# Centrifugal Pump (TL)

Centrifugal pump in thermal liquid network

**Library:**Simscape / Fluids / Thermal Liquid / Pumps & Motors

## Description

The Centrifugal Pump (TL) block represents a centrifugal pump that transfers energy from the shaft to a fluid in a thermal 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 pump drops to zero.

**Port Configuration**

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

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*_{ref}is the reference pressure gain, which is determined from a quadratic fit of the pump pressure differential between the**Maximum head at zero capacity**,**Nominal head**, and**Maximum capacity at zero head**.*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
demonstrates.

The block calculates the reference capacity as:

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

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

You can parameterize the pump performance as a 1-D function of capacity. 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}$$\Delta p=\rho g\Delta {H}_{ref}({Q}_{ref})\frac{{\omega}^{2}}{{\omega}_{ref}^{2}}{\left(\frac{D}{{D}_{ref}}\right)}^{2},$$

where:

*ω*is the shaft angular velocity.*ρ*is the fluid density.*g*is the gravitational acceleration.

This is derived from the affinity law that relates head and angular velocity:

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

where *ΔH* is the pump head.

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

*Q*:

_{ref}$$T={P}_{ref}({Q}_{ref})\frac{{\omega}^{2}}{{\omega}_{ref}^{3}}\frac{\rho}{{\rho}_{ref}}{\left(\frac{D}{{D}_{ref}}\right)}^{5},$$

where *ρ _{ref}* is the

**Reference density**parameter.

This equation is a formulation of the affinity law that relates brake power and angular velocity:

$$\frac{{P}_{ref}}{P}=\frac{{\omega}_{ref}^{3}}{{\omega}^{3}}\frac{{\rho}_{ref}}{\rho}{\left(\frac{D}{{D}_{ref}}\right)}^{5}.$$

The reference capacity is:

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

where $$\dot{m}$$ is the mass flow rate at the pump inlet.

When the simulation is outside of the normal pump operating conditions, the block extrapolates the pump head linearly and brake power to the nearest point.

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

You can parameterize the pump performance as a 2-D function of capacity and shaft
angular velocity. 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,
*P _{ref}*, which is a function of the
reference capacity,

*Q*, and the shaft speed,

_{ref}*ω*:

$$T=\frac{{P}_{ref}({Q}_{ref},\omega )}{\omega}\frac{\rho}{{\rho}_{ref}}{\left(\frac{D}{{D}_{ref}}\right)}^{5}.$$

The reference capacity is:

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

When the simulation is outside of the normal pump operating conditions, the block extrapolates the pump head linearly and brake power to the nearest point.

### 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:

### 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*_{A}is the energy flow rate at port**A**.*Φ*_{B}is the energy flow rate at port**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

Reverse flow or a pressure drop over the pump is not normal operation, and the simulation results in these situations 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

## Model Examples

## Extended Capabilities

## See Also

Centrifugal Pump (IL) | Fixed-Displacement Pump (TL) | Variable-Displacement Pump (TL)

### Topics

**Introduced in R2018a**