WIND ENERGY SYSTEMS - Cd3wd

Chapter 7—Asynchronous Loads 7–11
The centrifugal pump can be thought of as a turbine operating in reverse, so the power
input will be proportional to the cube of the speed of the fluid passing through the pump,
which is proportional to the pump rotational speed. The centrifugal pump, therefore, makes
a good load for a wind turbine, at least near the optimum operating point for the pump.
The important operating characteristics of a centrifugal pump are the capacity Q, the
head h, the input power P m , the efficiency η p , the rotational speed n, and the diameter d of
the rotating wheel or impeller which actually moves the liquid being pumped. Relationships
among these variables are usually expressed graphically. The number of possible graphs is
reduced by defining a dimensionless parameter called the specific speed n s which will be the
same for all geometrically similar pumps[12, 17]. It is given by
n s = nQ 0.5 h −0.75 (6)
The specific speed can be expressed in any consistent set of units. Historically, the units have
usually been r/min for n, gal/min for Q, and feet for h. This choice yields specific speeds
between perhaps 500 and 10,000 for most pump designs. Farm irrigation pumps would usually
have n s between 1500 and 5000. If the capacity is expressed in m 3 /s and the head in m, we
get a different specific speed n ′ s ,wheren′ s = n s/51.64. We shall use the non-SI version to
hopefully help the reader understand existing manufacturers data sheets.
Specific speed allows comparison among pumps in much the same way that the Reynolds
number allows comparison among pipe flows and airfoils. It is not intended to be a precise
value, so is always rounded off to no more than two significant digits. It is calculated at the
best or peak efficiency point of pump operation. That is, when it is desired to calculate the
specific speed from performance curves, the capacity and head values for the peak efficiency
point are used. If a pump has several stages, the specific speed is calculated on the basis of
the head per stage. For a given head and capacity, a higher specific speed pump will operate
at a higher speed and will be of smaller physical dimensions.
The peak efficiency of a pump varies with many parameters, but generally varies with
specific speed and capacity as shown in Fig. 4. We see that the very largest pumps have
a peak efficiency of about 90 percent at a specific speed of between 2000 and 3000. The
efficiency will decrease as operating conditions change from the optimum conditions for which
the pump was designed. Lower capacity pumps of the same quality of design will also have
lower peak efficiencies. A pump of one hundredth of the capacity of the largest unit may have
a peak efficiency of 65 percent at a specific speed of 2000. The equivalent quality of design for
a pump of the same capacity but built for a specific speed of 500 may have a peak efficiency
of only 48 percent. We, therefore, want to choose a pump for any wind driven application
that has a specific speed large enough to have a good efficiency.
The efficiencies in this figure are representative of what was considered good practice
in the days of cheap energy. We can expect pump efficiencies to improve as more efficient
pumps become cost effective with increasing energy costs. Candidate pump efficiencies should
be carefully investigated for those applications where total energy costs are significant when
Wind Energy Systems by Dr. Gary L. Johnson November 21, 2001