# Centrifugal Pump (IL)

**Libraries:**

Simscape /
Fluids /
Isothermal Liquid /
Pumps & Motors

## Description

The Centrifugal Pump (IL) block represents a centrifugal pump that transfers energy from the shaft to a fluid in an isothermal liquid network. The pressure differential and mechanical torque are functions of the pump head and brake power, which depend on pump capacity. You can parameterize the pump analytically or by linear interpolation of tabulated data. The pump affinity laws define the core physics of the block, which scale the pump performance to the ratio of the current to the reference values of the pump angular velocity and impeller diameter.

By default, the flow and pressure gain are
from port **A** to port **B**. Port
**C** represents the pump casing, and port **R**
represents the pump shaft. You can specify the normal operating shaft direction in the
**Mechanical orientation** parameter. If the shaft begins to spin
in the opposite direction, the pressure difference across the block drops to
zero.

**Port Configuration**

The figure shows the location of the block ports on a typical centrifugal pump.

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

When you set, **Pump parameterization** to ```
Capacity, head,
and brake power at reference shaft speed
```

, the block calculates the
pressure gain over the pump as a function of the pump affinity laws and the
reference pressure differential:

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

where:

*g*is the gravitational acceleration.*ΔH*is the reference pump head, which the block derives from a quadratic fit of the pump pressure differential between the values of the**Maximum head at zero capacity**,**Nominal head**, and**Maximum capacity at zero head**parameters.*ω*is the shaft angular velocity,*ω*_{R}–*ω*_{C}.*ω*_{ref}is the value of the**Reference shaft speed**parameter.$$\frac{D}{{D}_{ref}}$$ is the value of the

**Impeller diameter scale factor**parameter. This block does not reflect changes in pump efficiency due to pump size.*ρ*is the network fluid density.

The shaft torque is:

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

The reference brake power, *W*_{brake,ref}, is
calculated as capacity·head/efficiency. The pump efficiency curve is quadratic with its peak
corresponding to the **Nominal brake power** parameter, and it
falls to zero when capacity is zero or maximum as the pump curve figure
demonstrates.

The block calculates the reference capacity as:

$${q}_{ref}=\frac{\dot{m}}{\rho}\frac{{\omega}_{ref}}{\omega}{\left(\frac{{D}_{ref}}{D}\right)}^{3}.$$

You can choose 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 Tabulated Data Parameterization: Head and Brake Power as a Function of Capacity

When you set **Pump parameterization** to ```
1D tabulated data -
head and brake power vs. capacity at reference shaft speed
```

, the
pressure gain over the pump functions with the **Reference head
vector** parameter, *ΔH*_{ref},
which is a function of the reference capacity,
*q _{ref}*:

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

where *g* is the gravitational acceleration.

The block bases the shaft torque on the **Reference brake power
vector** parameter, *W*_{ref},
which is a function of the reference capacity:

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

where *ρ _{ref}* is the

**Reference density**parameter. The reference capacity is:

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

which the block uses to interpolate the values of the
**Reference capacity vector**, **Reference head
vector**, and **Reference brake power vector**
parameters as a function of *q _{ref}*.

When the simulation is outside the range of the provided tables, the block extrapolates head based on the average slope of the pump curves and brake power to the nearest point.

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

When you set **Pump parameterization** to ```
2D tabulated data -
head and brake power vs. capacity and shaft speed
```

, the pressure
gain over the pump is a function of the **Head table, H(q,w)**
parameter, *ΔH _{ref}*, which is a function of
the reference capacity,

*q*, and the shaft speed,

_{ref}*ω*:

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

The shaft torque is a function of the **Brake power
table, Wb(q,w)** parameter,
*W _{ref}*, which is a function of the
reference capacity,

*q*, and the shaft speed,

_{ref}*ω*:

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

The reference capacity is:

$${q}_{ref}=\frac{\dot{m}}{\rho}{\left(\frac{{D}_{ref}}{D}\right)}^{3}.$$

When the simulation is outside the range of the provided tables, the block extrapolates head based on the average slope of the pump curves and brake power to the nearest point.

**Missing Data**

If your table has unknown data points, use `NaN`

in place of these
values. The block fills in the `NaN`

elements by extrapolating
based on the average slope of the pump curves. Do not use artificial numerical
values because these values distort pump behavior when operating in that region.
When using unknown data:

The

`NaN`

elements in the table must be contiguous.The positions of the

`NaN`

elements in the**Head table, H(q,w)**and**Brake power table, Wb(q,w)**parameters must match each other.`NaN`

elements must be located in the lower-left portion of the table, which corresponds to the highest capacity and lowest shaft speed.

### Visualizing the Pump Curve

You can check the parameterized pump performance by plotting the head, power, efficiency,
and torque as a function of the flow. To generate a plot of the current pump
settings, right-click on the block and select **Fluids** > **Plot Pump Characteristics**. If you change settings or data, click **Apply** on
the block parameters and click **Reload Data** on the pump curve
figure.

The default block parameterization results in these plots:

### Predefined Parameterization

You can populate the block with pre-parameterized manufacturing data, which allows you to model a specific supplier component.

To load a predefined parameterization:

In the block dialog box, next to

**Selected part**, click the "<click to select>" hyperlink next to**Selected part**in the block dialogue box settings.The Block Parameterization Manager window opens. Select a part from the menu and click

**Apply all**. You can narrow the choices using the**Manufacturer**drop down menu.You can close the

**Block Parameterization Manager**menu. The block now has the parameterization that you specified.You can compare current parameter settings with a specific supplier component in the Block Parameterization Manager window by selecting a part and viewing the data in the

**Compare selected part with block**section.

**Note**

Predefined block parameterizations use available data sources to supply parameter values. The block substitutes engineering judgement and simplifying assumptions for missing data. As a result, expect some deviation between simulated and actual physical behavior. To ensure accuracy, validate the simulated behavior against experimental data and refine your component models as necessary.

To learn more, see List of Pre-Parameterized Components.

### Assumptions and Limitations

If the shaft rotates opposite to the specified mechanical orientation, pressure difference across the block drops to zero and the results may not be accurate.

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

Pre-defined parameterizations use available data and the block fills in missing data where necessary. Validate your model against expected results.

## Examples

## Ports

### Conserving

## Parameters

## Extended Capabilities

## Version History

**Introduced in R2020a**