The computational tools available for prediction of sound propagation through the atmosphere have increased dramatically during the past decade. The numerical techniques include analytical solutions for selected index of refraction profiles, ray trace techniques which include interaction with a complex impedance boundary, a Gaussian beam ray trace algorithm, and more sophisticated approximate solutions to the full wave equation; the fast field program (FFP) and the parabolic equation (PE) solutions. This large array of computational approaches raises questions concerning under what conditions the various approaches are reliable and concerns about possible errors in specific implementations. This paper presents comparisons of predictions from the several models assuming a complex impedance ground and four atmospheric conditions. For the cases studied, it was found that the FFP and PE algorithms agree to within numerical accuracy over the full range of conditions and agree with the analytical solutions where available. Comparisons to ray solutions define regimes where ray approaches can be used. There is no attempt to compare calculated transmission losses to measurements.
A wide-angle parabolic equation (PE) model is presented that is applicable to sound propagation in a steady (nonturbulent) atmosphere overlying a flat, loca, lly reacting ground surface. The numerical accuracy of the PE model is shown by comparing PE calculations to calculations from a "fast-field program" (FFP). For upward refraction, the PE and FFP solutions agree to within 1 dB out to ranges where the sound-pressure levels drop below the accuracy limits of both models. For downward refraction, the PE and FFP agree to within 1 dB except at deep interference minima. Parabolic equation calculations are also compared to measured values of excess attenuation for 15 different combinations of frequencies and ranges. In general, the PE model gives good agreement with the average experimental values. For upward refraction at the highest frequency (630 Hz), however, the PE predicts a strong shadow zone that is not observed in the data.
Cryogenic and high-temperature systems often require compact heat exchangers with a high resistance to axial conduction in order to control the heat transfer induced by axial temperature differences. One attractive design for such applications is a perforated plate heat exchanger that utilizes high conductivity perforated plates to provide the stream-to-stream heat transfer and low conductivity spacers to prevent axial conduction between the perforated plates. This paper presents a numerical model of a perforated plate heat exchanger that accounts for axial conduction, external parasitic heat loads, variable fluid and material properties, and conduction to and from the ends of the heat exchanger. The numerical model is validated by experimentally testing several perforated plate heat exchangers that are fabricated using microelectromechanical systems based manufacturing methods. This type of heat exchanger was investigated for potential use in a cryosurgical probe. One of these heat exchangers included perforated plates with integrated platinum resistance thermometers. These plates provided in situ measurements of the internal temperature distribution in addition to the temperature, pressure, and flow rate measured at the inlet and exit ports of the device. The platinum wires were deposited between the fluid passages on the perforated plate and are used to measure the temperature at the interface between the wall material and the flowing fluid. The experimental testing demonstrates the ability of the numerical model to accurately predict both the overall performance and the internal temperature distribution of perforated plate heat exchangers over a range of geometry and operating conditions. The parameters that were varied include the axial length, temperature range, mass flow rate, and working fluid.
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