Hub and Shroud are represented by 4th order Bezier-splines. The curve is determined by five Bezier points.

 

Points 0 and 4 are defining the endpoints of the curves while the other three points determining the shape of the curve. The middle point (2) can be moved without any restrictions whereas points 1 and 3 have only one degree of freedom. Point 1 is only movable on the straight line between points 0 and 2, point 3 between point 2 and 4. Therefore no curvature is occurring at the end of the curves. In conjunction with a continuous curvature gradient small velocity gradients can be expected. The two straight lines are defining the gradients in the end points of the curves.

 

Bezier point 2 can be limited in its mobility by the curve context menu option Limit stop. As a result the axial and radial position is limited in the area between the curve endpoints 0 and 4.

 

The above mentioned coupling between the Bezier points can be switched on or off by the curve context menu option Coupled Bezier points.

 

Start angle (line 0-1 or 0-1-2) and end angle (line 3-4 or 2-3-4) can be fixed optionally by the curve context menu option Fixed start angle or Fixed end angle. A fixed angle is illustrated by a dotted  line instead a dashed one and by a triangular marker on the curve endpoint.

 

 

 

For an automatic primary design of the contours the following values are used:

 

Point 1 is primary placed at 3/4 of the axial distance of points 0 and 2, point 3 at 2/3 of the radial distance of points 2 and 4.

 

The manipulation of the contours can be achieved by shifting the positions of the Bezier points. As an alternative the position of Bezier points can be realized by input of numerical values (see Graphical dialogs). Trailing edge can be rotate by moving Bezier points 4. If <Ctrl> key is pressed simultaneously the whole trailing edge can be moved in axial direction with constant inclination angle (change axial extension). Inclination angle of trailing edge can be numerically determined by clicking the right mouse button on it.

 

In the design process for the meridional contours the user should try to create curvatures which are as steady as possible in order to minimize local decelerations. The maximum values of the curvature should be as low as possible and should entirely disappear at the end of the contours. These requirements are met very well by Bezier curves showing the above mentioned limitations. Local cross section 2πrb should grow from the suction to the impeller diameter as uniformly as possible.

 

The points of maximum curvature are marked on hub and shroud while their numerical values are displayed in the Max. curvature section.

 

There are two different options to define hub and shroud contours that can be selected in the right-hand part of the dialog in the Design mode section:

 

In the first case hub and shroud can be designed separately or in the coupled mode. If you hit the Hub-Shroud Coupled check box hub and shroud will be modified simultaneously considering the same relative positions of the Bezier points.

 

In the second case only the geometric center line of the flow channel will be modified. The contours result in specifying a cross section distribution. It may either be linear or could be loaded from a file.

 

 

 

The leading edge is designed too by a 4th order Bezier spline. Regarding the Bezier points, the statements made above are applicable in a similar way. The only difference is the manipulation of the end points. For the leading edge there is no restriction on hub and shroud contour. The position of the leading edge always appears at the same relative position in a primary CFturbo design but this not mean to be a suggestion.

 

Leading edge can be designed as a straight line by selecting Straight in the context menu of the curve (controlled by 2 Bezier points). Additionally the edge can be strictly axial or radial (z = const. or r = const, controlled by 1 Bezier point).

 

For radial impellers having nq ≈ 10…30 the leading edge is often designed parallel to the z-axis. As the trailing edge is parallel to the axis too for such applications 2D-curved blades can be created. At higher specific speed nq or due to strength reasons the leading edge often is extended into the impeller suction area. Various diameters result in different leading edge blade angles - therefore 3D-curved blades are created. This leads to better performance curves, higher efficiencies and improved suction capacity for pumps.

 

The position of the leading edge should be chosen in a way that the energy transmission should be about equal on all meridional flow surfaces. A criterion is the approximately equal static moment S = ∫ r dx of the meridional streamlines on hub and shroud between leading and trailing edge. In the Static moment section the corresponding numerical values are displayed. Both ends of the leading edge should be perpendicular to the meridional contours of hub and shroud if possible. To obtain equal static moments on hub and shroud the trailing edge is often not parallel to axial direction - particularly at higher specific speeds (mixed-flow impellers).

 

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