Resultados obtenidos de la aplicación del modelo

Ü Blade | Leading edge

The previously designed blade has a blunt leading edge. To complete the blade design the leading edge should be radiused. For this purpose 4^th order Bezier splines are used.

Points 0 and 4 representing the transition between the blade sides and the rounded leading edge. You can move these points only along the corresponding blade side. Bezier points 1 and 3 can only be moved on straight lines which correspond to the gradient of the curve in points 0 or 4, respectively in order to guarantee smooth transition from the contour to the leading edge. Bezier point 2 is not restricted to move - it has the most influence to the shape of the leading edge.

In addition the m-value of the leading edge (corresponding to the radius) is represented. When designing the leading edge, you should make sure that the smallest radius of the rounded leading edge does not deviate too much from the value given in the meridian section.

4

0

1

3 2

There are two different possibilities to determine the shape of the leading edge. In the ^Edit  panel on the right top of the dialog window you can select between:

§ Coupled linear only leading edges of hub and shroud will be fixed, while anything between will be linearly interpolated

§ Uniform when designing leading edge on hub or shroud then Bezier points of all other leading edges have the same relative positions

You could click on the Frontal view button to show the designed blade profiles with their rounded leading edges in a frontal view, including diameters dN and d2.

V ^OLUTE

Inlet

Ü Volute | Inlet definition

The first design step of the volute is to define the inlet side. To do this, input the impeller data in the dialog box on the left hand side.

If the impeller was already designed using CFturbo^®, the data can be transferred directly from the corresponding CFT file (Load from Impeller CFT file).

General data:

§ Flow rate Q

§ Head H

§ Pump revolutions n

§ Density of the pumped fluid

r

Impeller outlet parameters:

§ Impeller diameter d2

§ Impeller outlet width b2

§ Angle of absolute flow

a

3

§ Axial position (centre of b2) z

The axial position, z, ensures correct positioning relative to the impeller concerned.

 Additionally, the direction of rotation of the impeller, seen from the drive side (looking at the backside of hub), must be defined.

Various calculated values are shown, for information purposes, in the bottom box:

Specific speed nq (SI units) Specific speed NS (US units) Type number

w

s (ISO 2548)

see section Design point page 21

Meridional component of the absolute velocity ^c_m3

⁼

^Q

( ^p

^d₂^b₂

)

Circular component of the absolute velocity c_u3

=

c_m3 tan

a

₃

Data concerning the volute are entered in the dialog box on the right hand side.

General data:

§ Volumetric efficiency

h

v

§ Flow factor FQ

(for overdimensioning, particularly for a better degree of efficiency at overload operation)

Volute inlet:

§ Inlet diameter d4

§ Inlet width b4

§ Axial displacement

D

z

(relative to the centre of the impeller outlet)

For

h

v and FQ, standard values of 1.0 are used. d4 and b4 are determined using the ratios d4/d2  and b4/b2, which are calculated from functions dependent on the specific speed nq (see section Approximation function).

Clicking on the Calculate-button, to the top right, recalculates the standard values.

 A short distance between the impeller and the cut-water is desirable for reasons of flow. For acoustic and vibration reasons, however, a certain minimum distance is necessary. The inlet width b4  should be chosen such that the width/height ratio at the end cross-section of the volute is close to 1. The ratio b4/b2  can be varied within a relatively wide range without significant negative effect on the efficiency. For radial impellers with open impeller sides, values up to b4/b2=2 are possible. At higher specific speeds (wider impellers), however, high width ratios have a negative effect on flow (intensive secondary flows, turbulence losses). In this case, b4/b2 should be between 1.05 and 1.2.

Various calculated values are shown, for information purposes, in the bottom box.

Calculated internal flow rate Qi Qi

=

FQ

×

Q

h

v

Inlet diameter ratio d₄ d₂

Inlet width ratio b₄ b₂

Geometry

Ü Volute | Geometry

The geometry of the volute can be designed and calculated in this dialog box. The wrap angle (standard: 360°) and the starting angle (standard:

0°= horizontally to the right of the centre) can be defined under Extension.

Design rule

The flow rate through a cross-section, A, of the circumferential angle,

j

, is generally calculated as:

( )

circumferential angle,

j

, dependent on the outer radius r a:

( )

b(r) is a geometrical function which is defined according to the shape of the cross-section. The velocity cu  is chosen in accordance with the design instructions. Under Design rule, two alternatives can be selected.

Œ Pfleiderer 

Experience has shown that the losses can be greatly minimised if the volute housing is dimensioned such that the fluid flows in accordance with the principal of conservation of angular momentum. The cross-section areas are therefore designed in accordance with the principal of conservation of angular momentum, i.e. angular momentum exiting the impeller is constant. In addition, an exponent of angular momentum, x, can be chosen so that the principle c_u

×

r ^x

=

const. is obeyed. When x=1,

the angular momentum is constant. For the extreme of x=0, the circular

The integral can be explicitly solved for simple cross-section shapes (rectangles, trapezoids, circles). For other, arbitrary, shapes, it can be solved numerically.

• Stepanoff 

 Alternatively, it can be beneficial to design the volute with a constant velocity in all cross-sections of the circumference. According to Stepanoff, this constant velocity can be determined empirically:

gH 2 k

c_u

 =

_s . The constant ks  can be determined dependent on the specific speed nq (see section Approximation function).

( )

The cut-water can be designed in the Cut-water  section:

Inner radius r 4 Informative, see section Inlet, page 51

Thickness (orig.) e Thickness of the cut-water at the start of the volute

Thickness (calc.) Realised thickness of the cut-water; deviates by

j

C,0<>0

Position

j

C,0  Angular position of the cut-water (standard:

0°=start of volute);

j

C,0<>0 indicates a

rounding-off between the actual volute and the diffusor

Position min. Minimum necessary angular position to prevent overlap of the actual volute and the diffusor

Compensation

j

C  Angle, above which cut-water correction begins (standard: 270°); only possible when

j

C,0=0

The cut-water does disturb the flow, since the cross-section of the flow is narrowed suddenly by the thickness of the cut-water. To weaken this negative influence, the cut-water can be corrected.

This is achieved by assuming that from the angle

j

C the inner radius r 4  increases linearly to a value of r 4+e at the end cross-section of the volute. This results in larger volute cross-sections in this area, so that the narrowing of flow caused by the cut-water becomes less significant.

By clicking on Default, you can return to the standard values for the cut-water.

Shape of the cross-section

The shape of the cross-section of the volute can be selected under Cross sections. In general, very small cross-sections width should be avoided. The achievable cross-section shape strongly depends on manufacturing and the space available.

Rectangle (exact)

most simple cross-section shape; cannot be achieved in cast parts; only sensible for low specific speeds, since otherwise the cross-section becomes too large

Trapezoid (exact)

cannot be achieved in cast parts; the angle

d

can be specified; results in a flatter cross-section than a rectangular cross-cross-section, with less intense secondary flow

Circle (symmetric)

simple geometry with a beneficial stress distribution; does not develop on rotation surfaces

Circle (asymmetric)

more favourable secondary flow structure than with a symmetrical circle cross-section; often with semi-axial impellers

User defined (Rectangle type)

analogous with Rectangle; with chamfers (cast radii)

User defined (Trapezoid type)

analogous with Trapezoid; with chamfers (cast radii)

Bezier cross-sections

The shape of a User defined  cross-section is described by a Bezier spline. A special dialog box is used for this purpose and it can be opened by clicking on the Design cross sections button.

One half of the shape of the cross-section is described using a 4th degree Bezier polynomial. Points 0 and 4 are the end points and cannot be changed. Point 1 can be moved along a straight line which corresponds to the cone angle of the cross-section (0° for a rectangle type,

d

 for a trapezoid type). Point 3 can only be moved in the horizontal direction in order to guarantee a smooth transition between the two symmetrical halves. The intersection of the two lines which points 1 and 3 are on is designated by the letter S and plays an important role in the positioning of Bezier points 1 and 3. Point 2 can be moved freely and therefore he has the major influence on the shape of the cross-section. In the first design, point 2 is identical with point S.

The basic shape of the cross-section can be selected in the upper right-hand corner of the dialog box, rectangular or trapezoid. Only the end cross-section of the volute is designed, all other cross-sections result from this. Under the heading Inner point position, you can select whether positioning of the inner points 1 and 3 should be relative (0=point 0 and 4; 1=point S) or absolute (distance from point S). The numeric values of the positions can be changed by right-clicking on

4

1

3 2

0

points 1 or 3. If the option Show all points under the heading Options is selected, the different positioning methods become apparent.

The minimum curvature radius of the designed contour is shown in the box to the bottom right.

End cross-section

Some informative values relating to the end cross-section are shown in the lower part of the left-hand area:

Radius r5

Height H5

Width B5

Side ratio H5/B5

Equivalent diameter D5

 Area A5

 Average velocity c5

In addition, the volute cross-sections can be viewed (Show cross sections) and the area distribution displayed (Show area distribution).

Diffusor

The options for the diffusor geometry are found to the right. In general, 2 basic shapes are differentiated:

Tangential diffusor Radial diffusor

The tangential diffusor is easier to manufacture, the radial diffusor has the advantage of minimising tangential forces.

The tangential diffusor has the added advantage that the angle deviation from the tangential direction,

g

, (standard: 0°) can be defined. In the case of a radial diffusor, either the angle

e

 between the outlet branch and the line connecting impeller-centre and outlet branch centre, or the radius RN

of the diffusor curvature can be selected.

The end cross-section of the diffusor can be either round or rectangular.

The diameter D6 can be directly defined or selected from standard tables (see page 27). In the case of a rectangular end cross-section the height H6 and width B6 can be chosen.

The length, L, of the diffusor can also be defined. The following values are shown for information purposes:

Equivalent diameter D6 Diameter of the equivalent circle at the diffusor outlet

Cone angle

J

cone angle from D5 to D6 over the length L  Allowable cone angle

^J

_max

⁼

^16.5°

(

^D₅ ²

)

^L

Deceleration ratio ²

6 2 5

R D D

 A

=

By clicking on Default, you can return to the standard values for the diffusor geometry.

Display options

Under Display options, changes can be made which affect only the graphics:

Cross section visualization Number of angle lines shown Show – refers to the image of volute + diffusor

Section lines radial angle lines

Cut-water compensation cut-water compensation as a larger inner radius

Cut-water original original cut-water geometry where

j

C,0<>0

Show in cross section – refers to the image of the cross-section Cut-water section cut-water cross-section

Equivalent diameter equivalent diameter D6 (dashed line) Outlet branch outlet branch as an area

Filled cross-sections filled cross-sections

R ^EFERENCES

Werner Fister 

Fluidenergiemaschinen Bd. 1 und 2, Springer-Verlag, 1984 und 1986

Gotthard Will

Kreiselpumpen, in: Taschenbuch Maschinenbau, Band 5, Edited by Hans-Joachim Kleinert, Verlag Technik Berlin, 1989

Joachim Raabe

Hydraulische Maschinen und Anlagen, VDI-Verlag, 1989

Kurt Holzenberger, Klaus Jung

Kreiselpumpen Lexikon, KSB AG, 1989

Carl Pfleiderer, Hartwig Petermann

Strömungsmaschinen, Springer-Verlag, 1991

Walter Wagner

Kreiselpumpen und Kreiselpumpenanlagen, Vogel-Verlag, 1994

Johann F. Gülich

Kreiselpumpen, Springer-Verlag, 1999

John Tuzson

Centrifugal pump design, John Wiley & Sons, 2000

In document Modelo de monitoreo de procesos en línea de una base de datos. (página 91-102)