The Wind Tunnel
Simulation
In these times, computers have replaced many procedures that would have once needed to be done in real life, such as crash testing for cars (1), which has been replaced with simulators as open-source as Beam NG (2), and for larger companies, programs like LS-DYNA (3), so that expensive prototypes would not need to be built, just to be immediately destroyed for data.
Interestingly, one area that is still predominantly not simulation-based in Fluid dynamics. Many programs do exist for modelling the movement of air around components, but in real-life testing, there is often a fatal discrepancy between how the simulated model reacts and how the model really reacts, which often rules CFD out of the question (4).
In order to understand why wind tunnels are necessary, it is required to understand how CFD works, so we can compare the differences between them. CFD works on the Navier-Stokes equations, which are the same equations we all know as the conservation of energy, the conservation of momentum, and the conservation of mass.
The physics
One of the Navier-Stokes equations is:
(5)
While this looks complicated, the mass per unit volume is density, or ρ, so when multiplied by a certain volume, it simplifies down to mass. The dV/dt is just the change of volume over time, which is dependent on the velocity of the fluid – if a fluid is moving faster, more volume is being pushed through a certain area in a given time, which is why many high-speed pumps for performance vehicles are rated in litres/minute. When mass and velocity are multiplied, the product is momentum, so the left side of this equation finds the momentum of a sample of liquid (6) , while the right side simplifies down to the same equation (mv) but with environmental factors in the equation so that the equation can be used to model liquid under certain conditions like gravity, drag coefficients and different temperatures (7).
How CFD works
CFD partitions what would normally be an infinite number of particles into a set of discrete packets, known as cells. The size of the cells is inversely proportional to the accuracy of the simulation; smaller cells are more akin to real, small air particles, while larger cells, while much easier to compute, are less representative of fluid particles (8). Different applications use different cell sizes – meteorological cases use cells that are around 3km wide, which is known as a ‘coarse’ mesh, while car companies can use cells that are one millimetre wide, and scenarios which need the upmost care such as Formula 1 use cells in the microns, which can take days to compute, even on the best hardware imaginable (9). CFD can provide incredibly precise data, such as providing the Reynolds’ Number, which is a value of how smooth airflow is, to within 5% of its true value (10).
All this seems to render wind tunnels obsolete, but while a percentage uncertainty of 5% may seem very accurate, in practice, complex systems in CFD can never give reliable results.
Real world scenarios
Consider the case of a Formula One team trying to simulate how air from another car in front of another will affect its performance, which is a phenomenon known as dirty air, where a car can lose a huge amount of its downforce simply by being behind another. It is, of course, in the interest of a racing team to ensure that their car is barely affected by the dirty air from the car in front, meaning their car can follow closely without losing performance. This helps the driver stay close and prepare for overtaking (11).
At the same time, the team wants their car to create a strong dirty air effect on the cars behind, disrupting their airflow and making it tougher for those cars to follow closely. This gives their driver a strategic advantage by making it harder for competitors to catch up or pass(12).
The team could try to use CFD to model this, but when looking at the pathway for air, it’s clear why this isn’t feasible for much more than a prototype.
Air initially hits the front wing, and the simulation can model this to a high degree of accuracy. Then, this air hits the rotating wheels, interacts with the air that the wheels have disturbed, runs along the body and over the wings, over the rear tyres with the same issues as the fronts, and then over the rear wing. Each one of these interactions adds that 5% uncertainty, and now the Reynolds’ number of the whole car can be very inaccurate. When you consider that this is just the simulation of one of the cars, and that the air from it has yet to even pass over the second car, it can become easy to understand why CFD has a long way to go before it can replace wind tunnels (11).
Considering miniature wind tunnels
One of the greatest innovations in aerodynamic simulation is the use of miniature wind tunnels. A full-sized wind tunnel, capable of pushing wind through it at 200mph, and with a rolling road that can reach similar speeds, easily costs over 30 million pounds, and this is just the initial building cost - operation and maintenance costs make 30 million look like a drop in the ocean.
This makes it clear that smaller wind tunnels seem to be the perfect solution – to model a 4m long car that goes 200mph, it seems obvious that you can just scale it down 10 times, and only need a wind tunnel around 40cm long, capable of just 20mph. If these were the case, then maybe large-scale wind tunnels would in fact be obsolete, but due to the nature of fluid dynamics, this intuition does not hold (13).
To measure the Reynolds number of air after an interaction, the general equation is VL/η, where V is the velocity of the air, L is the length of the subject, in this case the car, and η is the kinematic viscosity, which is just a fancy number that relates to the property of the fluid itself, so we can assume its constant since air is roughly always the same (14). The interesting part of this equation is the VL – if we want to make the length of the model 10 times smaller, the velocity of air over it must be 10 times larger – a model car 40cm long would need air flowing over it at 2000mph to match the Reynolds number of a real car that’s 4 metres long going 200mph (15).
This is one of the largest limitations of model wind tunnels; some constants can simply not be modelled effectively by a miniaturized model (16). Another example of this is boundary air, which is a thin layer of air that ‘sticks’ to something moving through the air. Ideally, this boundary air would be laminar (17), or smooth and uninterrupted, which it often is in full-sized cars, since an imperfection, like a dent, in a full-scale car is negligible when compared to its full size. In a small car, however, even a slightly bumpy paint job can completely throw off simulations (18).
Making the wind tunnel
I wanted to test for myself these limitations and the strengths of a wind tunnel at the 1:64th scale, which is the scale of every Hot Wheels car (19). I used a Datsun 510 Hot Wheel (20)(21) I had lying around, but unfortunately, there were no 3d models of this exact car online, so I had to model it myself.
I then uploaded this model to Sim Scale, which is an open-source source free CFD Software
I then modelled some walls to give it some similarity with a real wind tunnel. In the settings, I could set these walls to be non-slip, meaning air wouldn’t interact with them. This is another disadvantage to wind tunnels- the tunnel itself will always interact with the air, even if they are very smooth, since if the model redirects air upwards, the ceiling of the tunnel will slightly increase the pressure required to get this to happen - “The walls of a wind tunnel influence the airflow around a model, causing wall interference effects that must be considered to obtain accurate aerodynamic measurements (22). These effects can be minimized by increasing the size of the test section or by applying correction methods.”
Before this, I started work on the wind tunnel itself. It was very simple, just a PC fan powered by a simple circuit with a potentiometer, and a wood cage, then a water mist maker to visualise the path of air.
I used an LED strip backlight and got some great pictures of the airflow over the same Hot Wheel mentioned prior, then 3d modelled the car itself in Onshape, and uploaded it to a CFD program with identical parameters as the real wind tunnel:
Conclusion
Overall, I am happy with how the project turned out. The wind tunnel I made worked with showing key details about airflow over the model. Attached flow can be seen around the hood and front window, showing stable, laminar aerodynamic flow, while separation flow can be seen behind the roof rack and rear window. This separation is where wind is forced to spin into vortices, which takes a lot of energy out of the car to maintain, which causes drag. Since there is a large dark region lacking smoke behind the car, similar to the 3d model, this shows that a near vacuum has been created here, since the car has pushed away all the air around it, leaving almost no air behind it. This causes inefficiency for 2 reasons – the simple reason that the car is ‘sucked’ backwards into the vacuum, and the more noticeable effect of these vortexes getting amplified due to the huge pressure differences behind the car and next to the car. Even more vortex shedding is evident with smoke trails that curve downward or upward sharply near the back, that indicate pressure gradients.
References:
1 NHTSA. Vehicle Crashworthiness. National Highway Traffic Safety Administration. https://www.nhtsa.gov
2 BeamNG. “Soft-Body Physics for Vehicle Dynamics.” BeamNG Tech Docs. https://beamng.com/
3 Hallquist, J. O. LS-DYNA Theory Manual. Livermore Software Technology Corporation, 2006.
4 Versteeg, H. K., and Malalasekera, W. An Introduction to Computational Fluid Dynamics: The Finite Volume Method. Pearson, 2007.
5 Kundu, P. K., Cohen, I. M., and Dowling, D. R. Fluid Mechanics. Academic Press, 2012.
6 Batchelor, G. K. An Introduction to Fluid Dynamics. Cambridge University Press, 1967.
7 Fletcher, C. A. J. Computational Techniques for Fluid Dynamics. Springer, 1991.
8 Crowe, C. T., Sommerfeld, M., and Tsuji, Y. Multiphase Flows with Droplets and Particles. CRC Press, 1998.
9 Menter, F. R. Zonal Two Equation k-ω Turbulence Models for Aerodynamic Flows. AIAA, 1994.
10 White, F. M. Viscous Fluid Flow. McGraw-Hill, 2006.
11 Katz, J. Race Car Aerodynamics: Designing for Speed. Bentley Publishers, 2006.
12 FIA Formula 1 Technical Regulations, 2025 Edition. https://www.fia.com
13 Barlow, J. B., Rae, W. H., and Pope, A. Low-Speed Wind Tunnel Testing. Wiley, 1999.
14 White, F. M. Fluid Mechanics. McGraw-Hill, 2011.
15 Pope, A. Wind Tunnel Testing. Wiley, 2000.
16 Munson, B. R., Young, D. F., and Okiishi, T. H. Fundamentals of Fluid Mechanics. Wiley, 2009.
17 Spalart, P. R. Strategies for Turbulence Modelling and Simulations. International Journal of Heat and Fluid Flow, 2000.
18 Pope, A. Wind Tunnel Testing. Wiley, 2000.
19 Mattel Inc. Product Specifications. https://www.hotwheels.com
20 Nissan Heritage Collection. https://www.nissan-global.com
21 Rally Car Dimensions, Rallyways.com.
22 Houghton, E. L., & Carpenter, P. W. (2003). Aerodynamics for Engineering Students (5th ed.). Butterworth-Heinemann.
