Design Software for Radial & Mixed-flow Pumps
Software Manual 5.0
CFDnetwork Engineering
October 2005
CONTENTS System System Require Requirements ments ______________ ____________________ _____________ ______________ ______________ _________ __ 1 Features Features _____________ ____________________ ______________ ______________ ______________ _____________ _____________ _______1 1 General General _____________ ____________________ ______________ ______________ _____________ _____________ ______________ ________ _3 Licensin Licensing g ................ .................. ................. ................. ................. .............. 3 Prefere Preference nces s ............... ................. .................. ................. ................. ...........4 ........... 4 Approximation Approximation function functions s ......... ..... ......... .......... ......... ......... ......... ......... .......... ......... ......... ......... ......... .......... ......... ......... ........ ...5 5 Comparin Comparing g differen differentt design designs s ................. ................. ................. .................. ..8 Remove design steps.................................................................................9 Assembly.. Assembly....... ......... ......... .......... ......... ......... ......... ......... .......... ......... ......... ......... ......... .......... ......... ......... ......... ......... .......... ......... ......... ..... 9 Graphi Graphica call dialogs dialogs ................ ................. ................. ................. .................. 10 Main window____________ window__________________________________________________ ______________________________________ 12 Project.....................................................................................................12 Project information..............................................................................12 History................................................................................................13 Design information..............................................................................13 3D view view ............... .................. ................. ................. ................. ............... 14 Open/ Open/ Save Save design design................. ................. ................. ................. ................. ............... 17 Help.........................................................................................................17 Data export..............................................................................................18 Impeller - Meridional section_____________________________________ section _____________________________________ 21 Main dimensions......................................................................................21 Design Design point point ............... ................. ................. .................. ................. ...21 ... 21 Assumptions...... Assumptions........... ......... ......... ......... ......... .......... ......... ......... ......... ......... .......... ......... ......... ......... ......... .......... ......... ....... ... 24 Dimens Dimensions ions ................ ................. ................. .................. ................. ...27 ... 27 Meridion Meridional al contou contour.......................... r.......................... ................. .................. ................. ......30 ...... 30 Blade properties.......................................................................................35 Inlet triangle........................................................................................37 Outlet triangle.....................................................................................38 Meridional flow.........................................................................................42 Impeller Impeller - Blade design design ______________ _____________________ _____________ _____________ ______________ _______43 43 Mean line.................................................................................................43 Blade profile.............................................................................................47 Blade Blade leadin leading g edge edge ................ ................. ................. ................. ............... 49 Volute ______________ _____________________ ______________ ______________ _____________ _____________ ______________ _______51 51 Inlet Inlet ................ ................. ................. ................. .................. ................. ...51 ... 51 Geometry.................................................................................................53 Design rule.........................................................................................54 Cut-wate Cut-waterr ................ ................. ................. .................. ................. ......55 ...... 55 Shape Shape of the cross-s cross-sec ection................. tion................. ................. ................. ............... 56
CONTENTS System System Require Requirements ments ______________ ____________________ _____________ ______________ ______________ _________ __ 1 Features Features _____________ ____________________ ______________ ______________ ______________ _____________ _____________ _______1 1 General General _____________ ____________________ ______________ ______________ _____________ _____________ ______________ ________ _3 Licensin Licensing g ................ .................. ................. ................. ................. .............. 3 Prefere Preference nces s ............... ................. .................. ................. ................. ...........4 ........... 4 Approximation Approximation function functions s ......... ..... ......... .......... ......... ......... ......... ......... .......... ......... ......... ......... ......... .......... ......... ......... ........ ...5 5 Comparin Comparing g differen differentt design designs s ................. ................. ................. .................. ..8 Remove design steps.................................................................................9 Assembly.. Assembly....... ......... ......... .......... ......... ......... ......... ......... .......... ......... ......... ......... ......... .......... ......... ......... ......... ......... .......... ......... ......... ..... 9 Graphi Graphica call dialogs dialogs ................ ................. ................. ................. .................. 10 Main window____________ window__________________________________________________ ______________________________________ 12 Project.....................................................................................................12 Project information..............................................................................12 History................................................................................................13 Design information..............................................................................13 3D view view ............... .................. ................. ................. ................. ............... 14 Open/ Open/ Save Save design design................. ................. ................. ................. ................. ............... 17 Help.........................................................................................................17 Data export..............................................................................................18 Impeller - Meridional section_____________________________________ section _____________________________________ 21 Main dimensions......................................................................................21 Design Design point point ............... ................. ................. .................. ................. ...21 ... 21 Assumptions...... Assumptions........... ......... ......... ......... ......... .......... ......... ......... ......... ......... .......... ......... ......... ......... ......... .......... ......... ....... ... 24 Dimens Dimensions ions ................ ................. ................. .................. ................. ...27 ... 27 Meridion Meridional al contou contour.......................... r.......................... ................. .................. ................. ......30 ...... 30 Blade properties.......................................................................................35 Inlet triangle........................................................................................37 Outlet triangle.....................................................................................38 Meridional flow.........................................................................................42 Impeller Impeller - Blade design design ______________ _____________________ _____________ _____________ ______________ _______43 43 Mean line.................................................................................................43 Blade profile.............................................................................................47 Blade Blade leadin leading g edge edge ................ ................. ................. ................. ............... 49 Volute ______________ _____________________ ______________ ______________ _____________ _____________ ______________ _______51 51 Inlet Inlet ................ ................. ................. ................. .................. ................. ...51 ... 51 Geometry.................................................................................................53 Design rule.........................................................................................54 Cut-wate Cut-waterr ................ ................. ................. .................. ................. ......55 ...... 55 Shape Shape of the cross-s cross-sec ection................. tion................. ................. ................. ............... 56
Bezier Bezier cross-se cross-section ctions s ................ ................. ................. ................. ...... 58 End cross-s cross-sec ection tion .................. ................. ................. ................. ......... 59 Diffuso Diffusor.. r................... ................. .................. ................. ................. ................. ...... 60 Display Display option options s ................ ................. ................. .................. .............. 61 Reference References s _____________ ____________________ ______________ ______________ _____________ _____________ ___________ ____ 62 Contact Contact Addresses Addresses ______________ _____________________ ______________ ______________ _____________ _________ ___ 63
1
S YSTEM REQUIREMENTS ®
The CFturbo software runs on Windows NT4/ 2000/ XP. A valid license ® key must be obtained and installed before the first use of CFturbo . The key is linked to one specific computer and establishes the appropriate operation on that computer. Operation is based on the usual standards of the Windows operating systems. The user interface is in English language. An Online-Help in German and English is integrated.
FEATURES ®
CFturbo is made to design interactively radial and mixed-flow impellers and volutes for centrifugal pumps. The software is easy to use and does enable quick generation and variation of impeller and volute geometries. Several models can be displayed, compared and modified simultaneously. It contains numerous approximation functions that may be customized by the user in order to implement user specific knowledge ® into the CFturbo -based pump design process. In spite of the creation of semiautomatic proposals, fundamental experiences in pump design are helpful but not necessary. An experienced pump design engineer should be able to design new high-quality impellers and volutes more easily and quickly.
Main features of the program: § § § §
§
Approximation functions for characteristic parameters which may be individually customized by user Calculation of main dimensions of the impeller Calculation and modification of hub and shroud contours as well as leading edge using Bezier splines or polylines Calculation of blade angles at leading and trailing edge in consideration of obstruction by blades and output deficit (slip); representation of velocity triangles Meridional flow calculation by streamline curvature method; display of streamlines and velocity distribution
2 §
§ § § § § § §
Determination of blade mean lines on rotational-symmetric meridional flow surfaces using Bezier splines or polylines at m,t plane (conformal mapping); display of b-distribution Generation of blade profiles by defining blade thickness at 4 points; display of thickness distribution Radius design of blade leading edge by Bezier splines Volute design for various cross section shapes according to the theory of Pfleiderer or Stepanoff Radial or tangential diffusor with circular or angular cross section at the pressure side Complete 3D display of designed geometry according to design progress Design report as text file Geometry export to various CAD and CFD systems
3
GENERAL Licensing Ü Edit
| Register Register Menu item enables input of licensing information. The so-called Machine ID is calculated ® by CFturbo considering hardware and operating system. This Machine ID number is used to generate License key for each of the Design type (Radial+Mixed Flow Pump Impeller and/or Volute). A valid license key is ® necessary to run CFturbo on your computer.
Please send the Machine ID to
[email protected]. You could probably use the Send E-Mail… button if your email software does allow it. In this case the text to be submitted is shown in your standard email program. Alternatively you can copy the relevant data to clipboard by pressing the Copy to Clipboard button. You will get a license file that can be opened by pressing the button Read from file…. The table License Key contains the calculated license keys. Alternatively the user can insert the the license keys manually. The item Company is for information only. If the license key has expired, you can reactivate the program by entering a new key. A hint with remaining days appears on startup screen 20 days before expiration of the license. You can inform about expiration date in the dialog Help | About CFturbo. For the input of license information as well as for installation, System Administrator rights are required.
4
Preferences Ü Edit
| Preferences | General
Menu item Preferences - General is used for global options of the program. On tab sheet Units you can select physical units to be used in the dialogs. Following units are available: § Head m, ft § Geom. length mm, in § Flow rate m³/h, ft³/h, gpm, gps § Density kg/m³, lb/ft³ § Stress MPa, PSI § Pressure MPa, PSI § Power kW, hp You can simultaneously change all units to SI or US system by pressing the buttons above.
On tab sheet Other you can specify length unit for exporting geometry. Please select the appropriate units when importing data to the chosen CAE software. Furthermore, you can adjust the language of online help. The standard is English.
Ü Edit
| Preferences | Export
On dialog Preferences - Export you can specify how many data points are to be generated during export. The number of points can be selected separately in each case for all geometry parts. The available options depend on active desgn module: Impeller
Meridian: hub/ shroud, leading edge Blade: mean line, pressure/ suction side, leading edge
5 Volute
-
Spiral: cross sections, points per cross section Diffusor: cross sections, points per cross section
3 different global pre-settings can be selected.
Approximation functions Ü Edit
| Approximation functions ®
CFturbo uses many approximation functions. These functions are based on published measurement data of centrifugal pumps that facilitate the forecast of optimal or accessible values. In this dialog the approximation functions are graphically displayed and can be individually customized. Functions for the following physical quantity are available: § § § § § § § § § § § § §
Hydraulic efficiency Volumetric efficiency Side friction efficiency Mechanical efficiency Pressure number Intake number Number of blades Wrap angle Width number Meridional deceleration Flow angle inflow Flow angle outflow Inclination angle hub
hh hV hS hm y e z
ju b2/d2 cm3/cmS
b0A b3 eH
6 § § § § § § § §
Inclination angle shroud Inclination angle trailing edge Blade thickness leading edge Blade thickness trailing edge Blade thickness max. Cut-water diameter ratio Cut-water width ratio Stepanoff constant
eS g s1 s2 smax d4/d2 b4/b2 ks
On the left at File location, the name of the file is shown that contains all data of the functions. In general this file is called Functions.cftfu, and is ® located in the installation directory of CFturbo . Modifications to functions are saved automatically if you leave the dialog window by pressing the OK-button. In case the user has no write permissions one could choose a different directory to save the file. Renaming files is possible by using the Save as-function. By clicking the Open-button a previously saved functions file can be opened. ®
The user must first select Physical variable. CFturbo ’s internal function is displayed in the diagram if corresponding check box is active. On panel Function you can add any functions. Selected function is ® displayed in the diagram in addition to CFturbo internal function. ® Function with active check box is used by CFturbo for calculations. If no
7 function has active checkbox or no additional function is defined at all, ® then the CFturbo internal function is used. In panel Points you can edit curve points of selected function. You can add new points at the end of the table – the points are automatically sorted by x values. To remove a point you have to delete either x or y value. These 3 buttons are enabling the user to import points from file (one point per line) or export points to file or to clear the table. On panel Test you can test the active function. Saving of values is possible by clicking OK-button. 2 special features are existing: Functions depending on 2 variables Functions can depend on 2 variables whereas one serves as parameter. Separate curves exist for each particular parameter value that are used to calculate function values. These parameter curves can be added in the Parameter panel. The parameter value is displayed on endpoint of curve in the diagram.
Following functions with 2 variables exist: Function Hydraulic efficiency hh mechanical efficiency hm
depends on specific speed nq flow rate Q
curve parameter flow rate Q revolutions n
Range definition
The Pressure number has a recommended range (see page 24), which means an area that is defined by a higher and a lower limit. The definition of the 2 parameter curves can be done as written above.
8
Comparing different designs Ü Edit
| Reference designs
This functionality can be used for simultaneous display of various designs to compare each other and for purposeful modification. Using the Add-button any reference design (*.CFTfiles) can be added. Each design has its own color and line width (panel Options). On panel Hint some information about the selected design is provided. With the Remove-button selected reference design can be deleted from list. However reference design may be deactivated by the check box at the beginning of the line.
9 Reference geometries are displayed in the dialogs with selected color and line width. Numerical values appear as small hints on input fields when mouse is moved over it. Down to the right in the dialog windows you could completely switch off the display of reference geometries and start a dialog for new configuration.
Remove design steps Ü Edit
| Remove design steps
For impeller design only !
If you make any design changes on the impeller all initial design steps based upon this status are automatically adapted (automatic update). This is done to prevent repeating the same design steps. However, if you would like to start with an ® automatic generated CFturbo primary design, certain design steps can be ® removed manually. Then CFturbo continues with new primary design data. For that purpose you have to select the appropriate design step to be removed and then press the OK button.
Assembly Ü Edit
| Show assembly
In the assembly dialog it is possible to display impeller and volute simultaneously. There are the same settings available as shown at the 3D-representaion of the individual components (see 3D view, page 14).
10
Graphical dialogs All graphical representations are made in diagrams that are automatically scaled according to displayed objects. All diagrams have a popup menu (right click on empty diagram area) with basic functions. Alternatively you can use the buttons on the left side of the diagram: Zoom window by mouse Zoom all Fit view Lens magnification Copy to clipboard Save as WMF, BMP or JPG Print Add any polyline from file (x,y points) to compare different curves
11 or to visualize components Measure distance Configure diagram
If the mouse cursor is moved over a graphical object (e.g. polyline, Bezier point) then this is highlighted by color or by increased line width. Right mouse click is now related to this object and does open a special popup menu or a small dialog window for data input. Bezier splines are used for geometrical contours by default. This continuous polylines are described by the position of a few Bezier points. Therefore a simple modification of the curve is possible but on the other hand the numerical representation of the curve is accurate. For Bezier curves, a popup menu emerges that permits the user to switch between Bezier spline and polyline. Loading and saving of curve points (*.CFTPL) and a reset of the curve is also performed using this menu. An alternate method to specifying Bezier points by the mouse, you may enter the accurate coordinates of Bezier points in a small dialog window that appears by clicking the right mouse button on the chosen Bezier point. One or two coordinate values can be entered in dependence of geometrical boundary conditions. As a rule these values are normalized relative values describing the position of the point between extreme values left or bottom (0) and right or top (1). Normalized relative coordinates are giving the advantageous possibility of an automatic update of the entire design if a parameter is modified. Coordinates of mouse cursor are displayed in format x:y bottom left in the status bar. Position and size of dialogs are saved to restore it in the same way when they are called again. ®
If CFturbo generates primary design automatically you may see Initial design on the top right of the diagram. If numerical values are entered in tables, then a new value is only activated and the diagram is updated if the key is pressed or a new cell of the table is selected.
12
MAIN WINDOW The main window contains important information of the actual project. A 3D-view of the current design state can be displayed. Menu items and buttons only become active in accordance to the current design state. The user is able to return to former design status from any design step in the program. Design step updates dependent on its modifications are accomplished automatically. Manual removing of ® complete design steps is possible too in order to continue with CFturbo using its primary design (see chapter “Remove design steps”, page 9).
Project
Project information
For identification of the project it may be specified:
13 Project name § Classification (e.g. version or sub name) § User name § Comments §
This information is not mandatory and should support the identification of ® CFturbo projects & sessions. The working directory, the creation date and the date of last modification are displayed too. History
The history contains all design steps from opening of the project or session in chronological order. By pressing button Remove selected you can undo selected design steps. By pressing the button Clear history the complete history (and temporary files) can be deleted. Design information
The right part of main window shows a tabular form summary of the most important design parameters. You can print these data together with project information (File | Print) or save to file (see chapter “Data export”, page 18).
14
3D view
Tab sheet 3D view contains the three dimensional representation of the current impeller or volute design state. Above the representation you can find some buttons with the following functions: Reset of representation (default position) Save representation as JPG or BMP Print representation X
Viewing direction in positive x-axis direction
Y
Viewing direction in positive y-axis direction
Z
Viewing direction in positive z-axis direction Define view (see below) Define point resolution (see Preferences, page 4) Switch perspective view on/off Switch coordinate system on/off
15 The View dialog is to set, save and load special view points. The corresponding values for rotation, translation and scaling according to the current state are displayed and they can be modified.
3D display can be influenced by mouse and keyboard: Mouse Left button
Middle button/ wheel
Right button
Rotation around point of origin
Zoom in/ out
Move
Keyboard /
/
/
Rotation around x
y
x/ y/ z
< > x/ y/ z
viewing direction in z
positive
axis
negative
axis direction
In the panel Component all available parts are listed, whereby their visibility can be switched on or off alternatively. There is shown in detail: Impeller
Volute
Hub
Spiral
Shroud
Diffusor
Mean surface of blades
Connection surface hub
Blades
Connection surface shroud Spiral contour
16 The connection surfaces close the flow area between impeller and volute. These surfaces have no constructional relevance, but serve the CFD modelling.
For the marked component in each case the following attributes can be defined below: Wire frame display Surface display Color selection Transparency of foreground components
There exist some more features for impellers: In panel Options the display can be limited to single blade if the blades overlap too high. Additionally the shown material thickness of hub and shroud can be adapted only for visualization. In panel Animation you can generate uniform rotation of impeller around z axis, whereby velocity can be influenced by track bar.
17
Open/ Save design Ü File
| Open/ Save/ Save as ®
When opening an existing CFturbo design (*.CFT) you may explicitly select between current file format or version KREILA4 (*.KRE), but the different file formats are self-determined. Saving always takes place in the new format. To open a list of recently used files can be used by pressing the small arrow right beside the Open button or by selecting the menu File|Open recent. The user can modify filenames by the Save as- function in order to save modified designs under different file names.
Help Ü Help
The following features can be used in the help menu: Help topics
Help for main window, index of whole help
®
CFturbo website
Show www.cfturbo.com in the web browser
Check for updates
Check for available updates
®
About CFturbo
®
Information about CFturbo incl. licenses
18
Data export Ü File
| Export
Export submenu offers file formats of several CAE programs to export designed geometry. Thus a smooth further processing of the geometry data is possible. Menu
Description
Design report TEXT
*.CFT-REP
Short design information as text file Summary of most important design parameters
Geometry – *.CFT-GEO TEXT Text file containing geometry data of the design for any further processing Impeller: Meridional section: Blade mean lines, Blade profiles:
z, r of hub, shroud, leading edge x, y, z (cartesian coordinates), r (radius), t (angle)
Volute: Spiral cross sections, Diffusor cross sections x, y, z (cartesian coordinates) Outline: x, y (cartesian coordinates) BladeGen
(Impeller only)
*.rtzt
ANSYS CFX-BladeGen 4.1
Program for three-dimensional blade design and automatic impeller performance evaluation with CFD File | Open: select file type „Meanline File (*.rtzt)“ § select file §
19 TurboGrid
(Impeller only)
*.curve
ANSYS CFX-TurboGrid 1.6
Software to generate high-quality grids for turbomachinery 3 files will be generated: hub.curve, shroud.curve, profile.curve § § § §
Gridgen
Application Launcher: select directory, start TurboGrid File | New: select template define z axis as rotational axis, input number of blades, select XYZ coordinate system Grid | Create
*.curve
Gridgen 15 (Pointwise)
Software to generate high-quality grids for turbomachinery A model file and a curve file for each component are generated. Import by Glyph-script “CFturboImport.glf“ RBS-Q3D
*.RBS
(Impeller only)
Input file for program RBS-Q3D (quasi-three-dimensional frictional flow) of TU Dresden, which can be used for approximate flow calculation
Fluent
*.tur
(Impeller only) IGES
RBS-Q3D
GAMBIT (Fluent)
Input file for the Fluent preprocessor GAMBIT for meshing with G/Turbo *.igs
common format
File contains designed geometry as B-Splines PRO/E
*.ibl
PRO/Engineer Version 2001
File contains hub, shroud, blade profiles § § § §
File | New | (if no file is open) Insert | Datum | Curve | From file Define coordinate system (e.g. with menu) | Select select *.ibl file
20 Unigraphics
*-ug.dat
Unigraphics V16-18, NX
4 files will be generated: *hub-ug.dat, *shroud-ug.dat, *skl-ug.dat, *blade-ug.dat § §
File | New | (if no file is open) Application | Modeling
For hub and shroud: § § §
Insert | Curve | Spline | Through points Points from file select *.dat for hub and shroud
For blade surfaces: § § § §
Insert | Free form feature | Through points Row degree > 1 dr = = 1
Negative swirl is increasing the head and may often have no good affect to the suction behavior of the pump. Inflow through a straight pipe usually leads to swirl-free flow.
dr and and aS relate as follows: dr = 1 -
c mS us tan aS
= 1-
4Q
p2 (dS2 - dN2 )d n tan aS
The conversion dr 1 aS is only valid for certain diameters dN and dS. Conversion is updated if these diameters are modified.
23 Furthermore, you can define rotational direction of the impeller seen from the drive side (looking at the backside of hub) At the lower lower end of each each column column some related related values values are compute computed d - just for information: Specific speed nq (metric units)
points to pump type and general shape of impeller: nq
= n [min ]×
[
Q m3 s
-1
]
(H [m])3 4
10… 50 Radial Radi al impeller 50…170 Mixed-flow impeller 150…400 Axial impeller Specific speed NS (US-units)
Ns
„Type number“ ws (ISO 2548)
ws = 2 p n ×
Specific energy Y
Y = g H
Pressure difference Dp
Dp = r g H
Pump output PQ
PQ
= n [rpm]
Q [gpm ]
(H [ ft ])3 4 Q
(g H)3 4
=
nq 52.9
= rgHQ
In general for cost reasons single-stage & single-intake pumps are preferred covering a range of about 10 < nq < 400. In exceptional cases it may become necessary to design an impeller for extremely low specific speed values (nq < 10). These impellers impell ers are characterized by large impeller diameters and low impeller widths. The ratio of free flow cross section area to wetted surfaces becomes unfavorable and is causing high frictional losses. To prevent this one may increase either rotational speed n or flow rate Q if possible. An alternative solution could be the design of a multi-stage pump reducing the head H of the single-stage. If especially high specific speed values (nq > 400) do occur one can reduce rotational speed n or flow rate Q if feasible. Another option would be to operate several single-stage pumps - having a lower nq - in parallel. parallel. ®
Please note: CFturbo is preferably used between 10 < nq < 150 – radial and mixed-flow impellers.
24 Assumptions
At the middle column of the Main Dimension dialog window you have to put in or to modify Assumptions resulting from approximation functions in dependence on specific speed nq or flow rate Q (see chapter "Approximation functions“, page 5). The panel Characteristic numbers allows to define alternative values in each case for the calculation of all impeller main dimensions: suction diameter dS, impeller diameter d2 und impeller width b2: For dS calculation -
Intake number e
Ratio between meridional inflow velocity and specific energy
e = c0
2 Y ~ b 0a
0.05…0.4 (rising with nq) - high ’ smaller dimensions, lower friction losses ’ prevent the risk of cavitation < 20° ’ with regard to efficiency > 15° - 12°...17° ’ recommended for good suction capability small friction and shock losses only if no cavitation risk ! f dS=1.15...1.05 standard impeller, nq=15...40 f dS=1.25...1.15 suction impeller -
Inflow angle b 0a
Minimal relative velocity w
nSS Suction number nSS
[
]×
[
Q m3 s
-1
= n min
(NPSHR [m])3 4
Standard suction impeller Suction impeller, axial inflow Suction impeller, cont. shaft High pressure pump Standard inducer Rocket inducer -
2
Min. NPSH
]
u1>1000
c w NPSHR = l c 1m + l w 1 2g 2g lc suction pressure coefficient for absolute velocity c (inflow acceleration and losses) 1.1 axial inflow 1.2…1.35 radial inflow casing lw suction pressure coefficient for relative velocity w (pressure decrease at blade leading edge) 0.10…0.30 standard impeller 0.03…0.06 inducer
25 For d2 calculation -
Pressure coefficient y
Outflow angle b3
for b2 calculation Outlet width ratio b2/d2 Mer. deceleration cm3/cmS
dimensionless expression for the specific energy
y = Y u22 2 0.7 ...1.3 radial impeller 0.25...0.7 mixed-flow impeller 0.1 ...0.4 axial impeller - high ’ small d2, flat charactersitic curve - low ’ high d2, steep charactersitic curve 6°...13°: recommended for stable performance curve (with nq rising)
-
0.04...0.30 (with nq rising)
-
0.60...0.95 (with nq rising)
In panel Efficiency you have to specify several efficiencies: § § § §
Hydraulic efficiency Volumetric efficiency Side friction efficiency Mechanical efficiency
hh hv hS hm
The first three values form the internal efficiency because these losses result in dissipating energy from the fluid:
hi = hh × hv × hS Internal and mechanical efficiency form the overall efficiency (pump/ coupling efficiency):
h=
PQ PD
= hi × hm
PQ: pump output, see above PD: power demand (coupling/ driving power)
The obtainable overall efficiency correlates to specific speed and to the size and the type of the impeller as well as to special design features like bypass installations and auxiliary aggregates. Efficiencies calculated by approximation functions (please see page 5) are representing the theoretical reachable values and they should be corrected by the user if more information about the impeller or the whole pump are available.
26 The hydraulic efficiency (or blade efficiency) describe the energy losses within the pump caused by friction and vorticity. Friction losses mainly originate from shear stresses in boundary layers. Vorticity losses are caused by turbulence and on the other hand by changes of flow cross section and flow direction which may lead to secondary flow, flow separation, wake behind blades etc.. The hydraulic efficiency is the ratio between specific energy Y and the energy transmitted by the impeller ~ blades Y : Y
hh = ~ » h » 0.85 K0.93 Y
The volumetric efficiency is a quantity for the deviation of effective flow rate Q ~ from total flow rate inside the impeller Q which also includes the circulating flow within the pump casing: Q
hv = ~ » 0.93 K0.99 Q
(rising with impeller size)
The side friction efficiency contains losses caused by rotation of fluid between hub/ shroud and housing:
hS
P = 1- S P
< 40 » 0.985K 0.995 for nq > 40 0.5 K 0.985
for nq
The mechanical efficiency mainly includes the friction losses in bearings and seals:
hm = 1 -
Pm P
» 0.95 K 0.995
(is rising with impeller size)
Hydraulic and volumetric efficiency are most important for the impeller ~ ~ dimensioning because of their influence to Y and/or Q . Mechanical and side friction efficiency are affecting only the required driving power of the pump. Please note about the required consistency for Q- and H- values and for hh und hV too: they refer to the same control volume of the viewed fluid domain. For example if the head H is representing the desired head after the outlet of the spiral casing the assumed hydraulic efficiency hh must contain all hydraulic losses which occur at the flow through the impeller and through the volute. Clearly distinguish if you look at the whole pump stage or just viewing to the impeller alone!
27 Finally the blade number z has to be set as an assumption: the number is usually between 3 and 10. Many blades - causing low blade loading are related to higher friction losses. By choosing of fewer blades leading to a higher blade loading - the hydraulic losses may rise due to increased secondary flow and stronger deviation between blade and flow direction. In the lower area of the Assumptions column you will find again some calculated values for information: PQ
Required driving power
PD
=
Power loss
PL
= PD - PQ = PD (1 - h)
Internal efficiency
hi = hh × hv × hS
Overall efficiency
h=
h
PQ PD
= hi × hm
Dimensions
In the panel Shaft/ hub, the required shaft diameter is computed and the hub diameter is determined by the user. Dimensioning of the shaft diameter is made under application of strength requirements. It is a result of torque M = P w to be transmitted by the shaft and the allowable torsional stress t of the material. You can directly enter allowable stress or select the value from a list by pressing button right beside the input area. In a small dialog window you can see some materials and its allowable stress. The list can be extended or reduced by and button. You can confirm selected value by pressing the OK-button. At File location the file containing material properties is shown. The file is originally called Stress.cftst and is located in the ® installation directory of CFturbo . Modifications of the list will be saved if the user is leaving the dialog window by
28 clicking the OK-button. In case there are no write permissions the user can choose another directory to save the file. Renaming of files is possible by Save as- functionality. By clicking the Open-button a previously saved file can be opened.
To consider a higher load, e.g. due to operating conditions away from the design point, a safety factor SF may be specified leading to a modified proposed shaft diameter dw. dW
³
3
8 r Q Y × SF
p2 n t h
The hub diameter dN is usually selected as small as possible and depends on the kind of connection of hub and shaft.
The main dimensions of a designed impeller - suction diameter dS, impeller diameter d2, outlet width b2 - can be seen on Main dimensions panel. They can be recomputed by pressing the Calculate-button. The computation is based on "Euler's Equation of Turbomachinery", on the continuity equation and the relations for the velocity triangles. You may accept the proposed values or you can modify them slightly, e.g. to meet a certain normalized diameter. Regarding the impeller size one should try to attain d2 values as low as possible. But there is a limit for a specified task: lower impeller diameters are leading to higher blade loading - up to blade angles b 2 which may not be suitable anymore.
You can select a value for the diameters dS and d2 from standard specifications. For that purpose you have to press the button right beside the input field. The small dialog gives you the possibility to select a diameter from several standard specifications. If material, standard name and pressure range are selected the lower panel shows all diameters of the chosen standard. One diameter is highlighted as a proposal. Nominal diameter, outside diameter and wall thickness for the marked entry is displayed. Using of and buttons additional standard specifications and user defined diameters can be added or existing parameters can be removed from the list.
29 At File location the name of the file containing the diameters is shown. The file is originally called Diameter.cftdi and is located in the installation directory of ® CFturbo . Modifications of the list will be saved if the user is leaving the dialog window by clicking the OK-button. In case there are no write permissions the user can choose another directory to save the file. Renaming of files is possible by Save as- functionality. By clicking the Openbutton a previously saved file can be opened.
In the lower area you will find some calculated values for information which result from calculated or determined main dimensions: Pressure coefficient
y = gH u22 2
§
Average inlet velocity
cmS
=
hV p 4 dS2 - dN2
§
Average outlet velocity
cm3
=
Q hV pd2b2
§
§
Q
(
c m12
)
NPSHR
= lc
NPSHR
= H × (n q nSS )4 3
NPSH value
2g
+ lw
w12 2g
§
Outlet width ratio
b2/d2
§
Meridional deceleration
dcm
= cm3 cmS
§
Estimated axial force
Fax
= 0.9 r gH× p 4 dS2 - dN2
resp.
30
Meridional contour Ü Meridian
| Contour
The design of the meridional contour is the second important step to design the impeller. th
Hub and shroud are represented by 4 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.
4
4
3 3 2 1 0
0
1
2
31 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. For an automatic primary design of the contours the following values are used: § § § §
Main dimensions (see page 27): dN, dS, d2, b2 Inclination angle g of trailing edge to horizontal (see Approximation functions, page 5) Inclination angle e of hub and shroud to vertical (see Approximation functions, page 5) Axial extension Dz = (d2a - dS ) (nq 74 )
1.07
+ b2 2 cos g
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 page 10). Trailing edge can be rotate by moving Bezier points 4. If 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 2 pr × b 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 Edit section: Œ
Hub, Shroud
Direct design of the two contours
•
Cross section
Design of center line; the contours result from given cm course between suction (dS) and outlet (d2) cross sections
32 In the first case hub and shroud can be designed separately or in the coupled mode. If you hit the 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 relative shape of the meridional velocity cm. It may either be linear or could be loaded from a file. # Cross section progression # example # Beginning/end tangential, # linear in the middle section # Spline interpolation between # 9 points 0.00 0.00000 0.04 0.01728 0.08 0.03830 0.12 0.06368 0.16 0.09404 0.20 0.13000 0.24 0.17164 0.28 0.21687 0.32 0.26314 0.36 0.31018 0.40 0.36000 0.44 0.41404 0.48 0.47102 0.52 0.52898 0.56 0.58596 0.60 0.64000 0.64 0.68982 0.68 0.73686 0.72 0.78313 0.76 0.82836 0.80 0.87000 0.84 0.90596 0.88 0.93632 0.92 0.96170 0.96 0.98272 1.00 1.00000
On the left side you can see an example of cm progression. All lines starting with a # symbol are comments. All other lines contain the numerical values. The first value of each line is the relative meridional coordinate x along the center line, with x=0 at the suction cross and x=1 at the outlet cross-section. The second value is the relative meridional velocity cm,rel, which allows to compute the related absolute value: cm
= c m,0 + c m,rel × (c m,3 - c m,0 )
The meridional velocity is used to determine the width b vertical to the flow direction: b=
Q 2pr × c m
These considerations are based on the assumption of a constant meridional velocity cm over the cross section. This will becomes less applicable to wider impellers at the non-radial area of the impeller. th
The leading edge is designed too by a 4 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
33 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 Leading edge straight in panel Edit (controlled by 2 Bezier points). If the edge additionally should be parallel to z-axis then Leading edge parallel to z has to be selected (controlled by 1 Bezier point). For radial impellers having nq » (10…30) rpm the leading edge is often designed parallel to the 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 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 improved suction capacity, better performance curves and higher efficiencies. The position of the leading edge should be chosen in a way that enables the transmission of energy should be about equal on all meridional flow surfaces. A criterion is the approximately equal static moment S = ò 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).
In panel Extension on exit an extension downstream of the trailing edge can be modeled. This may be necessary for further processing in other CAE-systems, e.g. CFX-BladeGen. The values Exit diameter d2a and Exit width b2a refer to cross section behind trailing edge and can be determined in different ways. The designed outflow area is displayed.
In panel Show progressions the following curves can be displayed: Curvature
Static moment
Area progression
34 In the Options panel some graphical representations can be activated for illustration: Grid for later blade design
Width lines for calculation of hub and shroud
Area circles for calculation of cross section area
In the Information panel you can find some numerical values of above mentioned quantities.
35
Blade properties Ü Meridian
| Blade properties
When starting blade design, the number and the meridional position of blade profile sections must be specified as well as the blade angles. Blade angles b B1 and b B2 are calculated from the velocity triangles, whereby the blade blockage of the flow channel and the slip velocity is considered.
Procedure for calculation of blade angles: Œ
Defining the blade thickness values at leading (LE) and trailing edge (TE) in panel Blade thickness s
•
Estimation of slip velocity in panel 2: Deviation flow – blade: fully automatic by selecting WIESNER theory or input of coefficient a when selecting PFLEIDERER theory or manual selection of angular deviation b2B - b2 resp. velocity ratio cu 2 cu 2 ¥ by selecting Self
36 Ž
Panel Blade angle B: §
Specifying number of blade profile sections for further blade design using the vertical track bar
§
Calculation of blade angles using values from Œ and • by pressing button Calculate B
§
Manual adaptation of calculated blade angles if required
Calculation or input of blade angles can be executed for 2 up to 11 blade profiles. Further blade design is realized according to the defined blade profile number. Blade angles are computed under consideration of the equations listed below. They remain unchanged by default if they are determined once. If main dimensions or meridional contours are modified or, on the other hand, values of blade thickness or slip velocity are renewed, a recalculation of blade angles should be executed by pressing button Calculate B. On panel Blade lines all meridional lines are displayed which will be used for blade design. The number of lines can be adjusted with track bar on panel Blade angle B. Velocity triangles of inflow and outflow are displayed. Continuous lines represent flow velocities on hub (blue) and shroud (green). Velocities directly before and behind blade area can be displayed optionally (dashed lines) to show influence of blockage in the flow domain. Furthermore the blade angles can be displayed by thick lines in order to see the incidence angle on the leading edge and the flow deviation caused by slip velocity on trailing edge.
Numerical values of velocity components and flow angles are displayed in a table on the right side of the dialog window. A short description is at mouse cursor too: § § § § §
d
a b u cm
cu § c § wu §
§
w
§
t
Diameter Angle of absolute flow to circumferential direction Angle of relative flow to circumferential direction Circumferential velocity Meridional velocity ( cm = w m ) Circumferential component of absolute velocity Absolute velocity Circumferential component of relative velocity ( w u Relative velocity Obstruction by blades (see below)
+ cu = u )
37 §
i
Incidence angle i = b1B - b1
§
d
Deviation angle
§
wR
Deceleration ratio of relative velocity wR
d = b2B - b2 = w 2 w1
Inlet triangle
The inlet triangle is defined by inflow parameters and geometrical dimensions on leading edge. Between inlet area and leading edge the swirl is constant because transmission of energy from rotating impeller to fluid occurs in blade area only. Cross sections 0 and 1 (see “Main dimensions", page 21) are different only due to blockage of the flow channel by blades (t1) in section 1. This results in an increased meridional velocity cm. tan b1 =
c m1 w u1
c m1 = c m0
t1 = c m0
t1 t1
t1 - s1
with
t1 =
pd1 z
, s1 =
s1 sin b1
= Q (pd1b1)
w u1 = u1 - c u1
u1
= pd1n
cu1 = c uS
r S r 1
= uS (1 - dr )
r S r 1
constant swirl before blade
Selected blade angle b 1B does only indirectly influence the velocity triangle due to blade blockage. Differences between selected blade angle b1B and flow angle b1 is referred as the incidence angle i: i = b1B - b1 In general an inflow without any incidence is intended (i=0). If i ¹0 the flow around the leading edge shows high local velocities and low static pressure: i > 0 : i < 0 :
b1 < b1B Þ stagnation point on pressure side Þ > suction side
38 A small incidence angle i can be profitable for best efficiency point. ® Calculation of b1B inside CFturbo gives inflow without incidence. Because of cavitation b1B should be as small as possible; with regard to efficiency not smaller then 15…18°. If the radius of leading edge varies from hub to shroud the blade angle b1B does not remain constant. A higher radius on shroud results in a lower value for b 1B – the blade is curved on leading edge.
Outlet triangle
The outlet triangle is determined by geometrical dimensions of flow channel and selected blade angle b2B. The blade angle b 2B strongly affects the transmission of energy in the impeller therefore is has to be chosen very carefully. Similar to the inlet the velocity triangles in cross sections 2 and 3 are different due to blockage of the flow channel by blades t2 in section 2. tan b2
=
c m2 w u2
= c m3t2
cm2
t2 = with c m3 w u2
t2 t2
- s2
t2
p d2
=
z
, s2
=
s2 sin b2
= Q (pd2b2 )
= u2 - c u 2
u2 cu 2
= pd2n =
Y
hh + u12 (1 - dr ) u2
Y gH ~ from: Y = = = u 2 c u3 - u 1c u0
hh
hh
39 For determination of b 2B it is important to be aware about the deviation between flow angle and blade angle. The direction of the relative flow w2 at impeller outlet does not follow exactly with the blade contour at angle b2B. The flow angle b2 is always smaller than blade angle b2B due to the slip velocity. This difference is called deviation angle d:
d = b2B - b2 The deviation angle should not exceed 10°…14°, in order to limit increased turbulence losses by asymmetric flow distribution. A reduced flow angle b 2 results in smaller circumferential component of absolute speed cu2, which is - according to Euler's equation - dominant for the transmission of energy. Blade angle b 2B is estimated by cu 2¥ for blade congruent flow (see figure). Therefore an estimation of slip is necessary. Slip can be estimated by empirical models. Two different ® possibilities are available in CFturbo :
Œ
Theory of decreased output by PFLEIDERER
Reduced energy transmission is expressed by decreased output coefficient p: p=
~ Y¥ ~ Y
-1
This coefficient can be empirically calculated in dependence of experience number y’: p = y'
r 2
2
zS r 2
with S =
ò rdx
static moment from leading to trailing edge
r 1
y' = a (1 + b2 60° ) experience number Design coefficient a is supposed to be: Radial impeller with guided vanes : a = 0.6 with volute : a = 0.65…0.85 with plain diffusor : a = 0.85…1.0 Mixed flow/axial impeller : a = 1.0 …1.2 (for sufficiently high Re; y’ strongly grows with small Re).
40 More descriptive is the decreased output factor kL: kL
=
1 1+ p
=
~ Y ~ Y¥
=
D (rc u ) D (rc u )¥
(kL=1 for flow congruent to blade)
Circumferential component of the flow, which is congruent to blade, can be calculated as follows: cu2¥
•
=
cu2 kL
æ 1 ö çç - 1÷÷2pn(1 - dr ) r 2 è kL ø 2
-
r 1
Outflow coefficient by WIESNER
Outflow coefficient g is defined for decreased energy transmission:
g = 1-
c u2 ¥ - c u2 u2
Difference cu2¥
(g=1 for flow congruent to blade)
- cu2 is called slip velocity.
The smaller the outflow coefficient, the higher is the deviation of flow compared to the direction given by blade. Wiesner has developed an empirical equation for the estimation of outflow coefficient:
æ sin b2B ö÷ ç g = f 1 1 kw 0.7 ç ÷ z è ø with correction values 0.98 for radial impellers ìï üï = f 1 í ý -3 ïî1.02 + 1.2 × 10 (nq - 50 ) for mixed flow impellers ïþ
ì1 for d1m d2 £ eLim ü ï 3ï k w = í æ d1m d2 - eLim ö ý ÷÷ ï ï1 - çç 1 - e Lim ø þ î è d1m
= 0.5 * (d1,Shroud2 + d1,Hub 2 )
æ 8.16 sin b2B ö eLim = expç ÷ z è ø
41 Circumferential component of blade congruent flow can be calculated as follows: cu2¥
= c u2 + (1 - g )u2
Blade angle b 2B must be determined to reach the desired energy transmission - respectively the required head - under consideration of slip velocity. Common blade angles b2B for pumps are within the range of 15°…45°, commonly used 20°…27°.
Radial pumps with low specific speed nq usually have similar values for b2B. The blades for this type of impellers are often designed with a straight trailing edge (b2B=const.).
42
Meridional flow Ü Meridian
| Flow
The meridional flow is computed by a streamline curvature method. The flow domain is divided into thin layers of 11 meridional flow surfaces. There a two-dimensional flow computation is possible with sufficient accuracy. The calculation is made on 35 quasi-orthogonal lines - from the suction area up to the extension area behind the trailing edge. The leading and trailing edges are two of these quasi-orthogonal lines. Since this design program is supposed to deliver just a rough estimation of the meridional flow the influence of friction is neglected. Furthermore ® rotational symmetry has been assumed. After completing the CFturbo based pre-design process, one should use an appropriate CFD-code for flow recomputation of the impeller or of the whole pump stage. After calculation the meridional contour as well as the cm and w distribution is represented showing 6 streamlines and 35 quasiorthogonal lines. You could adjust the size of the diagrams by mouse.
43
IMPELLER - BLADE DESIGN Mean line Ü Blade
| Mean line
The blade mean lines are designed on the number of meridional flow surfaces which were determined in “Blade properties” (page 35). The spatially curved meridional flow surfaces are mapped to a plane by coordinate transformation. This coordinate system has the angle in circumferential direction t as abscissa and the dimensionless meridional extension m as the ordinate. Both quantities are created by the reference of absolute distances to local radius r: dm =
dM r
dt
=
r
t
z
m
dT r
This conformal mapping allows the uniform handling of various impeller types (radial, mixedflow, axial). It should be noted that for each meridional flow surface a separate m-coordinate is existing. rd
In general the mean lines are represented by 3 order Bezier splines. Boundary conditions are: § § §
Blade angles bB1, bB2 (see Blade properties, page 35) Meridional extension dm (see Meridional contour, page 30) Wrap angle j
44
3 2 1
0
®
CFturbo 's primary design is fixing point 0 (leading edge) for all cross sections due to wrap angle and meridian coordinate m=0, while point 3 is determined by the meridian coordinate of the trailing edge (dm) and t=0. The wrap angle j is initially constant for all cross sections (see Approximation functions, page 5), but it can be modified individually. In general j should be in the range of 70…150° (with nq decreasing). Wrap angle tremendously influences blade angle progression - bB along mean line. Beta-progression can be viewed in a separate diagram. Two points in the middle, 1 and 2, must be on a straight line at an angle of b B1 or bB2 to the horizontal in order to fulfill the boundary condition ( tan bB = dm dt ). The primary design shows points 2 at 1/4 of the wrap angle, and points 1 at 3/4. For continuous transition between the separate mean lines (blade surface), the matching points of each mean line have to be Coupled linear . Individual mean lines can be designed separately. If the linear coupling mode is active you can move and rotate the connecting line. The positions of Bezier points of all mean lines are modified correspondingly, to get uniform profiles. If you select a point of the inner cross sections you can move the entire connecting line. On the other hand, if you select any point of the inner or outer cross sections, you can move this point along the related straight line. This line is given by bB1 or b B2 (rotation of
45 the connecting line). Points 0 (leading edge) and 3 (trailing edge) can only be moved horizontally (m=const). Points 3 can be moved interactively (move/ rotate trailing edge). Points 0 (leading edge) can moved only by modifying wrap angles in table Boundary conditions. Additionally you can use option Coupled in t-direction. This results in smooth transition of connection lines in t direction regarding t difference between inner and outer mean line. This option makes sense only if different wrap angles for the mean lines are used.
You can display bB progression along every mean line in a separate diagram by pressing button Show Beta progression. Too high local extreme values should be avoided if possible.
Alternatively to the Bezier splines, the mean lines can also be represented as simple polylines. For this purpose you may read any curve coordinates from file.
The blades of a pump impeller representing a deceleration cascade for the relative velocity. Therefore the risk of flow separation exists. The user should try to obtain a continuous, smooth change of flow direction, as well as the cross section graduation of the flow channel should be as steady as possible.
46 You can click on the button Frontal view to represent the designed mean lines in a frontal view, including diameters dN and d2.
47
Blade profile Ü Blade
| Profile
To create blade profiles the orthogonal blade thicknesses are used located at leading edge, at trailing edge, after 1/3 and after 2/3 of the ® blade. The primary CFturbo -design is suggested typical values in dependence of the impeller diameter d2 (see Approximation functions, page 5). Blade thickness is interpolated linear between these 4 values.
In the Blade thickness table the corresponding blade thickness values are indicated. Considering impeller manufacturing a certain thickness distribution across the flow direction may be implemented, e.g. to ensure the molding process. The blade thickness values can be set constant, linear changing from leading to trailing edge or completely user defined. The orthogonal blade thickness values are converted into thickness values referred to the circumferential direction. By adding half the thickness to both sides of the blade mean line the pressure and suction sides of the blades will be created. The profile can be represented then in m,t - coordinates.
48 You may display thickness progression along mean lines in a separate diagram by pressing button Show thickness progression.
By clicking to the Frontal view button the designed blade profiles in frontal view are shown, including diameters dN and d2.
49
Blade leading edge 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 th 4 order Bezier splines are used.
0 1 4 3
2
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.
50 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.
51
VOLUTE 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 Head Pump revolutions Density of the pumped fluid
Q H n
r
Impeller outlet parameters: § § § §
Impeller diameter Impeller outlet width Angle of absolute flow Axial position (centre of b2)
d2 b2
a3 z
The axial position, z, ensures correct positioning relative to the impeller concerned.
52 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 ws (ISO 2548)
see section Design point page 21
Meridional component of the absolute velocity
cm3
= Q (pd2b2 )
Circular component of the absolute velocity
cu3
= cm3 tan a3
Data concerning the volute are entered in the dialog box on the right hand side. General data: § §
hv Volumetric efficiency Flow factor FQ (for overdimensioning, particularly for a better degree of efficiency at overload operation)
Volute inlet: § § §
Inlet diameter d4 Inlet width b4 Dz Axial displacement (relative to the centre of the impeller outlet)
For hv 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.
53 Various calculated values are shown, for information purposes, in the bottom box.
= FQ × Q hv
Calculated internal flow rate Qi
Qi
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.
54 Design rule
The flow rate through a cross-section, A, of the circumferential angle, j, is generally calculated as: r a (j )
ò
= cudA =
Qj
ò c b(r )dr u
r 4
= Qi × j (2p ) , results in an equation to calculate the circumferential angle, j, dependent on the outer radius r a: Using
j=
2p Qi
Qj
r a (j )
òc
u
× b(r )dr
r 4
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 crosssection 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 cu × r x
= const. is obeyed. When x=1,
55 the angular momentum is constant. For the extreme of x=0, the circular component of the absolute velocity cu remains constant at the impeller outlet.
j=
2pcu4r 4 Qi
x
r a (j )
ò
b(r ) r x
r 4
dr
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: cu = k s 2gH . The constant ks can be determined dependent on the specific speed nq (see section Approximation function).
j=
2pk s 2gH Qi
r a (j )
ò b(r )dr
r 4
By clicking on Default, you can return to the standard values for each design instruction.
Cut-water
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 jC,00
Position jC,0
Angular position of the cut-water (standard: 0°=start of volute); jC,00 indicates a rounding-off between the actual volute and the diffusor
56 Position min.
Minimum necessary angular position to prevent overlap of the actual volute and the diffusor
Compensation jC Angle, above which cut-water correction begins (standard: 270°); only possible when jC,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 jC 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 cutwater.
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.
57 Rectangle (exact)
most simple cross-section shape; cannot be achieved in cast parts; only sensible for low specific speeds, since otherwise the crosssection becomes too large Trapezoid (exact)
cannot be achieved in cast parts; the angle d can be specified; results in a flatter crosssection than a rectangular 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)
58 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.
3
4
2
1
0
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 righthand 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
59 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).
60 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
Jmax = 16 .5°
Deceleration ratio
A R
(D5 2) L
= D52 D6 2
By clicking on Default, you can return to the standard values for the diffusor geometry.
61 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 jC,00
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
62
REFERENCES 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
