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 June 24, 2000, 22:34 About the difference between steady and unsteady problems #1 Lisa Guest   Posts: n/a Dear readers, I'm solving 2-D driven cavity problems. I read several papers and found that some people used steady equations to solve this problem, but others used unsteady equations to solve it and even gave the animotion of their results. If physical problem is the same, why some get unique solution and some get time dependent solution? Can you tell me the reason. Thank you. Lisa

 June 25, 2000, 12:06 Re: About the difference between steady and unsteady problems #3 Lisa Guest   Posts: n/a Dear John C. Chien, Thank you for your response. I still have a question about this problem, If I calculate the case with Reynolds number as high as 20000 or higher, then this physical phenomena is unsteady, so I can't use steady equation to solve this problem, only unsteady equation can be used. is it right? Thank you very much. Lisa

 June 25, 2000, 15:12 Re: About the difference between steady and unsteady problems #5 Lisa Guest   Posts: n/a Dear John C. Chien, Thank you very much, you helped me a lot. Lisa.

 June 25, 2000, 16:20 Re: About the difference between steady and unsteady problems #6 Lisa Guest   Posts: n/a Dear John C.Chien, I have ever used 3-D time dependent NS equations to simulate the flow field around delta wing. I got the following results, the solution is steady when angle of attack is less than critical angle( before vortex breakdown), Increasing the angle of attack ( exceeding critical angle of attack, vortex breakdown occurs), I can't get steady solution, the solution is time dependent (transient solution). Can I say my simulation reflects the basic real physical phenomena( suppose my methods are correct)? In mathematical aspects, Is the solution changed from steady to unsteady caused by the angles of attack related to the Hopf bifurcation or chaos? Lisa

 June 25, 2000, 19:03 Re: About the difference between steady and unsteady problems #7 John C. Chien Guest   Posts: n/a (1). In general, when there is no streamwise flow separation, the flow is stable. This is the case for the flow over a delta wing where the the flow separation is in the cross-stream plane vortex with the vector pointing in the streamwise direction, when angle of attack is small. (2). As soon as the streamwise flow separation occur, as in the flow after the vortex breakdown, flow oscillations similar to the wake flow of a cylinder will occur. (3). Flow over a body at high angle of attack will create very complex separation patterns on the surface and in the flow field. So, I must say that, in general it is similar to the real flow behavior. (4). But then, it depends on the Reynolds number, the wing leading edge shape, and Mach number,etc... I mean whether it is initially laminar, or turbulent. (5). In additions, the votex pair can be either symmetric, or asymetric, depending upon the angle of attack. (6). What I am trying to say is that just because the solution has turned into unsteady motion, we can not say that the solution is real. There are several other factors need to be considered also. But in any case, it is the first step in the right direction.

 June 25, 2000, 21:34 Re: About the difference between steady and unsteady problems #8 Lisa Guest   Posts: n/a Dear John C. Chien, In your last response, in item 5, you wrote that the vortex pair can be either symmetric, or asymetric, depending upon the angle of attack. Yes, in my calculation, when the angle of attack reached a certain value, the vortex pair changed from symmetric to asymetric. Although I got the result similar to the experiment, but I don't understand that the same equation and boundary condition, and the geometry of delta wing is symmetric, why is the vortex pair asymetric? Thank you Lisa

 June 25, 2000, 22:24 Re: About the difference between steady and unsteady problems #9 John C. Chien Guest   Posts: n/a (1). It is fairly common in the missile aerodynamics, that is flow over a slender body at high angle of attack.

 June 26, 2000, 02:46 Re: About the difference between steady and unsteady problems #10 Duane Baker Guest   Posts: n/a Hi Lisa, it is actallly very common with strongly forced flows (in fact any nonliner problem with strong forcing eg. hi Re fluids, slender beams and shells under high loading, etc) with symmetric geometry, b.c's and source terms can lead to asymmetric solutions. One thing to note is that for these ideal conditions the asymmetric solutions often come in pairs or higher multiples. A numerical algorithm will often tend to one of these multiple solutions because of assymetries in the algorithm ie. iterating the i,j,k from 1,1,1 etc. The real physical solution will often have a preference due to asymmetries in the physical problem (often very tiny) which have been neglected in the model. For example, a small scratch in the wall of a diffuser will cause the flow to separate off of one wall or the other. Often the preference for a physical solution is not the same as the one from the code. This takes quite a bit of investigation.

 June 26, 2000, 17:31 Re: About the difference between steady and unsteady problems #11 Lisa Guest   Posts: n/a Thank you very much ! Lisa

 July 5, 2000, 14:37 Re: About the difference between steady and unstea #12 Adrin Gharakhani Guest   Posts: n/a If you solve an unsteady problem with a transient code and time-average the results (given you have let the simulation proceed through statistically sufficient number of cycles) you will get an answer similar to the so-called steady state solution. What is crucial to recognize here is the term time-averaged, which unfortunately many researchers corrupt by terming it "steady state", either due to ignorance of physics or lax attitude toward using the correct terminology. Adrin Gharakhani meangreen likes this.

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