# Linear Stability Analysis of Blasius Boundary Layer

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 June 14, 2015, 16:11 Linear Stability Analysis of Blasius Boundary Layer #1 Member   Obad Join Date: Sep 2013 Posts: 42 Rep Power: 7 Hi folks, I'm currently trying to solve the Orr-Sommerfeld equation (OSE) for Blasius flow. I want to use an approach where the equation is discretizes with chebychev polinomials (chebychev collocation) and then calculate the eigenvalues. I do all of that with Matlab. However, I'm already stuck with it for a couple of days... I have a Matlab code to solve the OSE for Poiseulle flow, which works fine. But it don't know how to adapt the code to the Blasius case. It seems to me that no one is using Chebychev Collocation to solve Blasius flow, at least Google doesn't tell me. Does anyone have a clue how to handle Blasius flow? Cheers!

 June 15, 2015, 00:58 #2 Senior Member   N/A Join Date: Mar 2009 Posts: 189 Rep Power: 11 Look into www.channelflow.org.

 July 21, 2015, 12:18 #3 Member   Jingchang.Shi Join Date: Aug 2012 Location: Xi'an, China Posts: 70 Rep Power: 8 I'm also stuck with blasius linear stability calculation! I've already written f90 program to solve poiseuille flow successfully. so did my spectral collocation method. however, blasius case is wrong for both codes. I suspect that the key is some algebra mapping on the coordinates between blasius similarly variable and collocation points. I'm not successful for the moment and I hope to discuss with you! sincerely

 July 22, 2015, 18:06 #4 Member   Obad Join Date: Sep 2013 Posts: 42 Rep Power: 7 Hi, well I made it If you worked it out for the Poiseuille flow then you are very close to solving the Blasius flow. The code is exactly the same. Concerning the coordinate system you might have look at this master thesis: http://tuprints.ulb.tu-darmstadt.de/3173/ There is a chapter about the linear stability analysis of laminar boundary layers with a spectral collocation method using Chebychev polynomials. Furthermore check out this website: http://www.lmm.jussieu.fr/~hoepffner/codes.php The important thing about solving the stability of a boundary layer is, that you use a base velocity profile that was calculated across a couple of times the boundary layer thickness, so that a substantial amount of the velocity profile lies withing the free stream. This has to do with the farfield boundary condition that you impose on the upper edge where you say that the perturbation goes to zero as the distance from the wall goes towards large values. If you are using a temporal theory approach then try to solve the equations for a range of alpha = 0.1 - 0.5. Cheers! abhi22 likes this.

July 23, 2015, 11:19
#5
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Jingchang.Shi
Join Date: Aug 2012
Location: Xi'an, China
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Quote:
 Originally Posted by Obad Hi, well I made it If you worked it out for the Poiseuille flow then you are very close to solving the Blasius flow. The code is exactly the same. Concerning the coordinate system you might have look at this master thesis: http://tuprints.ulb.tu-darmstadt.de/3173/ There is a chapter about the linear stability analysis of laminar boundary layers with a spectral collocation method using Chebychev polynomials. Furthermore check out this website: http://www.lmm.jussieu.fr/~hoepffner/codes.php The important thing about solving the stability of a boundary layer is, that you use a base velocity profile that was calculated across a couple of times the boundary layer thickness, so that a substantial amount of the velocity profile lies withing the free stream. This has to do with the farfield boundary condition that you impose on the upper edge where you say that the perturbation goes to zero as the distance from the wall goes towards large values. If you are using a temporal theory approach then try to solve the equations for a range of alpha = 0.1 - 0.5. Cheers!
I will read the paper in the link. I hope I can also make it.
And I have another question. Do you have any experience on shooting method to solve OS equation? I mean the compound matrix method. I've no idea why my shooting method does not work on Blasius case though it works on Poiseuille case. I want to show you my codes implementing shooting method and hope you could spare some time finding why it does not work. However, it's not an appropriate request. And you can ignore it.

 July 25, 2015, 18:39 #6 Member   Obad Join Date: Sep 2013 Posts: 42 Rep Power: 7 Hey, yeah at first I also wanted to solve the spatial theory by using the CMM. I tried it out, but left it unfinished since the Spectral method worked. Concerning your code I'm sorry, but I'm not familiar with Fortran coding.

December 2, 2017, 15:18
#7
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Join Date: Aug 2013
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Quote:
 Originally Posted by Obad Hi, well I made it If you worked it out for the Poiseuille flow then you are very close to solving the Blasius flow. The code is exactly the same. Concerning the coordinate system you might have look at this master thesis: http://tuprints.ulb.tu-darmstadt.de/3173/ There is a chapter about the linear stability analysis of laminar boundary layers with a spectral collocation method using Chebychev polynomials. Furthermore check out this website: http://www.lmm.jussieu.fr/~hoepffner/codes.php The important thing about solving the stability of a boundary layer is, that you use a base velocity profile that was calculated across a couple of times the boundary layer thickness, so that a substantial amount of the velocity profile lies withing the free stream. This has to do with the farfield boundary condition that you impose on the upper edge where you say that the perturbation goes to zero as the distance from the wall goes towards large values. If you are using a temporal theory approach then try to solve the equations for a range of alpha = 0.1 - 0.5. Cheers!
Hi, Good For you. I wanna do stability analysis for boundary layer. I confuse For doing that. I just can drive Orr Sommerfeld but I dont know How I should solve It. can You help me please?
best regards