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Roued August 1, 2000 07:28

Model scaling

It may be the wrong forum, but I will try anyway.

Does anyone know what to do, when scaling buildings/ airflow from full scale to windtunnels size:

( 1:1 ----> 1:10/1:20 )

Normally, one whould also scale the the Reynolds number as well(Re = 5000 for full scale). But this is clearly impossible !

Sofar we have tried to turbulent flow in the hole domain of the windtunnel. This includes both outside and inside the scaled building.

This is quite important when we move to CFD, since most of the current turbulence models are not good in very low turbulent regions.

Are there other ways proceed ???



John C. Chien August 1, 2000 09:22

Re: Model scaling
(1). You just calculate the wind tunnel test conditions. (2). In this way, both will be consistent. (3). You can then run the calculations for the real building conditions. (4). To interpret the wind tunnel test results in terms of the real building flow is something else.(that's why people are using cfd simulation. There, you don't have such limitations. assuming that the turbulence models are worked out already.)

Adrin Gharakhani August 1, 2000 13:24

Re: Model scaling
> Normally, one whould also scale the the Reynolds number as well(Re = 5000 for full scale).

Absolutely not! In fact, you would use the Reynolds number as your scaling contraint. That is the whole idea behind non-dimensionalizing the Navier-Stokes equations (and coming up with the Reynolds number)

What you need to do is to keep the Reynolds number fixed. Since you are reducing your length scales by 10 or 20, then you have the luxury of playing around with your free stream velocity and viscosity such that their ratio (10 or 20) will keep the Reynolds number fixed.

Which to modify? Velocity or viscosity or both? This depends on your measurement and equipment capabilities, as well as what it is that you are interested in. If vortex shedding frequency is of interest (and if you are not sure whether the Strouhal number is fixed with Reynolds number) then you will perhaps have to scale your velocities under the constraint of the Strouhal number as well as the Reynolds number.

Practically all introductory books on fluid mechanics devote a chapter on non-dimensionalization. You may have to revisit it.

Adrin Gharakhani

John C. Chien August 1, 2000 14:34

Re: Model scaling
(1). If a two story building is 20FT high, the hurricane wind is 100MPH, the (1/20)scale model building is 1FT high and the flow in the wind tunnel will be 2000MPH (20x100MPH), to keep the Reynolds number the same. (2). At this speed, it is about Mach 3 (three times the speed of sound). (3). Even at 30MPH wind, the tunnel condition will be 600MPH(30MPHx20), which is very close to Mach 1. So, both conditions (Mach 3 and Mach 1) in wind tunnel will generate shock waves in front of the building.

Adrin Gharakhani August 1, 2000 15:44

Re: Model scaling
Good. I hadn't done the math. But

(1) The stated Re is 5000 (didn't say based on what, but I'll assume based on the width and not the height, and will further assume it to be 1 ft in the model) The kinematic viscosity of air is approximately 2E-5 m^2/s, which give us a free-stream velocity of less than 0.33 m/s [33 cm/sec]. This is subsonic and will remain so even if I made the wrong assumption about the width (being 1 ft) by a factor of 10.

Clearly, since the Reynolds number, the geometry and the medium (air) are fixed, we don't have the choice to assume just any velocity (as I'm sure you know)

(2) I did mention that one has the choice to play with the velocity as well as the viscosity. So, in case the Reynolds number is high and we end up with a high Mach number flow in the model, we need to look into the viscosity as a parameter. I don't know what gasses could substitute air for this problem. Helium or Hydrogen have an order of magnitude higher kinematic viscosity. There is a reason why certain tests are done with water (or glycerine) analogues instead of air! (I know there are cases when one cannot avoid the Mach issue, but this is not one of them)

Adrin Gharakhani

John C. Chien August 1, 2000 15:52

Re: Model scaling
(1). It must be an interesting problem to study the flow around the building at 33cm/sec. I think, it is slower than the air coming out of the nose.

Adrin Gharakhani August 1, 2000 16:53

Re: Model scaling
> It must be an interesting problem to study the flow around the building at 33cm/sec.

Yes, I was actually going to make the same comment :) It is possible that the stated Re=5000 was the "scaled" value, so that the original would be Re=100,000. Even in this case we'd have about 6 m/s for the velocity.

Anyway, the point I made in my original post was that the Reynolds number _cannot_ be scaled, no matter what (shocks or no shocks). I was not interested in the numbers. If, we end up with large velocity values, etc., then we'll have to think of alternatives but we should still keep the same Re. Period.

Adrin Gharakhani

Roued August 1, 2000 17:39

Re: Model scaling
Hi, again

Here are just some information about what kind of building I am talking about.

The full scale building is 8 meters in height and 12 meter in width.

The "normal free streem wind velocity is about 10 m/s in 10 meters height. And a profile (exp) in fitted so that is matches that of common boundary layer profile.

In the wind tunnel using 1:20 scale model, the building is a open type, which means that in the side of the buidling there is a 1 meter opening (height)and in the full width of the building. (Natural ventilation).

The Reynolds number of the flow inside the building would be of about 5000 - 9000 based on the opening height.

AND since we were doing wind tunnel test in air, the viscosity stays the same. So only the wind velocity can be changed. And since we do not want to have compressiblity effect or any Mach number in the wind tunnel we can not have the same Reynolds number. The wind tunnel is 3m x 6m (height x width), lenght (test section) is about 20 meters.

Since we would like to have the same motion of eddies inside the building in full scale and scale model, we have assumed that by precerving a full turbulent motion inside the building would give some similarities to the flow in the full scale. (???)

Results obtained for wind tunnels velocity of 3, 4.5 and 6.3 m/s shown that only 4.5 m/s and 6.3 m/s gives full turbulent motion inside the building, where 3 m/s does not give a full developed turbulent motion,eg. the flow have transitional effect.

BUT DOES anyone know some papers about the kind of problem with scaling effect ???

Thanks very much in advance.

Regards Roued.

Adrin Gharakhani August 1, 2000 18:28

Re: Model scaling
At the risk of sounding repetitive (since I am), you cannot "scale" the Reynolds number. Call it anything else, like "we are trying to solve a _different_ problem by chosing a different Re", but do not call it scaling.

Anyway, I could not really understand the geometry specification, but given your numbers I don't see how you'll have _important_ compressibility effects. And why not use something else besides air. If you want a true scaling, you are not forced to use air. Check Tables for other gases with higher viscosity.

Having said that, there are problems where the flow characteristics are independent of the Reynolds number for a wide range of Re. In this case, you can safely solve a different problem (at different Re) and yet get all the relevant info (but you have to be careful with the interpretation)

However, at Re=5000 (and I couldn't figure out whether you are solving an internal or external flow problem) the probability that the flow will depend on Re is high.

Adrin Gharakhani

John C. Chien August 1, 2000 22:35

Re: Model scaling
(1). Based on your description, I think, there is one parameter involved, that is the Reynolds number.(Re=U*L/nu, where U is the free stream velocity, L is the height of the opening in the side of the building, and nu is the kinematic viscosity of the air). (2). To do the model testing, the Re for the model testing condition must be the same as the real world condition. In other words, the Re must be the same, even though the individual U,L, and nu can be different in the model testing. (3). If you use the same nu in the model test, then U*L should remain the same for both the real world building and the model testing. (4). If the L is reduced by a factor of 20, then U must be increased by a factor of 20. This will result in the wind tunnel velocity of 20x10m/s, which is 200 m/s. This is roughly equal to Mach 0.55. (5). In your tests, the velocity in the wind tunnel was roughly around 5 m/s, which is 40 times smaller than the real world Reynolds number. (6). If the Reynolds number of interest inside the building is of order 1,000,000 to 10,000,000 then a factor of 40 lower will be 25,000 to 250,000. In this range, it is likely that the physics of the flow will be roughly the same, and the wind tunnel test data will still be useful. (with a correction factor of Reynolds number) So, the test results can be corrected for the Reynolds number, that is from the test Reynolds number to the real world Reynolds number, if you can establish the trend or the formula. (7). In the case when the Re range is low in the scale, flow transition will occur, that is between the laminar flow and the turbulent flow. It will be difficult to establish a relationship between the wind tunnel test data and the real world results, because the physics of the flow has changed. (8). Other than this accuracy issue, the wind tunnel test data will still show you some effect due to the external flow. I mean you will still get the induced flow effect, although it is hard to quantify the result in this case.

Robin Bornoff August 2, 2000 01:47

Re: Model scaling
The often referenced paper below will certainly help:

Castro, I.P. ? Robins, A.G. (1977) The Flow Around Surface-Mounted Cube in Uniform and Turbulent Streams. Journal of Fluid Mechanics 79, 307-335


Brad Wescott August 29, 2000 11:58

Re: Model scaling->similitude
Try any first course in fluid mechanics book such as: Roberson/Crowe "Engineering Fluid Mechanics" and look under "similitude". They discuss proper scaling to ensure you have satisfied geometric as well as dynamic similitude to obtain meaningful results with a prototype.


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