# Using Simifarity Principles in Planning Experiments

It is useful to take similarity principles and dimensionless numbers into con­sideration when planning experiments. Experiments may involve different lev­els of velocities and temperature differences. It is important to select values that give a large variation of Archimedes number (12.56) to obtain a high pos­sibility of large physical effects in the measurements.

The assumption of a self-similar flow (Reynolds number-independent flow) simplifies full-scale experiments and is also a useful tool in the formula­tion of simple measuring procedures. This section will show two examples of self-similar flow where the Archimedes number is the only important para­meter.

Figure 12.41 shows the results of three experiments with a similar Archimedes number and different Reynolds numbers. The figure shows verti­cal temperature profiles in a room ventilated by displacement ventilation. The dimensionless profiles are similar within the flow rates shown in the figure, al­though the profile may involve areas with a low turbulence level in the middle of the room. A test of this type could indicate that further experiments can be performed independently of the Reynolds numbers.

Figure 12.42 shows another example of the use of similarity principles in experiments. The temperature effectiveness ET is measured in a room venti­lated by displacement ventilation. The measurements are made at different flow’ rates Qn to the room, at different loads (from 100 W to 500 W) and by

 0.0 0.2 0.4 0.6 0.8 1.0 T-T0 Tr-Tq

 0.00 0.02 0.04 0.06 0.08 0.10 0.12 ‘Jo (m3/s)

FIGURE 12.41 Vertical temperature profile in the room for three different experiments with iden­tical Archimedes number.16

 2 3 45

 10 20 304050 1 00 ATo «0

 (*)

(B)

Two different wall-mounted diffusers. Figure 12.42a shows eT values Between

1.5 And 2.3; however, it is difficult to reach other conclusions from This figure Such as, for example, the importance of the two different diffusers.

Figure 12.426 shows the measurements given as a function of the Archimedes number Ar ~ AT0/«5 • This figure is more informative than Fig.12.42a. The figure shows that the temperature effectiveness ET is a function of the Archimedes number. An identical level of eT for the two diffusers A and B at the same Archimedes number implies that the temperature effectiveness is rather independent of the diffuser design and the local induction close to the dif­fuser. The effectiveness is probably more dependent on other parameters that are constant in the experiments, such as heat source and heat source location.