VM157

VM157
3D Acoustic Modal Analysis with Temperature Change

Overview

Reference: C.L. Oberg, N.W. Ryan, A.D. Baer. “A Study of T-Burner Behavior”. AIAA Journal. Vol. 6, No. 6. 1131-1137.
Analysis Type(s):
Modal Analysis (ANTYPE = 2)
Element Type(s): 3D 8-Node Acoustic Fluid (FLUID30)
Input Listing: vm157.dat

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 and the rest is the “hot” gas. Determine the ratio of the amplitudes of pressure at the two ends of the T-burner.

Material PropertiesGeometric PropertiesLoading

Cool Gas:

ρc=1.1e-7 lbf s2 / in4
cc=13200 in/s2

Hot Gas:

ρh=2.2e-8 lbf s2 / in4
ch=29516 in/s2
Reference Pressure = 14.7 psi

R = 1.5 inches

L = 9 inches

Tc = 440.33 F

Th = 4040.33 F

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 is in the remainder. The first non-zero mode is of interest, and the mode is essentially 1D 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.

Results Comparison

TargetMechanical APDLRatio
Ratio of Hot/Cold Amplitude 0.4500.4471.007