On the Permissibility of Approximating Irregular Cavity Geometries by Rectangular Boxes and Cylinders

A general procedure for the three dimensional analysis of a gas cavity by the concept of four pole parameters has been developed by Kim and Soedel [1]; the procedure was later extended by Lai and Soedel [2] to two dimensional analysis, which is more efficient in computation than the 3~D analysis method and can solve some geometries which are difficult to solve by the 3-D method. In this study, the above procedures are applied to a realistic compressor head with irregular corners, flow obstacles, and a bullet shaped muffler by idealized rectangular box and circular cylinder approximations. The experimental tests are performed, discussed in this paper, and compared to the simulation results. The comparisons demonstrate the limitations of an overly idealized theoretical shape analysis for practical applications. Certain response frequencies which shift between idealized theory and experimental data are traced to certain acoustic path constrictions in the compressor head and the muffier which result in a geometric deviation from the idealized box and bullet shapes. It is concluded that while idealized shape approximations are useful for a qualitative understanding of gas pulsation muffiing behavior, precise geometric modeling is needed for precise predictions. Or one has to rely on transfer function measurements. ANALYTICAL MODELS Four pole parameters are very useful for the analysis of acoustic systems. Basic discussions of the concept and derivation of four poles of various acoustic elements are found in references [3, 4, 5, 6]. A gas cavity can be represented by the following format: (1) where Q1, P1 are the input volume velocity and acoustic pressure, Q 2, P2 are the output volume velocity and acoustic pressure. A, B, C, Dare the so~called four pole parameters. Compressor Head For the compressor head as shown in Figure 1, the 2-D model [2, 7] can be applied since the thickness is very small compared to the shortest wavelength of interest. Therefore, the four poles can be obtained: A h(r2,w) (2) !1(r2,w)' B 1 f1(r2,w)' (3) c f: C ) fl(h,w) f: C ) (4) 2 r1, w + f C ) 2 r2, w , 1 r2,w D fl(h,w) (5) /1(r2,w)'