[i.sabahi]

Hello dear forum members


I got a simple question regarding my thesis. Imagine a simple 2dof, 2D airfoil (NACA 0012, for example) in a wind-tunnel. The airfoil is considered a Rigid body, it has no elasticity. The 2 degrees of freedom are rotating and pitching movements and the constraints are a torsional spring and a normal spring both attached to an arbitrary point along the chord.



1. If the flow is considered laminar, can any dynamic instabilities occur at any high-enough wind speed(U)? If yes, how about flutter?


2. What if the wind is turbulent?



In general, what is the simplest(simplest to model and simulate) setup in which we can see the flutter phenomenon?




I searched the forum and the net for the answer first, but didn't find anything useful. My knowledge is more in structural mechanics, so please pardon me for the stupidity or the simplicity of the question.


Best regards
Iman

[FMDenaro]

Originally Posted by i.sabahi

Hello dear forum members


I got a simple question regarding my thesis. Imagine a simple 2dof, 2D airfoil (NACA 0012, for example) in a wind-tunnel. The airfoil is considered a Rigid body, it has no elasticity. The 2 degrees of freedom are rotating and pitching movements and the constraints are a torsional spring and a normal spring both attached to an arbitrary point along the chord.



1. If the flow is considered laminar, can any dynamic instabilities occur at any high-enough wind speed(U)? If yes, how about flutter?


2. What if the wind is turbulent?



In general, what is the simplest(simplest to model and simulate) setup in which we can see the flutter phenomenon?




I searched the forum and the net for the answer first, but didn't find anything useful. My knowledge is more in structural mechanics, so please pardon me for the stupidity or the simplicity of the question.


Best regards
Iman

In an air-wind tunnel, you should be aware of the role of the Reynolds number. Considering the kinematic viscosity and a small chord lenght of the airfoil (say 10^-1m), a velocity of 10m/s gives you Re=O(10^5) which on an 0012 airfoil can be still assumed laminar. However, the condition depends also on the inflow produced in the wind tunnel, of the level of turbulence intensity is quite small. Consider that the flow should be steady, no alternate shedding from the trailing edge should be present.


About the turbulence question, you should consider if the inflow is already turbulent or you want to study a turbulent separation along the airfoil.


I think you can find many references in internet

[msaravia]

You should determine the instability regions of the coupled aeroelastic system. The instabilities occur even in the laminar regime and even for small rotation angles. See for example, the Hodges book.

[Alex C.]

As far as I'm concerned, the simplest aeroelastic model that can have flutter instability is a rigid 2d airfoil mounted on a rotational spring.

Depending on the mounting position along the chord, flutter will occurs.

I see this as a very (very) rudimentary model of a fluttering flag.

[i.sabahi]

Thank you all for taking the time to answer,

Originally Posted by FMDenaro

About the turbulence question, you should consider if the inflow is already turbulent or you want to study a turbulent separation along the airfoil.

Dear Filippo, I understand that the inflow being turbulent or not is a condition which isn't determined naturally in a wind tunnel experiment, we ourselves dictate it(I intend for it to be non-turbulent), but when the flutter occurs, I assume that naturally the flow will become very unsteady and very turbulent around and downstream of the (largely)-moving airfoil. What I'm saying is that a turbulent simulation of the problem will surely be more accurate.(If I'm wrong please tell me.)
But the question was that even if we neglect the turbulent effects that will occur on the trailing edge and downstream and try to run the simulation with non-turbulent methods, will we ever see any flutter in the simulation?

Originally Posted by msaravia

You should determine the instability regions of the coupled aeroelastic system. The instabilities occur even in the laminar regime and even for small rotation angles. See for example, the Hodges book.

Dear Martin, I've studied the Hodges book and for the simple case of a 2d, 2DoF rigid airfoil such as the following picture in a steady-flow condition(L = 2πρ_∞b(U^2)θ & M_(1/4) = 0), the flutter analysis is preformed.




The example configuration in Hodges' book, is as follows:

a = −1/5, e =−1/10, μ = 20, r 2 = 6/25, and σ = 2/5. Here r is the dimensionless radius of gyration of the wing about the reference point P, σ is the ratio of uncoupled bending to torsional frequencies, μ is the mass ratio parameter reflecting the relative importance of the model mass to the mass of the air affected by the model, and V is the dimensionless freestream speed of the air, sometimes called the reduced velocity.
(For this configuration)The flutter speed is V F = U F /(bω θ ) = 1.843, and the flutter frequency is Ω F /ω θ = 0.5568.

I understand that "steady-flow" either means fully developed laminar or macro-scale turbulent flow. Does it mean that if i simulate the same configuration with laminar flow(either in FLUENT or OpenFOAM, the latter being the one I aim to use), I'd get the same results? And if I get the simulation right and the airfoil section movement amplitude starts to increase, surely the large displacement will cause turbulent separations and vortexes will be created, and because I'm using the laminar model, I won't be able to see them and include their effect.

Look at this quote from the hodges' book regarding the same problem:

However, the above analysis is deficient in its ability to accurately predict the flutter speed. Moreover, the damping of all modes below the flutter speed is predicted to be zero, which is known to be incorrect.
The main reason for these deficiencies is that the aerodynamic theory from Chapter 4 was used. Although the aerodynamic theory has obvious deficiencies, such as its linearity and two-dimensionality, a very significant deficiency as far as flutter analysis is concerned is that it neglects unsteady effects, which are in general very important for flutter problems.

I guess what I'm asking is:
1.How do I simulate the same steady-flow problem(I mean which flow models to use), and
2.How do I capture the flutter using this steady-flow, knowing that it'll make the flow very unsteady and "un-laminar"?


Thanks in advance