Data processing: measuring – calibrating – or testing – Measurement system – Performance or efficiency evaluation
Reexamination Certificate
2002-10-17
2003-12-30
Hoff, Marc S. (Department: 2857)
Data processing: measuring, calibrating, or testing
Measurement system
Performance or efficiency evaluation
C073S152180
Reexamination Certificate
active
06671657
ABSTRACT:
TECHNICAL FIELD
The present invention relates to a computer-implemented method of calculating various types of characteristic curves of a centrifugal fluid machine (pump or the like), and a computer-readable storage medium having a program recorded thereon for calculating various types of characteristic curves of a centrifugal fluid machine. The present invention also relates to a computer-implemented method of geometrically converting coordinates in drawing a high-order curve, and a computer-readable storage medium having a program recorded thereon for geometrically converting coordinates in drawing a high-order curve.
BACKGROUND ART
When customers have requested a pump having a prescribed performance (desired flow rate and head), the following method has heretofore been employed to supply a pump that meets the desired performance.
First, a pump capable of providing the requested performance (flow rate and head) is selected from among numerous types of pumps. Specifically, as shown in
FIG. 6
, a pump is selected to have such characteristics that coordinates A
1
which are determined by the requested flow rate and head are located between a flow-head characteristic curve (Q-H characteristic curve) Y
1
with an impeller having a diameter of 100 mm and a flow-head characteristic curve (Q-H characteristic curve) Y
2
with an impeller having a diameter of 50 mm, or half the size, in the cases where parts other than an impeller housed in a pump casing are not changed, but the impeller is changed only in diameter. In other words, the Q-H characteristic curves Y
1
and Y
2
are calculated for a plurality of types of pumps in advance, and pumps having pump characteristics which are located between the curves Y
1
and Y
2
are selected from the plurality of types of pumps.
It is possible to obtain a pump with the required flow rate by setting the diameter of the impeller of the selected pump to 100 mm and throttling the opening of the valve mounted on the discharge port of the pump to raise the head against the flow rate on the Q-H characteristic curve Y
1
.
However, since an unnecessary increase in head is caused by throttling the opening of the valve in this method, loss of the motor power or the like is increased, and hence the running cost is problematically increased due to the increase in electric power consumption.
In order to solve the above problems, there has been proposed a method of selecting an impeller having such a diameter that a Q-H characteristic curve passes through the requested flow rate and head, rather than a method of simply setting the diameter of the impeller housed in the pump casing to 100 mm.
The following method is employed to select such an impeller, for example. In
FIG. 7
, a Q-H characteristic curve Y
3
which is located intermediately between the Q-H characteristic curves Y
1
and Y
2
is calculated, and then it is determined whether the curve Y
3
passes through the coordinates A
1
for the requested flow rate and head. When the coordinates A
1
are larger than the Q-H characteristic curve Y
3
, a Q-H characteristic curve Y
4
which is located intermediately between the Q-H characteristic curves Y
1
and Y
3
is calculated, and then it is determined whether the curve Y
4
passes through the coordinates A
1
. This process of calculations is repeated until a Q-H curve passing through the coordinates A
1
is found. Based on the Q-H characteristic curve passing through the coordinates A
1
that is found above, the diameter of the impeller is calculated, and a pump incorporating the impeller having the calculated diameter is provided to the customer.
The following method has heretofore employed to calculate the Q-H characteristic curve Y
3
located intermediately between the two Q-H characteristic curves Y
1
and Y
2
in
FIG. 7
, based on these two Q-H characteristic curves Y
1
and Y
2
. As shown in
FIG. 8
, this method employs two Q-H characteristic curves Y
H
1
and Y
H
2
and Q-E characteristic curves (flow-efficiency characteristic curves) Y
E
1
and Y
E
2
which correspond to the Q-H characteristic curves Y
H
1
and Y
H
2
, respectively. The flow rates are calculated at a plurality of points on the Q-E characteristic curves Y
E
1
and Y
E
2
which have the same efficiency, including P
11
and P
21
, P
12
and P
22
, P
13
and P
23
, P
14
and P
24
, P
15
and P
25
, and P
16
and P
26
. The heads corresponding to the respective flow rates are then calculated. Although P
16
and P
26
are the best efficiency points, respectively, and do not have the same efficiency, they are assumed to have the same efficiency in this example.
For example, with regard to the points P
11
and P
21
, flow rates Q
11
and Q
21
which correspond to an efficiency E
R1
are calculated at the points P
11
and P
21
. However, it is not easy to calculate the flow rates Q
11
and Q
21
on the X-axis from the efficiency E
R1
on the Y-axis in a high-order curve, but many calculations are required. Moreover, since the number of points at which the flow rates are calculated is 12 in this example, the similar calculations should be performed 12 times.
Next, the flow rates Q
11
and Q
21
are substituted for the two Q-H characteristic curves Y
H
1
=f
H
1
(x) and Y
H
2
=f
H
2
(x) to calculate the respective heads H
11
and H
21
which correspond to the flow rates Q
11
and Q
21
calculated above. The other heads are also calculated in the similar manner.
A coordinate point R
1
(Q
R1
, H
R1
) is estimated with the following equations from the calculated flow rates Q
11
and Q
21
and the calculated heads H
11
and H
21
. The other coordinate points R
2
-R
6
are also calculated in the similar manner.
H
R1
={(
H
11
−
H
21
)/2
}+H
21
Q
R1
={(
Q
11
−
Q
21
)/2
}+Q
21
A new Q-H characteristic curve Y
H
3
is then calculated by the least-square approximation of the sequence of the calculated coordinate points R
1
-R
6
.
Next, because a coordinate point S
1
(Q
R1
, E
R1
) on a Q-E characteristic curve Y
E
3
which corresponds to the calculated Q-H characteristic curve Y
H
3
has been calculated in the above calculation, the Q-E characteristic curve Y
E
3
is calculated by the least-square approximation of the sequence of the calculated coordinate points S
1
-S
6
.
Complicated and massive calculations are required to derive a high-order equation with the least-square method. Since such calculations should be performed for deriving two high-order equations for the Q-H characteristic curve Y
H
3
and the Q-E characteristic curve Y
E
3
, further massive calculations are required.
Then, it is determined whether the Q-H characteristic curve Y
H
3
calculated with the above method passes through the coordinates A
1
for the requested flow rate and head as described with reference to FIG.
7
. If the Q-H characteristic curve Y
H
3
does not pass through the coordinates A
1
, the above calculation is repeated.
Assuming that the calculations for calculating the Q-H characteristic curve and the Q-E characteristic curve are repeated five times, for example, a value on the X-axis should be calculated from a value on the Y-axis in the high-order equation 60 times, and the least-square approximation should be performed 10 times. Therefore, it is necessary to perform massive and complicated calculations, which cannot be performed on a personal computer at a practical speed but requires a host computer.
The performance curve for a pump, such as the Q-H characteristic curve described above, is usually expressed by representing the flow rate as [m
3
/min] on the horizontal axis and the head as [m] on the vertical axis. While this system of units (coordinates) is usually used in Japan, the Q-H characteristic curve should be displayed with another system of units (coordinates) of another country in the case of selling products in that country, for example. Specifically, it may be necessary to display a Q-H characteristic curve in [USG(US gallon)/min] on the horizontal axis and in [feet] on the ver
Maruyama Junji
Shigehara Shinichi
Ebara Corporation
Hoff Marc S.
Raymond Edward
Wenderoth , Lind & Ponack, L.L.P.
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