Model Rotor Similarity Parameters

The effects of Reynolds number and Mach number becomes particularly important when studying the performance of subscaled rotors, and especially when attempting to use these results to predict the performance of the full-scale rotor. See Section 6.8 for a summary, but the problems are discussed in considerable detail by Philippe (1990). The dimensions of most wind tunnels do not permit the testing of model rotors much above 1 /4-scale. There are, however, some special wind tunnels that permit the testing of larger rotor models. For example, the DNW tunnel in the Netherlands has a 32 x 32 ft (9.75 x 9.75 m) section where 40% subscale rotor models may be tested. In another large wind tunnel at NASA Ames Research Center, which has both 40 x 80 ft (12.2 x 24.4 m) and 80 x 120 ft (24.4 x 36.6 m) working sections, full-scale rotors may be tested.

For a rotor in forward flight, the speed similarity parameter is the advance ratio ii = Too/QR. Normally, the advance ratio is fairly easy to simulate in a wind tunnel environment by a suitable choice of rotor tip speed and V^. To simulate the aerodynamic effects, the Reynolds numbers and Mach numbers on the model rotor must be as close as possible to the full-scale values. In practice, this is not easy to achieve. For example, consider the attainment of full-scale tip Mach numbers on a 1/5-scale rotor. If the rotational frequency of the full-scale rotor is S3, then for Mach number scaling the rotational frequency of the model must be 5S3. Yet, the Reynolds numbers for the model will still be a factor of 1/5 those on the full-scale rotor. Thus, the model rotor may operate with Reynolds numbers that are in the sensitive regime, that is, in Reynolds number regimes where the aerodynamic characteristics of the blade sections show a higher sensitivity to Reynolds number. The inability of model rotors to achieve tip Reynolds numbers above 106 is a serious factor when trying to extrapolate airloads and rotor performance measurements to full-scale.

Table 7.1. Relative Scaling Parameters for a 1/5-Scale Rotor in Air and Freon

Scaling factors

Air

Freon-12

Mach number

1.0

1.0

Lock number

1.0

1.0

Advance ratio

1.0

1.0

Froude number

5.0

1.0

Reynolds number

0.2

0.53

Time

0.2

0.446

Angular velocity

5.0

2.24

Linear velocity

1.0

0.448

Force

0.04

0.0334

Moment

0.008

0.00667

Power

0.04

0.01419

Mass

0.008

0.0334

Some of the problems in matching Reynolds numbers and Mach numbers on models have been overcome by changing the test gas from air to Freon. However, the use of Freon as a test medium is expensive and can be used only in very specialized wind tunnels. Freon will allow full-scale tip Mach numbers to be achieved with a rotational frequency of 2Q with a 1/5-scale rotor. Furthermore, the properties of Freon allow the Reynolds numbers to be as high as 0.53 those of full-scale. The general scaling parameters for a 1/5-scale model in air and Freon are summarized in Table 7.1, which is from Philippe (1990).

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