This content is not included in
your SAE MOBILUS subscription, or you are not logged in.
Mathematical Modelling of Linear/Non-Linear Wave Reflective Boundaries in Automotive Exhaust Systems
Annotation ability available
Sector:
Language:
English
Abstract
Time-domain numerical modelling of performance for complete engine systems is now routine in most automotive design offices. To achieve this with a minimal computer run-time overhead, drastic simplification of the exhaust silencer box models is required. Complete exhaust systems are often modelled as simple capacitances bounded by orifices. This is justified on the grounds that the influence of exhaust system geometric detail on the engine torque-speed characteristic is less significant than that of the backpressure of the ‘lumped’ system. In contrast to engine performance, acoustic modelling of silencer boxes is usually carried out in the frequency-domain, since this offers a computationally cost-effective means of including very complex internal geometries with minimal computer time overhead. One limitation of these models is the difficulty of characterising the engine as an acoustic source, though empirical methods are often employed.
This paper describes the development of a ‘hybrid’ model in which a frequency-domain silencer box boundary condition is integrated into the MERLIN time-domain engine code. The silencer box is modelled by its frequency dependent reflection and transmission coefficients at each boundary. These are calculated using the LAMPS frequency-domain acoustic model. An engine order-based scheme is used to map the time-domain silencer box boundary into the frequency-domain, and back again, on a once per cycle basis. The model is limited to steady engine speeds only. Predictions of time-pressure histories up and downstream of a silencer box are compared with time-domain measurements. Good agreement in both trend and magnitude is demonstrated.
Recommended Content
| Technical Paper | Study of Intake System Wave Dynamics and Acoustics by Simulation and Experiment |
| Ground Vehicle Standard | Spark Arrester Test Procedure for Medium Size Engines |
| Technical Paper | Numerical Simulation of Exhaust Flows and Tailpipe Noise of a Small Single Cylinder Diesel Engine |
Authors
Citation
Smith, L. and Thurgood, D., "Mathematical Modelling of Linear/Non-Linear Wave Reflective Boundaries in Automotive Exhaust Systems," SAE Technical Paper 970504, 1997, https://doi.org/10.4271/970504.Also In
References
- Banisoleiman, K. “MERLIN User Manual - Release 4.3” Lloyd's Register of Shipping Lloyd's Register House, Croydon, CR0 2AJ, UK
- Peat, K.S. Kelarijani, K.O. “LAMPS User Manual - Release 4.3” Department of Mathematical Sciences, University of Loughborough UK
- Harrison, M.F. “Time and Frequency-Domain Modelling of Vehicle Intake and Exhaust Systems” ISVR Southampton 1994
- Payri, F. Desantes, J.M. Torregrosa, A.J. “Acoustic Boundary Condition for Unsteady One-Dimensional Flow Calculations” J. Sound Vib. 1995 188 85 110
- Watson, N. Marzouk, M. “A Non-Linear Digital Simulation of Turbocharged Diesel Engines Under Transient Conditions” SAE Paper 770123 1977
- Blumberg, P.N. Lavoie, G.A. Tabaczynski, R.J. “Phenomenological Models for Reciprocating Internal Combustion Engines” Prog. Energ. Comust. Sci. 5 1979
- Watson, N. Janota, M.S. “Turbocharging the Internal Combustion Engine” Macmillan Publishers Ltd. 0-333-242290-4 1982
- Borman, G.L. “Mathematical Simulation of Internal Combustion Engine Processes and Performance Including Comparisons with Experiment” University of Wisconsin 1964
- Streit, E.E. “Mathematical Simulation of a Large Pule-Turbocharged Two-Stroke Diesel Engine” University of Wisconsin 1970
- Marzouk, M. “Simulation of Turbocharged Diesel Engines Under Transient Conditions” Imperial College, University of London 1976
- Bazari, Z. “Transient Response of High Output Turbocharged Diesel Engines” Imperial College, University of London 1978
- Shahin, M.A. “Performance of High-Output Turbocharged Vehicle Diesel Engines” Imperial College, University of London 1981
- Benson, R.S. “The Thermodynamics and Gas Dynamics of Internal Combustion Engines - Volume 1” Clarendon Press 0-19-856210-1 1982
- Blair, G.P. Johnston, M.B. “Unsteady Flow Effects in Exhaust Systems of Naturally Aspirated Crankcase Compression Two-Cycle IC Engines” SAE Paper 680594 1968
- Blair, G.P. Arbuckle J.A. “Unsteady Flow in the Induction System of a Reciprocating Internal Combustion Engine” SAE Paper 700443 1970
- Bingham J.F. Blair G.P. “An Improved Branched Pipe Model for Multi-Cylinder Automotive Engine Calculations” Proc. I.Mech.E. 199 1985
- Poloni, M. Winterbone, D.E. Nichols, J.R. “A Comparison of Unsteady Flow Calculations in a Pipe by the Method of Characteristics and the Two-Step Lax-Wendroff Method” Int.J.Mech.Sci. 29 1987
- Onorati, A. Winterbone, D.E. Pearson, R.J. “A comparison of the Two-Step Lax-Wendroff Technique and the Method of Characteristics for Engine Gas Dynamic Calculations Using the Fast Fourier Transform Spectral Analysis” SAE Paper 930428 1993
- Pearson, R.J. “Numerical Methods for Simulating Gas Dynamics in Engine Manifolds” UMIST 1994
- Smith, L.A. Banisoleiman, K. “MERLIN - A Modular approach to Diesel Engine Performance Simulation” Paper D70, 20th International Congress on Combustion Engines CIMAC 1993
- Smith, L.A. Banisoleiman, K. Bazari, Z. French, B.A. “Prediction of Performance and Emissions for a High-Speed DI Diesel Engine with Exhaust Gas Recirculation” IMechE Paper C465/054/93 1993
- Bazari, Z. Smith, L.A. Banisoleiman, K. French, B.A. “An Engineering Building Block Approach to Engine Simulation with Special Reference to New Application Areas” IMechE Paper C499/017/96 1996
- Prasad, M.G. Crocker, M.J. “Studies of Acoustical Performance of a Multi-Cylinder Engine Exhaust Muffler System” J. Sound Vib. 1983 90 491 508
- Davies, P.O.A.L. “Practical Flow Duct Acoustics” J. Sound Vib. 1988 124 1 91 115
- Munjal, M.L. “Acoustics of Ducts and Mufflers” John Wiley & Sons 0-471-84738-0 1987
- Alfredson, R.J. Davies, P.O.A.L. “Performance of Exhaust Silencer Components” J. Sound Vib. 15 2 1971
- Ericksson, L.J. Thwani, P.T. “Theory Practice in Exhaust System Design” SAE Paper 1985
- Callow, G.D. Peat, K.S. “Insertion of Engine Intake and Exhaust Silencers” IMechE C19/88 1988
- Peat K.S. Callow, G.D. Bannister, P.A. “Improving the Acoustic Performance of an Intake Systems” IMechE Paper C420/021 1990
- Matlab Version 4.2c.1 Software The Mathworks, Inc. 24 Prime Park Way, Natick, Mass. 01760-1500
- Burrus, C.S. Parks, T.W. “DFT/FFT and Convolution Algorithms” John Wiley and Sons 0-471-81932-8 1985
- Courant, R. Friedrichs, K. Lewy, H. Math. Ann. 1928 Inst. of Math. Sci., New York Univ. 1956