Centrifugal Pump (2P)

Centrifugal pump in a two-phase fluid network

Since R2023b

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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:

• ΔH_ref 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, where ω = 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. 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_ref, and the shaft speed, 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_ref, and the shaft speed, 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_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

• 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

A — Pump inlet

two-phase fluid

Two-phase fluid conserving port associated with the fluid.

B — Pump outlet

two-phase fluid

Two-phase fluid conserving port associated with the fluid.

R — Impeller shaft

mechanical rotational

Mechanical rotational conserving port associated with the impeller shaft.

C — Pump casing

mechanical rotational

Mechanical rotational conserving port associated with the case.

Parameters

Pump parameterization — Head and brake power parameterization

Capacity, head, and brake power at reference shaft speed (default) | 1D tabulated data - head and brake power vs. capacity at reference shaft speed | 2D tabulated data - head and brake power vs. capacity and shaft speed

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 the 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 the tabulated data of the head and brake power at a given capacity and shaft speed.

Nominal capacity — Pump volumetric flow rate

45 lpm (default) | positive scalar

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 head — Pump head

40 m (default) | positive scalar

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 brake power — Pump power

0.85 kW (default) | positive scalar

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 head at zero capacity — Maximum pump head with no flow

60 m (default) | positive scalar

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 capacity at zero head — Maximum flow rate with zero head

80 lpm (default) | positive scalar

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 shaft speed — Reference shaft angular velocity for affinity law calculations

1770 rpm | 3500 rpm | positive scalar

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

Dependencies

To enable this parameter, set Pump parameterization to Capacity, head, and break power at reference shaft speed or 1D tabulated data – head and break power vs. capacity at reference shaft speed.

Minimum shaft speed threshold as fraction of reference — Threshold for minimum shaft speed

1e-2 (default) | positive scalar

Threshold for the minimum shaft speed as a fraction of the reference shaft speed. The block uses this value to prevent the shaft speed from becoming zero and causing a division by zero error in the expression for q_ref.

Dependencies

To enable this parameter, set Pump parameterization to Capacity, head, and break power at reference shaft speed or 1D tabulated data – head and break power vs. capacity at reference shaft speed.

Reference capacity vector — Volumetric flow rate

[16.67, 30, 40, 53.33, 66.67, 83.33] lpm (default) | vector

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.

Reference head vector — Pump head vector

[50, 47.5, 45, 40, 35, 25] m (default) | vector

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.

Reference brake power vector — Pump brake power vector

[.6, .75, .85, .93, .98, .99] kW (default) | vector

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.

Capacity vector, q — Volumetric displacement vector

[16.67, 23.33, 30, 40, 53.33, 60] lpm (default) | vector

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 Head table, H (q,w) 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.

Shaft speed vector, w — Angular velocity vector

[2450, 2800, 3150, 3500] rpm (default) | vector

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 Head table, H (q,w) 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.

Head table, H(q,w) — Pump head matrix

[25, 32.7, 42.5, 50; 24, 31.7, 41, 49; 22.7, 30.5, 39, 47.5; 20, 28, 36, 45; 15.7, 24, 32, 40; 12.5, 21, 29.5, 37.5] m (default) | M-by-N matrix

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 Shaft speed vector, w 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 Head table, H(q,w) and Brake power table, Wb(q,w) parameters must match.

• 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.

Brake power table, Wb(q,w) — Pump brake power matrix

[.28, .38, .5, .6; .31, .41, .55, .68; .33, .44, .6, .75; .36, .48, .65, .83; .38, .53, .72, .93; .39, .55, .75, .97] kW (default) | M-by-N matrix

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 Shaft speed vector, w 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 Head table, H(q,w) and Brake power table, Wb(q,w) parameters must match.

• 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 density — Fluid density for listed pump performance data

998 kg/m^3 (default) | positive scalar

Reference fluid density for the pump performance data. 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.

Impeller diameter scale factor — Ratio of model diameter to reference diameter for affinity law calculations

1 (default) | positive scalar

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 model changes in pump efficiency due to pump size.

Mechanical orientation — Shaft normal rotational direction

Positive angular velocity of port R relative to port C corresponds to normal pump operation (default) | Negative angular velocity of port R relative to port C corresponds to normal pump operation

Shaft rotational direction for flow from port A to B.

Cross-sectional area at ports A and B — Flow area at pump inlet and outlet

0.01 m^2 (default) | positive scalar

Flow area at the pump inlet and outlet. The block assumes that the areas are equal.

Report when fluid is not fully liquid — Notification when fluid is not fully liquid

Warning (default) | None | Error

Whether the block does nothing, generates a warning, or generates an error when the vapor quality is greater than 0, which indicates that the fluid is not fully liquid.

Check if operating beyond normal pump operation — Option to notify when block is beyond operating bounds

None (default) | Warning | Error

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.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2023b