Calculate the wind tunnel box size
 

I am running a CFX simulation on a wing about 40m in half span. What wind tunnel box size should I use? As this is for a university year 3 project, could you please provide references to back your answer.

Is there a formula I could use to calculate this?

I am testing the A380's wing at a cruise speed of Mach 0.8 and an altitude of 13136.88 meters

Pressure: 16157.9 Pascal [29]
Dynamic Viscosity: 0.0000143226
Density: 0.259814 kg/m3 [29]
Wind speed: 250.75 m/s

You determine the boundary proximity by sensitivity analysis. You do a simulation with one proximity distance, and repeat with another proximity distance (say double the distance to the boundaries). Then you compare parameters of interest to you, which in your case are probably lift, drag and moment. If the parameters of interest to you do not change by a tolerance you are happy with then your boundary proximity is OK. If they are changing unacceptably then you double the boundary proximity distance again and rerun - and continue increasing the boundary proximity until the results converge to an accuracy you are happy to accept.

The concept of sensitivity analysis like this is fundamental to CFD. You should also do sensitivity analsyses of mesh size, convergence criteria and time step size (if transient). All these parameters are dependant on what you are modelling and how accurate you want to be, so need to be determined for your case.

Is there a rule of thumb sizing or is it more of a guess and test?

In general it is guess and test. If you can find other papers in the literature which have done similar analyses then that can give you a reasonable starting point.

Should I start with one chord length and then increase cord lengths until the value converges.

Also how about the distance away from the wing, above the wing, below the wing, in front of the wing, and behind the wing?

My supervisor said to calculate via Reynolds number but I can't imagine how that would be.

You can start anywhere you like, but a better starting guess will mean you need to do less iterations. I would be thinking 5 chord distances is a better starting point and you will probably end up around 10 for a final figure, but that is just a guess.

You can do all the directions individually if you like running lots of sensitivity analyses or you can do them all together by doubling all those distances together for each iteration.

I do not know of any way to get this from Reynolds number. Maybe your supervisor can tell us and then we will all learn something.