# Wind tunnel tests and Reynolds Number

I have a question about Reynolds Number and wind tunnel tests. Last semester a few students at my university were conducting wind tunnel tests on a small model of a truck, they were trying to find ways to reduce the drag in order to save fuel. I would guess they were testing at a Reynolds Number on the order of a few thousand which is no where near that of a full sized truck on a highway.

My question is, how valid are these tests if the Reynolds number is off a couple orders of magnitude?

When I brought it up they just said that they were only investigating the qualitative effects of various configurations. But based on my understanding even qualitative results may not be valid for very different reynolds numbers so I dont see how their results would be useful at all.

Thanks

## Answers and Replies

It depends on what they were specifically looking for. If they were simply looking for a certain effect to happen then the Reynolds number would not necessarily be important. However, if they were looking for an extent of an effect, then you would be correct in your assumption.

Here is a guess based primarily on unit analysis. The Reynolds number is approximately

Re = ρvD/μ where ρ is density, v is velocity, D is diameter of object, and μ is kinematic viscosity.

Re is a unitless number, so if D is reduced by a factor of 10, v would have to be increased by a factor of 10 to keep the Reynolds number the same.

Below a certain Reynolds number (like ~ 3000), the drag becomes Stokes Law for non-turbulent flow.

α β γ δ ε ζ η θ ι κ λ μ ν ξ ο π ρ ς σ τ υ φ χ ψ ω

I have a question about Reynolds Number and wind tunnel tests. Last semester a few students at my university were conducting wind tunnel tests on a small model of a truck, they were trying to find ways to reduce the drag in order to save fuel. I would guess they were testing at a Reynolds Number on the order of a few thousand which is no where near that of a full sized truck on a highway.

My question is, how valid are these tests if the Reynolds number is off a couple orders of magnitude?

When I brought it up they just said that they were only investigating the qualitative effects of various configurations. But based on my understanding even qualitative results may not be valid for very different reynolds numbers so I dont see how their results would be useful at all.

Thanks
They need to know what they are doing. Typically, experience will guide the wind tunnel engineer in knowing what range of Re the variables flatten out. For an airplane, typically Reynolds numbers below 0.6 million become iffy when comparing sub-scale models to full scale vehicles.

You should note, it's never possible to match the Reynolds number of a scale model in a wind tunnel that uses air at atmospheric pressure (this is true for nearly all wind tunnels).

Work out the dimensional analysis and you'll quickly see this for yourself.

When I brought it up they just said that they were only investigating the qualitative effects of various configurations. But based on my understanding even qualitative results may not be valid for very different reynolds numbers so I dont see how their results would be useful at all.
Here's a qualitative effect: air hitting the truck pushes on the truck to slow it down. Not very insightful, I'm afraid.

I'm with you, what sort of qualitative effect would be, at all, informative? So, ask them.

Here's a qualitative effect: air hitting the truck pushes on the truck to slow it down. Not very insightful, I'm afraid.

I'm with you, what sort of qualitative effect would be, at all, informative? So, ask them.
For a truck, they would like to know the coefficient of drag and side force, and how to reduce drag.

A reduction in drag is a reduction in drag (Most of the time, I'm not going to get into special cases because its outside the scope).

For a truck, they would like to know the coefficient of drag and side force, and how to reduce drag.
Those are quanitative. Maybe their just looking for ideas.

Those are quanitative. Maybe their just looking for ideas.
No, the coefficient of drag is a number. The quality of the number depends on what you're trying to do. For instance, if you want to reduce drag and a certain design feature causes a substantial reduction in drag, it's fairly safe to assume that the drag will also go down on the actual vehicle. Matching the number exactly gets dicey because of the transition point on the boundary layer, which is why people use trip strips.

The other day a Lockheed model of a C-130 was in the wind tunnel for drag reduction on the tail.

Well, they wouldnt be able to assume that the reduction in drag would be the same right? For instance, if the CD of the model decreased by 5% could you assume the CD of the truck would be reduced by 5%? Is there any way to scale this or is knowing drag will go down be the best you can do? What if the flow over the model is laminar whereas the flow over the prototype would be turbulent because of the difference in Re?

Well, they wouldnt be able to assume that the reduction in drag would be the same right? For instance, if the CD of the model decreased by 5% could you assume the CD of the truck would be reduced by 5%? Is there any way to scale this or is knowing drag will go down be the best you can do? What if the flow over the model is laminar whereas the flow over the prototype would be turbulent because of the difference in Re?
It won't be exactly 5% on the full scale vehicle, but it also wont be too far off. The only time you can assume that the drag coefficient of the car also goes down by 5% as long as the transition point is the same and that the Reynolds number is being matched.

If they are trying to designing a car, then they care about how to reduce drag. They'll probably use a smoke wand and/or tufts for flow visualization.

If, on the other hand, they are trying to improve an existing car, then they should already know where the full scale cars boundary layer transitions and use trip strips at that spot. Then the numbers should match up fairly well (provided the Re isn't in a range so low that it becomes sensitive to Re).

I don't do car aerodynamics, but since a car is a very unaerodynamic shape I would think the flow over it is not very laminar most of the time anyways. Cars are designed based on styling (for the most part) since rolling resistance causes more drag than the air does for speeds below 60mph.

I still strongly recommend that you write out an example problem doing dimensional analysis to see for yourself.

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Ok, lets forget about the truck and just consider a model of an aircraft. If you are testing at a much lower Re then the flow may be laminar even though on the prototype it would be turbulent, and with the laminar flow you are more likely to have separation bubbles that would not be present on the prototype. How do you correct for these things? You mention trip strips to induce turbulence so it matches that of the prototype but what if you dont know where transition occurs?

Ok, lets forget about the truck and just consider a model of an aircraft. If you are testing at a much lower Re then the flow may be laminar even though on the prototype it would be turbulent, and with the laminar flow you are more likely to have separation bubbles that would not be present on the prototype. How do you correct for these things? You mention trip strips to induce turbulence so it matches that of the prototype but what if you dont know where transition occurs?
"Much lower" is meaningless. If Cd is flat over a wide range of Reynolds numbers, then being an order of magnitude lower in Re than the full scale vehicle doesn't matter.

The point is, there is a range of Re you want to be in for certain vehicles. Once you go outside this range, the sensitivity to Re increases substantially. For most aircraft, 0.6< Re < 2 million is a good range to be in for testing.

Turbulent flow does not imply that you have separation bubbles, or that you are more likely to have them. Designing a new vehicle is tough because the use of trip strips is based on where you *think* the full scale vehicle will have separation. This is usually done by the tunnel engineer who has experience working with many aircraft models.

Higher angles of attack usually are better because the transition point moves forward, so less of the wing has laminar flow (which is where you are guessing it occurs when you use trip strips). It's lower angles of attack that comparison is not as good since you are using trip trips to guesstimate where transition is going to occur.

You should also look up a plot of Cd Vs Re.

as a side question, but not to get everyone off track, how did the students measure the drag? Strain gauges or pitot tubes?? I did something similar once and got some really sloppy data.

They used strain guages.

Why?

FredGarvin
How do you measure drag with pitot tubes?

you cant, it was my mistake. only lift can be found from pitot tubes. I was trying to relate lift and drag... but no go.

FredGarvin
Ummm...how do your measure lift with a pitot tube?

pressure difference on top and bottom of wing.

FredGarvin
Those are usually static pressure ports, not pitot tubes. What kind of configuration did you use?

I read this in a book or it was presented to me in my Aerodynamics class, but I must have mis-understood what configuration they used to measure the pressure. I thought they had an airfoil profile in a wind tunnel ( control volume) and lined the top and bottom of the tunnel with pressure gauges (maybe pressure transducers?) along the span of the wing. From that you can get lift.

As for my experiement, we used strain gauges to measure the drag on the sphere... but there were too many uncertainties and areas that produced noise and we got real sloppy data.

cant you measure static pressure with a pitot if you turn the inlet parallel to the flow?

Are you talking about a wake rake? Its a bunch of pitot static tubes lined up and traversed across the span of the airfoil to determine the loss of momentum in the wake of the airfoil. But Im pretty sure it can only measure drag.

The way I was thinking is if you have an airfoil in a control volume and air is running past it due to the curvature of the airfoil the air moves faster on the top than the bottom.

Due to bernoulli, the faster the air goes, the less pressure is exerted ( thats why wings have low pressure on top and high pressure on bottom)

Find the pressure difference and multiply by area... there is your lift force.

Static pressure ports would be the best way of measuring the pressure distribution along an airfoil. A pitot tube would interfere with the flow, and i would guess that it is difficult to maneuver a pitot tube around an airfoil especially ones with a lot of camber

russ_watters
Mentor
cant you measure static pressure with a pitot if you turn the inlet parallel to the flow?
Basically, yes - if you turn a pitot tube 90 degrees to the flow, it would essentially become a static port, though it wouldn't be in the wing, it would be on it.... I think you're just using the word wrong. In your previous post, you correctly describe drag measurment via pressure profile using static ports on the wing.