Fig. 1 - Description of basic angles: stall angle and stall delay angle.
In all of the following figures, points A, B, C, etc will denote points on the lift curve. The solid black line is the original lift curve. The red curve indicates that a parameter has been modified, and the resulting lift curve has been generated. The black dotted lines are used to locate points on the curves.
Figure 1 shows the basic approach taken in defining the cl-alfa curve in PROPID. The data input to PROPID via the *.pd file is indicated by the points A-B-C-E. The lift curve generated by PROPID is A-B-C-D. The stall angle at point B is specified by the user. The stall delay angle B-C is also user-defined. If no post stall models are on, PROPID adds the stall delay angle to the stall angle and holds the cl constant over that range (taking the constant from the value at point B). The flat-plate model starts at point C, and the lift curve proceeds to point D and beyond. The location of point C on B-E will depend on the magnitude of the stall delay angle. This is explained in Figure 2.
This approach to defining the airfoil cl-alfa curve is best when airfoil data up to stall is available, and the airfoil is known to have a gentle stall and data after stall is not available.
The history behind having a variable stall delay angle B-C traces to when a stall delay angle was used to model the stall delay effect of constant-speed stall-regulated wind turbines. This stall delay effect is largest over the inboard part of the blade and is reduced to a neglible amount outboard. In other words, the delay stall inboard can be modeled by using a higher stall delay inboard than outboard which should behave in a 2D manner with no stall delay other than that of the 2D performance. By varying the stall delay angle, the importance of blade rotation effects that cause stall delay can be examined.
Fig. 1 - Description of basic angles: stall angle and stall delay angle.
Figure 2 shows the effect of increasing the stall delay angle. A larger stall delay angle moves point C to C' as shown in the figure. The flat plate model will start at point C'. Points A-B-C'-D' will now describe the lift curve.
Fig. 2 - The effect of changing the stall delay angle.
Figure 3 shows that PROPID does not use any of the input data after the stall angle. As shown, the code takes the cl-value at the stall angle B' and holds that value until stall at point C'. Note that for the case shown, the stall delay angle B'-C' is increased over that used in Fig. 2. The flat plate model starts for angles higher than stall + stall delay.
In developing the code, this approach was taken so that the effects of a lower clmax could be rapidly modeled by simply changing the user-prescribed stall angle of attack B'.
Fig. 3 - The effect of changing the stall angle.
Figure 4 shows (among other cases) the approach to take when the entire stall behavior is known and represented in the tabulated airfoil data given in the *.pd file. First, A-B-C shows the cl-alfa data known from experiment. At the stall angle C, the flat plate model begins and extends the curve to point D and then to higher angles (not shown). To initiate the start of the flat plate model at point C, the stall delay angle has been set to zero. This approach is the prefered approach when the stall data is known and representative of the airfoil behavior on the blade.
Two other cases are also shown to illustrate and amplify the effects that the various angles can have. First, if the stall angle is set at point B' and a non-zero stall delay angle is used, the clmax is set to that value at point B' and held to point B'+C''. If on the other hand the stall delay angle is set to zero, point C'' moves to C' and the flat plate model then begins at point B'/C'. Thus, it is quite important to understand the meanings of these angles and to set them appropriately.
Fig. 4 - Various uses of the stall
delay angle and the prefered approach when given the experimental
stall data from clmax and beyond.
Figure 5 shows the data generation when using UIUC post-stall model. First, it is important to note that the post stall models can be used with stall delay, and the models build the 3D data based on the 2D data as partly defined by the stall and stall delay angles. In the case of the Corrigan model, the lift curve A-E-F-G will follow the shape of the input 2D lift curve A-B-C-D exactly (this is not the case shown). The Corrigan stall curve (though stalling at a higher angle) follows the 2D curve because the 3D data is generated by simply adding a constant increment to the 2D stall curve (past the insert angle) followed by a shift to the right so that the lift curve is continuous. In the UIUC model, point F (the "end" angle) is specified as desired. The "start angle" point E is also user-prescribed. The flat plate model then extends from point F to point G and beyond.
Fig. 5 - The UIUC post stall model (shown) and Corrigan model (not shown).