# Centrifugal Pump (2P)

**Libraries:**

Simscape /
Fluids /
Two-Phase Fluid /
Fluid Machines

## Description

The Centrifugal Pump (2P) block represents a centrifugal pump that transfers energy from the shaft to a fluid in a two-phase fluid network. The pressure differential and mechanical torque are functions of the pump head and brake power, which depend on the pump capacity. You can parameterize the pump analytically or by linear interpolation of the tabulated data. The pump affinity laws define the core physics of the block, which scales the pump performance by 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 pump drops to zero.

### Analytical Parameterization

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:

*Δp*is the reference pressure gain, which the block determines from a quadratic fit of the pump pressure differential between the_{ref}**Maximum head at zero capacity**,**Nominal head**, and**Maximum capacity at zero head**parameters.*ω*is the shaft angular velocity, where*ω*=*ω*–_{R}*ω*._{C}*ω*is the value of the_{ref}**Reference shaft speed**parameter.$$\frac{D}{{D}_{ref}}$$ is the value of the

**Impeller diameter scale factor**parameter. The 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 block calculates the reference brake power,
*W _{brake,ref}*, as capacity·head/efficiency. The pump efficiency curve is quadratic and its peak corresponds
to the

**Nominal brake power**parameter. The pump efficiency curve falls to zero when capacity is zero or maximum.

The block calculates the reference capacity as

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

The block returns a warning when the block flow rate becomes negative or exceeds the
maximum pump capacity if the **Check if operating beyond normal pump
operation** parameter is `Warning`

.

### 1-D Tabulated Data Parameterization

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 is a function of 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 value of 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 the head based on the average slope of the pump curves and brake power to the nearest point.

### 2-D Tabulated Data Parameterization

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 the 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 the **Head
table, H(q,w)** and **Brake power table,
Wb(q,w)** parameters 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.The

`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 the block and select **Fluids** > **Plot Pump Characteristics**. If you change the settings or data, click **Apply**
on the block parameters and click **Reload Data** on the pump curve
figure.

The default block parameterization creates these plots:

### Energy Balance

Mechanical work is a result of the energy exchange from the shaft to the fluid. The governing energy balance equation is

$${\varphi}_{A}+{\varphi}_{B}+{P}_{hydro}=0,$$

where:

*Φ*is the energy flow rate at port_{A}**A**.*Φ*is the energy flow rate at port_{B}**B**.

The pump hydraulic power is a function of the pressure difference between pump ports

$${P}_{hydro}=\Delta p\frac{\dot{m}}{\rho}.$$

### Assumptions and Limitations

If the shaft rotates opposite to the setting of the

**Mechanical orientation**parameter, the 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.

## Ports

### Conserving

## Parameters

## Extended Capabilities

## Version History

**Introduced in R2023b**