A Time-Delay Analog for Thermal-Acoustic Oscillations
Thermal-acoustic oscillations are thermally driven oscillations in low rate and fluid pressure and temperature which sometimes occur in forced convection. The oscillations are sustained and occur at frequencies which can be related to acoustic frequencies. A possible cause of these oscillations are perturbations during heat transfer. Following the perturbation, the flow relaxes toward steady conditions as the disturbance is propagated throughout the system by a pressure wave, traveling at the velocity of sound, and by a slower density wave, traveling at the velocity of the fluid. If there is a controlling downstream restriction, such as an orifice or a valve, the arrival of the slower density perturbation there will again perturb the flow rate, and hence heat transfer. The net effect is a delayed feedback of the perturbation to its source, which can sustain oscillations if the feedback is sufficiently strong. The mechanical analog for this system, which can generate oscillations having the characteristics of Helmholtz resonance, is a damped spring-mass system with the addition of a term that is proportional to displacement at an earlier time. The time delay corresponds to the time required to feed the perturbation back to its source. It will be shown that this analog can account for the qualitative differences in stability limits reported by Hendricks et al.  and by Thurston et al. . It also quantitatively accounts for the departure from acoustic Helmholtz frequencies which the latter authors experimentally observed.
KeywordsStrouhal Number Distribute Parameter System Helmholtz Resonance Cryogenic Engineer Observe Frequency Dependence
Unable to display preview. Download preview PDF.
- 1.R. C. Hendricks, R. W. Graham, Y. Y. Hsu, and R. Friedman, “Experimental Heat-Transfer Results for Cryogenic Hydrogen Flowing in Tubes at Subcritical and Supercritical Pressures to 800 psia,” NASA TN D-3095 (Mar. 1966).Google Scholar
- 2.R. S. Thurston, J. D. Rogers, and V. J. Skoglund, in: Advances in Cryogenic Engineering, Vol. 12, Plenum Press, New York (1967), p. 438.Google Scholar
- 3.N. Zuber, “An Analysis of Thermally Induced Flow Oscillations in the Near-Critical and Supercritical Thermodynamic Region,” NAS8–11422 (May 1966).Google Scholar
- 4.S. J. Bhatt and C. S. Hsu, in: ASME J. of Appl. Meck 33:13 (1966).Google Scholar
- 5.F. J. Sansom and H. E. Petersen, “MIMIC Programming Manual,” USAF Tech. Report SEG-TR-67–31 (July 1967).Google Scholar
- 6.J. C. Friedly, J. L. Manganaro, and P. G. Kroeger, in: Advances in Cryogenic Engineering, Vol. 14, Plenum Press, New York (1969), p. 258.Google Scholar