I have a fully developed pipe flow in with Inner radius (r) and outer radius (R), using pressure driven flow condition due to buoyancy,
- (1/rho) dP/dx = g
and velocity scaling u* = sqrt ( (-R/ (2 rho)) * (dP/dx)) [ friction velocity ], if Reynolds number is fixed ( Re = 600 ), along with r and R
we can get y+ value based on y values we give for cell size at both the walls,
But the question is when y+ calculated from this formula is y+ at the outer wall ( general pipe flow condition ) but how to get a y= for the inner annulus? ( concentric annular pipe flow ) ?
is there any analytical method to find this y+ or the only solution is to get us after simulation run when we have calculated friction velocities wall shear stresses at wall cell centers.
basically two different y+ to get analytically, in order to set up minimum cell size for my LES grid.
First of all, y+ is a function, not a value. It is the local Reynolds number in normal to wall direction.
Clearly, you need to consider the velocity utau that is a result of the total wall stress.
In a numerical simulation in a channel, if you use the utau velocity to make non dimensional the equations, you have a constant pressure gradient (=-1) that acts as forcing in the momentum equation and the Reynolds number is based on the velocity utau. Thus, the computed numerical velocity is u+
I guess, I have missed to mention y+ calculation before simulation run. I meant y+(1) basically y+ of the first cell near wall with no slip Boundary conditions.
And you are absolutely correct in terms of simulation results when I have the data and computed U_tau value. Filippo Maria Denaro
But my sole doubt was Is it possible to have a per-calculation of y+ before the simulation based of U_tau calculated from Friction Reynolds number ( As this is a flow condition I'm presetting for My simulation). I want this calculation to have an idea about where my first cell center i.e. y+(1) is located so that I could do appropriate wall function implementation in the code.
Nishidh Shailesh Naik Burye
if you work by prescribing the Re_tau number of your non dimensional solution, you have the y+ at the first cell known.
Since y+ = u_tau*y/ni = Re_tau *y/L you just scale your non dimensional first cell height by Re_tau.
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