# Centrifugal Pump (TL)

Centrifugal pump in thermal liquid network

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• 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:

• 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, Nominal head, and Maximum capacity at zero head.

• ω is the shaft angular velocity, ωRωC.

• ωref 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, Wbrake,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:

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

### 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, ΔHref, which is a function of the reference capacity, Qref:

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

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, Pref, which is a function of the reference capacity, Qref:

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

where ρref 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:

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

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

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

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, ΔHref, which is a function of the reference capacity, Qref, and the shaft speed, ω:

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

The shaft torque is a function of the Brake power table, Wb(q,w) parameter, Pref, which is a function of the reference capacity, Qref, and the shaft speed, ω:

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

The reference capacity is:

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

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 and 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:

### 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:

• ΦA is the energy flow rate at port A.

• ΦB is the energy flow rate at port B.

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

`${P}_{hydro}=\Delta p\frac{\stackrel{˙}{m}}{\rho }.$`

### 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.

## Ports

### Conserving

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Thermal liquid conserving port associated with the fluid.

Thermal liquid conserving port associated with the fluid.

Mechanical rotational conserving port associated with the shaft.

Mechanical rotational conserving port associated with the case.

## Parameters

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Parameterization of the pump head and brake power, specified as:

• ```Capacity, head, and brake power at reference shaft speed```: Parameterize pump pressure gain and shaft torque with an analytical formula.

• ```1D tabulated data - head and brake power vs. capacity at reference shaft speed```: Parameterize head and brake power from tabulated data of the head and brake power at a given capacity.

• ```2D tabulated data - head and brake power vs. capacity and shaft speed```: Parameterize head and brake power from tabulated data of the head and brake power at a given capacity and shaft speed.

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 determines the reference pressure differential over the pump, which the block uses to fit a quadratic equation for pressure in addition to the Nominal capacity, Nominal head, and 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 fluid load with zero head at a reference angular velocity. This parameter determines the reference pressure differential over the pump, which the block uses to fit a quadratic equation for pressure in addition to the Nominal capacity, Nominal head, and 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 the pump head or brake power. The elements in this vector correspond one-to-one with the elements in the Reference head vector and Reference brake power vector parameters. In normal operating conditions, the elements in this parameter are nonnegative, but the block does accept negative values. Negative capacity is a non-normal operating condition that may arise from certain situations.

#### 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 the pump head and brake power. This parameter corresponds one-to-one with the Reference capacity vector parameter. In normal operating conditions, the elements in this parameter are nonnegative, but the block does accept negative values. Negative head, or pressure drop, is possible in non-normal operating conditions at the end of the vector.

#### 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 the pump head and brake power. This parameter corresponds one-to-one with the Reference capacity vector parameter. In normal operating conditions, the elements in this parameter are nonnegative, but the block does accept negative values. Negative brake power is possible in non-normal operating conditions at the end of the vector.

#### Dependencies

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

Vector of volumetric flow rates for the tabular parameterization of the 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. In normal operating conditions, the elements in this parameter are nonnegative, but the block does accept negative values. Negative capacity is a non-normal operating condition that may arise from certain situations.

#### 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 the 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. In normal operating conditions, the elements in this parameter are nonnegative, but the block does accept negative values. Negative head, or pressure drop, is possible in non-normal operating conditions at the bottom of the table. The block employs linear interpolation between table elements. M and N are the sizes of the corresponding vectors:

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

• N is the number of elements in the parameter. All rows must be in strictly ascending order.

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 and 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.

#### 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. In normal operating conditions these values are nonnegative, but the block does accept negative values. 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. All rows must be in strictly ascending order.

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 and 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.

#### Dependencies

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

Reference fluid density. The reference or data sheet typically specifies this value. This parameter scales the pump performance between different fluids.

#### Dependencies

To enable this parameter, set Pump parameterization to ```1D tabulated data - head and brake power vs. capacity at reference shaft speed``` or ```2D tabulated data - head and brake power vs. capacity and shaft speed```.

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

Shaft rotational direction for flow from port A to B.

Option to notify if the block operates outside of the normal pump boundary. This situation occurs when the flow rate through the pump is negative or beyond the maximum capacity of the pump.

#### Dependencies

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

## Version History

Introduced in R2018a

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