"Analysis of acoustic scattering in ducts of continuously varying cross section, when compressible potential flow is passed through it, is of importance in many applications. It is the purpose of this study to develop the circular duct and the one dimensional finite element models for different ducts and to study their relative acoustic scattering characteristics.
Both finite element models are developed using similar formulation techniques. The equations of motion for circular duct model are re-formulated for the one dimensional model to take the local area into account. A velocity potential formulation is used. The code developed for evaluating the velocity potential for both models uses an LU decomposition linear equation solver. A convergence test is designed for the iterative solution of the flow code to get a user-defined level of accuracy between successive iterations.
The sound source at the source plane for both models is taken as a combination of positive and negative propagating modes (in the one dimensional model, however, there is only one positive and negative propagating mode). A hybrid finite element technique is developed which has modal degrees of freedom for the nodes located at the source and the exit planes and nodal degrees of freedom at the interior nodes.
The range of validity of results, in terms of the power transmission coefficient, is determined for one dimensional model and compared to the circular duct model for different duct profiles, their contraction ratios, steady flow mach numbers and for a range of source frequency spanning from plane wave to multi-mode propagation. Both models are compared with an established approximate analytical solution to determine their correctness"--Abstract, page iii.
Grow, David E.
Avula, Xavier J. R.
Mechanical and Aerospace Engineering
M.S. in Mechanical Engineering
University of Missouri--Rolla
xv, 120 pages
© 2000 Gurpreet Singh Narula, All rights reserved.
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Narula, Gurpreet Singh, "Acoustic analysis of a duct of varying cross section with steady flow in one dimension using finite element methods and its comparison with circular duct analysis" (2000). Masters Theses. 1870.
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