Range of Reynold's numbers (Drag Lab)

[yonese]

[Mentor Note -- Thread moved from the technical forums, so no Homework Template is shown]

Hi all,

Recently I 'did' (a virtual lab) a drag laboraty experiment that used a wind tunnel to measure drag coefficient of 3 different shapes (cylinder, airfoil, triangular prism) and I'm not convinced the graph I've plotted is right.

The aim of the experiment was to obtain the drag coefficients for each body, for a range of air flow rates. When the fan in the wind tunnel is on and the valve is open, air impacts the object installed in the test section and a drag force is generated on the object. The objective of the experiment is to measure this drag force at different valve openings (i.e. different flow speed).

From this experiment, I've plotted a graph of each shape's drag coefficient vs Reynold's number (See below). The characteristic length were the same for the cylinder and prism, and the airfoil had a slightly larger value. I had expected the airfoil to have a smaller drag coefficient as it is streamlined and I expected the prism to have the highest drag, both of which are shown in the graph, so that's fine. However, something doesn't seem right. Firstly, the airfoil has such a large range of Reynold's number compared to its other shapes. Secondly, the prism's Reynold's number has a minimum of 7400, which means it's in the transitional state rather than turbulent like the other two shapes.

I have included the actual values below, if it is any useful.

	Reynold's Number, Re
Valve pos. (mm)	Cylinder	Triangular Prism	Airfoil
1 (Fully opened valve)	2.57E+04	2.29E+04	1.33E+05
0.9	2.34E+04	1.93E+04	1.18E+05
0.7	2.15E+04	1.62E+04	1.09E+05
0.5	1.93E+04	1.32E+04	1.03E+05
0.3	1.48E+04	9.93E+03	9.00E+04
0.1	1.05E+04	7.40E+03	6.15E+04
0 (Closed valve)	0	0	0

The average drag coefficients were 1.08, 2.43 and 0.063 for the cylinder, triangular and airfoil prisms, respectively. I compared these to an external literatures which had values 1.20, 2.0 and 0.045 respectively. So, I wouldn't say I'm too far off but something about the graph doesn't seem right.
I'm also not sure whether I should be using the average drag coefficient when comparing it to other resources, or if I use the fully open valve values.

Thanks in advance.

 

[Arjan82]

You'll have to be a bit more specific than this. What exactly 'doesn't seem right'? And why? What did you expect? Did you compare with literature at equal Reynolds number? Certainly for a cylinder the Cd vs Re should be readily available (also look for 'drag crisis' for cylinders).

 

[yonese]

What did you expect? Did you compare with literature at equal Reynolds number?

Thanks for your comment.

The range for the prism and airfoil weren't what I expected. The prism didn't have values that were always turbulent like the cylinder (as I has expected it to as I expected both shapes to be fairly similar considering their characeristic length were the same). My data has shown that towards the closing of the valve that the prism experiences transitional flow, which just wasn't what I expected.

I didn't compare the equal Reynold's number (which I've just realized I haven't done). I just compared the drag coefficients at approximately 10^4 but I don't know whether I should be comparing every single data point or using an average instead?

 

[Chestermiller]

I don't think that the air foil had a larger range of Re than the other shapes. They varied by a factor of about 2x in all the cases. Plot the results using log scales and see what you get. Also, please tell us what you used for the characteristic lengths in the cases of the prism and the airfoil.

 

[boneh3ad]

Reynolds number depends on using a length scale, $L$, defined by the body. If the length chosen for each body varies by a fact of 2, then that will show up in the Reynolds number you calculate. A useful concept here is that of the unit Reynolds number, $Re^{\prime} = \rho u/\mu$ (units $[1/L]$). That is often a nice way to define the flow in a wind tunnel because it can just be multiplied by the relevant length scale for any model to come up with the Reynolds number for the specific case. Assuming your $L$ was diameter for the cylinder and chord length for the airfoil (likely considerably larger than the sphere diameter), then the ranges you have make sense assuming $Re^{\prime}$ was reasonably constant.

Indeed, your low $Re$ point for the airfoil is about 6 times that of the cylinder and the high point is a little more than 5 times larger, what this really implies is that you have a smaller $Re^{\prime}$ range for the airfoil.

Also, what basis are you using for determining laminar versus turbulent flow here? That part left me confused.

 

[yonese]

Also, please tell us what you used for the characteristic lengths in the cases of the prism and the airfoil.

Hi, all 3 shapes have the same length of (L = 12.5mm), but I used the chord (c=62mm) for the airfoil instead to find its planform area instead. I can imagine that because the airfoil used a different length, this would affect the results plotted?

 

[yonese]

Also, what basis are you using for determining laminar versus turbulent flow here? That part left me confused.

Hi,

I'm just using the basis that laminar flow is when Re > 4000.

Correct me if I'm wrong, but are you saying that because the planform area of the airfoil (where the chord is 62mm) is larger than the frontal area of the prism and cylinder (l = 12.5mm), the Re number is what's been presented?

 

[Arjan82]

First off, I think you mean turbulent flow when Re > 4000 and laminar flow below.

However, the Reynolds number is a similarity parameter. This means that for a flow with equal Reynolds number, the flow is similar. That is, if either there are no other relevant similarity numbers (e.g. Mach number, Prandtl number, Froude number, etc.) or if they are equal as well. Let's now suppose that the Reynolds number is the only relevant similarity parameter.

This is nice, because if you are concerned with the flow around a cylinder, the characteristics of the flow (drag coefficient, lift coefficient, etc.) are equal at equal Reynolds number, whether it is a small cylinder in a flow with high velocity or a large cylinder in a flow with low velocity. Now, for this flow you can determine at which Reynolds number turbulence starts, say at 4000 indeed (although, usually it is more of a range rather than a single number.

Now, notice that this number is only valid, strictly speaking, for cases where you have exactly the same setup, so same geometry and the flow coming from the same direction. Notice further that if you base Reynolds on, say the length of the side of the triangle, then this 4000 is also only valid for that case. If you take another experiment where everything is equal but you base the Reynolds number on the triangle height, then you'll get a different number, say 3000 (or whatever) at which turbulence starts. So it is rather important to know for which setup the Reynolds number for transition to turbulence is determined, and also on which length the Reynolds number is based on that case. So there is no 'general' Reynolds number at which all flow transitions to turbulence.

Now, it turns out to be that if you determine the critical Reynolds number for a prism, then it will be in the same ball park for another type of blunt body, say a cylinder, or a square. But then the critical Reynolds number is a rough approximate.

You put a triangular shaped prism, a cylinder and a streamlined body (airfoil) in a flow. If everything else is equal, i.e. velocity, density, viscosity (i.e. the Re' is equal, as per the definition of @boneh3ad) then only the typical length of your body determines the Reynolds number of your experiment. If you measure drag on a blunt body (triangle, cylinder) it is common to take some length of the frontal area as reference (in this case the height, because I presume the width is the same for all). For this case that is also what I would do for the airfoil, to get a better comparison. Although, indeed it is more common to base the Reynolds number of an airfoil on its chord length.

If you then indeed get a range in Reynolds number for the airfoil which is rather different compared to the other two objects, then it is actually not entirely valid to directly compare the airfoil with the other two shapes. This also means that the thickness of the airfoil is much thinner than the diameter of the triangle and cylinder. So to do a proper comparison and you cannot change the geometry, then you should use different free stream velocities for the airfoil to get an equal Reynolds number and thus a better comparison.

 

[Chestermiller]

Hi, all 3 shapes have the same length of (L = 12.5mm), but I used the chord (c=62mm) for the airfoil instead to find its planform area instead. I can imagine that because the airfoil used a different length, this would affect the results plotted?

View attachment 281726

Then there's no reason to expect them to be comparable (since this is pretty arbitrary).

 

[boneh3ad]

Hi, all 3 shapes have the same length of (L = 12.5mm), but I used the chord (c=62mm) for the airfoil instead to find its planform area instead. I can imagine that because the airfoil used a different length, this would affect the results plotted?

View attachment 281726

Ultimately, the choice of length scales for shapes in a free stream is arbitrary and should be chosen based on the physics being probed and the comparisons being made. Here, you are looking at a flow phenomenon that is really dominated by the wake, and comparing shapes of what seems to be similar thickness, so using $t$ instead of $c$ to determine Reynolds number for your streamlined shape is probably more appropriate in this case.

Hi,

I'm just using the basis that laminar flow is when Re > 4000.

Correct me if I'm wrong, but are you saying that because the planform area of the airfoil (where the chord is 62mm) is larger than the frontal area of the prism and cylinder (l = 12.5mm), the Re number is what's been presented?

Where did you get the number $Re \geq 4000$? Also, what is transitioning here? How you treat this aspect of the problem would be very different if you are talking about the wake transitioning or the boundary layer transitioning. These phenomena also typically occur over a wider range of $Re$ depending on conditions. For example, The wake typically transitions somewhere in the range $10^2\leq Re\leq 10^5$ and a boundary layer may transition anywhere from $10^5\leq Re \leq 10^7$ (all orders of magnitude, not exact).

So $Re\geq 4000$ is okay for estimating the wake transition, but it's still something where you need more precision in your language at the very least. It would also help if you had data backing up that transition occurred there.