I am doing numerical analysis of GM type pulse tube cryocooler. Before doing transient analysis, I want to do steady state analysis to get cooling power.
When the PTC system reaches to steady state, the temperature does not change. But what about other parameters like velocity, density? In numerical analysis, to do steady state analysis, we must drop transient term from corresponding equations. In PTC, we have got continuity equation, momentum equation and energy equation for both gas and matrix. My question is, if I start steady state analysis, should I drop transient term of continuity and momentum equation? As per my knowledge, at steady state only temperature remains constant as the system runs but velocity and density can vary as the flow is oscillating. (Please look at governing equations.)
My first impression is that the diffusion term causes a true steady state,
but no answer can be given to the question if no boundary conditions are given.
In practice, often the engineers have an excellent feeling what the answer to such questions should be. (A guideline to set up equations and BCs.)
Hemker is correct that it depends on the physical setup [BCs]. For example, the Benard problem has time independent BCs but can have parameter choices that never reach steady state. If I understand your question correctly, you see temp reaching a steady state but bot velocity? This would be hard to understand since (set dT/dt = 0) a time varying velocity would cause time varying temperature in the energy equation even with dT/dt = 0. The engineers possibly mean that the flow is oscillatory but the temperature is statistically stationary [e.g., heat flux on a wall doesn't vary much]. I think you need to talk to the engineers and dig into the physical problem to make the question much more precise.
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