A Brief Explanation of Reynolds Number.

Judging from many comments in this forum, there seems to be a bit of confusion regarding Reynolds number. This isn’t surprising because flow in the boundary layer is quite complex.

Although basic aerodynamics assumes a perfect fluid that is incompressible and without viscosity, in the actual world, air is both compressible and viscous. Fortunately, aircraft of moderate size and flying at moderate speeds behave almost as they would in a perfect fluid. At high speeds, the compressibility of air must be accounted for and at low speeds, viscosity becomes a factor to be considered. Of course, Mach number is used as a measure of the need to consider compressibility, and Reynolds number relates to the influence of viscosity.

Reynolds number is a dimensionless number that is inversely proportional to the coefficient of kinematic viscosity and proportional to the velocity and some arbitrary dimension. The dimension is usually the chord of the wing but in case of a sphere or cylinder, may be the diameter.

The effect of Reynolds number on flow is far from linear. In fact there are some definite breaks in the curve. At very low R the flow close to the body (boundary layer) is smooth and layered (laminar flow). It very closely resembles perfect fluid flow. As R is increased, the flow separates at the widest point but remains laminar, creating a large wake, and the drag increases noticeably. As R increases further, the flow changes from laminar to turbulent and doesn’t separate until further aft of the widest part, reducing the size of the wake. When this occurs, drag drops significantly. This point is called the critical Reynolds number. For a sphere, this is around R=385,000. Unlike compressibility effect, which begins sharply with formation of a shock wave, the critical R is a rather wide band, and can vary considerably depending on the energy in the stream.

The use of Reynolds number is twofold. One is to compare bodies of different sizes (scale effect). A large body moving at a slower speed will have similar flow characteristics to a smaller body moving at a faster speed provided that the Reynolds number in both cases is the same. (This assumes that the higher speed is not so great as to encounter compressibility effect.) The second is to predict flow characteristics based on test data collected at a different R. Here is where a problem arises. Boundary layer flow is so complex that it defies rational analysis without sufficient test data. And extrapolation very far out of the range of the data collected, can be almost a WAG.

As an example, engineers at Boeing, and Lockheed, when designing the B747, and the C5A respectively, estimated drag by extrapolating from data from smaller aircraft, as well as wind tunnel data. During flight testing, it was discovered that the drag estimates were too high and both aircraft exceeded their design range figures by a significant amount. In those cases, the final results were better than estimated. As more such large aircraft have been built, test data at these large Reynolds numbers has accumulated making drag estimates on large aircraft a bit more accurate. At the other end of the spectrum, with very low Reynolds numbers, the estimates are likely to be overly optimistic.

If the R being considered is near a transition such as that involving laminar separation, or near the critical Reynolds number, any extrapolation is libel to yield questionable results. If well away from a transition R, extrapolation can give good results.

Anything that adds energy to the stream will affect the critical R and usually keep the boundary layer attached reducing drag. Thus a turbulator wire can be of benefit when operating near the critical R, but note that for R well outside of the critical range, there is little or no effect.

In designing the typical R/C model, dependable test data in the range of Reynolds numbers encountered is pretty sparse. Without such data, design becomes sort of hit or miss. Fortunately if you don’t stray much beyond typical design parameters the results are likely to be satisfactory. If you are designing for specific competition, the secret is to test, test, and test. It also helps to keep good notes.

[One test is worth a thousand expert opinions.]