Abstract

Mathematical Treatment of Exhaus Systems with Acoustic Properties Using Mathlie II. Application

J.Volkmann, R.Schmid, G.Baumann (Department of Mathematical Physics, University of Ulm, Ulm , Germany)

e-mail: volk@physik.uni-ulm.de

The second part of our presentation contains the application of results from the first part to differential equations coming out from the consideration of reacting gas systems. From a physical point of view exhaust systems combine aspects of hydrodynamical or fluiddynamical properties, thermal properties resulting mainly from chemical reactions and the acoustic properties of the pipe system. The designing goals for an exhaust system are determined by optimizing the space, cleaning the exhaust gas and minimizing the noise. To simulate an exhaust system under the restriction of low sound and pollutation output we need an efficient mathematical model and efficient mathematical solution procedures. The basic equations describing the physical properties of an exhaust system are the gasdynamics equations. By using modern group analysis in connection with computer algebra we can apply tools to solve the basic equations analytically. Using the variaty of the friction as an arbitrary function as well as the heat flux we will demonstrate how the algebra and the solution of the equations depends on these terms. In addition we examine the influence of the gas model (ideal or real gas) on the algebra and solutions of the equations. The calculations carried out in our examination are supported by the computer algebra package MathLie [G. Baumann, Symmetry Analysis of Differential Equations using Mathematica, TELOS/Springer (1998)] and agebraic extensions.

Section : 12