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
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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 designs ................................. .................................................. .................................. .......................4 ......4 2 Theoretical Theoretical bases 6 2.1 Speed Speed conditio conditions ns at the impeller impeller .................................. ................................................... .................................. .............................6 ............6 2.2 Compression Compression in impeller and peeler .................. ........ ................... .................. .................. .................. ................... ................... ........... ..8 8 2.3 Determina Determination tion of the delivery delivery head ................................. .................................................. .................................. ........................ ....... 10 2.3.1 Influence of the finite number of blades .................. ......... .................. .................. ................... ................... ............ ... 10 * 2.3.2 Blade angle ß2 ................................ ................................................. .................................. .................................. ..............................12 .............12 2.4 Losses Losses and efficienc efficiencies ies .................................. ................................................... .................................. .................................. ........................ ....... 13 2.5 Operating Operating performan performance ce .................................. ................................................... .................................. .................................. ........................ ....... 14 2.5.1 2.5.1 Centrifuga Centrifugall pump characte characteristic risticss ................................. ................................................... ................................... ................... 15 2.5.2 2.5.2 Similarity Similarity laws........................................... 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 centrifu centrifugal gal pump.................................. pump................................................... .................................. .................................. ........................... ..........25 25 3.2 The drive of the centrifugal pumps...........................................................................27 3.3 Start-up of the centrifugal pump plant......................................................................28 3.4 Measured Measured variables variables................. .................................. .................................. .................................. .................................. ..............................29 .............29 3.4.1 Flow measure measuremen mentt .................................. ................................................... ................................... ................................... ................... 29 3.4.2 3.4.2 Pressure Pressure measurem measurement ent ................................ ................................................. .................................. .................................31 ................31 3.4.3 Measurement Measurement of torque, rpm measurement measurement ................... ......... ................... .................. .................. .............. ..... 31 4 Testing method and evaluation 32 4.1 Throttle Throttle characte characteristi risticc ................................. .................................................. .................................. .................................. ........................... ..........32 32 4.2 Number of revolutions characteristic........................................................................32 4.3 Collection Collection of formulae formulae and evaluatio evaluation n ................................. ................................................... ................................... ................... 32
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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, Springer-Verlag, 1977
4.
KSB:
Kreiselpumpenlexikon KSB-AG, Frankenthal, 1989
5.
Pfleiderer, C.; Petermann, H.:
Strömungsmaschinen Springer-Verlag, 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, 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 Duisburg-Essen
13.
Benra, F.-K.:
Berechnung und Konstruktion von Strömungsmaschinen Vorlesungsskript, Universität Duisburg-Essen Duisburg-Essen
14.
Simon, H.:
Strömungsmaschinen I Vorlesungsskript, Universität Duisburg-Essen Duisburg-Essen
15.
Simon, H.:
Strömungsmaschinen II Vorlesungsskript, Universität Duisburg-Essen Duisburg-Essen
4
List of used symbols Symbol
Unit Unit
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
m m T m/s m -1 s N 2 m/s m kg/s min-1 m 2 N/m Kw m m s m/s V m/s m/s m2 /s2 m 2 2 m /s
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 Reynolds-number distance Strouhal-number Strouhal-number time circumferential speed Voltage Speed Relative speed specific bladework Height specific loss
Unit Unit rad rad 3 kg/m s-1
Meaning angle Orifice-constant angle Difference Difference Orifice-constant Loss factor Efficiency Friction in pipes factor Density kinematic degree of reaction Pressure-n Pressure-numb umber er Angle-speed
2
Meaning
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, Infinite, environm environment ent
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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 management (water supply, Cellar drainage pumps, 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 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 u 1 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)
If one names with dp
ρ
= dY∞′ = ω 2 rdr
(2.3)
the specific flow work of centrifugal forces, then the work portion from cent rifugal forces can be determined by integration along the radius. Y∞′ =
1
p∞
ρ ∫ p
dp =
p∞ − p1
2 Y∞′ = ω
r 2
∫ rdr = ω r 1
(2.4)
ρ
1
2
r22 − r12
2
=
u 22 − u12
2
(2.5)
As a result of the introduction of acceleration due to gravity the delivery head portion arises due to centrifugal forces to:
2 2 Y∞′ p∞ − p1 u2 − u1 ′ = = H ∞ = ρg 2g g
(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:
d ω
dF ′′ = −dA ⋅ ds ⋅ ρ ⋅
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 = − ρωd ω
(2.8)
Names one this time
dp
ρ
= dY∞′′ = −ωd ω
(2.9)
the specific flow 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 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 theoretically to the liquid with infinitely many blades is: Yth∞ = Y∞′ + Y∞′′ + Y∞′′′
Y th∞ =
p2 ∞ − p1
ρ
=
(2.14)
2 2 2 2 2 2 u2 − u1 + ω1 − ω2 ∞ + c2 − c1
2
(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∞ = u2cu 2∞ − u1cu1
(2.16)
The theoretical delivery head results to:
H th∞ =
Y th∞ 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 − u1cu 1
(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: Y th Yth∞
=
1 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 ß 2
*
The angle of outlet ß 2* can theoretically be selected freely within a wide range. An angle * * * ß2 >90° leads to backwards curved blades. ß 2 =90° means radially ending blades and ß 2 <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 c 2. The transformation of this speed energy in * pressure energy in the peeler is connected with substantial losses. It is better to chose ß 2 >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 ß 2 =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 P i, 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. 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.
h
=
& 1 + V&sp / V
1 − (P ( Pr + Pm ) / p
A summary of all efficiencies is given in fig. 2-5.
⋅η
(2.20)
16
Efficiency
η=
Use
=
Output (Work )
Expe Expendi nditu ture re
) Inpu Inputt( Work Work
Blade efficiency or hydraulic efficiency
ηh =
Y
=
YSch
Y Y + Z h
Wheel friction efficiency
η r =
Pi − Pr
=
Pi
η r =
& +m & Sp )Y Sch (m
1
η Sp
Pi
⋅
Y Sch Y i
Gap efficiency & m
η Sp =
& +m & Sp m
Internal efficiency
ηi = i
& mY
Pi
=
Y Y i
= η h ⋅η r ⋅η Sp Sp
Mechanical efficiency
ηm =
Pi P
=
Pi Pi + Pm
Overall efficiency or clutch efficiency
=
& mY
P
=
& mYP i
Pi P
= ηi ⋅ηm
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 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 & , Y, n, P, ?, machine and/or operating parameters. With centrifugal pumps the parameters V NPSH have the greatest importance. For the representation of the characteristics frequently sizes such as delivery head head H, power P, efficiency ?, or the NPSH-value are laid over the volume flow rate. Geometry sizes such as impeller diameters D 2, 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 • •
• • • • • • •
•
& N: Nominal flow rate V 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. & opt : Best flow rate V The delivered flow in the point of the best efficiency with the rated speed and the liquid indicated in the contract. & < V & opt is called partial load, the range V & > V & opt is called overload The flow rate range V & max: Highest flow rate V Largest permissible delivered flow, which the pump can deliver continuously without without getting damaged. (Limitation (Limitation e.g. e.g. through thro ugh NPSHgiv , radial or axial forces etc.) & min: Minimum flow rate V Smallest Smallest permissible delivered delivered flow, which which the pump pum p can deliver deliver continuously cont inuously without without getting damaged. (Limitation e.g. through heating up, oscillations, NPSHneeded ) Upper delivery head border H max: 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 indicated in the contract is ordered. Best delivery head H opt: 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 H 0: Delivery head at the nominal number of revolutions nN, the pumping medium indicated in the contract and the flow & = 0. rate V Vertex delivery head H vert: Delivery head in the vertex (that means in the relative maximum of an instable centrifugal pump characteristic)
Fig. 2-7: Characteristics Characteristics of a centrifugal pump at a constant number of rrevolutions evolutions..
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. & , fig. 2-8) results in the & and V The view of speed conditions with two different flow rates ( V N
same circumferential speed u 2 and the same relative flow angle ß 28 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 Outgoing-velocity-triangles with different volume flow rates.
The meridional velocity is proportional the flow rate. Thus applies:
ωm 2 =
& V & V N
ωm 2 N
(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)
derives
Yth∞ = u2 + 2
& V
u2ωm 2 N
V& N A2 tan β 2 ∞
u2 & Yth∞ = u22 + V A2 tan β 2∞
(2.27)
(2.28)
Thus a theoretical characteristic in dependence of the volume flow rate can be represented (Fig. 2-9). The angle ß 28 determines thereby the upward gradient of this straight line, which cuts the ordinate at u22 and, with the usual obtuse angles ß 28 , has a falling tendency.
Fig. 2-9: Theoretical characteristic characteristic with loss-free current
If the less power factor p and thus the relationship 1/(1+p) are accepted as constant, then the & ) becomes again a straight line. char charac acte teri rist stic ic Yth = f (V Up to this moment the view without consideration of losses was accomplished. One generally differentiates between friction and collision losses. The friction losses ∆V V,R in the design point & ) are given by (V N
∆YV , R = (1 − ηh )Y th
(2.29)
and for operating conditions deviating from the design point for instance proportional to the square of the flow rate:
∆YV , R = (1 −η h )Y th (
& V & V N
)
2
(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
∆Y V , S
(
& V& N − V 2 ) & V N
(2.31)
By subtraction of the two loss portions ? Y V,R and and ? Y V,S from Yth the searched pump & ) results. Further from the relationship: char charac acte teri rist stic ic Y = f (V Y
= 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 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 Y
H=
H a Hb
g
=
D2, a
=(
u2 cu 2
g
D 2, b
)2 (
na nb
(2.33)
)2
(2.34)
Volume flow rate V& = cm 2 ⋅ D2 ⋅ B2 ⋅ π
V&a V&b
=
na D2, a 3 ( ) nb D2,b
(2.35)
(2.36)
Available power P = H ⋅ g ⋅ ρ ⋅V& Pa Pb
=(
D2, a 5 )3 ( ) nb D2, b na
(2.37)
(2.38)
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−
b
1 − ηa
=(
Re a Reb
)0,1
(2.39)
with Re =
u2 ⋅ D2
ν
(2.40)
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 & = 74,5 m3 /h and n = 1500 min -1. Into these theoretical radial-flow pump with design data V N N 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:
H =
p2 − p1 A
ρg
2 2 c2 − c1
+
2g
+ z2 − z1 + H + H VD
VS
(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: H V = λ ⋅
l c2 d 2g
(2.42)
resp. H V = ξ
c2
2g
(2.43)
24 ;if one assumes that the dependence of the friction number for pipes λ and the coefficients of & is negligible . drag ξ on the Reynolds number and thus on the delivered flow V
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 & ) through: - Change of the dynamic portions of the plant characteristic characteristic H A ,dyn = f( V
· 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 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. accomplished. The throttle regulation uses the change of the t he dynamic losses H V in the armatures, with which the slope of the plant characteristics H A can be affected within wide ranges of the delivered & till V & =0) (Fig. 2-13). The operating point B can be shifted thereby over the entire flow ( V 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 (H B-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 & -H) with throttle curves of different numbers of revolutions In the characteristic diagram ( V 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. 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
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 investigation of centrifugal pumps is represented 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 d i = 107,1mm) is reduced before the pump to the connection nominal DN 80 (d i = 82,5mm) size of the pump. In the pressure pipe of the nominal size DN 65 (d i = 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 Characteristics Movi 65/3 M3
3.2 The drive of the centrifugal pumps
Centrifugal pumps are in most cases cases driven by electric electric motors. The centrifugal pump 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 0,3n N = 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 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 i s 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 3 parallel legs (Fig. 3-5). With a small overlap range flow rates up to 10 m /h are measured in the measuring pipe A (DN 25), while delivered flows over 10 m 3 /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.
V& =
π D 4 KB
U
(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:
v f = St⋅ d
(3.2)
The dimensionless constant St is called Strouhal number and is a relevant parameter for eddy flow measurements. 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 standard orifice. From the continuity equation equation and the energy equation in the form after Bernoulli one receives the relationship for the determination of the volume stream: & = V
πd2 4
αε
2∆p
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 the pressures in the intake before before the pump, 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 closed after each measurement in as small as possible 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 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 -1 -1 rpm = 3000min and then the speed is reduced reduced in small small steps ? n ˜ 250min . 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 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&1 + V 2
2
(4.1)
Pressure: pi = p∞ + ∆ pM ,i + ( ρ ⋅ g⋅ ∆ zM ,i )
The ambient pressure p8 is given before the attempt.
(4.2)
35 Specific blade work, delivery head:
Y =
p D− pS
ρ H =
vD− v S 2
+ g ( z D − z S ) +
Y g
2
2
(4.3)
(4.4)
Output: PK = M d ⋅ ω
(4.5)
ω = 2 ⋅π ⋅ n
(4.6)
& Y = ρ ⋅ V& ⋅ Y P Nutz = m
(4.7)
Efficiency:
ηP =
P Nutz PK
(4.8)
36
Evaluation Lab-test “CP”
The following characteristics are to be drawn
Number
Designation 1 Delivery head characteristic characteris tic Stage 1 H1(V) 2 Delivery head characteristic characteristi c Stage 2 H2(V) 3 Delivery head characteristic characteristi c Stage 3 H3(V) 4 Pump characteristic 5 Rpm-charactersitic Rpm-characte rsitic of the pump 6 Rpm-charactersitic Rpm-characte rsitic 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 demanded values are are to be registered into the prepared diagrams. diagrams. The results should should be discussed discussed in detail in a critical view of the attempt. In particular a statement statement about the range of 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 2 2 Y1 [m /s ]
delivery head H1 [m]
Output P1,Nutz [kW]
Table 4-3a: Calculated data of the 1. stage
-1
Stage 2
rpm n = …….. min = const. Volume flow rate V [l/s]
Pressure [bar] p1 p2
Table 4-3b: Calculated data of the 2. stage
blade-work 2 2 Y2 [m /s ]
delivery head 2 H [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 2 2 Y3 [m /s ]
delivery head H3 [m]
Output P3,Nutz [kW]
Table 4-3c: Calculated data of the 3. stage
-1
Pump
rpm n= …….. min = const. Flow rate V [l/s]
Pressure
Velocity
Specific Delivery Power Required Required Efficiency work head Output Power pS pD vS vD Y H Pnutz PK ?P 2 2 [bar] [bar] [m/s] [m/s] [m /s ] [m] [kW] [kW] [-]
Table 4-3d: Calculated data of pump
Pump (Throttle position = const.)
39
Number of revolutions -1
[min ]
Flow rate V [l/s]
Pressure
Specific Specif ic Delivery Power Required Efficiency Effici ency 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 Velocit y
40
Diagramme 4-1: Single-Stage characteristic, Total characteristic characteristic
41
Diagramme 4-2 : rpm const.
42
Diagramme 4-3 : Throttle position constant
