Aerodynamics/Physics question: Drag

[D.P.]

Looking at that device in the youtuve video has made one thing clear in my mind anyway, stop listening to me None of the zero-lift drag stuff I've talked about will help you.

Tell me about it.

 

[Duff-Man]

Where are you getting this "scale with speed squared" may I ask?

The concept of an overall drag coefficient is well defined. Although this coefficient is NOT constant when the velocity is changed, the force still scales as CD*speed^2 linky

In such a simple model, the first approximation will be to use a constant drag coefficient as I suggested. This would technically only be valid in a particular flow regieme (ie the coptor travelling at a constant speed), but will do as a first approximation. As I said before, the calibration of this constant needs to be done empirically - a collection of theoretical approximations won't give you good results in this case.

A further approximation would be to vary the drag coefficient with the velocity field. Of course, this leaves you with extra parameterisations - you must first find an appropriate function shape for the variation of CD, then you must calibrate the magnitude.

Its a stupendously complicated thing to try to break down, I have to say. Unless you have access to some very good experimental data you will not be able to come up with any sort of appropriate approximation that you can simply tack on in an ODE.

Turbulence simulations of helicopter flows is something I know my old department (Aero at Imperial College) is very much involved in, but there are very few people brave enough to tackle it.

As for modelling the turbulent downwash: Yes, the turbulence will effect the value of CD, and yes it will vary with *both* the impinging fluid stream and the turbulence intensity from the rotars. However, whatever way you look at it, these effects will be taken into account by the drag coefficient. Since you are empirically calculating the drag coefficient anyway, there is nothing to be gained by trying to incorporate some kind of theoretical model for the turbulent effect.

As for why it is difficult to model the turbulent effects of helicopter rotors: The usual pressure-velocity model for solving navier-stokes (which is used by all major commercial codes) does not accurately model the "starting vortices" which are produced constantly by the trailing edge of the rotor blades. The vortices are (numerically) diffused far too rapidly. To accurately model the evolution of such vortices it is neccesary to take a vorticity-based formulation, which is more difficult to solve.

But anyway, all this is irrelevant since without building a full-scale computational model of the coptor and solving for all available factors at a variety of different speeds, or doing real-world experiments, the only realistic way to approximate the drag coefficient is empirically.

btw I did my masters at Imperial Aero dept. as well Good department, but living in London sucks

tl;dr Calculating a reasonably accurate value for the total zero-lift drag is easy and doable (ie, ignoring the spinning blades). The issue is the unsteady effect of the 4 rotor downwash regions. I don't know how to deal with that, but I don't agree its fair to model it simply as a "square of the velocity."

The global effect of ALL these factors would be to modify the shape of the drag coefficient as the flow regieme changes. But since this is being determined empirically anyway, what would be the point of determining part of it with expensive computational models?

Nobody is denying the complex and intractible nature of turbulent CFD. But since the aerodynamic force is being calculated only at the centre of mass (overall body-force), the sensible thing is to take the simplest approximation of the forces ( F_aero = CD*v^2 which is dimensionally and physically valid), and take an empirical approximation for the drag coefficient. In this way you CAN tack the force on to existing ODEs.

I realize he's stated that the lift is linked to the rotor RPM by that function, but the amount of drag /= amount of lift. The local effect of the rotor blades will depend on their rotational speed (ie, main rotor RPM). This velocity will in most cases, assuming the helicopter isn't doing 150 knots, dominate the overall problem. The tips of the rotor on Bell 206 for example typically travel at around 210m/s as opposed to its typical cruise speed of 40m/s.

I make no assumption about the lift-model used, only that the *overall drag* on the coptor will scale as CD*speed^2, where 'speed' includes the average resultant velocity from the air moving downwards from the rotors. While this is related to the rotor turn-speed and size etc, a rotor with tips travelling at 200m/s isn't going to produce an average downwash speed of anywhere near 200m/s. It need not neccesarily dominate the aerodynamic forces.

In conclusion, your real task in this case - as with any simple *global* models of aerodynamic objects - is to calibrate the drag coefficient. A constant value will give you your first approximation. A more accurate model will see CD vary with impinging flow speed, but will obviously be more difficult to calibrate (you would want to do experimental approximations of CD at several different speeds and fit a spline to the results).

 

[NicktheNorse]

snip

Yes I agree - the place to start is with a constant Cd then as a further step take into account the way the Cd varies with velocity.

I see what you mean now about varying with velocity squared. Given a constant Cd (emphasis on the coefficient and constant) the drag value will of course vary with v^2 (duh, lol). What I was trying to point out was that we have no real way of knowing how the Cd varies with velocity seeing as its such a complicated issue. I thought you were arguing that the Cd varied with velocity^2.

Its all very well talking about all this but I still think its going to be damn near impossible to come up with experimental data to extrapolate a meaningful Cd vs velocity relationship. To get accurate information for the total drag at varying free stream speeds with powered rotors using a wind tunnel model is a phd in itself, ignoring any of the control/modelling side of it.

 

[Duff-Man]

Agreed. Determining Cd(v) will not be easy, at least not to any degree of accuracy. But the biggest contribution to the change in aero forces for a given change in velocity will come from the (v*2) term, rather than change of Cd with velocity, so even a constant Cd should 'feel' reasonably physical when you're playing with the model.

Note though, that the Cd at the maximum velocity of the coptor should be fairly simple to approximate (at terminal velocity F_drag = F_forcing, so if you know F_forcing_max and the top speed of the model you can have a good guess). From here, I would probably look towards existing Cd plots for real helicopters (if they exist in the public domain) to approximate a curve shape for your Cd. To do much more is unrealistic in your time frame I suppose.

 

[NicktheNorse]

Note though, that the Cd at the maximum velocity of the coptor should be fairly simple to approximate (at terminal velocity F_drag = F_forcing, so if you know F_forcing_max and the top speed of the model you can have a good guess). From here, I would probably look towards existing Cd plots for real helicopters (if they exist in the public domain) to approximate a curve shape for your Cd. To do much more is unrealistic in your time frame I suppose.

Good idea, probably the best you're gonna get for an initial approximation in this case

 

[D.P.]

Thanks for the advice- i understand most of that.

I was assigned an Indian Intern yesterday who has studied aeronautical engineering at Bombay... I will still if she wants to model this....