Gas Pulsations in Thin, Curved or Flat Cavities due to Multiple Mass Flow Sources

If compressor manifolds are thin compared to the shortest wavel~ngth of i:r:tt~rest, the gene!al procedure developed by the authors [1, 2] for the analysis of curved, t~l? gas cav1hes can be apphed to the analysis of gas pulsations in multi-cylinder compres~?r head cav1t1es. The procedure for smgle input single output systems is extended to systems of multl-mputs. Four pole parameters and transfer functions for each input/output set are obtained separately. The pressu~e response at the output port excited by each input is calculated by multiplying the input volume velocity from each compressor valve with the cooresponding transfer functions. The total pressure response is obtained by superposition of the pressure response excited by each input. A rectangular box type compressor head cavity with refrigerant discharged from a two-cylinder compressor is analyzed as an application example. INTRODUCTION Four pole parameters are very useful for the analysis of composite acoustic systems and have been widely used in gas pulsations in cavities, sound propagation in porous media, and sound transmission in stiff panels and resistive screens. Basic discussions of the concept and derivation of four poles of some acoustic elements are found in references [3, 4, 5, 6]. A general formulation of four pole parameters for gas pulsations in thin, flat shell or plate like muffier elements, which can utilize limited narrow spaces, has been developed by the authors [1, 2]. In this study, this formulation is applied to cases of multiple inputs following the superposition schemes reported by Singh [7] and Kim [8]. The above procedure can be utilized in the analysis of gas pulsations in compressor or engine manifolds with thin head geometries. Specifically, a flat rectangular compressor head cavity with refrigerant discharged from a two-cylinder compressor is analyzed as an application example. The ability to analyze gas pulsations in compressor head cavities and manifolds is important since pulsations excite structural vibrations and also travel to the condenser where they become a major noise source. Soedel et al. [9] presented a simulation model for the discharge cavity and plenum chamber pressures of a two cylinder compressor. The discharge system was described as a multi-degree-of-freedom Helmholtz resonator. It was later extended to multi-cylinder compressor manifolds by Soedel and Baum [10, 11], and a four cylinder compressor was analyzed as an application example. Singh and Soedel [7, 12] derived the four pole parameters of a two-cylinder compressor discharge system by the lumped model approach and investigate the fluid interaction of each discharge plenum. The plenums were connected to each other by a common gas collection cavity. Kim and Soedel [8, 13] extended this work to the analysis of multi-cylinder compressors using a distributed modeling approach, since the lumped model is only valid if the largest gas cavity dimension is small enough compared to the shortest wavelength of interest. The multi-cylinder compressors investigated in the past generally consist of a discharge plenum attached to each cylinder and a common gas collection cavity connecting all the discharge plenums and discharging the gas through the exhaust pipe to the condenser. Sometimes, this design is unnecessarily complicated. A typical design by one compressor company uses only one flat, thin common gas collection cavity attached to both cylinders. The refrigerant is discharged directly into the common gas cavity from both cylinder valves without passing through any discharge restrictions or plenums. The advantage of this design is easy manufacturing and efficient utilization of narrow spaces. However, at least to the knowledge of the authors, a theoretical two dimensional analysis of these types of compressor manifolds has not been done. The three dimensional analysis by Kim and Soedel [14] can in principle handle these cases also, but while the three dimensional analysis has the advantage that it does not rely on a "thin" wave guide assumption, it is by nature more cumbersome.