Also i need to know how to exactly calculate the roughness element height
I have attached the required details and formula
any helping material or method or insights will be great for my master thesis research
For compressible flows because the airfoil is curved there is a transverse pressure gradient near the surface. In such cases it is necessery to compute the theoretical (ideal) velocity profile first (by taking total pressure equal to stagnation pressure of the inflow and using isentropic flow equations to get velocity which is not a constant value as in case of a flat plate flow). In the next step you need to find a point at which the velocity in your flow is reaching e.g. 99.5% of this theoretical (ideal) profile. This way you will find your boundary layer edge on a convex surface and be able to compute for example integral parameters, such as displacement or momentum thickness.
Check any Myring's publications for details...
Regards
Oskar
BL edge is arbitrarily chosen, the theory says it extends asymptotically up to Y-> Inf.
The assumption of the 99% of the external velocity is an engineering approximation that can be used.
External velocity means you are taking about the velocity of the air around the airfoil?? am I right?
Thank you for your answer
"External" means the velocity computed from the Euler equation, that is using the inviscid flow assumption.
Instead of velocity you can use voracity which can be get from the solution which will give you more clear idea
For compressible flows because the airfoil is curved there is a transverse pressure gradient near the surface. In such cases it is necessery to compute the theoretical (ideal) velocity profile first (by taking total pressure equal to stagnation pressure of the inflow and using isentropic flow equations to get velocity which is not a constant value as in case of a flat plate flow). In the next step you need to find a point at which the velocity in your flow is reaching e.g. 99.5% of this theoretical (ideal) profile. This way you will find your boundary layer edge on a convex surface and be able to compute for example integral parameters, such as displacement or momentum thickness.
Check any Myring's publications for details...
Regards
Oskar
If you need approximate solution use Euler equation and if you seek exact solution no doubt that full Navier Stokes equations to be solved.
Oskar Szulc what do you mean by Myring's publications, Can you please explain?
For example:
Myring D. F. 1970 An integral prediction method for three-dimensional turbulent boundary layers, RAE-TR 70147
Dear Naveenkumar Subramanian ,
You may find the velocity distribution in the boundary layer by experimental or numerical methods. By definition, the boundary layer thickness is the position where u/U = 0.99. However, in both the methods above, it is difficult to have a smooth boundary line. So, you may reduce the definition to be less than 0.99, i.e 0.98 or lesser until you have the smooth one. It is the same case when you want to find the boundary layer thickness by CFD. But if your calculation is accurate then you will find a smooth boundary layer line thickness by using a definition of near u/U = 0.99.
Have a nice job.
Best regards.
Nazaruddin Sinaga Hey when you mean u/U is it same as Uk/Us from the attachment i provided?
Dear Naveenkumar Subramanian ,
u = local velocity at a point
U = average free-stream velocity
I can recommend you take a look at a book by Alan Pope called Basic Wing and Airfoil Theory. There are specific chapter in this book explaining how to calculate the velocity at any point on an airfoil, both thick and thin. Starting on page 122, chapter 7.3 you'll find first the discussion as it applies to a thin airfoil. This will not be a constant, and most likely it will vary with the wing aspect ratio. Also Abbot & Doenhoff treats this subject in their book Theory of wing sections. Also G.D. McBain has an excellent book called Theory of Lift, that might be very helpful. Good luck.
Dear Naveenkumar Subramanian,
there are two publications that helped me in the past, and they might help you as well:
"Comparison of Methods for Determining Boundary Layer Edge Conditions for Transition Correlations", Liechty et al. AIAA 2003-3590
"Application of Laminar-Turbulent Transition Criteria in Navier–Stokes Computations", Cliquet et al. AIAA J, Vol. 46, No. 5, May 2008
In particular, the second approach was straightforward to implement and I found it quite robust.
Kind regards
Alberto
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