# How are wind tunnel models used when designing supersonic aircraft?

There are two things involved: wave drag and boundary layer separation. The wave drag depends on the Mach number while the latter depends on the Reynolds number of the flow. It's easy to maintain the incoming Mach number as it is independent of the geometry; however, the Reynolds number depends on the geometry of the model.

$$\text{Re} = \frac{\rho u d}{\mu}$$

If air is used as a medium, then assuming that the flow is to be maintained at a constant Mach number, $\rho$ and $u$ will be fixed by the gas dynamic relations. $\mu$ is pretty much out of our hands, so the only non-fixed parameter is $d$.

Since $d$ is much smaller for a model than for a real aircraft, the flow will have a lower $\text{Re}$ than a real aircraft would. This will give different flow separation characteristics for a model than for a real aircraft.

In subsonic testing, only thing that matters is $\text{Re}$, which can be fine tuned to match with the actual size by tweaking $u$ for given $d$. But in supersonic flow, we do not have that luxury, as $u$ is decided by the Mach number of incoming flow.

So how are wind tunnel models used for design of aircraft, spacecraft and missiles? Are there correction techniques to predict flow separation better? Can the same techniques be used for dealing with CFD data?

• The concepts involved in this topic are terrific and I don't want to discourage it. However, there essence of the question is answered in the second sentence of the wikipedia article on supersonic wind tunnels. I'd love to see more questions on the practicalities of scaling (I may post one of my own on a somewhat different topic soon).
– Dan
Feb 14, 2015 at 7:41

In the Fluid Dynamics community about 40 years ago, the group was primarily divided into experimentalists and theorists. However, at that time CFD was quite new, had to be run on expensive supercomputers, and untrusted. It was quite common that a theorist or experimentalist would at best discount the results of the CFD, while others may totally disregard the CFD results as useless. In fact, my former PhD advisor Dr. David Whitfield, was one of the early pioneers of using CFD alongside aerodynamics experiments at the Arnold Engineering Development Complex (AEDC). This reference explains well the thinking about CFD in those days:

At AEDC, CFD was used to supplement wind tunnel testing, but according to Dr. Whitfield, not a lot of people believed in CFD in the early 1970s.

"In fact," he said, "my efforts to promote CFD within AEDC in the early 1970s probably got me kicked-out, or through, most mahogany doors. However, when CFD was used to explain the source of the flow angularity problem in the test section of 16T, and when AEDC Fellow Dr. John Adams' CFD group in VKF explained how a tunnel there was actually operating at Mach 12 and not Mach 16 as previously thought, CFD found new life."

"I was told once that 'AEDC is a test-data place, and there is no place for CFD,'" he explained. "Our objective was to help those running the tunnels to be able to do their jobs better. I don't think AEDC should just be a 'test-data' place. Rather it should be a place for solutions and physical understanding of the problems, and this can be accomplished better by the mutual cooperation between those focusing on experiments and those focusing on numerics."

In those days, generally the designer would design a new prototype and send it to the wind tunnel to test, and maybe some CFD would be performed at the same time. There would generally be many prototypes built and tested, which was very costly. One such experimental facility where I used to work charged $16,000 per day of testing. On the other hand, with the development of robust open source CFD codes, such as OpenFoam, and cluster computers, CFD simulations are quite cheap. So, over time CFD began to mature, and with the popularization of cluster computers became quite feasible to run cheaply. With more and more validations with experiments being published in such journals as the AIAA Journal, CFD models have begun to be trusted more and more. Nowadays, the cost of running experiments is much more expensive than running CFD simulations. Therefore, more CFD simulations are used in the initial design stages, with many iterations back and forth, and even these days CFD-based design optimization (CDO) is often used in the design process. Nowadays, it is my understanding that wind tunnels are used these days primarily for the following reasons: (1) testing finalized prototypes, and (2) conducting fundamental research in supersonic flows, especially in order to develop more accurate numerical models. Regarding achieving flow similarity, when you have two different non-dimensional numbers, such as the Reynolds Number and the Mach number, the experimentalist must choose which number is most important to match. For subsonic flows, Reynolds number should be used, whereas for transonic and supersonic flows the Mach number should be used. Often times one is not able to match the Reynolds number of the actual prototype by using a model test in the wind tunnel. Consider for example a 747 which has a Reynolds number of 2,000,000,000 (reference). It is almost impossible to produce a wind tunnel which can match these types of Reynolds numbers. People have tried to increase the Reynolds number by decreasing the temperature and using low density gases at low temperatures. For example, the European transonic wind tunnel (ETW) is one of the world's largest cryogenic wind tunnels, which uses nitrogen as cold as -196$^{\circ}\$C, but only achieves a maximum Reynolds number of 50 million per meter. With a max test section length of 9 meters, the maximum possible Reynolds number would be 450,000,000, still less than half that of a Boeing 747. In these cases, people have developed scaling laws to deal with how to scale the results up to the larger Reynolds number. The scaling primarily has to do with the thickness of the boundary layer, which also effects other things like skin friction, and ultimately lift and drag. There was a special conference held at Princeton University in 2003 to discuss these issues. The results of that conference was this book: http://link.springer.com/book/10.1007/978-94-007-0997-3

From my experience experiments are only used to:

• validate numerical methods
• resolve flow-features which are not captured correctly by CFD (e.g. unsteady flow, differences in length and time scales, fluid-structure interaction)

As @Wes said the quality and accuracy of modern CFD is so high combined with the computing power of modern clusters that the conduction of simple experiments is normally not worth it anymore.