ABSTRACT
A good example of a complex fluid system22 in which impedance measurements have been found useful is shown in Fig. 4-26. The system under study is a boiler using as the working fluid Freon (a refrigeration fluid widely used at the time of the reference but now outlawed to protect the earth's ozone layer). Since in a boiler the working fluid enters as a liquid and leaves as a gas (vapor), the flow situation (called two-phase flow) is quite complex and difficult to analyze. Accurate dynamic performance data on the boiler is needed to properly design the larger thermal power system of which it will be a part, so an experimental fluid impedance study was run. To minimize the effect of nonlinearities, the impedance is taken for small perturbations around an equilibrium operating point. By running several such tests at different operating points, one can explore the degree of nonlinearity. (If all operating points gave exactly the same impedance curves, the system would be perfectly linear.)
The test procedure is to set the flow-control servovalve at some fixed position and establish steady flow. Then the valve is oscillated sinusoidally about the original position, causing a small oscillation of flow rate and, thereby, pressure. (For example, the data of Fig. 4-27 had an equilibrium flow rate of 445lbm/hr and a pressure of 25.5 psia. The flow rate oscillation was set at an amplitude of about 40 lbm/hr; the resulting pressure oscillation amplitude ranged from 0.04 to 0.28 psi.) The flow rate oscillation was measured with a turbine flow meter and the pressure with a piezoelectric pressure tranducer. 23 Measurements were made at 30 frequencies between 0.05 and 4.0 Hz, giving the sinuosidal transfer function of the impedance (P; 1 w;)(iw) as shown in Fig. 4-27. (Note that the flow rate is given as a mass
flow rate rather than our usual volume flow rate, but it can be easily converted if we know the density.) A theoretical model of this system has also been derived and comparison made24 with measured behavior. Good agreement was achieved under some, but not all, operating conditions, showing again the importance of experimental testing in validating theoretical models or revealing their defects so that improvements can be made.
