Use of scale models for aerodynamic test, dimensional analysis (similarity theory) and Reynolds number. Just to understand.

The concept of similarity theory in the study of the behavior of scale models, it is mainly used in the field of fluid dynamics.

Today there are many simulation systems (CFD – Computational Fluid Dynamic), but it maybe sometimes be useful to study a model reality such as wind tunnel where can make changes.

This article, without going into high-level theory arguments, to understand the importance or not of using a scale model for aerodynamic wind tunnel testing and discover the meaning of some technical term.

Literature tells us that the "scale-up" is satisfied when are observed the geometric similarity (same shape), kinematic similarity (same flow lines) and dynamics similarity (forces between the fluid and the surfaces of the real system and the model are constant).

At the same time while geometry can be reduced other sizes such as velocity, temperature, pressure etc. they are not immediately reduced; the similarity theory is based on the theorem π (pi-greek) or the Buckingham theorem*, but without going further on the literature regarding the subject we have considered a practical example of a test of a scale model in the wind tunnel to understand the benefit or downsides the use of this methodology rather than CFD software (that uses numerical analysis, finite volumes, finite elements method etc.) or rather than a real model, much depends on the budget available.

I took as reference an article of Simon McBeath (Racecar Engineering 2/2010) already author of texts, among others, like “Competition car composites” – Haynes Ed. or “Competition car preparation” – Haynes Ed.; seven years have passed, the technology has gone on but I think some evaluations are still current.

A scale model, that could be 1:2 scale, can be made by CAD drawings, if they are unavailable, it is used to scan through which to achieve the car body as well as all the parts that make it such as suspensions, wheels, etc.

The model is locked by horizontal sting and many scale wind tunnel offer the possibility to control some parameters by means of a data acquisition software that monitors the various model configurations; the moving ground is another important function available to some wind tunnels offering the possibility to know the interaction of the air flow between the ground and the bottom of the model; for the scale model is important to have the same air flow conditions (viscosity and density) of a real model so it is necessary that Reynolds number** of the scale model is the same as the real model, so for example in a scale model 1:4 the air velocity should be 2.5 times faster than the real model, so that the similitude is satisfied.

It is to be noted that things change when there is a moving ground situation that makes the test more likely, which is often adopted in the real model, other critical of a scale model occurs when the airflow enters the rear zone and the wheel lock systems which certainly have an airflow disturbance effect.

Whether a model will produce less reliable results for the possibility, for example, of assessing the effect of airflow with a less deep diffuser or lower wings incidence than a real model.

It is important to understand which reliable values can be derived from a scale model such as loads, moments, air resistance (drag), vertical load, roll, pitch and yaw moments; also the airflow behavior can be visualized through the use of smoke or wool tufts.

In a starting phase of analysis and study data obtained in a track test, with which good handling car can be found, can be used to compare these with those found in the model in the wind tunnel, is important to reduce evaluation errors.

** Reynolds number

from aeronautical and aero technique books we know that "aerodynamic resistance R is the sum of two resistances, one of friction and one of the shape, the first depends on the viscosity, the second from the game of pressures exerting on the surface, so proportional to the dynamic pressure."

Jumping some passages that relate the Reynolds number R and the coefficient of resistance we have directly R = V x l x σ / ? (adimensional number) where V : fluid velocity, l : body length characteristic, σ : fluid density, ? : fluid viscosity coefficient.

The forces to which a real fluid particle is subjected to in its motion are pressure forces, viscosity forces and forces of inertia; briefly it can be said that Reynolds number expresses the relationship between inertia forces (V, l, σ) and viscous forces (?)

Rpress + Rvisc = Finer

Rpress = Finer when viscous forces are very small

Rpress + Rvisc = 0 when viscous forces are very big

*Buckingham or pi-greek theorem

By way of example and without go into the subject the similarity theorem it’s based on this theorem that applied to a model through the Reynolds number :

Rm = Rr = Vm x lm x σm / ?m = Vr x lr x σr / ?r

Wanting to get the velocity of the model :

Vm = Vr x (σr/σm) x (lm/lr) x (?m/?r)

Where “r” is the real model and “m” is the scale model

This article does not claim to be an aerodynamic treaty but only manifest and express a desire for personal curiosity and for which I am looking for eventual comments.

Note : the wind tunnel model represented in the photos is our product.

References : Race car engineering (2010/2 - S. McBeath); Aero technique (1980 - G.Doria, C.Rovini - Pisa Italy)