Pump

The calculation process starts from the modelling of the pump and system. On the basis of pump nameplate and system information, program creates the characteristics model for the pumping system, so the required shaft powers for the pump with valve and VSD control can be solved at different flow rates. The entire calculation process for the pump and the system is illustrated in Fig. 3.1 and it is described in detail later in this chapter.

Throttle VSD

Fig. 3.1 Calculation process for the pump. Head, efficiency, rotational speed, and shaft power values for two control methods are calculated as a function of flow rate, based on the pumping system char-acteristics model created from the pump nameplate and the system information.

In almost all cases, the objective of a pump is to transfer liquid. Making the liquid flow requires production of pressure to overcome the losses in the system. These losses are de-scribed by the system head Hsys [m], which is divided into static and friction head. The static head Hst [m] is the height difference between the supply and destination reservoirs’ surface levels and friction head Hfr [m] is the loss caused by the friction of the liquid movement. The resulting system curve is calculated by the equation

𝐻_𝑠𝑦𝑠 = 𝐻_𝑠𝑡+ 𝐻_𝑓𝑟 = 𝐻_𝑠𝑡+ 𝑘𝑄², (3.1)

where k is the coefficient for friction head and Q [m³/h] is the flow rate. The locations of static and friction heads in a pumping system are illustrated in Fig. 3.2. The static head is assumed to remain constant, so the difference of reservoirs’ surface levels isn’t changing during the pumping.

H_st Hfr

Fig. 3.2 Pumping system with static and friction head. The static head Hst is the height difference between the supply and destination reservoirs’ surface levels and the friction head Hfr describes the friction of moving liquid through the pipes, valves, and other equipment in the system. The static head is assumed to remain constant during pumping, but the friction head grows quadratically as a function of the flow rate.

In addition to the system curve, also the pump curve is needed to describe the operating points of the pump in QH plane. Pump characteristic curves are usually published by the manufacturer and they describe the performance of the pump for instance at different rota-tional speeds and impeller sizes.

The operating point of the pump is always at the intersection of the pump- and system curves and two different ways to change it, throttle and variable speed drive control, are discussed in this thesis. With throttle control the pump is driven at fixed speed and the operating point is changed by throttling and opening the valve. When the valve is throttled, the friction head is increased due to greater flow resistance, which causes reduction of flow rate. With variable speed drive, the flow is controlled by changing the rotational speed of the pump so the flow resistance can be kept in the optimal value. The flow reduction with both control methods is illustrated in Fig. 3.3.

THROTTLE CONTROL

VSD CONTROL

Fig. 3.3 Example of flow control with throttle and VSD in QH plane. Produced flow rates in both graphs are 60, 80 and 90 m³/h. The operating point of the pump is always at the intersection of the red pump curve and the blue system curve. The power produced by the pump at each operating point, and pump rotational speed at each pump curve are shown in graphs.

0 20 40 60 80 100 120

As Fig. 3.3 illustrates, reducing the flow with throttle control will always cause greater head losses than with variable speed drive, because of increased flow resistance in the system.

Therefore, when system is controlled with VSD, same flow rate can be usually produced with less power than with throttle control. This is the main reason for VSD being more effi-cient control method than throttling.

3.1.1 Throttle controlled system

In a throttle controlled system, rotational speed is kept constant so the operating point is changed by moving the system curve as shown in Fig. 3.3. Therefore the head values are following the pump curve as a function of flow rate. The actual shape of the pump head and efficiency curves can be approximated on the basis of the pump specific speed. Specific speed nq is a dimensionless quantity that is used to describe the centrifugal pump character-istics regardless of pump size, and it’s defined by the equation

𝑛

_𝑞

= 𝑛

^√𝑄𝑛

𝐻_𝑛^3⁄4, (3.2)

where n [rpm] is the rotational speed, Qn [m³/s] is the nominal flow rate of the pump, and Hn

[m] is the nominal head of the pump.

The program creates nq based head and efficiency curves for pump on the basis of the digit-ized relative curves that are represented in J.F. Gülich’s Centrifugal Pumps (2008). The curves are relative to the pumps’ nominal head, efficiency, and flow rate values and they are digitized for specific speeds 20, 60, 100 and 250. Curves are digitized with the program Engauge Digitizer 4.1, which can be used to convert a graph to CSV file containing the values of the curve. The average resolution of digitized values is 2.52 % in the range 0 % to 120 % of relative flow rate (Q/Qn). The curves are shown in Fig. 3.4.

Fig. 3.4 Relative head and efficiency curves based on pump specific speed nq. Curves are digitized from J.F.

Gülich’s Centrifugal Pumps (2008). Curves are covering the range of specific speeds from 20 to 250 and they are relative to the pumps’ nominal head, efficiency and flow rate values.

Even though there are digitized curves for only four specific speed values, head and effi-ciency curves can be approximated for all specific speeds ranging from 20 to 250 by linear interpolation. If specific speed of the pump is for example 35, head- and efficiency curves for the pump are interpolated from the digitized curves, in this instance from curves nq=20 and nq=60. This is illustrated in Fig. 3.5.

Fig. 3.5 Solving the head curve for certain specific speed. In the figure above, head curve for the pump with specific speed nq=35 is created from the digitized curves for specific speeds nq=20 and nq=60 by linear interpolation. The efficiency curve is created the same way.

With throttle controlled system, pump head and efficiency values at each flow rate are solved from created curves. Values are relative so they are multiplied by the nominal values.

3.1.2 VSD controlled system

When the pump is controlled with VSD, the flow rate is regulated by changing the rotational speed so the flow resistance can be kept at the optimal value. Therefore the operating points are following the system curve, while pump curve is varied like shown in Fig. 3.3. Head values at different flow rates are solved from the system curve for VSD controlled system.

With VSD, pump rotational speed at each flow rate is necessary to calculate, because it has effect on the operation of pump, motor and drive. Rotational speed is dependent on head and flow rate. A low specific speed pump’s head curve has typically a parabolic shape so it can be fitted to the form (Leonow 2013)

𝐻₀(𝑄₀) = 𝐴𝑄₀²+ 𝐵𝑄₀+ 𝐶, (3.3)

where Q [m³/h] is the flow rate and H [m] is the head. The fitting is created by solving the coefficients A, B and C by using the least squares fitting method. With the high specific speed axial flow pumps, this fitting is not as accurate as with the low specific speed pumps,

0 20 40 60 80 100 120 140

but it is still used in the program for all pumps for simplicity. Rotational speed can be taken into account by extending the created fitting with the affinity laws

𝐻 = 𝐻₀(_𝑛^𝑛

0)², (3.4)

𝑄 = 𝑄₀(_𝑛^𝑛

0) . (3.5)

When pump efficiency is assumed to remain constant, extension leads to the equation (Le-onow 2013)

𝐻 = 𝐴𝑄²+ 𝐵𝑄 (_𝑛^𝑛

𝑜) + 𝐶 (_𝑛^𝑛

𝑜)². (3.6) Head values are already calculated from the system curve with flow rate values, so the rota-tional speed n can be solved with the quadratic formula

𝑛 =

^{−𝐵𝑄+√(𝐵𝑄)2−4𝐶(𝐴𝑄2−(𝐻𝑠𝑡+𝑘𝑄2))}

2𝐶

𝑛

_𝑛 . (3.7)

Because of rotational speed of the pump is varied, the digitized curves used to approximate the efficiency values with throttle control cannot be used with VSD. However, there exist several equations that can be used to estimate the pump efficiency as a function of rotational speed. In designed program, the efficiency is calculated by the equation (Sârbu 1998)

𝜂 = 1 − (1 − 𝜂_𝑛) (^𝑛_𝑛^𝑛)^0.1, (3.8)

where η [%] is the efficiency of the pump.

When flow rate, head and pump efficiency values are known, required shaft power from motor Pshaft [W] with two control methods can be calculated by the equation

𝑃

_{𝑠ℎ𝑎𝑓𝑡}

=

^{𝜌𝑔𝐻𝑄}

𝜂 , (3.9)

where ρ [kg/m³] is the liquid density and g is the acceleration due to gravity (~9.81 m/s²).

In document Savings Calculator for Centrifugal Pumps (sivua 18-26)