# Aerospace Modelling drag force of big spheres in air.

1. Oct 18, 2012

### Vigardo

Hi all, I´m a researcher in computational biology thinking on topics quite far from my field. Would you help me? Thanks in advance!

I want to calculate the drag force in air of big rigid spherical and cylindrical objects at speeds form 0 to 100 Km/h. Their diameter would range from 1 to 20m.

Does anybody know where would I find this information?
Would you recomend me some good book?

2. Oct 18, 2012

### Angry Citizen

Look at the Anderson book, Fundamentals of Aerodynamics. Look for the section in chapter 6 on spherical bodies, or if you know the coefficient of drag for your shape, you could check out the information on how to calculate D from Cd. Incompressible flow is a good assumption for the range you want. It also assumes inviscid flow, so if you have a viscous fluid, it won't be a great approximation.

May I ask what you're wanting to model?

3. Oct 18, 2012

Since you're into computational stuff. You could write a code to calculate the drag using Newton's Method. All you do is enter the inital conditions and angle of attack and it will return the drag, drag coefficient etc. This method uses very simple assumptions, but it would give nice estimates with your range. It works by cacluating the pressure and integrating it over the defined surace. You have to enter in the geometry as points in global coordinates. I use this to give rough approximations before running CFD simulations.

4. Oct 19, 2012

Because, you know, angle of attack actually means something to a sphere...

If he is using simple shapes like this at velocities this comparatively low, there is no reason not to use use the simple CD values that you can find all over the place.

5. Oct 20, 2012

### Vigardo

Now I´m reading Anderson´s book. I´ll let you know if I don´t understand something.

6. Oct 20, 2012

### bigfooted

A sphere of 20m going 100 km/hr? The Reynolds number for this would be of the order of $10^7$!

The explanation and values that you can find all over the place for calculating drag coefficients are for example here:
This will get you started hopefully.

Most people use something like this for the drag coefficient of solid spheres in air:
$C_D=\frac{24(1+0.15Re^{0.687})}{Re}$ with the Reynolds number based on diameter: $Re=\frac{\rho V D}{\mu}$

Most research involves non-deformable objects so if you're working with hot-air balloons you should take into account the deformation to get a better prediction of the drag coefficient

Last edited by a moderator: May 6, 2017
7. Oct 20, 2012

### Vigardo

Thanks a lot Bigfooted, I´ll use your equations as soon as possible!
In principle, the balloon would be rigid, so the approximations should be ok.

And Angry Cityzen, I´m modelling a dirigible or balloon like object.

8. Oct 21, 2012

Yeah, but where's the fun in that. It seemed to me like he wanted to actual model it somehow himself. The object might not of been fully spherical, and he might want to model other objects... Picky picky...

9. Oct 21, 2012

10. Oct 22, 2012

### Vigardo

Hi, thanks all again for your precious help and time!

I´ve been checking your equations and computing the Reynolds number for several speeds and diameters of a spherical particle. As you can check in the attached table I made (see below), these numbers surpase quickly the applicability range of the equation cited by "Bigfooted" (Re > 2·105 value). In fact, only some values below 10km/h and 10m diameter fall within this range.
http://www.freeimagehosting.net/t/ax422.jpg

So, what equation would I use around 3.5~7 x 107 Reynolds? Should I use the values extracted from the NASA´s plot cited by "Boneh3ad", i.e. Cd in the range [0.1-0.5] (see below)? Am I runing out of valid available data?
http://www.freeimagehosting.net/t/o95k2.jpg

By the way, perhaps I misunderstooded something, but in the links cited by "Bigfooted" the Cd equation valid range goes up to 2·105, but "Boneh3ad" says: "is only valid for roughly 1 < ReD < 1000 and doesn't apply here". What do you think?

Thanks again!

Last edited: Oct 22, 2012
11. Oct 22, 2012

The link cited by bigfooted had a couple of different CD equations. The one that he cited was for 1 < ReD < 1000. There is also one for ReD < 1. For 1000 < ReD < 105, the drag coefficient is approximately constant. Above ReD = 105, it is simply more complicated and there is almost certainly not a closed-form solution. Your best bet is to approximate from the plots.

12. Oct 23, 2012

### bigfooted

I agree with boneh3ad that for such high Re it is better to find measurement data (and with high Re I mean you are not anymore in the Stokes or linear regime, and Cd becomes more complicated). Depending on the exact shape of your object and your Re, you are before or after the regime where turbulent flow separation occurs so it might be important to know if your object can be approximated as a sphere. There are many studies on the drag of spheres, but for balloon-shaped objects you can probably find some useful data on e.g. the NASA Technical Report Server.

13. Oct 23, 2012

### Vigardo

Hi all,

1) The equation cited by bigfooted (eq. 35 in that reference) says "0 < Re ≤ 2x105". From what boneh3ad says... should I assume that that equation limits are wrong? Which one is the valid in 1<Re<1000 range? (the eq. number of the reference will be enough, thanks)

2) From what you said, for ReD greater than ≈2x105, the following drag force (D) formula is not valid anymore, am I right?
D = 0.5 * Cd * ρ * V2 * A
By the way,
- is this formula the one I should use below 2x105 Re?
- the "A" is the frontal sphere area, i.e. π·r2? This one may be a bit stupid question, but I need to know it. For me is strange that you need to put the sphere diameter in both the Re number and the drag force (via A)...

3) Where would I find more information for air flows with ReD ≥2 x105 and basic rigid shapes like spheres and cylinders? Do you remember some book, web, or whatever? (I already tried google without much success...)

If exact Cd data for such a high Re is not available or drag is so shape (or surface roughtness) dependant that can not be determined without some detailed computational study, for me it would be ok just having some "valid range" of Cd to do some approximate stimations. Ok?

Thanks a lot! I really appreciate this!

Last edited: Oct 23, 2012
14. Oct 23, 2012

In the first link provided by bigfooted, the exact same equation is cited as being valid for 1<ReD<1000 range rather than 0<ReD<105. How do we know this first source is correct instead of the second source? We know that for ReD>105, the drag coefficient is effectively constant, so some power law formula probably isn't correct. Further, we have an analytical solution for the drag in the Stokes regime, so even though the equation you cite asymptotically approaches the Stokes solution, it isn't going to be exact. If you plot the function itself, you can tell that it doesn't work above 1000. Seriously, go try it.

No. That formula is pretty much always valid as long as the CD you use is valid and rooted in reality for your situation. The problem is you can't always find a nice simple relationship for CD, especially for more complicated shapes. At that point, you have to rely on empirical data or CFD solutions. Empirical data is usually better in those cases.

You can get some information from books like Anderson's Fundamentals of Aerodynamics but you won't likely find an actual formula for the flows you are looking for most likely unless you find one that is just something like a triple-deck solution that is fit to the data. The best I have seen is essentially a curve fit that works up to 106, and even that is just fitting a curve to experimental data. You can find that here if you are interested, but it still doesn't cover all of your range of sizes.

And this has already been given to you via the NASA plots.

15. Oct 23, 2012

### Vigardo

Regarding CFD and assuming it is a very complicated field... would it be possible for me, a non expert in aerodynamics, to perform some CFD for relatively basic shapes like spheres or cylinders? Can you recomend me some manual or tutorial "for dummies" and some software (free, if possible)?

Thanks a lot!

16. Oct 23, 2012

CFD, even for simple shapes, is quite time consuming and has a steep learning curve. It is also expensive since the meshing software is expensive, the solvers are expensive and the post-processors are expensive, plus you need one beastly computer to run it if not a cluster or bigger. As much as I'd like to help you out here, I don't really have that sort of familiarity with any CFD package. I am, at this point in my life, an experimentalist, though I am considering looking for a post-doc in CFD.

17. Oct 23, 2012

### bigfooted

CFD can be quite time consuming, which is why a lot of people are using simple fluid flow models, where the focus is the model for turbulence. Unfortunately these models are not really general in the sense that some models perform better than others for certain cases, but worse for other cases.

Creating a good mesh for your geometry, choosing a good model, and also choosing good solver settings can be quite tricky. This is especially so when trying to get good drag estimates.

I have a quad core at home and sometimes run some small test cases. Creating a 5 million cell mesh and converging a simple 2-equation turbulence model for steady state will take me less than half a day.

As an introduction you could try the book of Ferziger and Peric. Free software: you could try openfoam, but the learning curve is steep.

18. Oct 23, 2012