# compressible laminar flow over flat plate

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 March 18, 2010, 05:44 compressible laminar flow over flat plate #1 Member   varun Join Date: Apr 2009 Posts: 35 Rep Power: 9 hello all! i'm writing my own CFD code for boundary layer eqns. over flat plate for laminar compressible flow, for mach no. 1.5... i'm using finite difference central-differencing scheme, and uniform grid spacing.... but the problem is, in order to stabilize the solution my deltaY=10^-8 and deltaX=10^-10, now even if i'm assuming a (5000,100)(x,y), practically my plate length is 5 x 10^-7, which is negligible.... can some one help me out, so that i can somehow increase my deltaX, and have a normal plate length.... if u want i can upload my code and graphs plotted.... thanks in advance varun

 March 18, 2010, 06:32 #2 Senior Member   Hamid Zoka Join Date: Nov 2009 Posts: 198 Rep Power: 9 these delta x and y seems to be good only for a DNS solution. please tell me how it can be possible to have a much number of 1.5 and a laminar flow as well? how mush is your reynolds number? it sounds that you can not have a laminar flow at this speed.

March 18, 2010, 06:57
#3
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varun
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Quote:
 Originally Posted by Hamidzoka these delta x and y seems to be good only for a DNS solution. please tell me how it can be possible to have a much number of 1.5 and a laminar flow as well? how mush is your reynolds number? it sounds that you can not have a laminar flow at this speed.
I am considering a supersonic flow, over a flat plate... i guess a laminar boundary layer will develop. Plz correct me if i'm wrong... So, if a laminar boundary layer is developed isn't the flow laminar...??? my calculations are all dimensional... I'm considering Uinf=500, therefore mach 1.47, and length of plate 0.1m, rest are all sea level conditions. so my reynolds no. is coming out to be 3.4083 X (10^6). I'm a newbie... trying to learn CFD all by myself... so a bit weak in concepts. thank u

 March 18, 2010, 08:52 #4 Senior Member   Join Date: Nov 2009 Posts: 411 Rep Power: 11 Hello, check J. D. Anderson's book Introduction to CFD, you will find exactly what you are looking for (laminar flat plate and supersonic speed). And yes you can have laminar flow at this speed if your flat plate is small enough, usually in an external flow the boundary layer will go from laminar to turbulent, so for a very small flat plate you can suppose the flow is laminar. If you need more help with this assignment send me a private message. Do

 March 19, 2010, 02:21 #5 Member   varun Join Date: Apr 2009 Posts: 35 Rep Power: 9 Thanks a lot Do you exactly got right what I am talking about. I have read that, chapter before getting started with this problem. But the thing is that chapter has solved using full N-S eqns. I am using the reduced N-S eqns or boundary layer eqns. (As mentioned in Ch-18, Fundamentals of Aerodynamics, by J.D. Anderson) I can always solve by doing what is suggested in the book(cfd by j.d. anderson), but if I'm using boundary layer eqns. then also i should obtain a solution right...??? So, just to keeping things simple for the time being, I am applying finite difference method, central differencing scheme, in the 4- boundary layer eqns. i.e. continuity, x-momentum, y-momentum and energy eqn. i'm assuming steady solution. marching in x-direction. so i'm calculating my Temp from energy eqn, then u from x-momentum eqn. rho from y-momentum eqn, and v from continuity eqn. I hope u r getting me. i will just try with dx and dy values they have mentioned and let u know... thank you once again varun

March 19, 2010, 06:02
#6
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L.Y LIN
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Quote:
 Originally Posted by varunjain89 hello all! i'm writing my own CFD code for boundary layer eqns. over flat plate for laminar compressible flow, for mach no. 1.5... i'm using finite difference central-differencing scheme, and uniform grid spacing.... but the problem is, in order to stabilize the solution my deltaY=10^-8 and deltaX=10^-10, now even if i'm assuming a (5000,100)(x,y), practically my plate length is 5 x 10^-7, which is negligible.... can some one help me out, so that i can somehow increase my deltaX, and have a normal plate length.... if u want i can upload my code and graphs plotted.... thanks in advance varun
hi ,i would like to say:
1,i suggest you use the dimensionless equations for the problems you concern(because few people use dimensional ones for its meaningless)
2,Hamid Zoka's reply seems right.u can get laminar boundary layer when the x is very small,and when x is larger it may changes to turbulence flow.but it is not important for DNS .we always set the min net size equaling to the value of 1/RE in experience.
that's it.

March 19, 2010, 06:34
#7
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varun
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Quote:
 Originally Posted by iilw1314 hi ,i would like to say: 1,i suggest you use the dimensionless equations for the problems you concern(because few people use dimensional ones for its meaningless) 2,Hamid Zoka's reply seems right.u can get laminar boundary layer when the x is very small,and when x is larger it may changes to turbulence flow.but it is not important for DNS .we always set the min net size equaling to the value of 1/RE in experience. that's it.
thank you.... so okay if my re no. is 3.4 X (10^6), then my dx would be somewhere around 10^(-7), that means i will have to consider 10^(6) points along x axis... well the desktop i'm working on is allowing me a max of 4000 points, so any suggestions.... should i reduce my plate length....???

 March 19, 2010, 14:08 #8 Senior Member   Join Date: Nov 2009 Posts: 411 Rep Power: 11 Actually from my experience it is more difficult to implement a boundary layer solver then a simple NS solver for a flat plate. You will also need an accurate potential solver for the external flow (a panel code). A BL code will use less resources then a NS code from a computation point of view, but it is more difficult to implement accurately. If you really need BL check this book: "Modeling and Computation of Boundary-Layers Flow" Cebeci and Cousteix Do

 March 19, 2010, 23:02 #9 Member   L.Y LIN Join Date: Mar 2010 Posts: 47 Rep Power: 8 e...u cannot use the uniform net size all the domain,u need refine the nets around the boundary,and larger size far from the boundary.and the shape of the net can be rectangle ,so it means you can use less points along the flow direciton,the 1/RE value means the net size of the net near the boundary in normal direction.keep more than 20 points inside the boundary layer if it is laminar.

 March 19, 2010, 23:06 #10 Member   L.Y LIN Join Date: Mar 2010 Posts: 47 Rep Power: 8 anybody can help me with my problem,Title:problems for the flow over flat wall , i appreciate your suggestions.

March 20, 2010, 05:21
#11
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Hamid Zoka
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Quote:
 Originally Posted by varunjain89 I am considering a supersonic flow, over a flat plate... i guess a laminar boundary layer will develop. Plz correct me if i'm wrong... So, if a laminar boundary layer is developed isn't the flow laminar...??? my calculations are all dimensional... I'm considering Uinf=500, therefore mach 1.47, and length of plate 0.1m, rest are all sea level conditions. so my reynolds no. is coming out to be 3.4083 X (10^6). I'm a newbie... trying to learn CFD all by myself... so a bit weak in concepts. thank u
Dear Varunjain;
Of course you have a laminar flow at the first. but it is limited to a very small region and is going to become fully turbulent rapidly. so you should consider the flow field to be turbulent. you should use momentum, continuity and energy equations in its original form. what is important is your mesh generation. you should use meshes with high aspect ratio next to the wall. wall function method may be appplied to capture flow details in regions near to wall. you can use a hybrid scheme in your code like this: you can calculate Y+ parameter in cells adjacent to wall. if it falls below a certain amount(say 11 which depends to flow type) flow will be laminar. but if it axceeds the 11, it is turbilent and you should use turbulent equations.
since you are going to solve a boundary layer problem, i suggest you to study near wall treatments in turbulent flows. there are different techniques for that. but one of most popular and economic methods is wall funcion technique. you can find useful topics regarding wall functions in the web. UMIST pdf files are very useful. one of most important aspects of flow modeling is boundary layer modeling which is source of turbulence generation withinh the flow. you do not need to modify your equations, you need to learn how to adjust your code for near wall regions.

 March 20, 2010, 12:01 #12 Member   varun Join Date: Apr 2009 Posts: 35 Rep Power: 9 Thank you everyone, i will try to implement what all you suggested and let you know the progress. i really appreciate your help. varun jain

 March 22, 2010, 16:05 boundary conditions.... #13 Member   varun Join Date: Apr 2009 Posts: 35 Rep Power: 9 okay here's another doubt.... a very simple and basic one.... if i am considering a supersonic flow, over a flat plate... then i should have a shock wave @ leading edge. i'm still using boudary layer eqns. only, and i'm getting decent results... i'm assuming steady flow. So what should be my boundary conditions @ leading edge.... they certainly cannot be the free stream conditions, if i need a shock wave.... if i'm assuming free stream conditions i'm getting a normal output, without any shock... suggestions...??? should i simply switch to unsteady flow and eventually it will give me the desired steady results. is there any way i can work this out using steady flow....???

March 24, 2010, 09:20
#14
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L.Y LIN
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Quote:
 Originally Posted by varunjain89 okay here's another doubt.... a very simple and basic one.... if i am considering a supersonic flow, over a flat plate... then i should have a shock wave @ leading edge. i'm still using boudary layer eqns. only, and i'm getting decent results... i'm assuming steady flow. So what should be my boundary conditions @ leading edge.... they certainly cannot be the free stream conditions, if i need a shock wave.... if i'm assuming free stream conditions i'm getting a normal output, without any shock... suggestions...??? should i simply switch to unsteady flow and eventually it will give me the desired steady results. is there any way i can work this out using steady flow....???

i am sorry ,i cannot understand your meaning?...if you want to solve the problem of flow voer flat plate,you need not corcern the shock at leading edge,if i were doing the problem,i would add a short flat plate in front of the plate,and the velocity over the flat plate that you add should be uniform flow.
if you corcern the problem of the shock at the leading edge.i am not sure that the boudary layer eqns can solve this problem.you may use NS eqns.and the M number over the flat plate may be below the M no. you used before(1.5?)
....

March 24, 2010, 10:01
#15
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varun
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Quote:
 Originally Posted by iilw1314 i am sorry ,i cannot understand your meaning?...if you want to solve the problem of flow voer flat plate,you need not corcern the shock at leading edge,if i were doing the problem,i would add a short flat plate in front of the plate,and the velocity over the flat plate that you add should be uniform flow. if you corcern the problem of the shock at the leading edge.i am not sure that the boudary layer eqns can solve this problem.you may use NS eqns.and the M number over the flat plate may be below the M no. you used before(1.5?) ....
well i am writing the NS code, and almost through with it, may be half an hour more... but i did not understood your funda of short plate in front of plate.

and yeah i think u are right, B-L eqns can not solve this problem, but may be unsteady B-L can, in fact they should... but for the time being, i'm really bored with doing this problem, and i want to end it so i think i will complete my N-S solution only.... as Do said i'm referring CFD by anderson, ch10. I hope it works....

but i would still like to know how to solve supersonic flow, using BL eqns. so that i can get shock waves.... my program is running fine with sub-sonic flow.

thanks once again.

varun

 March 24, 2010, 12:59 #16 Super Moderator     Praveen. C Join Date: Mar 2009 Location: Bangalore Posts: 255 Blog Entries: 6 Rep Power: 10 Here is a suggestion. Say your domain is a rectangle. At left face you give uniform inflow. The bottom side of rectangle is y=0. Bottom left corner is (0,0). L=length of plate. Between x=0 to x=x1, specify mirror boundary condition, basically a slip boundary or symmetry boundary. Between x=x1 to x=x1+L, specify no slip condition. This should allow you get the leading edge shock.

March 24, 2010, 14:02
#17
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varun
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Quote:
 Originally Posted by praveen Here is a suggestion. Say your domain is a rectangle. At left face you give uniform inflow. The bottom side of rectangle is y=0. Bottom left corner is (0,0). L=length of plate. Between x=0 to x=x1, specify mirror boundary condition, basically a slip boundary or symmetry boundary. Between x=x1 to x=x1+L, specify no slip condition. This should allow you get the leading edge shock.
oh! i get your point, u want me start the flow a bit before the actual plate starts right...??? yeah! this should work... i'll let u know.... thanx a lot praveen, u dont know how thankful i am....

warm regards
varun

 March 25, 2010, 00:51 #18 Member   varun Join Date: Apr 2009 Posts: 35 Rep Power: 9 hi! praveen thanks for your last post, there's this another problem which i'm facing. well in subsonic flow the flow conditions at the edge of the boundary layer, over plate, were same as free stream conditions. but now in super sonic flow as the boundary layer edge lies in shock layer, so flow conditions, or pressure, is varying along the x-direction, so any suggestions how can i calculate pressure on the upper edge of the boundary layer...??? i guess this should be the last thing that is bothering me.... so basically i think i need to apply shock wave boundary layer equations. thanks once again varun Last edited by varunjain89; March 26, 2010 at 01:35.

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