Parameters

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Parameters

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On page Parameters one has to put in or to modify parameters resulting from approximation functions in dependence on specific speed nq (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  rotor main dimensions:

suction diameter dS

rotor diameter d1

inlet width b1

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

The design concept is based on a mean flow area, therefore a mean blade angle βB1 as well as a mean incidence angle i has to be given. In order to yield best efficiency the angle of incidence should be 20..30°. The relative flow angle β1 based on these two parameters is:

.

One of the following parameters has to be specified for the calculation of the rotor diameter d1.

Work coefficient ψ

(= pressure and head coefficient)

dimensionless expression of the specific enthalpy

big small d1
small big d1

Guideline ~ 2

Flow coefficient φm

dimensionless mass flow

in accordance to Cordier-Diagramm

Tangential force coefficient

ct = ψ/φm

Coefficient of a flow force pointing in tangential direction

3 ... 4 Francis high-speed turbine

4 ... 8 Normal-speed turbine

8 ...10 Low-speed turbine

 

Coefficient ratio

cR = ψ/φm2

Ratio of work to the square of the meridional speed

6  ...10 Francis high-speed turbine

10...12 Normal-speed turbine

12...30 Low-speed turbine

 

Between the work coefficient ψ, the relative flow angle β1 and the tangential force coefficient ψ/φm there is the following relation:

At a relative flow angle of β1= 90° the work coefficient becomes ψ = 2. In this case the work coefficient should not be chosen as a design parameter in the tab sheet Parameters. Otherwise one has no influence on the meridional flow coefficient and therefore meridional flow, see last equation.

 

For all further geometric variables guess values have to be given:

Diameter ratio d2/d1

~0.5

Meridional acceleration
cm2/cm1

 
1.005..1.05

Meridional acceleration (suction side) cmS/cm2
or

Diameter ratio dS/d1

 
1.005..1.05

 

~0.7

Diameter ratio dH/dS

~0.3

 

There are three modes for the definition of the hub diameter dH:

Direct input in the tab sheet Dimensions (check box "Calculate hub diameter" deactivated)

Combo box option "Diameter ratio dH/dS": automatic calculation with dH = dH/dS * dS.

Combo box option "Diameter ratio d2/d1": automatic calculation with dH = dH/dS * dS. Here the diameter ratio dH/dS will be adjusted in a way that the guideline of the geometrical ratios will be met.

With option "diameter ratio dS/d1" for the dS-calculation the option "Diameter ratio d2/d1" is not available.

Efficiency

In the group Efficiency the following efficiencies need to be given:

Design relevant

Rotor efficiency ηtt (total-total)

Information only

Mechanical efficiency ηm

Internal and mechanical efficiency form the overall efficiency (coupling efficiency):

PQ: (isentropic) Rotor power

PD: Power output (coupling/ driving power)

The rotor efficiency (or blade efficiency) ηtt describes the energy losses within the turbine 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 rotor efficiency is the ratio between the actual specific work Y and the specific work at loss less transmission:

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

(rising with impeller size)

 

If the check box "Use η for main dimensions (otherwise for βB1 only)" is set, then main dimension calculation is done on the basis of Δh=Δhis·η. Otherwise Δhis - the isentropic specific enthalpy - is used.

Information

In the right panel of the tab sheet Parameter some variables are displayed for Information:

actual Power PD

PD = PQ·ηttSt

Power loss PL

PL = PQ - PD

Flow Q

calculated with total density in the outlet:

Total pressure inlet pt1

pt1 = π⋅pt2

Pressure ratio total-total

Pressure ratio total-static

Stage efficiency total-total

ηttSt

Efficiency total-static

ηts

Polytropic efficiency

(n .. polytropic exponent

κ .. isentropic exponent)

In general for cost reasons single-stage & single-intake machines are preferred covering a range of about 10 < nq < 400. In exceptional cases it may become necessary to design a rotor for extremely low specific speed values (nq < 10). These rotors are characterized by large rotor diameters and low rotor 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 mass flow rate ṁ if possible. An alternative solution could be the design of a multi-stage turbine reducing the pressure drop of a single-stage. If especially high specific speed values (nq > 400) do occur one can reduce rotational speed n or mass flow rate ṁ if feasible. Another option would be to operate several single-stage turbines - having a lower nq - in parallel.

Please note: CFturbo® is preferably used between 10 < nq < 150 – radial and mixed-flow rotors.