Calculating the drag force on a spherical object with holes

[Taylor_1989]

I am looking for a bit of guidance on how one could calculate the drag force of a sphere with holes in the sphere falling through a fluid, in my case water.

So I know for a low Reynolds number the drag force on a sphere is given by stoke law, but what I would like to do is calculate the drag force on a sphere with holes in it.

I am very new to fluid mechanics and more or less want guidance on where to look, i.e should I be looking a Bernoulli equation for example, or could I form more of a drag equation from dimensional quantities?Any advice and guide would be much welcome.

 

[Chestermiller]

What is the nature of these holes? Dimples like a golf ball, or holes all the way through? And, what is their spacing and geometry?

 

[coquelicot]

Are you sure it will be possible to calculate it? a sphere with holes seems to me an incredibly complex thing for fluid dynamics. In my opinion, the best that can be done is to find a good simulator or solver that solves the Navier-Stokes equations step by step, and to find a way to extract from there some information.

 

[Chestermiller]

Are you sure it will be possible to calculate it? a sphere with holes seems to me an incredibly complex thing for fluid dynamics. In my opinion, the best that can be done is to find a good simulator or solver that solves the Navier-Stokes equations step by step, and to find a way to extract from there some information.

Maybe what the OP means is that the sphere is porous, and described by Darcy's (continuum) law. In that case, an analytic solution might still be possible for the case of creeping flow.

 

[boneh3ad]

A few things stand out to me here.

1. It is unlikely that this would qualify for Stokes flow, for which the criterion is $Re_D \ll 1$. Water is generally not viscous enough to cause objects to flow slowly enough through it to qualify. Unless the sphere has a specific gravity that is just barely greater than 1 and therefore buoyancy nearly counteracts the weight, then you probably can't use this approximation.
2. In general, "calculating" drag from first principles is very difficult to impossible for most flow examples. Fluid motion is too complex and varied for exact analytical solutions in most cases, and simulating the Navier-Stokes equations directly on a computer is prohibitively time-consuming for most real problems.
3. Depending on the exact situation here (which is not clear), you may be able to come up with an approximate solution based on something like Darcy's law per @Chestermiller's suggestion. At any rate, though, it will be approximate.
4. Why not just build a rig and test it?

 

[coquelicot]

A few things stand out to me here.
It is unlikely that this would qualify for Stokes flow, for which the criterion is $Re_D \ll 1$. Water is generally not viscous enough to cause objects to flow slowly enough through it to qualify. Unless the sphere has a specific gravity that is just barely greater than 1 and therefore buoyancy nearly counteracts the weight, then you probably can't use this approximation.

Do you mean that the Navier-Stokes equations are not suitable for water ?

 

[boneh3ad]

Do you mean that the Navier-Stokes equations are not suitable for water ?

No, I mean that the Navier-Stokes equations are remarkably complex, and fully-resolving them requires resolving such a wide range of length scales that many, many grid points are required and supercomputers often require months to solve even small problems. Google "direct numerical simulation."

 

[coquelicot]

No, I mean that the Navier-Stokes equations are remarkably complex, and fully-resolving them requires resolving such a wide range of length scales that many, many grid points are required and supercomputers often require months to solve even small problems. Google "direct numerical simulation."

I agree. But to estimate the drag force, you need only the solution during a very small amount of time, so, this still may be feasible for a standard computer (well, probably assuming some additional assumptions about the flow).

 

[boneh3ad]

I agree. But to estimate the drag force, you need only the solution during a very small amount of time, so, this still may be feasible for a standard computer.

You may only need it at a small instant in time, but you need time to solve every point in the flow, and depending on the method used, there may be substantial iteration and mesh refinement. It takes a very long time to do that.

 

[coquelicot]

We agree about everything. This can be tried though, it depends on the motivation of the OP.

 

[boneh3ad]

Yes, if he has months (years?) to spare to learn about gridding and numerical methods, and then program a DNS solver, and then wait for the solution to be finished, then the OP could try it. I suspect that's not really in the scope of the question, though, given the "very new to fluid mechanics" line.

 

[coquelicot]

Usually, it is more simple to find solvers others have already coded and released in the Web. Who want to reinvent the wheel ?

 

[Chestermiller]

We haven’t even heard back from the op since Monday. So we don’t even know the details of the geometry yet. So why speculate now?

 

[coquelicot]

We haven’t even heard back from the op since Monday. So we don’t even know the details of the geometry yet. So why speculate now?

Just for the fun

 

[boneh3ad]

A good reason to reinvent the wheel is because, if you don't know how your scientific tool works, then the answer it gives you is just as likely to be complete nonsense as it is to be useful, and you'd never know. Most commercial codes are not DNS codes anyway, and instead solve things like the RANS equations.

 

[coquelicot]

A good reason to reinvent the wheel is because, if you don't know how your scientific tool works, then the answer it gives you is just as likely to be complete nonsense as it is to be useful, and you'd never know. Most commercial codes are not DNS codes anyway, and instead solve things like the RANS equations.

Well, my opinion is that you don't need to know how to build a car, if you only need to drive it. Assuming for example the OP is an engineer with some math background, but with no or few knowledge in fluid mechanics, that has to engineer a product that has something to do with water. In one or two months, he can learn some basics of fluid mechanics, to seek a free or commercial equation solver, and to learn how to use it. Moreover, these solvers have in general a doc that explains roughly their method of resolution, the associated problems and how to program them. I used this strategy several times in my career, and for me that was just enough. Moreover, that gives our engineer an added knowledge and professional value worth of the spent time, even if this eventually don't provide him the solution of his problem.

 

[Taylor_1989]

Firstly sorry for the lateness, I have been having trouble accessing my account. The geometry is just a sphere with four holes place around the centre, I have realized since then this is a very difficult take on in general, and have tried to think of maybe fundamental ways of exploring the idea, one method I tired was think of creeping flow around a cylinder and then comparing this to the holes in the sphere of same size, another method I am trying is exploring the idea fluid flow through a hollow cylinder, these ideas are probably of the mark, but the general concept of this was for me to explore fluids on a fundamental level, a get an intuition to why I am wrong a get a feeling for how stoke equations play a role in fluids.

My background is I am undergrad, in physics and we never cover anything on fluids in great detail, actually very very little and I came up with the idea as it would be a way for me to explore fluids, maybe I have bitten more than I can chew, but it more of a learning curve.

I am trying to aviod looking for answers or code of the internet as I have mentioned, I am trying to do more of a free think approach.