https://www.atmos-meas-tech-discuss.net/amt-2018-354/amt-2018-354.pdf

With respect

Dušan

hello Dusan, in my opinion you should try to calculate the drag coefficient on the scaled vehicle inside the tunnel. That coefficient will be calculated using the drop pressure trough the model and a characteristic length associated to the scaled vehicle. For the real scale vehicle then you could use the same drag coefficient the real characteristic length and calculate the drop pressure.

Dear Apostolos,

The validity of wind tunnel results obtained in testing of scale models is based on the fluid mechanics Principle of Dynamic Similarity (White, F.M., Fluid Mechanics, 6 ed., Boston, USA: McGraw-Hill, 2003, p. 866) which states that: "If two physical phenomena can be described using the same formulation (same equations and same initial and boundary conditions), the solutions for one of the phenomena are valid for the other one."

For the motion of air around and obstacle, this Principle guarantees that the non-dimensional results measured in a wind tunnel for a scale model (e.g., lift, drag, and pitching moment coefficients) will be the same as for the real, full-scale obstacle if the following conditions are fulfilled:

For CFD, this is not usually a problem, since you have much flexibility in defining the boundary conditions and other settings such that these 4 conditions are satisfied and, for example, Re and M match those of the real fluid problem.

Now the dilemma comes when trying to extrapolate wind tunnel results to the real fluid problem: If the fluid properties for both the tests and real case are the same (i.e., same speed of sound (T), ρ and μ), and the scale model is smaller or larger than the real obstacle, it is obvious that it is not possible to have simultaneously the same M and Re as in the real problem. If we cannot replicate simultaneously both parameters, it is then necessary to choose which one will be kept similar to the real case. Generally, we choose the parameter with a stronger influence on the flow. For instance, roughly speaking M is dominant for supersonic flows and Re for subsonic flows (your case). Thus, for example, in high-subsonic testing, we would strive to work with the same Re as in the real case, and would not pay so much attention to M. Effectively, this means that we are not complying fully with the requirements of the Principle of Dynamic Similarity, and thus the test results have some error respect to the behavior in the real case. Many researchers have characterized the Re and M scaling effects to be able to correct for this error when extrapolating the wind tunnel results to the real case, if the Re and/or M in the tunnel are different than those of the real case.

If the fluid properties for both your tests and real case are the same, you should try to work with a model as similar as possible in dimensions the real obstacle, bearing in mind also these recommendations (Barlow, J.B., Rae, W.H., Pope, A., Low-speed Wind Tunnel Testing, 3 ed., NY, USA: Wiley & Sons, 1999, p. 713):

• Blocking coefficient (ratio of frontal area of model to frontal area of test chamber): should be less than 0.1
• Wingspan (or width) of the model: should be less than 4/5 (80%) of test chamber width

If you manage to have same Re and M, then the lift and drag coefficients (cL = Lift/(0.5*rho*V^2*S) and cD = Drag/(0.5*rho*V^2*S)) that you obtain from the tunnel can be extrapolated to the real vehicle. If you manage to have only the same Re, the lift and drag coefficients that you obtain should be corrected, but this error should not be very large and maybe the values from the tunnel are still valide to you. If you don't manage to have the same Re, then you could correct the cL and cD following the procedure described in the attached image from White's book Fluid Mechanics, for which you need to have values of cL or cD at several flow velocites (i.e., at several Reynolds numbers).

Hope this is useful,

Jose