Centrifugal Pump (IL)

A centrifugal pump in an isothermal fluid network.

blockType: EngeeFluids.IsothermalLiquid.Turbomachinery.CentrifugalPump

Path in the library:

/Physical Modeling/Fluids/Isothermal Liquid/Pumps & Motors/Centrifugal Pump (IL)

Description

Block Centrifugal Pump (IL) simulates a centrifugal pump that transfers energy from a shaft to a fluid in an isothermal fluid network. Differential pressure and mechanical torque are functions of the pump head and effective power, which depend on the pump performance. The pump can be parameterized analytically or by linear interpolation of tabular data. The laws of pump similarity define the basic physical principles of the unit’s operation, which scale pump performance depending on the ratio of the current values of the angular velocity of the pump and the diameter of the impeller to the reference values of the angular velocity and diameter, respectively.

By default, the flow rate and pressure drop generated by the pump are directed so that the flow and pressure gradient are directed from port A to port B. Port C is the pump body, and port R is the pump shaft. The normal direction of rotation of the shaft can be specified in the parameter Mechanical orientation. If the shaft starts rotating in the opposite direction, the pressure difference on the block drops to zero.

configuration of ports

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

centrifugal pump il 1

Analytical parameterization: productivity, pressure and effective power

If set for the parameter Pump parameterization meaning Capacity, head, and brake power at reference shaft speed, the unit calculates the pressure gain at the pump as a function of the laws of similarity of the pump and the difference in set pressures:

where

— acceleration of free fall;
— the reference pressure value, which the unit calculates by quadratically approximating the pump pressure difference between the parameter values Maximum head at zero capacity, Nominal head and Maximum capacity at zero head;
— angular velocity of the shaft, ;
— parameter value Reference shaft speed;
— parameter value Impeller diameter scale factor; this block does not reflect changes in pump efficiency depending on its size;
— the density of the liquid in the network.

The torque on the shaft is

Reference effective power calculated as . The efficiency curve of the pump has a quadratic shape, the peak of which corresponds to the value of the parameter Nominal brake power, and it drops to zero when the productivity (consumption) is zero or maximum.

The unit calculates the reference flow rate as follows:

Parameterization of one-dimensional tabular data: pressure and effective power as functions of productivity

If set for the parameter Pump parameterization meaning 1D tabulated data - head and brake power vs. capacity at reference shaft speed, the pressure increase at the pump is a function of the parameter Reference head vector, , which is a function of the flow reference value :

where — acceleration of free fall.

The unit calculates the shaft torque based on the parameter Reference brake power vector, , which is a function of the reference flow rate:

where — parameter value Reference density. The reference flow rate is

it is used by the block to interpolate parameter values. Reference capacity vector, Reference head vector and Reference brake power vector in relation to .

When the simulation results exceed the range specified in the tables, the unit extrapolates the pressure based on the average slope of the pump curves and effective power to the nearest point.

Parameterization of two-dimensional tabular data: head and effective power as functions of productivity and angular velocity of the shaft

If set for the parameter Pump parameterization meaning 2D tabulated data - head and brake power vs. capacity and shaft speed, the pressure increase at the pump is a function of the parameter Head table, H(q,w), , which is a function of the reference flow rate and the angular velocity of the shaft :

The torque on the shaft is a function of the parameter Brake power table, Wb(q,w), , which, in turn, is a function of the reference flow rate and the angular velocity of the shaft :

The reference flow rate is

When the simulation results exceed the range specified in the tables, the unit extrapolates the pressure based on the average slope of the pump curves and effective power to the nearest point.

The missing data

If your table has unknown values, use NaN instead of these values. The block fills in the elements NaN by extrapolating based on the average slope of the pump curves. Do not use artificial numerical values, as they distort the pump’s behavior when operating in this range. When using unknown data:

Elements NaN the table should be arranged sequentially;
Positions of the elements NaN in the table in the parameters Head table, H(q,w) and Brake power table, Wb(q,w) must match;
Elements NaN They should be located in the lower-left corner of the table, which corresponds to the highest productivity and the lowest angular velocity of the shaft.

Assumptions and limitations

If the shaft rotates in the opposite direction to the set mechanical position, the pressure difference on the block drops to zero, and the results may be inaccurate.
The unit does not take into account the dynamic pressure in the pump. The unit only takes into account the pump head due to static pressure.

Ports

Conserving

# A — Isothermal liquid port
Isothermal liquid

Details

A non-directional port connected to the pump inlet section.

Program usage name

port_a

# B — Isothermal liquid port
Isothermal liquid

Details

A non-directional port connected to the pump outlet section.

Program usage name

port_b

# R — shaft of the impeller
rotational mechanics

Details

A non-directional port connected to the shaft.

Program usage name

rod_flange

# C — pump housing
rotational mechanics

Details

A non-directional port connected to the case.

Program usage name

case_flange

Parameters

# Pump parameterization — parameterization of pressure and effective power
Capacity, head, and brake power at reference shaft speed | 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

Details

Parameterization of the pressure and effective power of the pump, set as follows:

Capacity, head, and brake power at reference shaft speed — parameterization of pump pressure gain and shaft torque using analytical methods;
1D tabulated data - head and brake power vs. capacity at reference shaft speed — parameterization of pressure and effective power based on tabular pressure and effective power data for a given performance;
2D tabulated data - head and brake power vs. capacity and shaft speed — parameterization of head and effective power based on tabular data of head and effective power at a given output and angular velocity of the shaft.

Values	`Capacity, head, and brake power at reference shaft speed` \| `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`
Default value	`Capacity, head, and brake power at reference shaft speed`
Program usage name	`paramerization`
Evaluatable	No

# Nominal capacity — volumetric flow rate of the pump
m^3/s | mm^3/s | cm^3/s | m^3/hr | m^3/min | l/hr | l/min | l/s | gal/hr | gal/min | gal/s | ft^3/hr | ft^3/min | ft^3/s

Details

The nominal volumetric flow rate of the pump at a given angular velocity of the shaft.

Dependencies

To use this parameter, set for the parameter Pump parameterization meaning Capacity, head, and brake power at reference shaft speed.

Units	`m^3/s` \| `mm^3/s` \| `cm^3/s` \| `m^3/hr` \| `m^3/min` \| `l/hr` \| `l/min` \| `l/s` \| `gal/hr` \| `gal/min` \| `gal/s` \| `ft^3/hr` \| `ft^3/min` \| `ft^3/s`
Default value	`45.0 l/min`
Program usage name	`Vdot_nominal`
Evaluatable	Yes

# Nominal head — pump pressure
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

The nominal pressure drop of the pump, normalized relative to gravity and liquid density, at a given angular velocity of the shaft.

Dependencies

To use this parameter, set for the parameter Pump parameterization meaning Capacity, head, and brake power at reference shaft speed.

Units	`m` \| `um` \| `mm` \| `cm` \| `km` \| `in` \| `ft` \| `yd` \| `mi` \| `nmi`
Default value	`40.0 m`
Program usage name	`nominal_head`
Evaluatable	Yes

# Nominal brake power — pump power
W | uW | mW | kW | MW | GW | V*A | HP_DIN

Details

Rated mechanical power on the shaft at a given angular velocity.

Dependencies

To use this parameter, set for the parameter Pump parameterization meaning Capacity, head, and brake power at reference shaft speed.

Units	`W` \| `uW` \| `mW` \| `kW` \| `MW` \| `GW` \| `V*A` \| `HP_DIN`
Default value	`0.85 kW`
Program usage name	`nominal_mechanical_power`
Evaluatable	Yes

# Maximum head at zero capacity — maximum pump pressure in the absence of flow
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

Maximum pump pressure in the absence of flow at a given angular velocity. This parameter defines the reference pressure drop at the pump, which the unit uses to approximate the quadratic equation for pressure in addition to the parameters Nominal capacity, Nominal head and Maximum capacity at zero head.

Dependencies

To use this parameter, set for the parameter Pump parameterization meaning Capacity, head, and brake power at reference shaft speed.

Units	`m` \| `um` \| `mm` \| `cm` \| `km` \| `in` \| `ft` \| `yd` \| `mi` \| `nmi`
Default value	`60.0 m`
Program usage name	`max_head_at_zero_Vdot`
Evaluatable	Yes

# Maximum capacity at zero head — maximum flow rate at zero pressure
m^3/s | mm^3/s | cm^3/s | m^3/hr | m^3/min | l/hr | l/min | l/s | gal/hr | gal/min | gal/s | ft^3/hr | ft^3/min | ft^3/s

Details

The maximum volumetric flow rate generated by the pump at zero pressure at a given angular velocity. This parameter defines the reference pressure drop at the pump, which the unit uses to approximate the quadratic equation for pressure in addition to the parameters Nominal capacity, Nominal head and Maximum head at zero capacity.

Dependencies

To use this parameter, set for the parameter Pump parameterization meaning Capacity, head, and brake power at reference shaft speed.

Units	`m^3/s` \| `mm^3/s` \| `cm^3/s` \| `m^3/hr` \| `m^3/min` \| `l/hr` \| `l/min` \| `l/s` \| `gal/hr` \| `gal/min` \| `gal/s` \| `ft^3/hr` \| `ft^3/min` \| `ft^3/s`
Default value	`80.0 l/min`
Program usage name	`Vdot_max_at_zero_head`
Evaluatable	Yes

Details

The reference angular velocity for calculations according to the law of similarity.

Dependencies

To use this parameter, set for the parameter Pump parameterization meaning Capacity, head, and brake power at reference shaft speed or 1D tabulated data - head and brake power vs. capacity at reference shaft speed.

Units	`rad/s` \| `deg/s` \| `rad/min` \| `deg/min` \| `rpm` \| `rps`
Default value	`1770.0 rpm`
Program usage names	`w_nominal`, `w_reference_1D`
Evaluatable	Yes

# Minimum shaft speed threshold as fraction of reference — threshold value for the minimum angular velocity of the shaft

Details

The threshold value for the minimum shaft rotation speed as a fraction of the reference angular velocity of the shaft. The unit uses this value to prevent the shaft rotation speed from being reset to zero and a division by zero error from occurring in the expression for .

Dependencies

Default value	`0.01`
Program usage name	`w_threshold_factor`
Evaluatable	Yes

# Impeller diameter scale factor — the ratio of the model diameter to the reference diameter

Details

The ratio of the model diameter to the reference diameter for calculations based on the law of similarity. Change this value if there is a difference between the reference and system diameters of the impeller, for example, when checking the pump scaling. For system pumps with a smaller diameter than the reference pump, use a value less than one. For system pumps with a larger diameter than the reference pump, use a value greater than one. The unit does not reflect changes in pump efficiency depending on its size.

Default value	`1.0`
Program usage name	`diameter_ratio`
Evaluatable	Yes

# Mechanical orientation — direction of rotation of the shaft
Positive angular velocity of port R relative to port C corresponds to normal pump operation | Negative angular velocity of port R relative to port C corresponds to normal pump operation

Details

The direction of rotation of the shaft to create a flow from port A to port B.

Values	`Positive angular velocity of port R relative to port C corresponds to normal pump operation` \| `Negative angular velocity of port R relative to port C corresponds to normal pump operation`
Default value	`Positive angular velocity of port R relative to port C corresponds to normal pump operation`
Program usage name	`orientation`
Evaluatable	No

# Check if operating beyond normal pump operation — the option to notify when the block goes beyond the operating parameters
None | Error

Details

The option to notify when the unit goes beyond the normal operating parameters of the pump. This situation occurs when the flow rate through the pump is negative or exceeds the maximum pump capacity.

Dependencies

To use this parameter, set for the parameter Pump parameterization meaning Capacity, head, and brake power at reference shaft speed.

Values	`None` \| `Error`
Default value	`None`
Program usage name	`Vdot_assert_action`
Evaluatable	No

# Reference capacity vector — volume flow rate
m^3/s | mm^3/s | cm^3/s | m^3/hr | m^3/min | l/hr | l/min | l/s | gal/hr | gal/min | gal/s | ft^3/hr | ft^3/min | ft^3/s

Details

A vector of volumetric flow rates for tabular parameterization of pump head or effective power. The elements of this vector correspond one-to-one to the elements of the parameters Reference head vector and Reference brake power vector. Under normal operating conditions, the elements of this parameter are non-negative, but the block allows negative values. Negative performance is an abnormal working condition that can occur in certain situations.

Dependencies

To use this parameter, set for the parameter Pump parameterization meaning 1D tabulated data - head and brake power vs. capacity at reference shaft speed.

Units	`m^3/s` \| `mm^3/s` \| `cm^3/s` \| `m^3/hr` \| `m^3/min` \| `l/hr` \| `l/min` \| `l/s` \| `gal/hr` \| `gal/min` \| `gal/s` \| `ft^3/hr` \| `ft^3/min` \| `ft^3/s`
Default value	`[16.67, 30.0, 40.0, 53.33, 66.67, 83.33] l/min`
Program usage name	`Vdot_vector_1D`
Evaluatable	Yes

# Reference head vector — pump pressure vector
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

A vector of pump head values for a one-dimensional tabular parameterization of pump head and effective power. This parameter corresponds to one-to-one parameter elements Reference capacity vector. Under normal operating conditions, the elements of this parameter are non-negative, but the block allows negative values. In abnormal operating conditions, negative pressure or pressure drop is possible at the end of the vector.

Dependencies

To use this parameter, set for the parameter Pump parameterization meaning 1D tabulated data - head and brake power vs. capacity at reference shaft speed.

Units	`m` \| `um` \| `mm` \| `cm` \| `km` \| `in` \| `ft` \| `yd` \| `mi` \| `nmi`
Default value	`[50.0, 47.5, 45.0, 40.0, 35.0, 25.0] m`
Program usage name	`head_vector_1D`
Evaluatable	Yes

# Reference brake power vector — effective pump power vector
W | uW | mW | kW | MW | GW | V*A | HP_DIN

Details

A vector of effective pump power values for a one-dimensional tabular parameterization of pump head and effective power. This parameter corresponds to one-to-one parameter elements Reference capacity vector. Under normal operating conditions, the elements of this parameter are non-negative, but the block allows negative values. In abnormal operating conditions, negative effective power is possible at the end of the vector.

Dependencies

To use this parameter, set for the parameter Pump parameterization meaning 1D tabulated data - head and brake power vs. capacity at reference shaft speed.

Units	`W` \| `uW` \| `mW` \| `kW` \| `MW` \| `GW` \| `V*A` \| `HP_DIN`
Default value	`[0.6, 0.75, 0.85, 0.93, 0.98, 0.99] kW`
Program usage name	`mechanical_power_vector_1D`
Evaluatable	Yes

# Reference density — the density of the liquid for the specified pump performance data
kg/m^3 | g/m^3 | g/cm^3 | g/mm^3 | lbm/ft^3 | lbm/gal | lbm/in^3

Details

The reference density of the liquid. This value is usually indicated in the reference document or technical description. This parameter scales the pump performance for different liquids.

Dependencies

To use this parameter, set for the parameter Pump parameterization meaning 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`.

Units	`kg/m^3` \| `g/m^3` \| `g/cm^3` \| `g/mm^3` \| `lbm/ft^3` \| `lbm/gal` \| `lbm/in^3`
Default value	`998.21 kg/m^3`
Program usage names	`rho_reference_1D`, `rho_reference_2D`
Evaluatable	Yes

# Capacity vector, q — vector of volume expenses
m^3/s | mm^3/s | cm^3/s | m^3/hr | m^3/min | l/hr | l/min | l/s | gal/hr | gal/min | gal/s | ft^3/hr | ft^3/min | ft^3/s

Details

Vector of volumetric flow rates for tabular parameterization of the pump head. This vector forms an independent axis with the parameter Shaft speed vector, w for two-dimensional parameters Head table, H(q,w) and Brake power table, Wb(q,w). The elements of the vector must be listed in ascending order. Under normal operating conditions, the elements of this parameter are non-negative, but the block allows negative values. Negative performance is an abnormal working condition that can occur in certain situations.

Dependencies

To use this parameter, set for the parameter Pump parameterization meaning 2D tabulated data - head and brake power vs. capacity and shaft speed.

Units	`m^3/s` \| `mm^3/s` \| `cm^3/s` \| `m^3/hr` \| `m^3/min` \| `l/hr` \| `l/min` \| `l/s` \| `gal/hr` \| `gal/min` \| `gal/s` \| `ft^3/hr` \| `ft^3/min` \| `ft^3/s`
Default value	`[16.67, 23.33, 30.0, 40.0, 53.33, 60.0] l/min`
Program usage name	`Vdot_vector_2D`
Evaluatable	Yes

Details

The vector of values of the angular velocities of rotation of the shaft for tabular parameterization of the pump head. This vector forms an independent axis with the parameter Capacity vector, q for two-dimensional parameters Head table, H(q,w) and Brake power table, Wb(q,w). The elements of the vector must be listed in ascending order and must be larger 0.

Dependencies

To use this parameter, set for the parameter Pump parameterization meaning 2D tabulated data - head and brake power vs. capacity and shaft speed.

Units	`rad/s` \| `deg/s` \| `rad/min` \| `deg/min` \| `rpm` \| `rps`
Default value	`[2450.0, 2800.0, 3150.0, 3500.0] rpm`
Program usage name	`w_vector_2D`
Evaluatable	Yes

# Head table, H(q,w) — pump pressure matrix
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

Matrix size the values of the pump head at a given volume flow rate and angular velocity. Under normal operating conditions, the elements of this parameter are non-negative, but the block allows negative values. In abnormal operating conditions, negative pressure or pressure drop is possible at the bottom of the table. The block uses linear interpolation between table elements. and — the sizes of the corresponding vectors:

— the number of elements in the parameter Capacity vector, q;
— the number of elements in the parameter Shaft speed vector, w. All lines must be arranged in strictly ascending order.

Elements NaN the table should be arranged sequentially;
Positions of the elements NaN in the table in the parameters Head table, H(q,w) and Brake power table, Wb(q,w) They must match;
Elements NaN They should be located in the lower-left corner of the table, which corresponds to the highest productivity and the lowest angular velocity of the shaft.

Dependencies

To use this parameter, set for the parameter Pump parameterization meaning 2D tabulated data - head and brake power vs. capacity and shaft speed.

Units	`m` \| `um` \| `mm` \| `cm` \| `km` \| `in` \| `ft` \| `yd` \| `mi` \| `nmi`
Default value	`[25.0 32.7 42.5 50.0; 24.0 31.7 41.0 49.0; 22.7 30.5 39.0 47.5; 20.0 28.0 36.0 45.0; 15.7 24.0 32.0 40.0; 12.5 21.0 29.5 37.5] m`
Program usage name	`head_matrix_2D`
Evaluatable	Yes

# Brake power table, Wb(q,w) — effective pump power matrix
W | uW | mW | kW | MW | GW | V*A | HP_DIN

Details

Matrix size values of the effective pump power at a given volume flow rate and angular velocity. Under normal operating conditions, the elements of this parameter are non-negative, but the block allows negative values. The block uses linear interpolation between table elements. and — the sizes of the corresponding vectors:

— the number of elements in the parameter Capacity vector, q;
— the number of elements in the parameter Shaft speed vector, w. All lines must be arranged in strictly ascending order.

Elements NaN the table should be arranged sequentially;
Positions of the elements NaN in the table in the parameters Head table, H(q,w) and Brake power table, Wb(q,w) must match;
Elements NaN They should be located in the lower-left corner of the table, which corresponds to the highest productivity and the lowest angular velocity of the shaft.

Dependencies

To use this parameter, set for the parameter Pump parameterization meaning 2D tabulated data - head and brake power vs. capacity and shaft speed.

Units	`W` \| `uW` \| `mW` \| `kW` \| `MW` \| `GW` \| `V*A` \| `HP_DIN`
Default value	`[0.28 0.38 0.5 0.6; 0.31 0.41 0.55 0.68; 0.33 0.44 0.6 0.75; 0.36 0.48 0.65 0.83; 0.38 0.53 0.72 0.93; 0.39 0.55 0.75 0.97] kW`
Program usage name	`mechanical_power_matrix_2D`
Evaluatable	Yes