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Solving Linearized Euler Equation in frequency space using Weak Form PDE module
Posted 2019年7月26日 GMT-4 22:23 Fluid & Heat, Acoustics & Vibrations, Equation-Based Modeling Version 5.4 0 Replies
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Hi,
I am trying to solve the Linearized Euler Equation (LEE) in frequency space using 'Weak form PDE' module. For 1-D, uniform mean quantity assumptions, the LEE is given by:
Momentum: rho_mean(iomegau+u_meanux)+px = 0 Energy: iomegap+u_meanpx+gammap_mean*ux = 0
If the BCs are rigid at both ends, the first theoretical eigen-frequency is given by:
f1 = c/(2L(1-M^2))
This works perfect when there is no mean flow, i.e, M=0, (eigenfrequency = 1075.7 rad/s with c = 343m/s, L = 1m). However, when I include the mean flow effect (let's say, M=sqrt(10)), it gives a different answer (968.17 rad/s) from the theoretical one (1195.2 rad/s). And their difference from the solution without mean flow is the same:
1075.7/968.17 = 1.1111 1195.2/1075.7 = 1.1111
I guess COMSOL is subtracting something instead of adding it, but not sure exactly.
The attached files contain the ppt that summarized the procedure I took as well as the COMSOL file.
Thanks,
Attachments:
Hello JW Kim
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