Thanks.

But in this paper, any thing is not said about blade thickness.

The BL thickness increases over a flat plate because the farther the fluid flows over the plate the more viscous shear drag it has to overcome, so this gradually increases the thickness of the BL.

Considering the problem you have described , the answers are :

1)  The flow on a blade shall be guided according to the requirements ( velocity, pressure and direction) ; The  thickness of the boundary layer increases along the x- direction to a certain point where there may be the re-attachment of the flow to the blade or the laminar separation of the flow may cause a reversed flow boundary layer leading to stalled conditions( creation of turbulence wake) .

2)  Depending on the shape of the blade, It may decrease or increase. 

   A very sharp edge ( sudden increase of thickness)  of the blade may lead to a separation of flow , so one has to consider the trade off between the friction and pressure on the surface.. I Hope you may get some idea from this discussion

Thanks.

Charbel Bou-Mosleh, Can you explain more? I don't understand the following sentence:

" the farther the fluid flows over the plate the more viscous shear drag"

Thanks.

The thickness of the BL is proportional to the distance traveled by the fluid over the flat plate, whether it's a laminar or turbulent BL. This is what I meant by "the farther the fluid flows over the flat plate".

Thanks again professor Charbel Bou-Mosleh,

Can you explain more about "more viscous shear drag it has to overcome, so this gradually increases the thickness of the BL."?

Another way to understand it is studying how information is transmitted.

 In fluid Dinamics ,  the main way to code information is through difference of velocities an pressure. Pressure information is mostly transmitted At sounds speed. But velocity information can be transfered at much lower velocity.  In particular,  vorticity code most of this subsonic information.

Vorticity  is produced by difference of velocities and can convect and diffuse as velocity. In a planar configuration with no density variations as the pictured one, there is no other way to generate or modify vorticity.

The presence of the plane modify  the velocities field and this change of velocities it's coded in te vorticity.

We have a  nearly horozontal velocity V, the and the information diffusivity (D=diffusion divided by density with dimension  L2 /T)  is the same as that of the fluid. So, in the time that the information is connected  a distance x (t=x/V)  is has diffused to a height y (t=y^2/D). That means that the information of the presence of the plane follows a square root  shape (y=(xD/V)1/2).  The information of the presence of the plane starts at its edge,  so x can be considered 0 there.

Another way to understand qualitatively the growth  of the boundaries layer is thar friction reduce velocidad close to the plane  so  the velocity Laplacian decreases and viscosity effets becomes less important as we go farther form the edge

Is a more general case  the advertise and the pressure play a more important role,  the information dinamics is still quite similar (Taking x as the coordinate along the surface and V as the local velocity)

you can find the standard BL theory on the textbooks of fluid mechanics (White, Kundu, etc.) as well as searching in internet some brief reports can help you.

http://essay.utwente.nl/63314/1/BSc_report_Peter_Puttkammer.pdf

Mathematical descriptions of boundary layers can be found in many textbooks and technical papers on fluid dynamics.  Perhaps Ali Sam is looking for a simple depiction, something one can intuitively relate to.  How about this:

Imagine that a stream of fluid consists of molecules which have the peculiar property of sticking to any solid object with which they come into contact.  Molecules of fluid next to a solid surface stick to the surface, while the molecules farther away from the surface slowly stumble over those in the layer closer to it, trying to catch up with the mainstream.  The farther you go from the stationary surface, the higher the speed of the air molecules until they reach the full speed of the mainstream (the “relative wind”).  

Also, the longer the distance x from the leading edge of the solid surface, the more molecules are entrained in the process, and the (boundary) layer affected thickens (with distance x) because of this.

As regards the effect of turbine blade thickness on its boundary layers, no general rule exists.  Boundary layer development depends not only on distance x but also on local changes in the velocity of the relative wind surrounding the blade:  in locations where the flow is decelerating (diffusing), the boundary layer becomes thicker and vice versa.  Such local changes in velocity are quite prevalent on turbine blades, caused by streamwise changes to flow passage cross-sectional area (by the amount of divergence of endwalls and the degree of reaction) as well as local changes to curvature on blade surfaces (where, in the case of the suction surface of the blade, high curvature followed by reduced curvature will cause diffusion).  

When optimizing the aerodynamic design of a turbine blade it helps to think in terms of the flow passage between adjacent blades rather than in terms of the cross-sectional shape of the blade. This is especially true of rotor blades for turbines having a low degree of reaction.  The design of a turbine blade is an art which involves many design variables, including spanwise distribution of the cross-sectional area of the blade (to keep centrifugal stresses within acceptable limits).  

For a more comprehensive, non-mathematical discussion of boundary layers, I can recommend Chapter 5 and Appendices A and B of Part I of “Why Does It Fly?”, available at     www.okapuu.com

Thanks Ulo Okapuu ,

what is your exact meaning of the bold part of the following sentence?

"in locations where the flow is decelerating (diffusing), the boundary layer becomes thicker and vice versa. "

How does decelerating flow  process happens in turbines simulation?

I saw many paper about accelerating flow and decelerating flow process in turbines simulation....these simulation are unsteady.

Thanks.

As we all know, the velocity of fluid next to the surface a turbine blade varies from point to point.  In the streamwise direction, when velocity changes from fast to slow, that means decelerating, and slow to fast means accelerating.  For fluids in motion, another term for deceleration is diffusion:  when total pressure remains constant, static pressure increases when speed is reduced (by Bernoulli’s theorem), that is, the flow is diffusing.

An analogy with flow within a pipe would be the transition from a portion of pipe having small diameter to a portion having a larger diameter.  Velocity reduces, static pressure increases, i.e. the flow is diffusing.

The flow within turbine blade passages is indeed unsteady.  This is due to viscosity (which produces wakes at trailing edges of the row of blades upstream) and, more importantly, the cross-channel velocity gradient generated by the curvature of the flow passage in the cascade (row) of blades upstream.  Both these phenomena produce a periodic fluctuation, at blade passing frequency, of both angle of attack and relative inlet velocity to the following row of blades.

This is all very interesting, and makes for a good subject for graduate studies focused on CFD, with all its intricacies of grid generation and turbulence models.  However, the designer of a turbine needs to understand what the results of analysis mean in practical terms, how a certain amount of local diffusion on a given point on the blade translates into pressure loss (which he tries to minimize).  For this, he needs to simplify the results of analysis by focusing in on their AVERAGE values of inlet velocity and flow angle.  Then, based on previous corporate experience with cascade and rotating rig testing, he can assess the acceptability of any new turbine design.  

Fluent does not design the optimum turbine for you. It can’t even predict the efficiency of a turbine with any degree of reliability.  It is just a tool, an approximation to help you assess the quality of a trial design.  This tool needs to be calibrated with test results with actual turbines, or it will be next to useless.   It is easy to be sidetracked onto solving the many operational problems of CFD programs, and see them as the end in itself.  It is not, if your goal is the design of a turbine (or compressor).  “Design rules” and experience with previous turbine designs, which  form the link between results of analysis and actual turbine performance, are closely guarded corporate secrets which influence the relative competitive positions of companies which design and manufacture gas turbine engines. 

Dear Ali,

particles are decelerated along a plate within boundary layer due to the friction between the blade (plate surface) and the fluid particles. The particles attached at the plate surface have zero velocity (no-slip boundary condition) and the adjacent particles are slowdown accordingly. A the beginning of the plate the boundary layer consisting of such fluid particles is very thin. But further downstream more particles are decelerated causing to increase the boundary layer thickness.

But as the laminar boundary layer thickness increases along the plate, the particles become more freedom to move in vertical direction. So a fluctuation perpendicular to the flow takes place, which dissolves the laminar flow and flow becomes turbulent.

So for more scientific (theoretical) aspects regarding boundary layer development I can recommend you the following book:

Boundary layer theory : from Hermann Schlichting.

Best regards