148-7191, e-ISSN: 2688-3627
Published April 02, 2019 by SAE International in United States
This content contains downloadable datasetsAnnotation ability available
In this paper, a new solution method is presented to study the effect of wave propagation in engine manifolds, which includes solving one-dimensional models for compressible flow of air. Velocity, pressure, and density profiles are found by solving a system of non-linear Partial Differential Equations (PDEs) in space and time derived from Euler’s equations. The 1D model includes frictional losses, area change, and heat transfer. The solution is traditionally found by utilizing the Method of Characteristics and applying finite difference solutions to the resulting system of ordinary differential equations (ODEs) over a discretized grid. In this work, orthogonal collocation is used to solve the system of ODEs that is defined along the characteristic curves. Orthogonal polynomials are utilized to approximate velocity, pressure, sound speed, and the characteristic curves along which the system of PDEs reduce to a system of ODEs. The approximation polynomials are defined over the whole manifold domain, transforming Euler’s equations into a system of ODEs that can be solved using a generic ODE solver. This reduction is done symbolically using a computer algebra system (Maple). The method results in a system of ODEs that has a higher spatial order along the whole space compared to methods based on finite differences, reducing the number of nodes required to find an acceptable solution that captures the state dynamics at different locations inside the manifold in real time. The proposed model is compared against the Method of Characteristics (MOC) that is used as a reference model; this comparison includes the states at the inlet, outlet, and midpoint. In summary, a high order method that can calculate solutions of the 1D manifold model equations is developed by finding the respective polynomial approximations along the 1D space and solving the resultant system using a generic solver in real time.
CitationKeblawi, A. and McPhee, J., "A 1D Real-Time Engine Manifold Gas Dynamics Model Using Orthogonal Collocation Coupled with the Method of Characteristics," SAE Technical Paper 2019-01-0190, 2019, https://doi.org/10.4271/2019-01-0190.
Data Sets - Support Documents
|[Unnamed Dataset 1]|
- Benson, S.R., The Thermodynamics and Gas Dynamics of Internal-Combustion Engines (Oxford: Clarendon Press, 1982).
- Boyd, J.P., Chebyshev and Fourier Spectral Methods (Dover Publications, Inc, 2000).
- Cavina, N., Migliore, F., Carmignani, L., and Di Palma, S., “Development of a Control-Oriented Engine Model Including Wave Action Effects,” SAE Technical Paper 2009-24-0107, 2009, doi:10.4271/2009-24-0107.
- Cipollone, R. and Sciarretta, A., “The Quasi-Propagatory Model: A New Approach for Describing Transient Phenomena in Engine Manifolds,” SAE Technical Paper 2001-01-0579, 2001, doi:10.4271/2001-01-0579.
- Courant, R., Isaacson, E., and Rees, M., “On the Solution of Non-Linear Hyperbolic Differential Equations by Finite Differences,” Communications of Pure and Applied Mathematics 243-255, 1952.
- Hassanpour, S. and McPhee, J.M., “A Control-Oriented Modular One-Dimensional Model for Wall-Flow Diesel Particulate Filters,” International Journal of Engine Research 19(3):329-346, 2018.
- Jenny, E., “Unidimensional Transient Flows with Consideration of Friction and Change of Section,” Brown Boveri Rev. 37:447-461, 1950.
- Keblawi, A., Hassanpour, S., and McPhee, J., “A Reduced Control-Oriented Model for Quasi One Dimensional Flow in Area Varying Channels,” in Proceedings of the 24th International Congress of Theoretical and Apllied Mechanics, Montreal, QC, Canada, 2016.
- Lax, P.D. and Wendroff, B., “Systems of Conservation Laws,” Communications on Pure and Applied Mathematics 217-237, May 1960.
- Payri, F., Corberan, J.M., and Boada, F., “Modifications to the Method of Characteristics for the Analysis of the Gas Exchange Process in Internal Combustion Engines,” Journal of Automobile Engineering 10:259-266, 1986.
- Pearson, R.J. and Winterbone, D.E., “A Rapid Wave Action Simulation Technique for Intake Manifold Design,” SAE Technical Paper 900676, 1990, doi:10.4271/900676.
- Shapiro, A.H., The Dynamics and Thermodynamics of Compressible Fluid Flow (The Ronald Press Company, 1954).
- Stockar, S., Canove, M., Guezennec, Y., and Della, A., “Modeling Wave Action Effects in Internal Combustion Engine Air Path Systems: Comparison between Numerical and System Dynamics Approaches,” International Journal of Engine Research 391-408, 2012.
- Zhang, G. and Assanis, D.N., “Manifold Gas Dynamics Modeling and Its Coupling with Single-Cylinder Engine Models Using Simulink,” Journal of Engineering for Gas Turbines and Power 563-571, 2003.