1
Practical course
Turbomachinery
Measurement of the characteristics
of a centrifugal pump
University Duisburg-Essen
Faculty of Engineering Sciences
Department of Mechanical Engineering
Turbomachinery
Prof. Dr.-Ing. F.-K. Benra
2
Table of contents
1 General about centrifugal pumps
4
1.1 Range of application of centrifugal pumps .................................................................4
1.2 Impeller forms and pumping designs .........................................................................4
2 Theoretical bases
6
2.1 Speed conditions at the impeller ................................................................................6
2.2 Compression in impeller and peeler ...........................................................................8
2.3 Determination of the delivery head .......................................................................... 10
2.3.1 Influence of the finite number of blades .......................................................... 10
2.3.2 Blade angle ß2*................................................................................................ 12
2.4 Losses and efficiencies ............................................................................................ 13
2.5 Operating performance ............................................................................................ 14
2.5.1 Centrifugal pump characteristics ..................................................................... 15
2.5.2 Similarity laws................................................................................................ 19
2.5.3 Operating point of the pump............................................................................ 21
2.5.4 Regulation of centrifugal pump plants............................................................. 22
3 The centrifugal pump test stand
25
3.1 The centrifugal pump............................................................................................... 25
3.2 The drive of the centrifugal pumps........................................................................... 27
3.3 Start-up of the centrifugal pump plant...................................................................... 28
3.4 Measured variables .................................................................................................. 29
3.4.1 Flow measurement ....................................................................................... 29
3.4.2 Pressure measurement .................................................................................. 31
3.4.3 Measurement of torque, rpm measurement ................................................... 31
4 Testing method and evaluation
32
4.1 Throttle characteristic .............................................................................................. 32
4.2 Number of revolutions characteristic........................................................................ 32
4.3 Collection of formulae and evaluation ..................................................................... 32
3
Bibliography
1.
Bohl, W.:
Strömungsmaschinen Bd. 1 und 2
Vogel-Verlag
2.
Bohl, W.; Mathieu, W.:
Laborversuche an Kraft- und
Arbeitsmaschinen
Hanser-Verlag, 1975
3.
Schulz, H.:
Die Pumpen
Springer-Verlag, 1977
4.
KSB:
Kreiselpumpenlexikon
KSB-AG, Frankenthal, 1989
5.
Pfleiderer, C.; Petermann, H.:
Strömungsmaschinen
Springer-Verlag, 1990
6.
Sigloch, H.:
Strömungsmaschinen
Hanser-Verlag, 1993
7.
SIHI:
Grundlagen für die Planung von
Kreiselpumpenanlagen
SIHI-Halberg, Ludwigshafen, 1978
8.
Spengler, H.:
Technisches Handbuch Pumpen
Technik-Verlag, 1987
9.
Stepanoff, A.:
Radial- und Axialpumpen
Springer-Verlag, 1959
10.
Troskolanski, A.T.; Lazarkiewicz, S.:
Kreiselpumpen
Birkhäuser-Verlag, 1976
11.
Sulzer:
Kreiselpumpen Handbuch
Vulkan-Verlag, 1990
12.
Benra, F.-K.:
Hydraulische Strömungsmaschinen
Vorlesungsskript, Universität Duisburg-Essen
13.
Benra, F.-K.:
Berechnung und Konstruktion von
Strömungsmaschinen
Vorlesungsskript, Universität Duisburg-Essen
14.
Simon, H.:
Strömungsmaschinen I
Vorlesungsskript, Universität Duisburg-Essen
15.
Simon, H.:
Strömungsmaschinen II
Vorlesungsskript, Universität Duisburg-Essen
4
List of used symbols
Symbol
Unit
Meaning
A
B
B
c
D
f
F
g
H
K
m
n
nq
NPSH
p
p
P
r
Re
s
St
t
u
U
v
w
Y
z
Z
m2
m
T
m/s
m
s-1
N
m/s2
m
kg/s
min-1
m
N/m2
Kw
m
m
s
m/s
V
m/s
m/s
m2/s2
m
m2/s2
Surface
Impeller width
magnetic induction
absolute speed
Impeller diameter
Frequency
Power
Acceleration due to gravity
Delivery head
A constant
Mass-flow
Number of revolutions
specific number of revolutions
Energy height
Less power factor
Pressure
Output
Radius
Reynolds-number
distance
Strouhal-number
time
circumferential speed
Voltage
Speed
Relative speed
specific bladework
Height
specific loss
Unit
rad
rad
kg/m3
s-1
Meaning
angle
Orifice-constant
angle
Difference
Orifice-constant
Loss factor
Efficiency
Friction in pipes factor
Density
kinematic degree of reaction
Pressure-number
Angle-speed
Greek letters
Symbol
a
a
ß
?
e
?
?
?
?
?h
?
?
5
Indices
a
A
b
d
dyn
D
el
erf
h
i
i
K
m
max.
min.
M
N
Opt.
P
r
R
stat
S
Sch
Sch
Sp
th
u
vorh
V
0
1
2
8
Impeller a
Plant
Impeller b
Torque
dynamic
Pressure-site
electric
needed
hydraulic
internal
optional
Clutch
mechanic
maximum
minimum
measured value
Nominal size
Optimum
Pump
friction-caused
Friction
static
Suction-site
Vertex
Blade
Gap
theoretic
in circumferential direction
given
Loss
at zero delivering
Stage 1, Place
Stage 2, Place
Infinite, environment
6
1 General about centrifugal pumps
1.1 Range of application of centrifugal pumps
The first type of a centrifugal pump was already built 1689 by the French physicist Denis
Papin. Since then the centrifugal pump found entrance in many fields of the technology. In
particular radial-flow pumps are used for liquid-delivering in a dominant number of
constructions. Beside water every other liquid is applicable as delivery medium. In particular
oil, but in addition, aggressive liquids or liquid solid mixtures can be delivered with
centrifugal pumps.
Plant
Pump designation
•
Water management (water supply, Cellar drainage pumps, water supply
irrigation, drainage, sewage
disposal)
pumps, booster pumps, sprinkling and
irrigation pumps, sewage pumps
•
Power plants, heating systems
Circulation pumps, feed water pumps,
condensate pumps, storage pumps,
reactor pumps
•
Chemistry and petrochemistry
Diaphragm pumps, fuel and gasoline
pumps, chemical pumps, pipeline
Pumps, process pumps, inline pumps,
liquid gas pumps
•
Shipbuilding
Bilge pumps, ballast pumps, dock pump,
ship pumps, fuel pumps
•
Other intended purposes
fire-fighting pumps, drainage pumps,
dry-sump lubrication pump, dialysate
feed pump
Fig. 1-1: Operating areas of centrifugal pumps
1.2 Impeller forms and pumping designs
Despite the various application types of centrifugal pumps in technical plants the operating
ranges of the different designs can be summarized in a H,V-diagram (Fig. 1-2). Depending
upon size of the delivered flow, the delivery head and the number of revolutions another
characteristic impeller form results in the case of aiming at an optimal efficiency. With the
help of the rapidity and/or the specific number of revolutions
nq = 333
n V
( gH )3 / 4
(1.1)
7
the impellers can be split up according to their targeted application (Fig. 1-3).
1. Low rapidity (nq = 10-30): Radial-flow impeller with simply curved blades. Pumps
with low delivered flow and large delivery head.
2. Medium rapidity (nq = 30-50): Impeller with radial discharge and double curved
blades. Pumps with a middle delivered flow and middle delivery head.
3. Helicoidic impeller (nq = 50-80): Impeller with double curved blades. Pumps with
larger as middle delivered flow and smaller than middle delivery head.
4. Diagonal impeller with high rapidity (nq = 80-135) with double curved blades. Pumps
with high delivered flow and a low delivery head.
5. Propeller impeller with highest rapidity (nq = 135-330) and rotor blades in the form of
wings. Pumps with highest delivered flow and lowest delivery head.
If very large volume flow rates are needed, or if the velocity of flow is limited in the entrance
for reasons of the suction behaviour, radial flow pumps are frequently implemented in a
multi-flow way. Thereby two impellers with same dimensions deliver in a common housing.
With same delivery head the two flow rates are added together.
Since the maximum delivery head of an impeller is fixed by the pressure factor in dependence
of the design and upward the number of revolutions limited by firmness reasons, for the
achievement of large delivery heads several pump stages are connected in series. The delivery
heads of the single stages are added with same flow rate.
Fig. 1-2: Ranges of application of centrifugal pumps
8
Fig. 1-3: Impeller forms
2 Theoretical bases
Pumps are mechanisms for delivering from a state of lower static pressure to a state of higher
static pressure. At the centrifugal pumps the impeller stud with blades transfers mechanical
work to the liquid which is in the impeller channels. The liquid is displaced by centrifugal
forces from the impeller. The increase in pressure in the impeller is a consequence of
centrifugal forces and possibly also the retarded relative flow in the impeller channels. The
absolute speed of the delivery medium increased at the same time and is afterwards converted
in a system of static and extending channels into static pressure energy.
2.1 Speed conditions at the impeller
With the current of a liquid through the channels of a rotary impeller it is to be differentiated
between absolute and relative movement. The movement of the liquid particles is called
absolute, if they can be noticed by an outside of the impeller standing observer. The relative
movement of the liquid particles notices an observer, who moves with the impeller.
9
In fig. 2-1 speed conditions in the impeller are represented for a backwards curved blading.
r
The current joins with the relative velocity ω1 the blade channel. At this with "A" designated
r
place the impeller has the peripheral speed u1 . From the vectorial addition of the relative
r
r
r
velocity ω1 and the peripheral speed u1 the absolute speed c1 results.
Fig. 2-1: Speed conditions at the impeller
With flowing through the blade channel the relative velocity generally decreases. At this with
r
r
"B" designated place the fluid has the peripheral speed u2 and the relative speed ω 2 . As
r
resulting the absolute outgoing speed c2 results, which is substantially larger due to the
r
transfer of energy than c1 . The transformation of the kinetic energy happens in the following
r
guidance mechanism. Here the current with the speed c2 occurs and is retarded to the speed
r
c3 .
10
2.2 Compression in impeller and peeler
The work transferred in the impeller to the liquid is converted to pressure energy on the one
hand by the increase of the circumferential speed from u1 to u2 and on the other hand by the
delay of the current in impeller and peeler.
In order to be able to determine the compression in the impeller and in the peeler, one makes
the assumption that all liquid particles follow accurately the course of the rotor blades (Bladecongruent current). Thus the flow conditions (pressure and speed) are alike in each case along
concentric circles around the perpendicularly arranged wheel axle. This condition can be
fulfilled by the assumption of infinitely many and infinitely thin blades.
Further the transformation from speed energy in pressure energy should happen in the blade
r r
channels and the repeating-condition ( c3 = c1 ) should be fulfilled.
The increase in pressure from the work of centrifugal forces can be determined, if a mass
particle of the pumping medium is regarded, which is limited by the lateral surfaces of two
cylinders with the radii r and r+dr as well as two neighbouring blades and the wheel walls of
cover- and wheel disk (Fig. 2-2a). Thus the centrifugal force of the mass particle can be
expressed as follows:
dF ′ = dA ⋅ dr ⋅ ρ ⋅ r ⋅ ω 2
2.1)
From this follows for the increase in pressure:
dp = ρω 2 rdr
(2.2)
dp
= dY∞′ = ω 2 rdr
ρ
(2.3)
If one names with
the specific flow work of centrifugal forces, then the work portion from centrifugal forces can
be determined by integration along the radius.
Y∞′ =
1 p∞
p − p1
dp = ∞
∫
ρ p1
ρ
2
2
r
u22 − u12
2 2
2 r2 − r1
′
Y∞ = ω ∫ rdr = ω
=
r1
2
2
(2.4)
(2.5)
As a result of the introduction of acceleration due to gravity the delivery head portion arises
due to centrifugal forces to:
Y∞′ p∞ − p1 u22 − u12
′
H∞ =
=
=
g
ρg
2g
(2.6)
11
The increase in pressure from the delay of the relative velocity w can be derived by fig. 2-2b
from the dynamic Basic Law:
dF ′′ = − dA ⋅ ds ⋅ ρ ⋅
dω
dt
(2.7)
Thereby dw is negative since w decreases with rising pressure. With ds/dt = w and dp =
dF´´/dA can be written:
dp = − ρω dω
(2.8)
dp
= dY∞′′ = −ωd ω
ρ
(2.9)
Names one this time
the specific flow work from the delay of the relative velocity, then this work portion can be
determined by integration along the entire flow channel:
Y∞′′ =
1
ρ
∫
Y∞′′ = − ∫
p p∞
p∞
ω2 ∞
ω1
p p∞ − p∞
dp =
ρ
ω12 − ω22∞
ωd ω =
2
(2.10)
(2.11)
With acceleration due to gravity the delivery head results
H ∞′′ =
p p∞ − p∞
ρg
=
ω12 − ω22∞
2g
(2.12)
With fig. 2-2c for the transformation of the speed energy in the peeler accordingly derives:
H ∞′′′ =
p2 ∞ − p p∞
ρg
=
c22 − c12
2g
(2.13)
12
Fig. 2-2: Compression in peeler and impeller
2.3 Determination of the delivery head
The entire specific work transferred theoretically to the liquid with infinitely many blades is:
Yth∞ = Y∞′ + Y∞′′ + Y∞′′′
Yth∞ =
p2 ∞ − p1 u22 − u12 + ω12 − ω22∞ + c22 − c12
=
2
ρ
(2.14)
(2.15)
By the use of the appropriate relations from the velocity triangles the relative velocities can be
eliminated and one receives the Euler Main-equation for the current in turbo machinery:
Yth∞ = u2 cu 2 ∞ − u1cu1
(2.16)
The theoretical delivery head results to:
H th∞ =
Yth∞
g
(2.17)
2.3.1 Influence of the finite number of blades
The continuous pressure ratios along concentric circles are no longer present with an impeller
with finite blade number (Fig. 2-3). The uneven distribution of velocity can be explained after
Pfleiderer with the help of the relative channel eddy.
13
On the blade front small and on the blade back large relative velocities result. That leads to a
diversion of the thread of stream in opposite to the direction of rotation. The by this caused
enlargement of the relative flow angle ß2 causes a reduction of the circumferential component
of cu28 to cu2. Thus, according to the Euler equation,
Yth = u2 cu 2 − u1cu1
(2.18)
with a finite blade number a smaller specific work is exchanged (Fig. 2-3). The relationship
of these two blade work can be described with the less power factor p:
Yth
1
=
Yth∞ 1 + p
(2.19)
The less power does not represent a loss, but a correction of the for the current in the pump
impeller to inaccurate linear theory. With one against infinitely going rotor blade number the
less power factor p goes against the limit value zero and the relationship of the two blade
work goes against one.
Addition of single currents to the total current
Imaging A
Imaging B
Fig. 2-3: Influence of a finite blade number
14
2.3.2 Blade angle ß2*
The angle of outlet ß2* can theoretically be selected freely within a wide range. An angle
ß2*>90° leads to backwards curved blades. ß2 *=90° means radially ending blades and ß2 *<90°
means forward curved blades. With equation and velocity triangles results that the specific
blade work is the larger, the smaller ß2 * is. From fig. 2-4 it is to be recognized that a small
angle ß2* means also a large absolute speed c2. The transformation of this speed energy in
pressure energy in the peeler is connected with substantial losses. It is better to chose ß2*>90°
for getting a lower c2. In addition, a large angle ß2 * has the disadvantages that it requires with
same delivery head a larger circumferential speed and so it causes larger wheel friction losses.
Because of the larger difference of pressure between entrance and exit of the impeller, larger
gap leakages are caused. However, these disadvantages cannot cover the crucially better
hydraulic efficiency. Therefore in centrifugal pumps only backwards curved blades with
angles of outlet ß2*=140°-160° are used.
Fig. 2-4: Blade angle ß2 *
15
2.4 Losses and efficiencies
The kinds of loss of centrifugal pumps can be differentiated in:
•
Internal losses:
Ø Hydraulic losses or blade losses by friction, variations of the effective area or
changes of direction.
Ø Losses of quantity at the sealing places between impeller and housing, at the
rotary shaft seals and sometimes at the balance piston.
Ø Wheel friction losses by friction at the external walls of the wheel.
•
external or mechanical losses:
Ø Sliding surface losses by bearing friction or seal friction.
Ø Air friction at the clutches.
Ø Energy consumption of directly propelled auxiliary machines.
With pumps the work for the covering of the internal losses must be additionally transferred
to the demanded specific work Y by the blades to the delivery medium. The internal losses
have the common characteristic that they turn into as warmth to the pumping medium. Their
summary with the available power results in the internal power Pi, which must be supplied at
the drive shaft. In contrast to it the dissipated heat of the outside or mechanical losses turns
not into the pumping medium. It is outward exhausted.
One can directly determine the overall efficiency ? and also the internal efficiency ? i by
attempt, but as for the blade efficiency and the hydraulic efficiency ?h this is not possible. It
must be computed from ? or ? i by excluding the losses, which are not pressure losses.
ηh =
1 + V&sp / V&
1 − (Pr + Pm ) / p
A summary of all efficiencies is given in fig. 2-5.
⋅η
(2.20)
16
Efficiency η =
Use
Output (Work )
=
Expenditure
Input (Work )
Blade efficiency or hydraulic efficiency
ηh =
Y
Y
=
YSch Y + Z h
Wheel friction efficiency
ηr =
& Sp )YSch
Pi − Pr (m& + m
=
Pi
Pi
ηr =
1 YSch
⋅
η Sp Yi
Gap efficiency
η Sp =
m&
m& + m& Sp
Internal efficiency
ηi =
&
mY
Y
=
Pi
Yi
ηi = η h ⋅η r ⋅η Sp
Mechanical efficiency
ηm =
Pi
Pi
=
P Pi + Pm
Overall efficiency or clutch efficiency
η=
&
& i
mYP
mY
=
= ηi ⋅η m
P
PP
i
Fig. 2-5: Efficiencies of pumps
2.5 Operating performance
By the operating performance of a centrifugal pump one understands the connection between
the flow rate supplied by the pump with the delivery head prescribed by the plant.
During the evaluation of the operating performance it must be considered that the pump is not
an isolated machine, but that it is integrated always into a complete plant and all parts of the
plant have to be considered.
17
2.5.1 Centrifugal pump characteristics
The co-operation of the pump with the consumer can be described therefore by the
characteristics of pump and plant.
Characteristics of turbo machineries represent the functional connection between different
machine and/or operating parameters. With centrifugal pumps the parameters V& , Y, n, P, ?,
NPSH have the greatest importance. For the representation of the characteristics frequently
sizes such as delivery head H, power P, efficiency ?, or the NPSH-value are laid over the
volume flow rate. Geometry sizes such as impeller diameters D2, position of the peeler a or
the machine number of revolutions n are often used as parameters. Thus result further
characteristics of constant parameter, which represent the characteristic diagram of the pump
(e.g. positive spin-characteristic, rpm-characteristic…).
Fig. 2-6: Pump characteristics
From the characteristics some characteristic delivering data can already be read off. After fig.
2-7 these are for the characteristics of a radial centrifugal pump at constant number of
revolutions:
18
•
•
•
•
•
•
•
•
•
•
Nominal flow rate V& N:
Delivered flow, for that the pump with the number of revolutions, the nominal delivery head and the pumping
medium indicated in the contract is ordered.
Best flow rate V& opt:
The delivered flow in the point of the best efficiency with the rated speed and the liquid indicated in the contract.
The flow rate range V& < V& opt is called partial load, the range V& > V& opt is called overload
Highest flow rate V& max:
Largest permissible delivered flow, which the pump can deliver continuously without getting damaged. (Limitation
e.g. through NPSHgiv , radial or axial forces etc.)
Minimum flow rate V& min:
Smallest permissible delivered flow, which the pump can deliver continuously without getting damaged. (Limitation
e.g. through heating up, oscillations, NPSHneeded)
Upper delivery head border Hmax:
Largest permissible delivery head, which the pump can deliver continuously without getting damaged.
Nominal delivery head HN:
Delivery head, for that the pump with the number of revolutions, the nominal delivery head and the pumping
medium indicated in the contract is ordered.
Best delivery head Hopt:
The delivery head in the point of the best efficiency with the rated speed and the liquid indicated in the contract.
Lower delivery head border Hmin:
Lowest permissible delivery head, which the pump can deliver continuously without getting damaged.
Zero delivery head H0:
Delivery head at the nominal number of revolutions nN, the pumping medium indicated in the contract and the flow
rate V& =0.
Vertex delivery head Hvert:
Delivery head in the vertex (that means in the relative maximum of an instable centrifugal pump characteristic)
Fig. 2-7: Characteristics of a centrifugal pump at a constant number of revolutions.
19
The determination of such characteristics succeeds with sufficient accuracy only by
experiment. To improve the understanding a theoretical view is quite useful. First one
proceeds from a frictionless, blade-congruent current and considers only afterwards the
influence of the finite blade number and the losses.
The view of speed conditions with two different flow rates (V& and V&N , fig. 2-8) results in the
same circumferential speed u2 and the same relative flow angle ß28 in the case of same
number of revolutions. In the case of spin-free inflow results from the Euler' main equation:
Yth∞ = u2cu 2 ∞
(2.21)
Fig. 2-8: Outgoing-velocity-triangles with different volume flow rates.
The meridional velocity is proportional the flow rate. Thus applies:
V&
ωm 2 = & ωm 2 N
VN
(2.22)
From the velocity triangles at the blade exit can be derived:
ωu 2 ∞ =
ωm 2
tan(180° − β 2 ∞ )
(2.23)
and with
r
r r
cu 2 ∞ = u2 + ωu 2 ∞
(2.24)
20
cu 2 ∞ = u2 − ωu 2 ∞
(2.25)
Yth∞ = u2 (u2 − ωu 2 ∞ )
(2.26)
V& u2ωm 2 N
Yth∞ = u22 + &
VN A2 tan β 2 ∞
(2.27)
derives
Yth∞ = u22 + V&
u2
A2 tan β 2 ∞
(2.28)
Thus a theoretical characteristic in dependence of the volume flow rate can be represented
(Fig. 2-9). The angle ß28 determines thereby the upward gradient of this straight line, which
cuts the ordinate at u22 and, with the usual obtuse angles ß28 , has a falling tendency.
Fig. 2-9: Theoretical characteristic with loss-free current
If the less power factor p and thus the relationship 1/(1+p) are accepted as constant, then the
characteristic Yth = f (V& ) becomes again a straight line.
Up to this moment the view without consideration of losses was accomplished. One generally
differentiates between friction and collision losses. The friction losses ∆VV,R in the design point
(V&N) are given by
∆YV , R = (1 − ηh )Yth
(2.29)
and for operating conditions deviating from the design point for instance proportional to the
square of the flow rate:
V&
∆YV , R = (1 − η h )Yth ( & ) 2
VN
(2.30)
The stronger the flow rate from its design value to larger flow rates deviates, the larger are the
friction losses.
21
The deviation of the direction of the relative flow against velocity connected with the change
of the volume stream causes additional collision losses. This reduction of the specific work is
for instance proportional to the square of the flow rate difference ( V&A − V& ):
∆YV , S : (
V&N − V& 2
)
V&N
(2.31)
By subtraction of the two loss portions ? YV,R and ? YV,S from Yth the searched pump
characteristic Y = f (V& ) results. Further from the relationship:
Y
=η h
(2.32)
Yth
the process of the hydraulic efficiency of the pump results. Instead of the specific work also
the delivery head is often represented as a function of the flow rate.
Fig. 2-10: Real pump characteristic
2.5.2 Similarity laws
The determined characteristic applies to a certain centrifugal pump at a special number of
revolutions. Often it is however necessary to know either for a pump curves at different
numbers of revolutions or to conclude from a machine already built to a machine which is to
be developed. In addition one uses the similarity-mechanical model laws (affinity laws). With
the use of similarity-mechanical conversions of the main data of turbo machineries the
following conditions must be kept:
•
The machines, which have to be compared, must be geometrically similar in their
dimensions and forms.
•
The currents in the channels, in particular in the impellers, must run kinematically
similarly. That means that the velocity triangles of the corresponding machines must
be geometrically similar, which means that the dimensionless velocity triangles are
equal.
•
The currents, which have to be compared, must run dynamically similarly. The
appropriate forces of inertia and friction forces must behave similarly, which means
that the Reynolds number of the machines should almost agree.
22
The comparison of two geometrically similar impellers a and b with same dimensionless
velocity triangles results under the condition of spin-free incident flow and same efficiencies
in the following connections:
Delivery head
H=
Y η
= u2cu 2
g g
(2.33)
D
Ha
n
= ( 2, a )2 ( a )2
Hb
D2,b nb
(2.34)
V& = cm 2 ⋅ D2 ⋅ B2 ⋅ π
(2.35)
V&a na D2,a 3
= (
)
V&b nb D2,b
(2.36)
P = H ⋅ g ⋅ ρ ⋅V&
(2.37)
D
Pa
n
= ( a )3 ( 2, a )5
Pb
nb D2,b
(2.38)
Volume flow rate
Available power
The accepted equality of the efficiencies is only approximately correct, since as a result of
change of the machine size, the number of revolutions or the viscosity of the delivery medium
a deviation of the efficiency arises. The change of efficiency can be considered by so-called
empirical revaluation formulas. By Pfleiderer applies:
1 − ηb
Re
= ( a )0,1
1 − ηa
Reb
(2.39)
u2 ⋅ D2
ν
(2.40)
with
Re =
The regularities indicated here can be proven for a pump with different numbers of
revolutions. In fig. 2-11 the appropriate curves in a diagram are represented for a two-stage
radial-flow pump with design data V& N = 74,5 m3/h and nN = 1500 min-1. Into these theoretical
curves the measured values for water delivering are drawn in.
23
Fig. 2-11: Proof of the affinity laws at a two-stage pump
2.5.3 Operating point of the pump
The operating point of a centrifugal pump in a plant is determined not only by the pump
characteristic, but also by the plant characteristic. The plant characteristic indicates the
delivery head, which is necessary for delivering the fluid against the existing resistances in the
piping for any flow rates. From the continuity equation and the energy equation for stationary
currents an appropriate relationship for the delivery head can be derived:
HA =
p2 − p1 c 22 − c12
+
+ z2 − z1 + HVD + HVS
ρg
2g
(2.41)
This plant characteristic contains static portions, which are independent of the flow rate and
dynamic portions, in which squared flow rates and the fall in meters arise. The allocation into
static and dynamic portions is represented in fig. 2-12 for a simple centrifugal pump plant.
The fall in meters on the suction and the pressure site can be computed after Darcy-Weisbach
for straight pipings by:
l c2
HV = λ ⋅
d 2g
(2.42)
resp.
HV = ξ
c2
2g
(2.43)
24
;if one assumes that the dependence of the friction number for pipes λ and the coefficients of
drag ξ on the Reynolds number and thus on the delivered flow V& is negligible .
Fig. 2-12: Plant characteristic
The operating point of the pump adjusts itself, where the delivery head of the centrifugal
pump and the plant are the same size. That is the case in the intersection of pumping and plant
characteristic. An extremely important condition for working the pump in the adjusting
operating point is the demand:
NPSHgiven = NPSHneeded
(2.44)
Only under keeping this condition a cavitation-free running is ensured.
2.5.4 Regulation of centrifugal pump plants
With changing plant conditions a control procedure is released, with which the intersection of
the two characteristics is shifted, until the requested flow rate is reached. In order to reach
this, the following possibilities are available:
•
Measures on sides of the plant
- Change of the dynamic portions of the plant characteristic H A,dyn = f (V& ) through:
· Throttling
· Opening of bypasses in the pressure pipe
- Change of the static portion of the plant characteristic HA,stat through:
· Adapt the counter-pressure in the tank
· Change of the geodetic differences in height of the water levels
•
Measures on side of the pump
- Change of the pump parameters
· Number of revolutions
· Positive Spin before the impeller by spin throttle or arranged bypass
25
· Rotor blade position
· Switching on or off parallel-working pumps
· Correction of the impeller diameter
· Sharpen of the vane ends
•
Measures on side of the medium
- Change of the middle density ? of the delivery medium by steered content of steam
bubbles (self-regulation by cavitation)
In the practical course which is accomplished here as measure on side of the plant the
throttling (Throttle characteristic) and as measure on side of the pump the speed-regulation
(number of revolutions characteristic) are accomplished.
The throttle regulation uses the change of the dynamic losses HV in the armatures, with which
the slope of the plant characteristics HA can be affected within wide ranges of the delivered
flow ( V& till V& =0) (Fig. 2-13). The operating point B can be shifted thereby over the entire
pump characteristic from N to O. Throttle armatures (which in consideration of the A-value
should be built in only on the pressure site of the pump into the piping) are relative cheap
controlling means, they have however always the disadvantage that they in particular convert
considerable portions (HB-HA)/HB of the hydraulically usable energy in (mostly not usable)
warmth with stronger interferences and that they remove the operating point B from the
design point N of the centrifugal pump at the same time and causes thus the additional loss
portion (? N-? B)/? N.
Fig. 2-13: Throttle regulation
26
In the characteristic diagram ( V& -H) with throttle curves of different numbers of revolutions
the points of the best efficiency are on an origin parabola, which can coincide with the plant
characteristics without static portion ( H A : V& 2 ) more or less accurately. If one regulates, in
such cases, the pumping-rpm as a function of the need, then the operating point of the pump
always lies within the area of the best efficiency. At the same time the pump doesn't deliver
more delivery head, than the plant for the transmission of the delivered flow requires. Thus,
this kind of regulation is economically unsurpassed.
The larger the static portions HA,stat of the plant characteristic HA are, the more this economic
advantage is lost. Also in these cases no more delivery head H as if required is delivered, but
the pump drives out of its efficiency optimum with a lower number of revolutions n<nN.
Fig. 2-14: Speed regulation of plant characteristics HA with large static portion
With pump drive by turbines or combustion engines speed regulation can be realized more
easily. With drives by three-phase motors an additional expenditure on capital assets is
unavoidable, e.g. by hydraulic transmissions and/or induction couplings or increasingly by
Frequency inverter.
27
3 The centrifugal pump test stand
The plant for the investigation of centrifugal pumps is represented in fig. 3-1. It consists of an
open cycle and is operated with industrial water of ambient temperature. The open water store
tank made of PL (1) seizes maximally 8000 litres and is provided with several pipe unions as
well as a level monitoring and an exhaust.
The suction pipe (3) of the nominal size (DN) 100 (measured inside Diameter di = 107,1mm)
is reduced before the pump to the connection nominal DN 80 (di = 82,5mm) size of the pump.
In the pressure pipe of the nominal size DN 65 (di = 70,3mm) a flat slide is inserted behind
the pump, which serves as shutoff device. Subsequently, an extension of the piping DN 100 as
well as a regulating valve DN 100 follows. With its assistance the operating point of the pump
can be adjusted. After the valve the piping branches out to the two measuring sections A and
B, which are provided with two volumetric flow meters switched into row in each case.
Depending upon the operating point of the plant the measuring section A or the measuring
section B can be released over the ball valves (9). Over the return pipe (14) of the nominal
size DN 100 the water flows back into the store tank.
Fig. 3-1: Plant scheme
3.1 The centrifugal pump
The centrifugal pump (4) is a product of the company Klein, Schanzlin und Becker (KSB /
Frankenthal). It’s a three stage, horizontal arranged high-pressure pump in segmental-type
way out of the series MOVI with uncooled axial face seal and fat-lubricated grooved ball
bearings. Pumps of this series predominantly used for general water supply, spray irrigation -,
28
irrigation and pressure increasing systems. In addition they are used for warm water -, hot
waters -, cooling water circulation, for condensate-delivering, boiler supply and in fireextinguishing systems.
The rating data as well as the most important technical details are summarized in the
following table.
Pump
KSB Movi 65/3 M3
Nominal flow rate
VN = 0,02 m3/s
Nominal delivery head
HN = 140 m
Pumping medium
Water
Nominal rpm
nN = 2900 min-1
Power requirement
P = 45 kw
Max. pressure
pmax = 40 bar
Characteristics
Fig. 3-2
Intake joint
DN 80 PN 40 (d i = 82,5mm)
Pressure joint
DN 65 PN 40 (d i = 70,3mm)
Housing material
Gray cast iron
Impeller material
Tin bronze
The adaption to the demanded nominal dates was reached by differently strong turning off the
normally similar impellers of the three stages. The impeller diameters of the three stages
amount to:
Stage 1 : D2,1 = 203 mm
Stage 2 : D2,2 = 185 mm
Stage 3 : D2,3 = 172 mm
Thus the characteristics marked in fig. 3/2 by D result.
29
Fig. 3-2: Characteristics Movi 65/3 M3
3.2 The drive of the centrifugal pumps
Centrifugal pumps are in most cases driven by electric motors. The centrifugal pump used
here is in such a way conceived that it can be coupled e.g. directly with the shaft of a threephase alternating current asynchronous engine (5). The synchronous number of revolutions of
the used engine with a pair of poles amounts to, with the existing frequency of 50 cycles per
second, n = 3000 rpm. The actual number of revolutions lies due to the load-rate slip with
approximately n = 2900 rpm. By change of the frequency with the help of a currentsteered
frequency changer the number of revolutions can be adjusted steplessly in the range 0,3nN = n
= 1,0 nN. The lower speed limit is given by the cooling performance of the blower at low
numbers of revolutions, while the upper speed limit arises as a result of the maximum
capacity of the engine.
30
The characteristic torque characteristic of a three-phase alternating current asynchronous
engine with squirrel-cage rotor is represented in fig. 3. The parabola-similar process of the
load-moment corresponds to the conditions available with a pump drive.
For the determination of the taken up electrical power of the engine the current and the
voltage of one of the three phases can be measured.
Fig. 3-3: Characteristic torques of asynchronous engines
3.3 Start-up of the centrifugal pump plant
The centrifugal pump described in chapter 3.1 belongs to the group of the normalsucking, i.e.
no self-priming pumps. Since the water store tank is set up in the basement under the actual
test stand, the pump works in priming mode and must suck in the delivery medium depending
upon the water level over a certain geodetic height-difference. Normal priming pumps only
produce a very small difference of pressure during air delivering. Therefore they are not able
to air out their intake independently, if they are running in the priming mode. In order to fill
the pump with liquid, a pneumatically operated ejector (6) is arranged as external ventilation
system on the pressure site of the pump (Fig. 3-4).
31
Fig. 3-4: Arrangement of a priming-automat
After switching on the centrifugal pump on first only the priming-automat is activated. In the
case of completion of the exhaust procedure a float switch response, the vent line is locked by
a valve, the priming-automat is set out of operation and the centrifugal pump can be switched
on.
3.4 Measured variables
3.4.1 Flow measurement
For the determination of the characteristics of a centrifugal pump the measurement of the
volume flow rate is of elementary importance. The delivered flow rate of the pump is
determined by two different measuring procedures switched into row. Due to the limited
measuring range of the volumetric flow meters the measuring section is divided into two
parallel legs (Fig. 3-5). With a small overlap range flow rates up to 10 m3/h are measured in
the measuring pipe A (DN 25), while delivered flows over 10 m3/h in the measuring pipe B
(DN 100) are measured.
Fig. 3-5: Flow measurement area
32
Magnetically inductive flow measurement
The principle of a magnetically inductive flowmeter (MID) is based on inducing a voltage by
a constant magnetic field with the magnetic induction B by moving electrically conductive
measuring material through it (Fig. 3-6). This voltage is proportional to the middle velocity of
flow of the measuring material. With the knowledge of the distance of the test electrodes the
flow can be determined with the help of an equipment constant K.
π D
V& =
U
4 KB
(3.1)
Fig. 3-6: Function mode of a MID
Eddy flow measurement
The principle of the eddy flow measurement is based on the fact that at a flowed against body
(Vortex-body) at both sides eddies are produced, which separates and form a vortex trail. The
mutually forming eddies shift the vortex-body in oscillation with a frequency, which results
from the flow rate and the thickness of the vortex-body according to the definition for the
Strouhal number:
f = St ⋅
v
d
(3.2)
The dimensionless constant St is called Strouhal number and is a relevant parameter for eddy
flow measurements.
Fig. 3-7 shows the typical dependence of the Strouhal number of the Reynolds number for a
cylindrical vortex-body. Within a large range of the Reynolds number the vortex-body
frequency is directly proportional to the flow velocity and independent of the density and the
viscosity of the medium. If the Strouhal number of a vortex-body is known, the flow can be
determined by the vortex-body frequency.
33
Fig. 3-7: Principle of the eddy flow measurement
Effect pressure flow measurement
The measurement of the volume flow rate according to the effect pressure principle takes
place with a standard orifice. From the continuity equation and the energy equation in the
form after Bernoulli one receives the relationship for the determination of the volume stream:
πd2
2∆ p
V& =
αε
4
ρ
(3.3)
The constants of a and e can be inferred from the DIN 1952 for standard orifices.
3.4.2 Pressure measurement
For the determination of the delivery head characteristic of the several stages as well as the
entire pump the pressures in the intake before the pump, after the 1. stage, after the 2. stage
as well as in the pressure pipe after the pump has to be measured. Note that the pressure of the
intake is a pressure below the atmospheric pressure, which is indicated in the measuring
cabinet as absolute pressure!
3.4.3 Measurement of torque, rpm measurement
In order to be able to determine the achievement taken up by the pump, torque and number of
revolutions of the pump drive shaft must be known. For the measuring of the torque a torque
measuring shaft of the company Höttinger Baldwin Meßtechnik of the type T1 (15) is used.
On the measuring shaft strain gauges (DMS) are fastened, which are tossed or stretched, if the
wave is torqued. The Ohm's resistance of the DMS changes thereby proportionally to the
stretch and is a measure for the torque.
The number of revolutions is determined over a disk with 60 teeth in connection with an
inductive giver, attached on the shaft, by an impulse counter.
34
4 Testing method and evaluation
The range of the practical course attempt "measurement of the characteristics of a centrifugal
pump" includes the taking down of a throttle curve at a certain number of revolutions as well
as a number of revolutions characteristic during a certain throttle position. Apart from the
machine characteristics also only for the throttle curve the delivery head characteristics of the
individual stages are to be determined and to be represented in the prepared diagrams.
4.1 Throttle characteristic
At a given number of revolutions, which has to be kept constant during this attempt, the valve
in the pressure pipe is completely opened after starting the pump. The maximum flow rate
adjusting by the leg B (DN 100) is divided into a certain number of measuring points (max.
15). Subsequently, the valve is closed after each measurement in as small as possible
appropriate flow rate steps. When falling below the smallest measuring range of the leg B it is
to be switched to the parallel leg A (DN 25), as first A is additionally opened, before B is
closed. For the examination of the agreement of both measuring legs the last measuring point
of the leg B is to be measured again in the leg A.
The measured values are to be registered into the prepared table 4-1.
4.2 Number of revolutions characteristic
With a given position of the throttle valve on the pressure-site different numbers of
revolutions are to be examined. To avoid an overload of the engine, the attempt starts with an
rpm = 3000min -1 and then the speed is reduced in small steps ? n ˜ 250min-1. The lower speed
limit of 1000rpm shouldn’t substantially fall below. Also here a change of the volume
measuring legs is to be made according to chapter 4.1 at given time. The read off measured
values are to be registered into the prepared table 4.2. To reduce the extent of work only the
values of the entire pump without view of the single stages has to be taken up.
4.3 Collection of formulae and evaluation
Volume flow rate:
V& + V&
V& = 1 2
2
(4.1)
Pressure:
pi = p∞ + ∆pM ,i + ( ρ ⋅ g ⋅ ∆z M ,i )
The ambient pressure p8 is given before the attempt.
(4.2)
35
Specific blade work, delivery head:
Y=
pD − pS
v2 − v2
+ g ( zD − zS ) + D S
ρ
2
(4.3)
Y
g
(4.4)
PK = M d ⋅ ω
(4.5)
ω = 2 ⋅π ⋅ n
(4.6)
& = ρ ⋅ V& ⋅ Y
PNutz = mY
(4.7)
H=
Output:
Efficiency:
ηP =
PNutz
PK
(4.8)
36
Evaluation Lab-test “CP”
The following characteristics are to be drawn
Number
Designation
1 Delivery head characteristic Stage 1 H1(V)
2 Delivery head characteristic Stage 2 H2(V)
3 Delivery head characteristic Stage 3 H3(V)
4 Pump characteristic
5 Rpm-charactersitic of the pump
6 Rpm-charactersitic of the pump
Table
Diagramm
4-3a
4-1
4-3b
4-1
4-3c
4-1
4-3d
4-1, 4-2
4-4
4-1
4-4
4-3
In addition first the missing values are to be computed according to the equations (4.1) till
(4.8) in the tables 4-3a till 4-3d and 4-4. Subsequently, the demanded values are to be
registered into the prepared diagrams. The results should be discussed in detail in a critical
view of the attempt. In particular a statement about the range of validity of the affinity law is
to be made. In addition are to compare, related to the measuring point at largest adjusted
number of revolutions of the series of measurements during constant throttle position, the
theoretical characteristics of the affinity law (Equations 2.34, 2.35, 2.38) with the measuring
data.
37
rpm n = …….. min-1 = const.
Stage 1
Volume flow
rate
V [l/s]
Pressure [bar]
ps
p1
blade-work
Y1 [m2/s2]
delivery head
H1 [m]
Output
P1,Nutz [kW]
Table 4-3a: Calculated data of the 1. stage
rpm n = …….. min-1 = const.
Stage 2
Volume flow
rate
V [l/s]
Pressure [bar]
p1
p2
Table 4-3b: Calculated data of the 2. stage
blade-work
Y2 [m2/s2]
delivery head
H2 [m]
Output
P2,Nutz [kW]
38
rpm n = …….. min-1 = const.
Stage 3
Volume flow
rate
V [l/s]
Pressure [bar]
p2
p3
blade-work
Y3 [m2/s2]
delivery head
H3 [m]
Output
P3,Nutz [kW]
Table 4-3c: Calculated data of the 3. stage
rpm n= …….. min-1 = const.
Pump
Flow
rate
V
[l/s]
Specific Delivery Power Required Efficiency
work
head Output Power
pS
pD
vS
vD
Y
H
Pnutz
PK
?P
[bar] [bar] [m/s] [m/s] [m2/s2]
[m]
[kW]
[kW]
[-]
Pressure
Velocity
Table 4-3d: Calculated data of pump
Pump (Throttle position = const.)
39
Number of
revolutions
[min-1]
Flow
rate
V
[l/s]
Pressure
Specific Delivery Power Required Efficiency
work
head Output Power
pS
pD
vS
vD
Y
H
Pnutz
PK
?P
[bar] [bar] [m/s] [m/s] [m2/s2]
[m]
[kW]
[kW]
[-]
Table 4-4: Calculated data of pump
.
Velocity
40
Diagramme 4-1: Single-Stage characteristic, Total characteristic
41
Diagramme 4-2 : rpm const.
42
Diagramme 4-3 : Throttle position constant