y+ and boundary layers.
 

Hi!

I am just wondering what y+ means with regards to boundary layers...I am doing a project in college using CFD and my lecturer has spoken about y+ and a few other parameters...could some one explain these or simple tell me where I can find a good simple explaination... thank you. Jack.

Re: y+ and boundary layers.
 

"Turbulence Models and Their Applications To Prediction of Internal Flows: A Review", M.Nallasamy, 1987, "Computers and Fluids", v15,No.2 pp. 151-194. Also Search papers by Prof. Rodi, AiAA, 1982.

All the best

Re: y+ and boundary layers.
 

y+ is the non-dimentional wall distance. What our fluid mechanics fore-fathers found was that they could express the velocity and distance from the wall using non-dimentional numbers. Using these numbers they found that turbulent flow over a flat plate (for example) was always the same. You could have a small flat plate, or a flat plate the size of Manhattan. You could have a low free stream velocity, or a larger free stream velocity. When you plot the non-dimentional velocity (u+) as a function of the non-dimentional distance from the wall (y+) the curve you get in the boundary layer is the same.

As for books with good information, "Convective Heat and Mass Transfer" by Kays and Crawford has a good chapter on this stuff. Most other upper undergrad level fluid mechanics books should explain it also.

Re: y+ and boundary layers.
 

Let me add a little bit to this. First of all, the definition of y+ is

y+ = y*u_tau/nu

where y is the normal distance from a wall, u_tau is called the "friction velocity" and is defined by

sqrt(tau_w/rho)

where tau_w is the shearing stress at the wall and rho is the density of the fluid (assuming incompressible constant density flow). nu is the kinematic viscosity of the fluid. That's what y+ IS. But why is it useful?

Its useful because when plotted against u+ which is u/u_tau, for a *turbulent* boundary layer, there is a region for sufficiently small y+ where the velocity profile is UNIVERSAL. You always get the same shape (for a flat plate with dp/dx=0, anyway). Any time you can find universal behavior such as this, it becomes a very powerful tool for analysis, because you can solve the universal relationship for variables which would otherwise be unknown.

Hope this helps.

Bob

Re: y+ and boundary layers.
 

another suggestion -- whenever your professor uses terms in class that he hasn't defined just ask him what they are. if you get lost in one part of the lecture the entire remainder of it is wasted time for you.