# Centrifugal Pump (IL)

Rotational conversion of energy in an isothermal liquid network

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• Simscape / Fluids / Isothermal Liquid / Pumps & Motors

## Description

The Centrifugal Pump (IL) block models rotational conversion of energy from the shaft to the fluid in an isothermal liquid network. The pressure differential and mechanical torque are modeled as a function of the pump head and brake power, which depend on pump capacity and are determined either analytically or by linear interpolation of tabulated data. All formulations are based on the pump affinity laws, which scale pump performance to the ratio of current to reference values of the pump angular velocity and impeller diameter.

Normal pump operation is when flow travels from port A to port B with a pressure gain from port A to port B. Port C is a mechanical reference port and port R is the mechanical port associated with the pump shaft. The shaft torque can only be positive. You can specify the normal operating shaft direction for your system in the Mechanical orientation parameter. If the simulation results in an angular velocity opposite that of your selected configuration, the returned shaft velocity remains at 0.

Centrifugal Pump Block Ports

### Analytical Parameterization: Capacity, Head, and Brake Power

The pressure gain over the pump is calculated as a function of the pump affinity laws and the reference pressure differential:

`${p}_{B}-{p}_{A}=\Delta {p}_{ref}{\left(\frac{\omega }{{\omega }_{ref}}\right)}^{2}{\left(\frac{D}{{D}_{ref}}\right)}^{2},$`

where:

• Δpref is the reference pressure gain, which is determined from a quadratic fit of the pump pressure differential between the Maximum head at zero capacity, the Nominal head, and the Maximum capacity at zero head.

• ω is the shaft angular velocity, ωRωC.

• ωref is the Reference shaft speed.

• $\frac{D}{{D}_{ref}}$ is the Impeller diameter scale factor, which can be modified from the default value of 1 if your reference and system impeller diameters differ. This block does not reflect changes in pump efficiency due to pump size.

• ρ is the network fluid density.

The pump brake power, or the power extracted by the pump from the fluid, is:

`${W}_{brake}={W}_{brake,ref}{\left(\frac{\omega }{{\omega }_{ref}}\right)}^{2}{\left(\frac{D}{{D}_{ref}}\right)}^{5}.$`

The reference brake power, Wref, is related to the reference torque, τref:

`${\tau }_{ref}={\tau }_{ref,ideal}+{\tau }_{ref,fr}=\frac{{W}_{brake,ref}}{{\omega }_{ref}},$`

where the ideal reference torque is calculated as:

`${\tau }_{ref,ideal}=\frac{{q}_{ref}\Delta {p}_{ref}}{{\omega }_{ref}},$`

and the reference friction torque, τref,fr is determined from a linear fit of $\frac{{W}_{brake,ref}}{{\omega }_{ref}}-{\tau }_{ref,ideal}$ between the Nominal break power and the Brake power at zero capacity.

You can select to be warned when the block flow rate becomes negative or exceeds the maximum pump capacity by setting Check if operating beyond normal pump operation to `On`.

### 1-D Parameterization: Head and Break Power as a Function of Capacity

You can model pump performance as a 1-D function of capacity, the volumetric flow rate through the pump. The pressure gain over the pump is based on the Reference head vector, ΔHref, which is a function of the reference capacity, qref:

`$\Delta p=\rho g\Delta {H}_{ref}\left({q}_{ref}\right){\left(\frac{\omega }{{\omega }_{ref}}\right)}^{2}{\left(\frac{D}{{D}_{ref}}\right)}^{2},$`

where g is the gravitational constant.

The shaft torque is based on the Reference brake power vector, Wref, which is a function of the reference capacity:

`$\tau ={W}_{ref}\left({q}_{ref}\right)\frac{{\omega }^{2}}{{\omega }_{ref}^{3}}{\left(\frac{D}{{D}_{ref}}\right)}^{5}.$`

The reference capacity is set as:

`${q}_{ref}=\frac{\stackrel{˙}{m}}{\rho }\left(\frac{{\omega }_{ref}}{\omega }\right){\left(\frac{{D}_{ref}}{D}\right)}^{3},$`

which is then used for interpolation between the , the Reference head vector, and Reference brake power vector.

When the simulation is outside of the normal pump operating conditions, the pump head and brake power are linearly extrapolated.

### 2-D Parameterization: Head and Brake Power as a Function of Capacity and Shaft Speed

You can model pump performance as a 2-D function of volumetric flow rate and angular velocity. The pressure gain over the pump is a function of the Head table, H(q,w), ΔH, which is a function of the capacity, q, and the shaft speed, ω:

`$\Delta p=\rho g\Delta {H}_{ref}\left(q,\omega \right){\left(\frac{D}{{D}_{ref}}\right)}^{2}.$`

The shaft torque is calculated as a function of the Brake power table, Wb(q,w), W, which is a function of the capacity, q, and the shaft speed, ω:

`$\tau ={W}_{ref}\left(q,\omega \right)\frac{1}{\omega }{\left(\frac{D}{{D}_{ref}}\right)}^{5}.$`

When the simulation is outside of the normal pump operating conditions, the pump head and brake power are linearly extrapolated.

### Predefined Parameterization

There are multiple available built-in parameterizations for the Centrifugal Pump (IL) block.

This pre-parameterization data allows you to set up the block to represent a specific supplier component. To load a predefined parameterization, click on the "Select a predefined parameterization" hyperlink in the Centrifugal Pump (IL) block dialog and select the specific part you want to upload from the list of available components.

Note

Predefined parameterizations of Simscape components use available data sources for supplying parameter values. Engineering judgement and simplifying assumptions are used to fill in for missing data. As a result, deviations between simulated and actual physical behavior should be expected. To ensure requisite accuracy, you should validate simulated behavior against experimental data and refine component models as necessary.

### Assumptions and Limitations

• The block does not account for dynamic pressure in the pump. The calculated head is only due to static pressure.

• The block does not account for pressure loss due to friction or variable flow areas.

Note

In the Centrifugal Pump (TL) block, the ratio $\frac{D}{{D}_{ref}}$ is not a user-defined parameter and remains constant. In the Centrifugal Pump (IL) block, the diameter ratio can be changed by adjusting the Impeller diameter scale factor parameter.

## Ports

### Conserving

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Liquid entry or exit point to the pump.

Liquid entry or exit point to the pump.

Shaft angular velocity and torque.

Reference angular velocity and torque.

## Parameters

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Parameterization of the pump head and brake power. By selection ```Capacity, head, and brake power at reference shaft speed```, you can model the pump pressure gain and shaft torque empirically. By selecting ```1D tabulated data - head and brake power vs. capacity at reference shaft speed```, you can model head and brake power by interpolating between the user-provided pump capacity, head, and brake power vectors. By selecting ```2D tabulated data - head and brake power vs. capacity and shaft speed```, you can model head and brake power by interpolating between the user-provided pump capacity and shaft speed vectors and the head and brake power tables.

Nominal pump volumetric flow rate at a reference shaft angular velocity.

#### Dependencies

To enable this parameter, set Pump parameterization to ```Capacity, head, and brake power at reference shaft speed```.

Nominal pump pressure differential, normalized by gravity and the fluid density, at a reference shaft angular velocity.

#### Dependencies

To enable this parameter, set Pump parameterization to ```Capacity, head, and brake power at reference shaft speed```.

Nominal mechanical shaft power at a reference angular velocity.

#### Dependencies

To enable this parameter, set Pump parameterization to ```Capacity, head, and brake power at reference shaft speed```.

Maximum pump head with no flow at a reference angular velocity. This parameter is used to determine the reference pressure differential over the pump in the analytical parameterization by providing the roots of the quadratic equation for pressure in conjunction with the Nominal capacity, the Nominal head, and the Maximum capacity at zero head parameters.

#### Dependencies

To enable this parameter, set Pump parameterization to ```Capacity, head, and brake power at reference shaft speed```.

Maximum pump power without flow at a reference angular velocity. This parameter is used to determine the reference pump torque in the analytical parameterization by providing the roots of the equation for reference friction torque, in conjunction with the Nominal brake power.

#### Dependencies

To enable this parameter, set Pump parameterization to ```Capacity, head, and brake power at reference shaft speed```.

Maximum fluid load with zero head at a reference angular velocity. This parameter is used to determine the reference pressure differential over the pump in the analytical parameterization by providing the roots of the quadratic equation for pressure in conjunction with the Nominal capacity, the Nominal head, and the Maximum head at zero capacity parameters.

#### Dependencies

To enable this parameter, set Pump parameterization to ```Capacity, head, and brake power at reference shaft speed```.

Reference angular velocity for affinity law calculations. The default value depends on the setting.

#### Dependencies

To enable this parameter, set Pump parameterization to either:

• ```Capacity, head, and brake power at reference shaft speed```.

• ```1D tabulated data - head and brake power vs. capacity at reference shaft speed```.

Vector of volumetric flow rates for the tabular parameterization of pump head or brake power. This parameter corresponds one-to-one with the Reference head vector and Reference brake power vector parameters. The vector elements are listed in ascending order and must be greater than 0.

#### Dependencies

To enable this parameter, set Pump parameterization to ```1D tabulated data - head and brake power vs. capacity at reference shaft speed```.

Vector of pump head values for the 1-D tabular parameterization of pump head and brake power. This parameter corresponds one-to-one with the Reference capacity vector parameter. The vector elements must be listed in descending order and must be greater than 0.

#### Dependencies

To enable this parameter, set Pump parameterization to ```1D tabulated data - head and brake power vs. capacity at reference shaft speed```.

Vector of pump brake power values for the 1-D tabular parameterization of pump head and brake power. This parameter corresponds to the Reference capacity vector parameter. Vector elements must be greater than or equal to 0.

#### Dependencies

To enable this parameter, set Pump parameterization to ```1D tabulated data - head and brake power vs. capacity at reference shaft speed```.

Reference angular velocity for affinity laws.

#### Dependencies

To enable this parameter, set Pump parameterization to either:

• ```Capacity, head, and brake power at reference shaft speed```.

• ```1D tabulated data - head and brake power vs. capacity at reference shaft speed```.

Vector of volumetric flow rates for the tabular parameterization of pump head. This vector forms an independent axis with the Shaft speed vector, w parameter for the 2-D and Brake power table, Wb(q,w) parameters. The vector elements must be listed in ascending order and must be greater than or equal to 0.

#### Dependencies

To enable this parameter, set Pump parameterization to ```2D tabulated data - head and brake power vs. capacity and shaft speed```.

Vector of shaft angular velocity values for the tabular parameterization of pump head. This vector forms an independent axis with the Capacity vector, q parameter for the 2-D and Brake power table, Wb(q,w) parameters. The vector elements must be listed in ascending order and must be greater than 0.

#### Dependencies

To enable this parameter, set Pump parameterization to ```2D tabulated data - head and brake power vs. capacity and shaft speed```.

M-by-N matrix of pump head values at the specified volumetric flow rate and angular velocity. All table elements must be greater than 0. Linear interpolation is employed between table elements. M and N are the sizes of the corresponding vectors:

• M is the number of vector elements in the Capacity vector, q parameter. All columns of the array must be in descending order. For example, H(1,1) must be the largest value in the column, and H(M,1) must be the smallest.

• N is the number of vector elements in the parameter.

#### Dependencies

To enable this parameter, set Pump parameterization to ```2D tabulated data - head and brake power vs. capacity and shaft speed```.

M-by-N matrix of pump brake power values at the specified volumetric flow rate and angular velocity. All values must be greater than or equal to 0. Linear interpolation is employed between table elements. M and N are the sizes of the corresponding vectors:

• M is the number of vector elements in the Capacity vector, q parameter.

• N is the number of vector elements in the parameter.

#### Dependencies

To enable this parameter, set Pump parameterization to ```2D tabulated data - head and brake power vs. capacity and shaft speed```.

Ratio of model diameter to reference diameter for affinity law calculations. Modify this value if there is a difference between your reference and system impeller diameters, such as when testing pump scaling. For system pumps smaller than the reference pump, use a value less than 1. For system pumps larger than the reference pump, use a value grater than 1. This block does not reflect changes in pump efficiency due to pump size.

Shaft normal rotational direction. When the block simulates shaft rotation in the opposite direction of that indicated by the Mechanical orientation setting, the returned shaft velocity remains at 0.

Whether to notify if the block operates outside of the normal pump functionality. Select `Warning` to be notified when the flow rate through the pump is less than 0 or beyond maximum pump capacity. Select `Error` to stop the simulation when the flow rate through the pump is less than 0 or beyond maximum pump capacity.

#### Dependencies

To enable this parameter, set Pump parameterization to ```Capacity, head, and brake power at reference shaft speed```.