Gas-filled spherical resonators: Theory and experiment

Gas-filled spherical resonators are excellent tools for routine measurement of thermophysical properties. The radially symmetric gas resonances are nondegenerate and have high Q’s (typically 2000–10 000). Thus they can be used with very simple instrumentation to measure the speed of sound in a gas with an accuracy of 0.02%. We have made a detailed study of a prototype resonator filled with argon (0.1–1.0 MPa) at 300 K, with the objective of discovering those phenomena which must be understood to use gas-filled spherical resonators to measure the thermodynamic temperature and the universal gas constant R. The resonance frequencies fN and half-widths gN were measured for nine radially symmetric modes and nine triply-degenerate nonradial modes with a precision near 10−7 fN. The data were used to develop and test theoretical models for this geometrically simple oscillating system. The basic model treats the following phenomena exactly for the case of a geometrically perfect sphere: (1) the thermal boundary layer near the resonator wall, (2) the viscous boundary layer (for nonradial modes), (3) bulk dissipation, and (4) the coupling of shell motion and gas motion. In addition, the following phenomena are included in the model through the use of perturbation theory: (5) ducts through the shell, (6) imperfect resonator geometry, and (7) the seam where the two hemispheres comprising the shell are joined. Some estimates of the effects of (8) roughness of the interior of the shell have also been made. Much of the lower pressure fN and gN data can be explained by our model of these phenomena to within ±5×10−6 fN when a single parameter c0/(V0)1/3 is fit to a single resonance frequency at a single pressure. In this parameter, c0 is the ideal-gas speed of sound and V0 is the resonator volume. If this volume were known, the prototype resonator could be used to measure the speed of sound of a gas with an accuracy approaching ±0.0005%. Improvements in resonator design which will circumvent difficulties discovered in this work are expected to lead to much better agreement between theory and the measured fN and gN.