Parameters

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Parameters

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On page Parameters you have to put in or to modify parameters resulting from approximation functions in dependence on specific speed nq or flow rate Q (see Approximation functions).

For details of how to handle the parameter edit fields please see Edit fields with empirical functions.

 

Parameter and efficiency values can be handled manually or can be switched to automatic update by the checkbox on top of the page. Then the default values are used always, even after design point modifications (see Global setup).

If the automatic mode is not selected the current default values can be specified by one of the following options:

globally by the button on top of the page

regionally by the default button within the Parameters or Efficiency region

individually by the default button within the input field when selected

Parameters

The panel Parameters allows defining alternative values in each case for the calculation of the following impeller main dimensions:

suction diameter dS

impeller diameter d2

impeller width b2

For d2-calculation

Work coefficient Ψ

(= pressure and head coefficient)

dimensionless expression for the specific enthalpy Δhis=Y and Δh=Yeff resp.

high small d2, flat characteristic curve
low high d2, steep characteristic curve

Flow coefficient φ

dimensionless flow rate

0.01  narrow centrifugal impeller, untwisted blades

0.15  mixed-flow impeller, twisted blades

Diameter coefficient δ

according to Cordier diagram (see Dimensions)

Machine Mach number Mau

dimensionless peripheral speed of impeller related to total inlet speed of sound

Peripheral speed u2

Limiting values due to strength as a function of the material

 

For b2-calculation

Outlet width ratio b2/d2

0.01...0.15 (with nq rising)

Meridional flow coefficient φm

dimensionless flow rate

0.10...0.50 (with nq rising)

 

For d1-calculation (optional)

Diameter ratio d1/d2

d1/d2=0.3...0.8

Relative deceleration w2/w1

w2/w1>0.7  or  f(b2/d2)

 

For b1-calculation (optional)

Meridional deceleration cm2/cm1

cm2/cm1 = 0.8...1.25

 

for dS-calculation

Meridional deceleration
cm1/cmS     or
cm2/cmS

 
cm1/cmS = 0.9...1.1
cm2/cmS = 0.7...1.3

Relative inlet flow angle βS

Relative inlet Mach number MwS

Diameter ratio dS/d2

dS/d2 = 0.65...0.8

The relative inlet Mach number can be implemented in a certain range only. The lower limit is given by the fact that small values for dS (high meridional velocity cmS) as well as high values for dS (high rotational speed uS and therefore wuS) result in an increasing relative velocity wS. Due to the square root equation of MwS two different values of dS are possible. For certain boundary conditions a minimal relative velocity and therefore a minimal relative inlet Mach number is existing always.

In this context it's important to know that the fluid density is dependent on the velocity and therefore on the geometrical dimensions.

Efficiency

In panel Efficiency you have to specify several efficiencies. You have to distinguish between design relevant efficiencies and efficiencies used for information only:

Design relevant

total-total efficiency ηtt

volumetric efficiency ηv

additional total-total efficiency ηtt+ (displayed for information only, see Global setup)

Information only

mechanical efficiency ηm

motor efficiency ηmot

The additional total-total efficiency ηtt+ is used for impeller dimensioning in order to compensate additional flow losses.

The losses resulting in energy dissipation from the fluid form the internal efficiency.

Impeller and mechanical efficiency form the overall efficiency (coupling efficiency) of the stage ηSt.

When considering motor losses additionally the overall efficiency of the stage incl. motor ηSt* is defined.

PQ: output power, see above

PD: mechanical power demand (coupling/ driving power)

Pel: electrical power demand of motor

 

The following summary illustrates the single efficiencies and their classification:

classification


efficiencies


Relevant for impeller design

stage

 

ηC

additional casing

yes: for energy transmission



ηtt

total-total



impeller

ηV

volumetric

yes: for flow rate


 

ηm

mechanical

no: for overall information only

stage incl. motor

electrical

ηmot

motor


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 are representing the theoretical reachable values and they should be corrected by the user if more information about the impeller or the whole machine are available.

The impeller efficiency ηtt describes the energy losses 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 impeller efficiency is the ratio between the actual specific energy Y and the energy transmitted by the impeller blades without any losses:

The volumetric efficiency is a quantity for the deviation of effective flow rate Q from total flow rate inside the impeller which also includes the circulating flow within the casing:

(rising with impeller size)

The mechanical efficiency mainly includes the friction losses in bearings and seals:

(rising with impeller size)

Impeller efficiency and volumetric efficiency are most important for the impeller dimensioning because of their influence to and/or . The mechanical efficiency is affecting only the required driving power of the machine.

 

If the check box "Use η for main dimensions (otherwise for βB2 only)" is set, then main dimension calculation is done on the basis of Δh= 0.5(Δhis/η+Δhis). Otherwise Δhis - the isentropic specific enthalpy - is used.

Information

In the right panel of the tab sheet Parameter you can find again some calculated values for information:

Required driving power

Power loss

Internal efficiency

Stage efficiency

Stage efficiency incl. motor

Total-to-static efficiency

(perfect gas model)

Polytropic efficiency

(n .. polytropic exponent

κ .. isentropic exponent)