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Performance prediction |
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Ü Project | Project | Performance prediction 
The Performance prediction is an empirical based estimation of the performance map of the machine.
Please note: This is an estimation. The actual performance may differ from the prediction.
General
A performance curve of the current design is estimated on the basis of the Euler-Equation:
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Kinds of losses
There are different kinds of losses that are considered in different curves:
Kind |
Description |
Parameter |
Decreased power |
Based on the Euler-Equation and the decreased power that is calculated in the Blade properties. In the design point the decreased power line is shifted by a pressure head loss equivalent to the decreased power (HDecr=Hth-ΔHDecr). The decreased power line can be parallel to the Euler-Line as well as positioned that way, that it intersects the Euler-Line at Q = 0. |
cl: cl = 1...parallel position, cl = 0...intersection with Euler-Line at Q = 0. |
Hydraulic losses |
Based on the Euler-Line including the decreased power minus the losses due to friction. Yields a downwards opened parabola, that touches the decreased power curve at Q = 0. |
ζ: General approach:
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Turbulence and separation |
Includes all the effects listed above plus turbulence and separation losses at the inlet and outlet. Yields a downwards opened parabola. It touches the curve, in which decreased power and hydraulic losses are considered, in the design point. |
ct: General approach:
with ct > ζ |
Separate curves considering the pure losses (dashed) as well as the resulting performance curves (solid) can be displayed. The display of these curves can be prevented by the check boxes "All performance curves" and "Pure losses". In case the display has been prevented only the actual performance curve (red color) considering all losses will be visible.
The scope to be displayed can be controlled by the check boxes "x (Flow)" and "y (Energy)" as well as by giving the scope limits in the panel "Operating range".
A loss coefficient, that describes the hydraulic losses, can be calculated by pressing "Calculate ζ" in a way, that as a result the actual performance curve (red) of the flow efficiency will go through the best point. Here it is assumed that hydraulic losses of impeller and volute will occur with a ratio of 4:1.
Variables
All types of turbo machines have in common: The characteristics can be displayed in a diagram with dimensions as well as without dimensions.
Variable |
Pump |
Ventilator |
Compressor |
Turbine |
H |
head |
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Δp |
total pressure difference |
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ψ |
work coefficient |
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H/Hopt |
dimensionless head |
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Δp/Δpopt |
dimensionless total pressure difference |
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ptt |
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pressure ratio (total-total) |
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pts |
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pressure ratio (total-static) |
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ηimp |
flow efficiency |
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η |
total efficiency |
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P |
required driving power |
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Q |
flow rate |
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φ |
flow coefficient |
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Q/Qopt |
dimensionless flow |
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Qt |
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total flow rate |
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mass flow |
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reduced mass flow
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corrected mass flow
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All combinations of flow and energy variables are possible.
It is common practice in the case of turbines - contrary to all other type of turbo machines - that the flow variable is given as a function of the energy variable. Beyond it characteristics of different rotational speeds will not be displayed over the whole theoretical pressure interval but only piecewise.
The choice of the variables is to be made in the panel "Variables".
Surge - compressor and fans only
The prediction of surge line is based on the following model: The pressure difference between outlet and inlet yields a back flow within the compressor. Amongst pressure difference and back flow a correlation exits, that can be found in the table "Kinds of losses", column "Hydraulic losses". Within the applied model the compressor is thought as a parallel connection between a flow source and a hydraulic resistance. Then, surge will occur when the back flow in the hydraulic resistance becomes as big as the flow in the flow source.
The surge line can be controlled by the pressure loss coefficient "Equivalent surge hydraulic resistance". Of course it is impossible to consider non-steady effects that are characteristic for the onset of the surge with this model. The surge line can be displayed only in case dimensional variables has been chosen and the checkbox "Surge line" has been set.
With centrifugal fans surge may only happen if the pressure difference is big enough (~0.3 bar).
Choke - compressor only
Choked flow will happen if the flow reaches sonic speed somewhere in a duct. As the rothalpy is constant at any point in the flow channel the temperature (critical temperature within the narrowest cross section) at a flow at sonic speed can be calculated by:
and critical sonic speed becomes:
With an approximation of the critical density and the influence of the boundary layer blockage the choked mass flow is:
The blockage of the boundary layer is expressed by the factor B that is 0.02 by default.
Characteristics with different rotational speeds
With the current set of parameters performance curves with different rotational speeds can be calculated and displayed. This procedure is feasible only if the rotational speeds are not too far from the design point. If they are, similarity relations are not valid any longer.
Characteristics with different diameters - pumps and ventilators only
Performance curves for impellers with decreased diameter can be calculated and displayed too. The decrease of the impellers means that the geometric similarity is not given anymore. Therefore performance curve are calculated by the following empirical correlations: H' = H (d'/d)mH and Q' = Q (d'/d)mQ. The exponent mH should be within 2..3, mQ should be 1 or slightly bigger.
Reference curves
For comparison purposes with the present design saved designs can be loaded (soft button"configure").
System characteristic - pumps, ventilators and compressors only
An operating point, in which a turbo machine could possibly run, can be determined by a fictive system characteristic. The display of a system characteristic can be controlled by the checkbox "System Characteristic". The system characteristic consists of a static and a dynamic part. The static part is dependent on the parameter "Geodetic Head" (pumps only) and "Static part" respectively, whereas the dynamic part is dependent on the parameter "System hydraulic resistance". The system characteristic can only be displayed if head or total pressure difference have been chosen as variable.
Page url: http://www.cfturbo.com/fileadmin/content/manual/en/index.html?performance_prediction.html
