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:
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, ωR – ωC.
ωref is the value of the Reference shaft speed parameter.
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:
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:
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:
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:
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:
where ρref is the Reference density parameter.
This equation is a formulation of the affinity law that relates brake power and angular velocity:
The reference capacity is:
where 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:
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:
The reference capacity is:
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.
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 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:
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:
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.