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The difference between steady state and transient

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Old   February 11, 2015, 10:53
Default The difference between steady state and transient
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I know this is a rookie question to ask: a simple answer is that transient is time dependent and steady state is not.

But delving deeper into this question...

Suppose you had a simple pipe flow problem.

Let's say you perform a transient run, and stop the simulation after 4 simulation seconds, where the centreline velocity is 2 m/s.

If you then performed a steady state simulation, with a small enough physical time step, and implemented a stop control such that the simulation should stop when the centreline velocity is 2 m/s, would the steady state results be the same as the transient ones?

I.e. can you completely bypass the transient solution from 0s to 4s by performing a steady state simulation and applying a stop control when the centreline velocity is 2 m/s?

When we analyse the conservation equations, in steady state the time dependent partial derivatives disappear and we no longer have a time marching problem - I can't see how the two can compare unless you compare a steady state solution achieved by running a transient simulation long enough, and a steady state solution achieved by running a steady state simulation.
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Old   February 11, 2015, 12:07
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Due to the false-transient scheme used by CFX, technically yes, if you use a very small timestep for both the transient (with a first order approach for the time derivative) and the steady state simulation, you should arrive at the same result after the same number of timesteps are run in each. But this also means you're not bypassing the transient solution at all; you're just solving it by other means.

Also, this completely defeats the purpose of running a steady-state simulation, which is to fastly arrive at a time independent solution.
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Old   February 11, 2015, 18:28
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The steady state solver does not include some of the transient terms (I forget which, you will have to look up the doco to find that out). Also the steady state solver can advance different equations with different pseudo-timesteps. This is to make the simulation converge faster, but it does mean the result is not time accurate.

But these neglected terms are not important for all simulations, and the advancing of different equations at different speeds can be stopped by specifying a physical time step. Then a steady state simulation will be pretty close to a transient simulation.
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Old   February 12, 2015, 08:54
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If you use the First Order scheme for the transient equations, there should be no extra terms compared to the steady state equations. It is just

\frac{\partial}{\partial t}\left( \rho \phi \right) \rightarrow \frac{\rho \phi - \rho^0 \phi^0}{\Delta t}

for both.

The only thing missing on the SS solution will be the transient non-linearities corrections (\rho^0 \phi^0) between timesteps, but then again a small enough timestep (one that uses only 1 iteration per transient timestep) should solve this.

Cheers
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Old   February 12, 2015, 10:02
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Thanks for that - it's quite insightful.

So if I understand correctly you're saying you can make a good comparison between stopping a steady state simulation mid way and a transient simulation using first order numerics for the transient scheme?
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Old   February 12, 2015, 13:19
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A steady state simulation with a very small physical timestep, one that would require only one iteration for the transient solver, yes. But again, that basically means running a transient simulation anyway, so there is no gain in here. Quite the other way, actually: a transient simulation with adaptative timestepping would probably be able to arrive much faster at the desired physical time value.

May I ask why do you want to do this?
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Old   February 17, 2015, 13:31
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Hi,

Thanks for your input.

I'm undertaking a project which involves heating a tank of water and modelling the evaporation process from water to vapour. It's an Eulerian-Eulerian simulation, with the interface modelled using the CFX Mixture Model.

I am interested in the results when around 5% of the water in the tank is evaporated.

So far I am running these simulations in transient mode, with a stop control telling the solver to stop the simulation when 5% of the water has evaporated (I implement this by monitoring the absolute pressure at the bottom of the tank and using a conditional if statement [i.e. if abs pressure at the bottom of the tank is less than the abs pressure @ 95% water then stop the sim]).

I wanted to see if I can bypass the long transient runs by implementing a steady state analysis, and stopping the simulation at when 5% has evaporated.

Sorry I should have explained this much earlier.
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Old   February 17, 2015, 16:51
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I would say no. How can you justify the SS solution partway?

The SS solution will want to equilabrate towards a set amount of water evaporation (100% if the tank is open and heat is always on, some other percentage if the tank is closed, etc..). How it gets there is totally not time accurate if you utilize the SS as it should be used (no need to capture the transients).

Like brunoc said, trying to get a time accurate solution from a SS run, is probably not efficient.
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Old   February 17, 2015, 18:11
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This simulation sounds like one where significantly different time scales are relevant. I guess the fluid and/or heating time scale is of the order of seconds, but it takes hours or days to evaporate the tank? If that is the case then running it as a full transient will be slow and not very efficient.

Am I correct in saying you have a fast fluid/thermal time scale and a slow evaporation time scale?
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Old   February 18, 2015, 05:56
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Quote:
Originally Posted by singer1812 View Post
I would say no. How can you justify the SS solution partway?

The SS solution will want to equilabrate towards a set amount of water evaporation (100% if the tank is open and heat is always on, some other percentage if the tank is closed, etc..). How it gets there is totally not time accurate if you utilize the SS as it should be used (no need to capture the transients).
This was my understanding after reading various CFD books and the theory guide. My understanding is that the steady state solver tries to find a steady state solution (in my case the steady state solution is an empty tank where all water is evaporated). As I understand it, the solver doesn't adopt a time marching approach due to the lack of transient terms.

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Originally Posted by ghorrocks View Post
This simulation sounds like one where significantly different time scales are relevant. I guess the fluid and/or heating time scale is of the order of seconds, but it takes hours or days to evaporate the tank? If that is the case then running it as a full transient will be slow and not very efficient.

Am I correct in saying you have a fast fluid/thermal time scale and a slow evaporation time scale?
You are completely correct Glenn. There is a large difference in time scales that are involved. I'm trying to find ways to cheat and get around this. Hence why I questioned the steady state approach in my first post
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Old   February 18, 2015, 06:41
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If there is a big separation in time scales then you should try to uncouple them if this is possible. This is not cheating, this is being smart

If the rate of change of the fluid level is slow then you can do a steady state simulation of the fluid flow and thermal stuff with a fixed fluid level. From this model you can predict the condition at the surface and therefore the evaporation rate. Repeat this at a few fluid surface heights and you have the trend of evaporation rate versus fluid height. Then it is a simple matter of working out the fluid height versus time as a ODE.

This is an example of decoupling the different time scales, and using CFD to get the fast time scales and a simple ODE to get the slower fluid height time scale. And the simulation is a simple series of steady state simulations (real steady state simulations, not weird phoney ones) rather than a single extremely long transient simulation.

You will also find getting accurate results for the long time scale effect is difficult as the convergence criteria are based around the short time scale. Adding imbalances to the convergence criteria will help, but even the small imbalance you are left with will add up over a long time scale to a significant error. If you separate the time scales like I recommend you avoid this problem.
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Old   February 18, 2015, 13:25
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Hi, that's pretty clever!

All of the evaporation occurs at the free surface at the top of the tank. So your method of reducing the level a little bit each time and doing a steady state simulation could work.

The rate of evaporation from the free surface is characterised simply as

\dot{m}=\frac{\dot{q}_{free surface}}{\Delta H_{lg}}

So if I can determine the free surface heat flux for each level then I could derive some sort of relationship (ODE) for the free surface heat flux with water level. Since I know the enthalpy of vaporisation (see steam tables) then I can work out the rates of evaporation.

Is that the kind of direction you were hinting at?
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Old   February 18, 2015, 18:40
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Yes, you got it.
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Old   February 19, 2015, 11:51
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Thanks for the tip. I'll update the thread later to let you know how I get on.
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