Dimensionless wall distance

messik · March 2, 2014, 20:32

Hi there!

I would like to ask about the dimensionless wall distance. In many papers are three-dimensional domains described using

,

,

. I am not sure how to compute it for other axis (

,

).

Wall

can be computed as
$y^+ \equiv \frac{u_* \, y}{\nu}$ .
Where

is the friction velocity at the nearest wall, y is the distance to the nearest wall and $\nu$ is the local kinematic viscosity of the fluid.
** $u_* \equiv \sqrt{\frac{\tau_w}{\rho}}$
Where $\tau_w$ is the wall shear stress and $\rho$ is the fluid density at the wall.
*** $\tau_w = \mu \left(\frac{\partial u}{\partial y} \right)_{y=0}$
Where $\mu$ is the dynamic viscosity, u is the flow velocity parallel to the wall and y is the distance to the wall.

Is it computed for let's say

as follows?
$z^+ \equiv \frac{u_* \, z}{\nu}$
but
$u_* \equiv \sqrt{\frac{\tau_w}{\rho}}$
$\tau_w = \mu \left(\frac{\partial u}{\partial y} \right)_{y=0}$
are without change?

I am not sure about the wall shear stress component (gradient of u)
Thank you for any hints or recommendations.

Bazinga · March 3, 2014, 04:26

As far as I know the dimensionless wall distance is measured orthogonal to the wall which is usually called yplus and sometimes zplus. Never heard of xplus but it might just be dependent on how you set you coordinate system.

messik · March 3, 2014, 08:41

Thank you. I thought as you do, but you can find

,

widely used in domain descriptions. For example as shown here:

in LES of three-dimensional wing (http://www.iccfd.org/iccfd7/assets/p...3604_paper.pdf). It is possible to find it in other papers too.

I am not sure if

and

are "normalized" with respect to the wall

. I could not find any source with explanation. Probably, there is a trivial answer (that's why..).

Any idea guys? Thank you.

Rami · March 13, 2014, 05:33

Hi Messik,

I guess there are two issues in your post requiring consideration:
1. The "u" should actually be interpreted as the velocity parallel to the wall, not the x-velocity component.
2. The "y" in wall shear stress needs be interpreted as the normal-to the wall coordinate rather than the y-coordinate.
Then the

and the

follow naturally by merely changing components.

I hope this helps,
Rami

cfdivan · March 15, 2014, 07:55

Hi messik,

In 3D flows u may have the other commonents of shear stress, which IMHO makes sense to have the dimless in all three components. Although the boudary layer develops mainly normal to the wall, the resolution of the mesh in all the other two components is also important for the accuracy of your results. If you consider that u are resolving the laminar sub-layer (y+=1) it may be also important that your mesh in the other components fits within (x+/z~30). I think that u use the half of the mesh size and the velocity gradients in the right directions u can find those dimless.

Regards,

March 2, 2014, 20:32	Dimensionless wall distance	#1
messik New Member Join Date: Nov 2011 Posts: 7 Rep Power: 15	Hi there! I would like to ask about the dimensionless wall distance. In many papers are three-dimensional domains described using ,,. I am not sure how to compute it for other axis (, ). Wall can be computed as $y^+ \equiv \frac{u_* \, y}{\nu}$ . Where is the friction velocity at the nearest wall, y is the distance to the nearest wall and $\nu$ is the local kinematic viscosity of the fluid. ** $u_* \equiv \sqrt{\frac{\tau_w}{\rho}}$ Where $\tau_w$ is the wall shear stress and $\rho$ is the fluid density at the wall. *** $\tau_w = \mu \left(\frac{\partial u}{\partial y} \right)_{y=0}$ Where $\mu$ is the dynamic viscosity, u is the flow velocity parallel to the wall and y is the distance to the wall. Is it computed for let's say as follows? $z^+ \equiv \frac{u_* \, z}{\nu}$ but $u_* \equiv \sqrt{\frac{\tau_w}{\rho}}$ $\tau_w = \mu \left(\frac{\partial u}{\partial y} \right)_{y=0}$ are without change? I am not sure about the wall shear stress component (gradient of u) Thank you for any hints or recommendations. Thumper likes this.

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
Minimum Allowable Wall Distance	rks171	Main CFD Forum	7	June 16, 2012 16:39
Dimensions on Dimensionless Wall Distance (y+)	minger	Main CFD Forum	0	July 6, 2011 08:45
distance between particle and wall	Worth	FLUENT	2	June 13, 2009 04:04
How can I do the dimensionless wall heat flux ?	Luke	FLUENT	0	March 15, 2006 12:42
udf: dimensionless wall coordinate	Chris	FLUENT	0	June 22, 2004 07:10

March 3, 2014, 04:26		#2
Bazinga Senior Member Join Date: Jun 2012 Location: Germany, Bochum Posts: 230 Rep Power: 16	As far as I know the dimensionless wall distance is measured orthogonal to the wall which is usually called yplus and sometimes zplus. Never heard of xplus but it might just be dependent on how you set you coordinate system.

March 3, 2014, 08:41		#3
messik New Member Join Date: Nov 2011 Posts: 7 Rep Power: 15	Thank you. I thought as you do, but you can find , widely used in domain descriptions. For example as shown here: in LES of three-dimensional wing (http://www.iccfd.org/iccfd7/assets/p...3604_paper.pdf). It is possible to find it in other papers too. I am not sure if and are "normalized" with respect to the wall . I could not find any source with explanation. Probably, there is a trivial answer (that's why..). Any idea guys? Thank you.

March 13, 2014, 05:33		#4
Rami Senior Member Rami Ben-Zvi Join Date: Mar 2009 Posts: 155 Rep Power: 17	Hi Messik, I guess there are two issues in your post requiring consideration: 1. The "u" should actually be interpreted as the velocity parallel to the wall, not the x-velocity component. 2. The "y" in wall shear stress needs be interpreted as the normal-to the wall coordinate rather than the y-coordinate. Then the and the follow naturally by merely changing components. I hope this helps, Rami

March 15, 2014, 07:55		#5
cfdivan Member Join Date: Jun 2011 Posts: 51 Rep Power: 15	Hi messik, In 3D flows u may have the other commonents of shear stress, which IMHO makes sense to have the dimless in all three components. Although the boudary layer develops mainly normal to the wall, the resolution of the mesh in all the other two components is also important for the accuracy of your results. If you consider that u are resolving the laminar sub-layer (y+=1) it may be also important that your mesh in the other components fits within (x+/z~30). I think that u use the half of the mesh size and the velocity gradients in the right directions u can find those dimless. Regards,