**3.5. Corners**

Diffuser 3 guides the flow to the power plant which is strongly affected by flow separation. In order to avoid it, the criterion imposing a maximum value of the semi-opening angle is maintained here as well. The cross-sectional shape may change along this diffuser because it must connect the exit of corner 2, whose shape usually resembles that of the test chamber, with

a

/2

b/2

H**ent**

**Flow direction**

W**ent**

**Length**

The same can be said about diffuser 4 because pressure oscillations travel upstream and therefore may affect the power plant. Analogically to the previous case, it provides a connec‐ tion between the exit of the power plant section and the corner 3, which has a cross-section

Diffuser 5 connects the corners 3 and 4. It is going to be very short, due to a low value of the dynamic pressure, which will allow reducing the overall wind tunnel size. This will happen mainly when the contraction ratio is high and the diffusion angle may be higher than 3,5°. It can also be used to start the adaptation between the cross-section shapes of the tests section

An accurate calculation of the pressure loss coefficient can be done with Idel´Cik´s (1969) method. A simplified procedure, derived from the method mentioned above, is presented here

the entrance of the power plant, whose shape will be discussed later.

shape resembling the one of the test chamber.

W**exit**

14 Wind Tunnel Designs and Their Diverse Engineering Applications

to facilitate a quick estimation of such coefficient.

and the power plant.

H**exit**

**Figure 6.** Rectangular section diffuser.

Closed circuit wind tunnels require having four corners, which are responsible for more than 50% of the total pressure loss. The most critical contribution comes from the corner 1 because it introduces about 34% of the total pressure loss. To reduce the pressure loss and to improve the flow quality at the exit, corner vanes must be added. Figure 7 shows a typical wind tunnel corner, including the geometrical parameters and the positioning of corner vanes.

The width and the height at the entrance, *Went* and *Hent* respectively, are given by the previous diffuser dimensions. The height at the exit, *Hexit*, should be the same as at the entrance, but the width at the exit, *Wexit*, can be increased, giving the corner an expansion ratio, *Wexit*/*Went*. This parameter can have positive effects on the pressure loss coefficient of values up to approxi‐ mately 1,1. However, it must be designed considering specific geometrical considerations, which will be discussed, in greater details in the general arrangement.

The corner radius is another design parameter and it is normally proportional to the width at the corner entrance. The radius will be identical for the corner vanes. Although increasing the corner radius reduces the pressure loss due to the pressure distribution on corner vanes, it increases both the losses due to friction and the overall wind tunnel dimensions. According to previous experience, it is recommended to use 0,25 *Went* as the value of the radius for corners 1 and 2, and 0,20 *Went* for the other two corners.

The corner vanes spacing is another important design parameter. When the number of vanes increases, the loss due to pressure decreases, but the friction increases. Equal spacing is easier to define and sufficient for all corners apart from corner 1. In this case, in order to minimise pressure loss, the spacing should be gradually increased from the inner vanes to the outer ones.

The vanes can be defined as simple curved plates, but they can also be designed as cascade airfoils, which would lead to further pressure loss reduction. In the case of low speed wind tunnels the curved plates give reasonably good results. However, corner 1 may require to further stabilise the flow and reduce the pressure loss. Flap extensions with a length equal to the vane chord, as shown in Figure 7, is a strongly recommended solution to this problem.

Other parameters, such as the arc length of the vanes or their orientation, are beyond the scope of this chapter. For more thorough approach the reader should refer to Idel´Cik (1969), Chapter 6. As mentioned above, the pressure loss reduction in the corners is very important. Therefore,

**Figure 7.** Scheme of a wind tunnel corner, including vanes, flaps and nomenclature.

an optimum design of these elements, at least in the case of corner 1 and 2, has a significant impact on the wind tunnel performance.

In order to allow a preliminary estimation of the pressure loss in the corners we will follow the method presented in Diagram 6.33 from Idel´Cik (1969) mentioned above. In this approach, we take an average number of vanes, *n*= 1,4\**S*/*t1*, *S* being the diagonal dimension of the corner, where *t1* is the chord of the vane. The pressure loss coefficient is given by the expression:

$$\zeta = \zeta\_M + 0.02 + 0.031^\* \frac{r}{W\_{\text{out}}}.$$

*ζM* depends on *r*/*Went*, and its values are 0,20 and 0,17 for *r*/*Went* equal to 0,20 and 0,25, respective‐ ly.Asaresult,thecorrespondingvaluesof*ζ*are0,226and0,198respectively,alwayswithrespect to the dynamic pressure at the entrance. This proves the validity of the recommendations given before with regard to the value of the curvature radius and the length of diffusor 1.
