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 this purpose some specific edit fields are used.

 

 

One of the following parameters have to specified for the calculation of the rotor diameter d1:

 

Work coefficient

dimensionless expression of the specific work

big small d1
small big d1
Guideline ca. 2

Flow coefficient

φm

dimensionless mass flow

in accordance to Cordier-Diagramm

Tangential force coefficient

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

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 ψ̃ the relative flow angle β1 and the tangential force coefficient ψ̃/φm there is the following relation:

At a relative flow angle of β1= 90° the work coefficient becomes ψ̃=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/cm1 or

Diameter ratio dS/d1

1.005..1.05

 

 

~0.7

Diameter ratio dN/dS

~0.3

 

There are three specification modes of the diameter ratio dN/dS:

Direct input
Automatic calculation: option "Automatic". Here the diameter ratio will be adjusted in a way that the guideline of the geometrical ratios will met.
Direct specification of dN in the tab sheet Dimensions. Here the diameter ratio is not necessary.

With diameter ratio dS/d1 option "Automatic" is deactivated.

 

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

Rotor efficiency ηtt (total-total)
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)

 

MD_Parameters_Turb

 

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

 

actual Power PD

PD = PQ·ηtt

Power loss PL

PL = PQ - PD

Specific speed nq
(SI-Unit)

points to machine type and general shape of rotor:

Specific speed NS
(US-Unit)

„Type number“ ωs
(ISO 2548)

Speed coefficient σ

Guideline: 0.16..0.32. This has to be matched with the design.

Flow Q

calculated with total density in the outlet:

Total pressure inlet pt1

pt1 = π⋅pt2

Total density inlet rt1

Pressure ratio total-total

Pressure ratio total-static

Efficiency total-total

Efficiency total-static

 

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 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 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.

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