# How can I create uniform laminar flow in a short duct?

I have a small vessel with a rectangular cross-section which needs to be ventilated at a relatively slow rate, ~$3\ \tfrac{\text{L}}{\text{hr}}$. The connections to the vessel will be tubes with an approximately 0.5" diameter, but the cross-section of the vessel is 4" x 1". The diagram below gives a rough idea of the cross-section (viewed from above) with the height of the chamber being about 1". The part circled in orange is the topic of this question. The flow will be forced in from the left and will exit passively from the right (or vice versa).

How can I couple the 0.5" tube to the chamber such that the flow in the chamber is uniform across the entire cross-section for the entire length of the duct? In addition, how can I couple the two in the smallest amount of space possible? • I'm curious if this is possible. Intuitively this much of a change in size and shape in the flow path seems like it should be a source of turbulence but with this slow of a flow rate maybe not. Oct 22 '15 at 15:28
• Can you pass the air through a packed granular bed? Air will come out turbulent but will diffuse laterally quite a bit. Oct 22 '15 at 15:34
• Based on the dimensions, it looks like you've got Reynolds numbers of about 5.5 and 13.5 in the tube and duct, respectively. Those are both well below the transition to turbulence. So the flow should be laminar everywhere. Uniformity near the ends might be a problem...
– Dan
Oct 22 '15 at 15:47
• Similar to the packed bed suggestion, I've seen some people suggest that flow straighteners can make a flow more uniform in addition to reducing the turbulence (an advantage over the packed bed). I'm not sure how true this is. You'd also expect the velocity profile to transition to the parabolic laminar one after the flow straightener. How quickly that occurs is not clear to me. Oct 22 '15 at 17:08
• According to this paper flow straighteners tend to preserve the velocity profile. So this suggests they wouldn't work for this. Otherwise, I know that contractions can be used to create more uniform velocity profiles, but there's an expansion here. Oct 22 '15 at 19:22

Quick and dirty CFD simulation of your problem using ANSYS Fluent 14.5: I used a 2D duct, 8" x 4" with a 45-degree angle going from the inlet pipes to the main chamber. Assuming 3 liters per hour flow through a half-inch diameter pipe gave me an inlet velocity of 6.6 mm/s. Air enters from the left and exits through the right. Inlet and outlet were set to a constant pressure of 101 kPa. I used the realizable $k-\epsilon$ turbulence model with standard wall functions. Computed velocity contours are below: You can see that the flow becomes very uniform by the time the angled parts meet the main duct. It may be hard to read off the image, but the difference in velocity between points A and B is about 1 mm/s.

Update

I re-ran the problem with the inlet going directly into the main duct - no expander section. Velocity contours are as follows: Velocity at point A is nearly zero (a dead-spot). Velocity at B is about 4 mm/s. The flow through the duct becomes uniform after about 1 inch into the duct, where I'm defining uniformity as when the velocity at the center of the duct is within 1 mm/s of the velocity near the wall.

The most interesting thing about the second case is the formation of dead spots in the corners. The flow is fairly uniform, but the dead spots may be bad if you need good ventilation there.