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How to determine whether flow is steady or unstead 

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October 2, 2006, 02:20 
How to determine whether flow is steady or unstead

#1 
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Dear all,
I have a question about flow state. we all know steady state means flow quantities do not change with time while unsteady one not. If there is no experiment for reference, how could we judge whether the flow is steady or not. In some time, steady solutio can not got by steady alogrithm. Unsteady alogrithm could generate steady solutioin. Any comments are welcome. Maliya 

October 2, 2006, 05:15 
Re: How to determine whether flow is steady or uns

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Dear Maliya,
In a strict sense, no flow can be aprioir judged to be steady or unsteady, when a computation is being performed, unless you have a knowledge of the same from experiments. The right thing to do is to run an unsteady flow solver on the problem, and the result will automatically emerge; either you get a steady converged solution or an unsteady oscillating solution. In fact, all FVM codes solve an unsteady problem, they march to steady state (if you are solving a steady state problem) by some time integration procedure. Hope this helps Regards, Ganesh 

October 2, 2006, 08:34 
Re: How to determine whether flow is steady or uns

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The numerical determination can be difficult. Near the transition from steady to unsteady, convergence can be rather slow. And apparent convergence or not to steady can depend on methods used. One mathematicallymotivated method used by some authors is to generate a quasisteady solution using a steady method. This can be done by a little smoothing of the convective velocity. Then introduce a series of perturbations and integrate in time with an unsteady solver and see if the perturbations grow or die away in time. Unsteadyness is likely to develop around irregularities in the boundary first, then spread to the whole domain as the Reynolds number increases.


October 2, 2006, 11:42 
Re: How to determine whether flow is steady or uns

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>In fact, all FVM codes solve an unsteady problem, they march to steady state (if you are solving a steady state problem) by some time integration procedure.
Is this true? Are there no codes in use, based on the steady state equations (without time derivatives) and using an iterative approach other than some kind of time integration (e.g. something like approximate factorization)? It's safe to say all unsteady methods can produce a steady result (if the flow is indeed steady, or the time resolution is not sufficient). If you don't know if there is an unsteady solution, you're kind of tapping in the dark. The problem is, if you don't even know if it's unsteady, you probably have no clue about the dominant time scales of a possibly unsteady problem. In other words, you don't know what time steps to choose to resolve the (possible) unsteadiness. You may use extremely small time steps (in the extreme: resolving turbulent fluctuations) but that's going to cost you. And as Jonas says, you also don't know how many time steps you need to compute before the possibly weak unsteadiness finally shows up. Your solution might look steady for a very long time, before it becomes unsteady. So what should you do? Perform a stability analysis of the assumed steady state! 

October 2, 2006, 12:11 
Re: How to determine whether flow is steady or uns

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hi let me ask u something from the radical structure. when u iterate, what u do is u get a solution based on assumed solutions(which is not accurate) . Now let us look at the basic structure of an algorith of an unsteady scheme. u(some timestep) = u(previous time step) + the corrections now an iteration also has a similar structure u(more accurate) = u(less accurate) + the corrections. its just the names that we use are different. isnt it? doesn' this apply for implicit schemes too. Expecting edifications from Mr.Mani. (i am just a novice)


October 2, 2006, 12:53 
Re: How to determine whether flow is steady or uns

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The idea of a numerically steady flow can be based on a solution change tolerance, for example: if we say that a solution change (based on the magnitude of the time derivative, e. g.) of 10^3 defines a steady condition, so, you'll have a reference to stop your *unsteady* computation and say: "My solver reached a steady state condition defined by some tolerance". In turbulent computations the term "steady in average" or quasisteady can be used to define a condition when the solution fluctuations tends to become fix, but also bounded by some tolerance.
Regards Renato. 

October 2, 2006, 13:58 
Re: How to determine whether flow is steady or uns

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>u(some timestep) = u(previous time step) + the corrections
>u(more accurate) = u(less accurate) + the corrections No it's not the same, for several reasons. The first statement could stand for a time accurate computation, where the solution at each time step is accurate. However, even in the context of steady state computations, these two different approaches are not equivalent. The first approach is using the unsteady equations (or a modified form of the unsteady equations) to advance the flow. It's a special case of the second approach which is more general. Although both methods may arrive at the same solutions, the paths to the solution will be different. One interesting aspect (and in my mind still an open question) is the possible link between unsteadiness and convergence problems of a steady state computations. Since the (pseudo)time integration essentially retains the form of the unsteady equations, this approach may be more prone to convergence issues, if the real flow is unsteady (i.e. the steady state is unstable when described by the unsteady equations). Other resolution methods, directly applied to the steady equations (without the time derivatives), may not be affected by unsteadiness. Any experience in that regard? 

October 7, 2006, 02:26 
Re: How to determine whether flow is steady or uns

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In the software CFDesign, transient only available for the turbomachinery where time is playing more role. Since there is no steady state, you can confirmedly move further.


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