The one-port acoustical source in a duct system can be characterized by the source impedance and strength using the linear frequency-domain modeling. It is known that the direct method yields different results from the indirect method, in other words, load method, in measuring the source parameters of many fluid machines. Although the real part of the source impedance is expected to be non-negative, the indirect method comes up with a negative source resistance at some frequencies.
In the first part, this study is focused on the effect of the time-varying nature of fluid machines on the output results of two typical measurement methods: direct and indirect methods. For this purpose, a simplified fluid machine consisting of a reservoir, a valve, and an exhaust pipe is considered as representing a typical periodic, time-varying system and the measurement situations are simulated using the method of characteristics. The equivalent electro-acoustic circuits for such simulations are also analyzed by considering the system as having a linear time-variant source. It is found that the results from the indirect method are quite sensitive to the change of cylinder pressure and/or valve profile, in contrast to those from the direct method. In the indirect method, the source admittance turns out to be predominantly dependent on the valve admittance at the calculation frequency as well as the valve and load admittances at other frequencies. In the direct method, however, the source resistance is always positive and the source admittance depends mainly upon the zeroth order of valve admittance.
In the second part of this study, the source model and measurement techniques are modified in order to evaluate the effect due to nonlinear and periodically time-varying source character as well as the linear property of the reflectivity of in-duct fluid machine source. With the a priori known kinematical information of the source, the types of nonlinear time-variant terms can be presumed by a simple physical model, in which there is practically no restriction on the form of the model. The concept of source impedance can be extendable by introducing the linear frequency response function for each nonlinear or time-variant component. Extending the conventional method and adapting the reverse MI/SO technique, it is possible to develop a direct method that can deal with the nonlinear time-variant source parameters. The proposed direct method has a novel feature that there is no restriction on the probability or spectral natures of the excited sound pressure data. In addition, the indirect method for dealing with the nonlinear time-variant source parameters is also suggested: different loads are applied to the same source and the equations are formulated, which can be solved simultaneously to extract the source parameters. The proposed direct and load methods can utilize the same input data with the conventional linear methods. The present methods are verified by the simulated measurements for simplified fluid machines and applied to measure the nonlinear time-variant characteristics of the blower and compressor sources. It is thought that the proposed method in this study would be useful in predicting the insertion loss or the radiated sound level from intake or exhaust systems of fluid machines.