VM-WB-MECH-100
VM-WB-MECH-100
3-D Acoustic Modal Analysis with Temperature Change
Overview
| Reference: | Oberg, C. L., Ryan, N. W., & Baer, A. D. (1968). A study of T-burner behavior. AIAA Journal, 6(6), 1131-1137. |
| Solver(s): |
Ansys Mechanical |
| Analysis Type(s): | Modal Analysis |
| Element Type(s): | Solid |
Test Case
A cylindrical region (single-ended T-burner) is filled with propellant. The temperature distribution in the propellant is discontinuous, where 31% of the length is occupied by "cool" gas, with the remaining volume filled with "hot" gas. Determine the ratio of the amplitudes of pressure at the two ends of the T-burner.
This problem is also presented in VM157 in the Mechanical APDL Verification Manual.
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Analysis Assumptions and Modeling Notes
The T-burner is represented as a cylindrical volume. The cool gas occupies 31% of the length at 440.3 °F, while the hot gas of 4040.3 °F occupies the remaining volume. The first non-zero mode is of interest, and the mode is essentially 1-D in nature. Using the ideal gas relationship, the ratio of the temperatures can be used to determine the ratio of the speed of sound and density:
The temperature is applied in the cool and hot regions with a discontinuity at 31% of the length. Based on the reference, the relative amplitude at the hot end should be 0.45.