ANSYS,FLUENT CFD, Turbulent flow

[sandpants]

I have an assignment involving a duct vent and turbulent flow.

Flow enters a duct vent of a certain cross-section, it then reaches another section with a smaller area, at the beginning of which there is a horizontal plate that is radiating heat.

It's a 2D problem.
Fluid is Air, inflow T=20C and velocity is 30m/s

I have 2 primary design constraints:
1)The entrance length must be sufficiently long enough so that the turbulent flow is fully developed by the time it reaches the second section, so as to have the fully developed flow entering the narrower section and going over the hot plate.
2)The exit length needs to be sufficiently long enough so that it doesn't affect the flow around the plate.

My attempts:
1)White M. Frank describes in his book "Fluid Mechanics" that the entrance length to achieve a fully developed turbulent flow is Le=4.4DRe^(1/6), where D is the hydraulic diameter. Somewhere on the internet I saw an expression for hydraulic diameters in duct vents to be... something, but I worked it out and for a thickness of 0.2m it was still 0.2m.
However, @30m/s and density of 1.2kg/m3 the Re is 400,000 and the matching Le for D=0.2 is ~7.5m.
Which is huge. Is there any other way to check if the flow is fully developed?
Would looking for a velocity profile work, even though the flow is turbulent, and how could I do that in ansys?
What other verification methods can be used?

2)I am not sure how the exit geometry can affect the flow around the plate upstream.

Please advise.

 

[SteamKing]

The hydraulic diameter Dh of a non-circular duct is given by the formula:

Dh = 4A/P

where A is the cross sectional area and P is the perimeter of the duct. You should be able to find this formula in White, especially when dealing with open-channel flow and Manning's eqn. 'Somewhere on the internet' is incredibly vague and slapdash. IDK why you are using the thickness of anything to determine the Dh.

If you have an Re = 400,000 and a duct with a hydraulic diameter of 0.2 m, then using the relation Le/D = 4.4(Re)^1/6 should give an Le of about 7.55 m.

 

[sandpants]

T

If you have an Re = 400,000 and a duct with a hydraulic diameter of 0.2 m, then using the relation Le/D = 4.4(Re)^1/6 should give an Le of about 7.55 m.

It does give me exactly that. And that's for a 0.2m duct width.
My question is whether this is waayyy too long or not.

 

[SteamKing]

It does give me exactly that. And that's for a 0.2m duct width.
My question is whether this is waayyy too long or not.

I think you should be using the hydraulic diameter to determine the entrance length, and not necessarily the the duct width,if the duct has a non-circular cross section.

These relations for calculating entrance length are somewhat imprecise. I think that in order to guarantee that the flow in a pipe or duct has gone fully turbulent, a greater entrance length is required, unless some artificial means to stimulate turbulent flow are employed.