.ThermoSysPro.WaterSteam.Machines.StaticCentrifugalPump

Information

## Copyright © EDF 2002 - 2026   
## ThermoSysPro Version 4.2  
This component model is documented in Sect. 12.2 of the ThermoSysPro book.   

# Static centrifugal pump  

Centrifugal pumps are used to generate flow or to increase the pressure of a liquid by conversion of mechanical energy into kinetic energy.   
For the static centrifugal pump, either the rotational speed of the pump is a fixed input, or the mechanical power is provided as a fixed input and the rotational speed is calculated.  

Because energy losses cannot be neglected, the Bernoulli equation cannot be used to describe them. Instead, the momentum balance equation is replaced by a more general homologous relation called *pump characteristic*.  
The model depends on the available characteristics from the manufacturer.   

Usually, characteristics are only provided for the operating domain limited to:  
- positive pump rotational velocity: \\(\bar{\omega} > 0 \\),  
- positive flow rate through the pump: \\(q > 0 \\),  
- positive pump head: \\(h_n > 0\\).  

Such characteristics are sufficient if the simulation occurs near the nominal operating.  
If not, see [Centrifugal pump](modelica://ThermoSysPro.WaterSteam.Machines.CentrifugalPump).  

## Modelica component model  

The equations mentioned below are implemented in the component *StaticCentrifugalPump*, located in the *WaterSteam.Machines* sub-library.  
The component has 3 connectors:  
- C1: fluid inlet,  
- C2: fluid outlet,  
- rpm_or_mpower: rotational speed or mechanical power.  

![modelica://ThermoSysPro/UsersGuide/Documentation/ThermoSysPro.WaterSteam.Machines.StaticCentrifugalPump.svg](modelica://ThermoSysPro/UsersGuide/Documentation/ThermoSysPro.WaterSteam.Machines.StaticCentrifugalPump.svg)  

## Nomenclature  

| Symbol | Description | Unit | Definition | Modelica name |  
|---------------- |------------------------------------------------------------------ |----------------------------- |--------------------------------- | -----------------|  
| \\( a_i \\) | Coefficient of degree \\( i \\) of the parabolic pump characteristic \\(h_n=f_h(\frac{q}{\omega}) \\) | \\( \mathrm{s^i/m^{2i + 1}} \\) | |a1 (x^2), a2 (x), a3 (-) |  
| \\( b_i \\) | Coefficient of degree \\( i \\) of the parabolic pump characteristic \\(\eta_h=f\_{\eta}(\frac{q}{\omega}) \\) | \\( \mathrm{s^i/m^{3i}} \\) | | b1 (x^2), b2 (x), b3 (-) |  
| \\( F(\theta) \\)  | Pump head full characteristic | | | - |  
| \\( g \\) | Gravity constant | \\( \mathrm{m/s^2} \\) | | g |  
| \\( h_i \\) | Fluid specific enthalpy at the inlet| \\( \mathrm{J/kg} \\) | | C1.h |  
| \\( h_o \\) | Fluid specific enthalpy at the outlet| \\( \mathrm{J/kg} \\) | |C2.h |  
| \\( h_n \\) | Pump head | \\( \mathrm{m} \\) | \\( h_n = \frac{P_o − P_i}{\rho \cdot g}  \\) | hn |  
| \\( \dot{m} \\) | Fluid mass flow rate through the pump | \\( \mathrm{kg/s} \\) | | Q |  
| \\( N \\) | Rotational speed of the pump | \\( \mathrm{rev/min} \\) | \\( \frac{30}{\pi} \cdot \omega\\) | Vr |  
| \\( N_{nom} \\) | Nominal rotational speed of the pump | \\( \mathrm{rev/min} \\) | \\( \frac{30}{\pi} \cdot \omega\_{nom}\\) | VRotn |  
| \\( P_i \\)  | Fluid pressure at the inlet | \\( \mathrm{Pa} \\) | | C1.P |  
| \\( P_o \\)  | Fluid pressure at the outlet | \\( \mathrm{Pa} \\) | | C2.P |  
| \\( q \\) | Volumetric flow rate through the pump | \\( \mathrm{m^3/s} \\) | \\( \frac{\dot{m}}{\\rho} \\) | Qv |  
| \\( q_{nom} \\) | Nominal volumetric flow rate through the pump | \\( \mathrm{m^3/s} \\) | | - |  
| \\( \bar{q} \\) | Reduced volumetric flow rate through the pump | | \\( \frac{q}{q\_{nom}} \\) | - |  
| \\( W_h \\) | Hydraulic power | \\( \mathrm{W} \\) | | Wh |  
| \\( W_m \\) | Mechanical power | \\( \mathrm{W} \\) | | Wm |  
| \\( \eta_h \\) | Hydraulic efficiency | - | | rh |  
| \\( \eta_m \\) | Product of the pump mechanical and electrical efficiencies | - | | rm |  
| \\( \theta \\) | Angle beween coordinates \\( (\omega, q) \\) | \\( \mathrm{rad} \\) | \\( \\arctan \left( \frac{\bar{q}}{\bar{\omega}} \right) \\) | - |  
| \\( \\rho \\) | Average fluid density between the inlet and the outlet | \\( \mathrm{kg/m3} \\) | | rho |  
| \\(\omega\\) | Pump angular velocity | \\( \mathrm{rad/s} \\) | | - |  
| \\(\omega\_{nom}\\) | Nominal pump angular velocity | \\( \mathrm{rad/s} \\) | |  - |  
| \\(\bar{\omega}\\) | Reduced pump  rotational velocity | - | \\( \frac{\omega}{\omega_{nom}}  = \frac{N}{N_{nom}} \\) | R |  


## Governing equations  


### Energy balance equation  

- Validity domain:  
   
 \\( \forall \bar{\omega}, \forall q \\neq 0 \\; \text{such that} \\; \eta_h \\in ]0,1] \\)  

- Mathematical formulation:   

$$ g \cdot h_n = \eta_h \cdot (h_o - h_i) $$  


### Energy balance equation: mechanical power  

- Validity domain:  
   
 \\( \forall \bar{\omega}, q \\; \text{such that} \\; \eta_h \\in ]0,1] \\)  

- Mathematical formulation:  
      
    $$ W_m = \frac{\rho  \cdot q \cdot  (h_o - h_i)}{\eta_m} $$  


### Energy balance equation: hydraulic power  

- Validity domain:  
   
 \\( \forall \bar{\omega}, q \\; \text{such that} \\; \eta_h \\in ]0,1] \\)  

- Mathematical formulation:  
      
$$ W_m = \frac{q  \cdot (P_o - P_i)}{\eta_h} $$  


### Pump full characteristic  

- Validity domain:  
   
 \\( \forall \bar{\omega} \\; \text{and} \\; \forall q \\; \text{such that} \\; \bar{\omega} \\; q \\neq 0 \\)  

- Mathematical formulation:  
      
$$ \frac{\bar{h}\_n}{\bar{q}^2 + \bar{\omega}^2} = F(\\theta) $$  

- Comments:  

The characteristic \\( F(\\theta) \\) depends on the specific speed.  


### Hydraulic parabolic efficiency  

- Validity domain:  
   
 \\( \forall \bar{\omega} > 0 \\; \text{and} \\; \forall q > 0 \\; \text{such that} \\; \eta_h \\in ]0,1] \\)  

- Mathematical formulation:  
      
$$ \eta_h = b_2  \cdot \frac{q \cdot |q|}{\bar{\omega}^2} + b_1 \cdot \frac{q}{\bar{\omega}} + b_0 $$  


### Fluid average density  

- Validity domain:  
   
 \\( \forall P \\; \text{and} \\; \forall h \\; \text{inside the domain of valifity of } f_p, \\) the state equation for the density.  

- Mathematical formulation:  
      
$$ \rho = f_p \cdot  \left( \frac{P_i + P_o}{2}, \frac{h_i + h_o}{2} \right)$$  

- Comments:  
      
The pump does not follow the upwind scheme: the average density is calculated at the mid-point of the compression.  

## References  

El Hefni, Baligh and Bouskela, Daniel (2019). [Modeling and Simulation of Thermal Power Plants with ThermoSysPro](https://link.springer.com/book/10.1007/978-3-030-05105-1), sect. 12.2. Springer Nature Switzerland AG.  
    

Revisions