Measuring and testing – Blower – pump – and hydraulic equipment
Reexamination Certificate
2000-08-07
2002-09-17
Williams, Hezron (Department: 2856)
Measuring and testing
Blower, pump, and hydraulic equipment
C073S861690
Reexamination Certificate
active
06450023
ABSTRACT:
BACKGROUND AND SUMMARY OF THE INVENTION
The present invention is directed to a method and apparatus for centrifugal testing pumps, and more particularly, a method and apparatus for determining pumping efficiency of large quantity centrifugal slurry pumps using air as a test medium to predict pump performance and efficiency. The use of air as a testing medium requires less power to operate the pump, and a open test loop consisting of a light construction flow tube, section pipe and discharge pipe sections making for a simpler, less costly, easier to use test rig.
Centrifugal slurry pumps are large quantity pumps, such as large dredge pumps, for moving a large volume of solid-liquid mixture. As described, for example, in Applicants commonly assigned U.S. Pat. No. 4,923,369, which issued May 8, 1990, a centrifugal-type pump consists basically of a rotatable impeller enclosed by a collector or shell. As the impeller is rotated, it generates velocity head at the periphery of the shell. The shell collects the velocity head and converts it to a pressure head. There are many configurations within the framework of this basic design. In one common configuration illustrated in
FIG. 1
, the flow enters the shell on one side along the axis of rotation of the impeller, that is, the flow enters the shell at a point adjacent to the center of the impeller, referred to as the “eye” of the impeller, while the discharge of the shell is located at a point tangent to the shell outer periphery.
The impeller is connected to a drive shaft
20
, which protrudes away from the shell and is rotatably supported by suitable bearings blocks
21
. A motor (not shown) rotates the shaft
20
and the impeller within shell. The usual packing (not shown) for surrounding shaft
20
in the central portion of the back side of the shell, prevents leakage.
The efficiency and performance of a centrifugal slurry pump is normally determined by pumping water around a test loop and recording the differential head across the pump, the flow through the pump and the pump input power. The head and power at constant rotational speed (rpm) varies with the flow as shown in FIG.
2
. Head quantity performance at constant rpm has a characteristic curve that is usually established from ten or so sets of head measurements at different flows.
To determine performance of the pump, calculations for head and efficiency are made. The volume of liquid pumped is referred to as capacity and is generally measured in liters per second. The height to which liquid can be raised by a centrifugal pump is called total dynamic head (TDH) and is measured in meters. This does not depend on the nature of the liquid (its specific gravity) so long as the liquid viscosity is not higher than that of water. Water performance of centrifugal pumps is used as a standard of comparison because practically all commercial testing of pumps is done with water.
The head (H), or TDH as it is commonly called, is determined from the differential pressure across the pump and with appropriate velocity head and datum corrections using the well known Bernoulli's Equation 1:
H
=
TDH
=
V
B
2
-
V
A
2
2
g
+
P
B
-
P
A
ρ
f
g
+
(
z
B
-
z
A
)
(
1
)
where
TDH is usually in meters of H
2
O
V is usually in meters/sec.
P is usually in Newton/meters squared (or Pascal)
&rgr; is the density of water in kg/m
3
g is 9.81 meters/second squared
z is in meters of H
2
O.
The performance shown in
FIG. 2
varies with speed according to well-established laws, which may be used to establish the hydraulic performance of the pump at other speeds. When testing a pump, it is normal to test at or near the expected pump operating speed. The following discussing will be limited to constant speed.
The power output of the pump is determined by the product of Q, which represents the quantity of fluid pumped (m
3
/sec) and H, and is given by:
(Power)
out
=&rgr;gQH
(2)
This relation applies in any consistent system of units. Thus for SI units, equation (2) gives the power out in watts, which is usually divided by 1000 to obtain kilowatts. In the units in common use in the United States, Q is expressed in US gallons per minute, and H in feet and a numerical coefficient is required in the equation.
The input power to the pump can be defined as (T)(&ohgr;), where T is the torque on the shaft of the pump and &ohgr; is the angular velocity. Using seconds as the unit of time, &ohgr; is equal to 2Πn where n is measured revolutions per second. In practice, the speed of rotation is usually measured in revolutions per minute, even where SI units are generally employed. The symbol N (or rpm) will be reserved for revolutions per minute, and thus:
&ohgr;=2Π
n=
2
ΠN/
60 (3)
and the input power is then defined as:
(
Power
)
in
=
2
π
nT
=
2
π
(
NT
60
)
(
4
)
With torque in Newton-meters, this equation gives power in watts. In the United States, torque is generally measured in foot-pounds, and the input power is known, for historic reasons, as brake horsepower. When defined in this manner, a further numerical coefficient is required.
A final point, and in fact the main point concerning the pump's input and output, is pump efficiency, denoted &eegr;, which is the ratio of output power to input power, i.e.;
η
=
(
Power
)
out
(
Power
)
in
(
5
)
This relation applies in any system of units. For ideal pump efficiency, &eegr; is 1.00 or 100%. However, in practice, pumps necessarily have lower values. Efficiencies of over 90% can be achieved for large water pumps. Efficiencies of slurry pumps tend to be somewhat less.
The resulting measured efficiency of a normal slurry pump (at constant speed) has a characteristic (curve) as shown in FIG.
2
. The highest value along the curve is usually called the Best Efficiency Point Efficiency (BEPE) and the flow (Q) and head (H) corresponding to the BEPE are referred to as the BEPQ and BEPH, respectively. The theoretical head of a centrifugal pump may be defined as:
H
t
=[u
2
c
t2
−u
1
−c
t1
]/g
(6)
where
u is the tangential velocity; and
c
t
the tangential component of the absolute flow velocity.
As losses have been disregarded, H is a theoretical head.
Equation (6) is often called the Euler equation, after its originator (Euler, 1756). The term u
1
c
t1
refers to the flow entering the eye of the impeller. At the best efficiency point this term effectively reduces to zero. Thus it is ignored when considering the idealized machine with efficiency of 100%. The vector diagram at the exit of the impeller shows that:
c
2t
=u
2
−c
m2
cot &bgr;
f
(7)
where &bgr;
f
is the angle between the relative velocity vector and the circumferential direction. It is somewhat smaller than the vane outlet angle. The term c
m2
is the meridional component of outlet velocity (directed radially outward for most slurry pumps), which in turn is given by the discharge Q divided by the exit area of the impeller, i.e.:
c
m2
=
Q
π
D
2
b
2
(
8
)
where b
2
is the breadth between the shrouds at the outlet of the impeller.
All of the above are in terms of a fluid being pumped. Normally, this is thought of as some type of liquid as the fluid, or even air, noting then that the head produced value must also be in units of air. Centrifugal water and slurry pumps have been run on air. Provided the Reynolds (Re) number is high enough (>10
5
), the head quantity performance data based on air as the flow medium has been found to be identical (within a normal commercial testing code tolerance) with that obtained on water. Recent tests carried out at the inventor's test laboratory on a pump with an impeller diameter of 1.58 meters, for example, show that separate water and air tested head quantity values were within 1% of each other.
If a large slurry pump could have performance and efficiency tests carried out using air rather than a liquid, with sufficient accuracy, establishing pump performance could be
Addie Graeme
Hergt Peter
Crowell & Moring LLP
Frank Rodney T.
GIW Industries, Inc.
Williams Hezron
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