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Selection criteria for suction impellers of centrifugal pumps
Selection criteria for suction impellers of centrifugal pumps Part 1: Suction specific speed - a criterion for flow recirculation and pump reliability? In the first part of a three-part feature, J.F. G~lich, of Sulzer Pumps Ltd, challenges the historical approach to choosing reliable centrifugal pumps based on calculating suction specific speed. ased on statistics compiled 20 years ago on failures with centrifugal pumps designed in the late 1960s, sorae pump users specify limits on the suction specific speed with the objective of buying more reliable pumps. In the light of the progress made in pump technology over the past 30 years, this article examines the relationship (if any) between suction specific speed n~ and impeller inlet recirculation and associated vibrations. Part 1 reviews the history and literature on the subject, gives a rationale for selecting NPSH margins, compares modern design concepts for high nss impellers with the design methods of the past and provides a method to select the optimum suction specific speed for a given NPSH available. In Part 2, impeller inlet recirculation is discussed. Four case histories of cavitation damage and of cavitation induced noise and vibrations demonstrate that neither of these phenomena can be related directly to the suction specific speed, but that such failures are more related to unsuitable design, wrong pump selection or changing operation conditions. Part 3 provides rationales to prevent cavitation damage and provides a number of hydraulic criteria for pump selection.
B
1. H i s t o r y Statistical evaluations of failures with centrifugal pumps showed a trend that the frequency of failures increased above a suction specific speed of nss = 213 (about 11000 in USunits) [1]. This finding was explained by reasoning that high values of the suction specific speed need unnecessary large impeller eye diameters which cause impeller inlet recirculation to start at high flow rates. Strong suction recirculation could thus become responsible for cavitation damage and/or high excitation fi3rces causing noise and vibration, premature wear and all sorts of component failures - in particular on bearings and shaft seals. The analysis involved 480 process pumps observed over a period from 1976 to 1981. It can be assumed that these pumps had been installed on average at least 5 years before the observation period reported. Since process pumps usually are standardised machines (and developing a pump range takes some time) it is concluded that the pumps were designed in the mid to the late 1960s, if not earlier. These failure statistics [1] were extremely useful in drawing the attention of both pump users and manufacturers to a serious lack in product reliability. However, a thorough analysis of the root causes of the failures and the necessary remedies should have followed this work. Unfortunately such an analysis was not included in that report nor in subsequent publications. During the same period studies of partload recirculation at impeller inlet and outlet were published [2], in which the
28
WORLD
PUMPS
onset of impeller inlet recirculation was related to just one parameter - an average impeller blade inlet angle - and in a further simplification to the suction specific speed. The onset of inlet recirculation was plotted against the suction specific speed nss with the hub-to-tip diameter ratio v = dn/d 1 as parameter. This seemingly provided pump users with a procedure to "predict" the onset of inlet recirculation from the NPSH 3 at the BEP without knowing any specifics of the pump at all. Poor mechanical design and pump concepts of doubtful reliability - such as two-stage overhung or double-entry overhung impellers - contributed to the frustration of pump operators in that period [3]. In the late 1970s also a serious accumulation of power plant pump failures were reported in the USA [4], which triggered a comprehensive research project, sponsored by EPRI, on pump hydraulics, partload flow phenomena, cavitation, hydraulic excitation forces and rotordynamics, [5]. The problems reported in [1] and [3] occurred in the hydrocarbon industry, where hundreds of small to medium size pumps are required to ensure the reliable operation of complex plants. Since it is costly to do an in-depth technical analysis of every pump required for installations of that scale, the pump buyer likes simple criteria to assess the adequacy of the pumps offered to him. Based on the above studies part of the hydrocarbon processing industry elected to limit the suction specific speed to nss = 213 (US-units: 11000) with the object to improve pump reliability in their installations. Hydrocarbons are not very aggressive with respect to cavitation erosion; it can therefore be assumed that this limit mainly focuses on hydraulic excitation caused by impeller inlet recirculation rather than on cavitation erosion. There is indeed a general tendency that the onset of impeller inlet recirculation, with the associated excitation forces, increases with the impeller inlet diameter - or to be more precise - with the ratio dl/d u of the impeller eye diameters at outer streamline and inner streamline. This means that the onset of inlet recirculation increases, tendency-wise, with the specific speed nq and with the suction specific speed nss. Unfortunately there is no simple relationship between these parameters; and a reliable method to predict the onset and intensity of inlet recirculation has not yet been published. A large number of the pump failures reported in [1] may therefore be attributed to poor design, wrong material selection, poor quality and/or unsuitable pump selection. Typical examples might be: application of a singlevolute, where a double volute would have been appropriate to reduce bearing loads and shaft deflection; insufficient
0262 1762/01/$ - see front matter © 2001 Elsevier Science Ltd. All rights reserved
FEATURE *
shaft stiffness causing shaft seal failure due to high vibration amplitudes; excessive casting tolerances leading to high ~ynchronous excitation due to hydraulic unbalance; insufficient rotor damping due to inappropriate labyrinth design; insufficient bearing capacity; too small a gap between impeller and volute cutwater or diffuser vanes causing pressure pulsations and component failure. Any pump failure caused by such design insufficiencies may easily be interpreted as being caused by excitation from partload recirculation - which may have occurred, but was "excessive" only with respect to weak components and would have gone unnoticed with an appropriate design. The development of high energy boiler feed and injection pumps as well as rocket fuel pumps has triggered substantial efforts in pump research during the past 30 years; as a result there is today a much better understanding of the mechanisms and avoiding strategies of impeller inlet and outlet recircu[ation, cavitation damage, hydraulic excitation forces and vibrations. As discussed in detail below a new concept for the design of suction impellers with flat pressure distributions has emerged from that effort, from which process pumps have benefited as well as high energy pumps. At the time when the failure statistics were established, pumps with large impeller eye were designed with large incidence and very spiky pressure distributions - hydraulic design rules which must be considered today as obsolete and inadequate. While it is recognised that the pump buyer needs some simple engineering methods to assess the suitability of the pump selected; such methods must permit, however, to take full advantage of what present-day pump technology can offer to provide the most economic and reliable solution. Several investigators have stressed the fact that inlet recirculation and cavitation damage depend on a large number of design and operational parameters and that the use of the n~-criterion is an over-simplification which does n o t ensure safe operation, e.g. [8] to [10], [21], [35], [36]. In [8] inlet tip speed ul, type of pump, specific gravity and vane overlap were introduced as additional criteria, but the data and recommendations are essentially applicable f o r avoiding cavitation damage to cast iron impellers operating with marginal NPSHA.
2. Suction specific speed as cavitation criterion Consider an impeller blade moving with the velocity wl relative to the fluid. Due to high local velocities around the blade leading edge the static pressure decreases (Bemoulli's law) resulting in a pressure distribution with a pronounced minimum Pmin as sketched in Fig. 1. When the static pressure drops down to the vapour pressure (as imposed by the fluid temperature) a small portion of the liquid evaporates creating a vapour pocket or "cavity". Downstream of the leading edge, where the local pressure increases above the vapour pressure, the bubbles condense violently in a water-hammer-like manner; they "implode" and can damage the impeller, if the hydraulic cavitation intensity exceeds the cavitation resistance of the material. For a given pump at a given speed and flow rate the suction pressure necessary to avoid cavitation completely
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is expressed by the "incipient net positive suction head" NPSH i. If the available NPSHA exceeds the NPSHi (Pmin > Pv) there is no cavitation; but as NPSHA decreases successively below NPSH i (i.e. Pmin < Pv) cavities of increasing length are created. If the cavity length reaches the impeller throat area (sometimes even earlier), performance is impaired and the head created by the impeller drops. Cavitation is thus a phenomenon which develops gradually as the suction pressure (or NPSHA) is lowered. W h e n referring to "cavitation" it is therefore necessary to specify exactly what extent of cavitation is meant. This may be expressed by the following "cavitation criteria": • NPSHi: visual cavitation inception; i.e. first cavitation bubbles are visible • NPSHx: the cavitation causes a drop in x percent of the head developed by the suction impeller; x = 0, 1 or 3% • NPSHFc: full cavitation or head break down ("choking flow") representing the maximum flow limit, which is reached when the curves of NPSHA = f(Q) and NPSHFc = f(Q) intersect. • NPSH required for a specified amount of cavitation erosion, impeller life or increase in noise. These cavitation criteria, or the extent of cavitation, depend for a given pump on the flow rate and the rotor speed, which determine the relative velocity w 1 and the incidence i 1 ~ ]~IB - [31 (difference between blade and flow angle), which in turn generate the pressure distribution around the leading edge. The pressure distribution - and therefore the extent of cavitation - depends on the inlet flow distribution, i.e. the geometry of the inlet of the pump as well as suction pipe layout, and on the geometry of the impeller: blade profile, blade angles and 3D-contours of blades, shroud and hub. The only practical means to predict the pressure distribution as per Fig. 1 are numerical flow calculations; no simple procedure of adequate accuracy is available. In the industry a head drop of 3% is mostly used as a cavitation criterion and is represented as NPSH 3 = f(Q) on the performance curves provided by pump manufacturers. Some pump users also request the NPSH curves for zero and/or one percent head drop NPSH 0 or NPSH 1. Near BEP the NPSH ratio between cavitation inception and 3% head drop typically is NPSHi/NPSH 3 =
&
Total pressure static pressure
t/(P/2~c,2
I[-' , pDS[////~ ~
cavity
~pss without cavitation
pmi(wi n thout
cavitation)
Figure 1. Pressure distribution at blade leading edge, Pss = pressure on suction side of blade.
WORLD P U M P S
January2001
1.0 0.9
q*= 1; nss = 209 q* =0.67; nss=209 q" = 1; case 5.3, concept L q* = 0.78; case 5.3, concept L q* = 1, c a s e 5.1, concept H q* = 1, case 5.1, concept L NSPH0
•
0.8 0.7
•
0.6 la
4
0.5 car 0.4
•
"•0
/T
4•
•
e
0.3 C[••~• \,
0.2 0.1 0.0 1
2
3
FNPSH 4
5
II Figure l(a). Cavity l e n g t h as f u n c t i o n o f NPSH m a r g i n FNPSH = NPSHA/NPSH 3
4 to 6 (with special leading edge profiles also down to 2), while the ratio NPSH0/NPSH 3 = 1.1 to 1.3 [6]; in [4] N P S H 0 / N P S H 3 = 1.5 is proposed. It is important to note that the cavity length at N P S H 3 is of a size similar to the blade pitch at the impeller inlet, i.e. Lea,, ~ rt dl/ZLa. Even at N P S H 0 and N P S H 1 the impeller operates with extended cavitation. This fact is well illustrated by Fig. l(a) which shows measured cavity lengths plotted against the ratio FNPSH = NPSHA/NPSH 3 for different impellers and flow rates. The points where head drop starts are marked as N P S H 0. The intersection
NPSH A = NPSH3+
U2
0.05+2
of the curves with the x-axis gives the points of cavitation inception. As discussed above all these data and features depend on the pressure distribution and can vary in a wide range depending on the impeller geometry. Fig. l(a) gives an impression of the variations encountered. In order to reduce the risk of noise, vibrations or cavitation erosion, a safety margin between NPSHA and NPSH 3 is required in most pump applications. 20 years ago - when [I] to [4] were published - this requirement was less widely accepted than it is today. The NPSH-margin necessary to avoid damage, noise and vibrations depends on the eye tip speed u 1, type of pump (approach flow), type of fluid, impeller material and impeller geometry. Guidelines as to the margin are given in Table 1 (abbreviated and adapted from [7]). Table 1 l~rovides a consistent method to define N P S H margins as a continuous function of the tip speed u 1 which can be considered as the single most significant parametercontrolling cavitation erosion and vibration phenomena induced by inlet recirculation. The coefficients used in the method can be easily adapted to define more or less
U1
FtypeFF Fq. Eq. (T1.1)
URe f = 100 m/s.
Use only for
u 1 < 65 mls and NPSH A < NPSH i
Fq. =1+2q* (l-q*) 2
Fluid factors
I FF
water w i t h t < 200 °C seawater, corrosive fluids hydrocarbons
I 1.0 _> 1.15 1 0.75
Pump type factors
I Ftype
axial inlet, smooth approach f l o w radial inlet (multi-stage and double-entry pumps) unfavourable approach f l o w conditions
I 1.0 t 1.05 >_1.1
FNPSH-
30
WORLD I~UMPS
January2001
NPSH A = G._A_~_ NPSH3 (~3
FNPS.= 1.16 NPS,H3 l T M Nt-'UM Ref]
Eq. (T1.2)
conservative margins or to reflect the special features of various pump types and applications. A recent guideline from the Hydraulic Institute [37] recommends N P S H margins in terms of "low", "high" and "very high suction energy level" (SEL). The limit between low and high SEL is given by a graph which can be approximated by an impeller inlet tip speed H1,SE L = URef (nss,Ref /nss) 1"26with Ul,Re~ = 18 m/s and nss,Ref = 243 (12500 in US units). Recommended N P S H margins are low SEL: FNPSH= 1.1 to 1.3; high SEL: FNpsu = 1.3 to 2.0 and very high SEL: FNpSH = 2 to 2.5. No limit is specified between "high" and "very high" SEL. Another drawback is the step change between the different SEL. The guideline states that pumps operating with high SEL may still be susceptible to elevated noise levels and erosive damage to the impeller. The suction specific speed nss is a parameter which allows to compare geometric dissimilar pumps in terms of their suction capability:
nss = n
NPSH3,BEp 0'75
(1)
2g NPSH R ~-
2
(la)
LI t
The suction specific speed nss is thus defined with the flow rate per impeller eye at the best efficiency point (BEP) and the NPSH3,BE p i.e. the N P S H required for a specific pump to operate with exactly 3% head drop of the first stage in the case of a multi-stage pump. The nss is no criterion whatsoever for either cavitation inception, N P S H 0, NPSH 3 or the risk of cavitation erosion. By definition the suction specific speed has nothing to do with impeller inlet recirculation or hydraulic excitation forces. Nor does the nss say anything about pump reliability - even under cavitation performance. Only the safety margin FNPSH can give some clue as to the reliability and this only with respect to cavitation induced noise, vibration or damage. Another useful parameter is the cavitation coefficient c defined by Eq. (1 a) as the ratio of the required N PSH (for any of the cavitation criteria
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FEATURE •
C
mentioned above) to the impeller eye tip speed squared. It allows to assess the quality of the hydraulic design; for ,example: cavitation inception at ~i = 0.6 at BEP would represent a sophisticated blading while % = 2 would mean usually a poor hydraulic design of the impeller inlet (which may - or may not - imply trouble). To use the NPSH 3 as a cavitation criterion on performance curves is a matter of convenience only, because this value can be determined with some accuracy on the test bed, while the determination of the NPSH 0 leaves more room for individual interpretation, and measuring the NPSH i would require special test rigs, where the impeller inlet can be observed by means of a stroboscope. At high flow, q* > 1, the NPSH 3 = f(Q) is significant since the rise of this curve describes approximately the flow limit of the pump (NPSH 3 and NPSHFc being then close).
3. Design of impellers for high suction specific speed 3.1 Design concepts There are essentially two concepts that can be used to design an impeller with high nss: ( 1) A conventional design, concept "H", using a high incidence at the impeller inlet to increase the throat area. (2) A modern design able to achieve a high suction specific speed with low incidence, concept "L". The appreciation of the differences between these two design methods is the key to the evaluation of the suitability of pumps with high n~s. The features of these concepts are discussed in the following: Concept H: The impeller is designed to "swallow" the high vapour volume created by extensive cavitation. This is accomplished by providing a large impeller eye and large blade inlet angles in order to increase the impeller throat area. Excessive flow deceleration created by the oversized throat induces premature partload recirculation of high intensity. The blade leading edge profile used to be either wedge-like or even of constant blade thickness with a semicircular leading edge; the latter giving o i > 2. The large blade angles lead to high incidence even at BEP flow. This creates a sharp low-pressure spike, a zone of flow separation downstream of the leading edge filled by a cavity of considerable thickness, a high cavity volume, and strong pressure gradients in the zone where the cavitation bubbles implode (see Figs. 2 and 3). The thick cavity leads to the shedding of cavitation vortices which contribute strongly to the risk of cavitation erosion [13]. The potential for cavitation damage and surge is high because of the energy stored in the large cavity volume. Cavitation inception starts at high NPSH a (typically ~i = 1.5 to 2.5) because of the high incidence and non-optimum leading edge profiles. Concept L: During the 1970s the head per stage of large boiler feedpumps increased to levels of 600 to 800 m, with impeller eye tip speeds reaching u| up to 80 m/s. Severe cavitation damage was then observed on impellers designed according to the old rules (i.e. concept "H"). Superior impellers where developed subsequently by means of stroboscopic cavity observations and modifying, by trial
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~
Concept,,L"
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Wl
.
.
.
Wl
Wl
Wl
thick cavity, separated flow, vortices
-
thin sheet cavitation
![ _ _ Figure 2. Blade shapesof concepts "H" versus"L" a) U Cu
b)
1
o,s ! !
I ps~t
0,6 --unfa ourabl
0,4 0,2
avoura le
0 0
~
0,2
n
0,4
0,6
0,8
Lsch
:
Lseh
a) work transfer; b) pressuredistribution.
and error, leading edge profiles and blade angles until cavity length and volume were reduced sufficiently to achieve an acceptable impeller life. Later, advances in computing allowed the calculation of blade pressure distributions and thus optimisation of the impeller inlet through a reduction of the low pressure spikes. In the 1980s computer programs essentially used non-viscous flow models allowing only to calculate the single-phase pressure distributions, which were useful to optimise cavitation inception but failed to catch developed cavitation [29] [31]. Recently it has even become possible to calculate the development of a cavity and to estimate performance impairment [22]. The impeller designs emerging from these development feature a low blade loading u c u near the leading edge and consequently a flat pressure distribution to minimise the low-pressure spike, Fig. 3. Cavitation inception can be as low as (~i 0.5 tO 0.7. This is achieved by an aerofoil-like leading edge profile designed to be as insensitive as possible to a variation of incidence (hence flow rate). The leading edge is far advanced into the axial portion of the impeller eye (see Fig. 6) in order to obtain a small blade loading in the zone where bubbles are likely to implode (small driving pressure differential for bubble implosion). The increase of the blade angle from the leading edge to the impeller throat needs careful attention to get a sufficient suction capacity at flow rates above BEE but to avoid excessive local deceleration of the flow. Typically the cavity starts downstream of the leading edge, it increases rapidly in length once cavitation starts, but the cavity volume is very small since the cavity forms a thin transparent =
WORLD PUMPS
January2001
L. . . . . . . . . . . .
sheet. Because of the weak pressure gradient and the low cavity volume the risk of cavitation erosion, cavitation noise and surge is much lower than with design concept "H". At the author's company concept "H" was gradually abandoned from the early 1970s when a second generation of suction impellers for "advanced class" boiler feedpumps with a head per stage of 1200 m was being developed. Development efforts at that time led to suction impellers with very low cavitation inception above 60% of BEP flow [14]. The physical mechanisms behind concept L were recognised since the early 1980s when methods were also developed for the quantitative prediction of cavitation damage [15 and 12], and since then this knowledge has been applied systematically to the development of suction impellers. More recent publications show that major manufacturers now design impellers for high tip speeds essentially according to concept "L" with flat pressure distributions [16], [17] and [28] to [32]. Problems with impellers designed with high incidence and their elimination by applying in essence concept "L" were reported for example in [16] and [18] to [20].
other words there is a definite relationship between suction specific speed and impeller eye diameter as expressed by Eq. (5) for radial and semi-axial impellers and Eq. (6) for inducers. Equations (3) to (6) are derived from test data in [7]. Typically such test data show a very large scatter and can thus describe only a general trend. Graphs in [6] show similar trends as expressed by Eqs. (4) and (5).
12,5~n ,/nq "[0.19 nss = (p10,455 [ " ~ J
52 n s s - £011.075
Traditionally the NPSH required is expressed by Eq. (2) in which the coefficient 5Lc represents the acceleration of the fluid and inlet losses, while ;Lw is the blade coefficient describing the low pressure zone around the blade leading edge, Fig. 1.
C2 W2 NPSH=X c ~lm +;Lw -1 2g 2g
(2)
For pumps with an axial inlet we may set Xc = 1.05 to 1.15; for radial inlet bends 5% = 1.25 to 1.5 depending on the design. Different cavitation criteria - such as inception, zero, one and three percent head drop or full cavitation require different values of the blade coefficient i.e. Xw,i; )Vw,0;)Vw,1; )Vw,3 or Xw,FC. Furthermore Xw depends on the leading edge profile, inlet flow distribution and flow rate. Most significantly all of the blade coefficients k w depend on the stagger angle of the blades 131B,a or the flow coefficient q)l = tan ~l,a (approaching flow without prerotation); for inception and 3 % head drop Eqs. (3) and (4) give an idea of these relationships. Xw, i = 3(tanJ31B,a) 0'9 (3)
Xw,3 = 0,3(tan ~l,a) 0'53 (4) Unfortunately many publications leave the reader with the impression that k w can be considered as constant - in fact the "classical" concept of optimising the impeller eye diameter through a plot of NPSH = f(dl) fails when using such data as represented by Eq. (3) and (4)! Since the coefficient Xw decreases with decreasing flow coefficient (or increasing impeller eye diameter for given flow rate and speed) the NPSH required decreases with increasing dl; in
32
WORLD P U M P S
January2001
(inducers)
15 %ofor nq < 170
(5)
(6)
Equation (5) covers more than 50 single- and multi-stage pumps in the range of nq = 10 to 160 with a standard deviation of + 15 %. If one wants to design an impeller (or inducer) for a selected suction specific speed, Eqs. (5) and (6) may be solved for the flow coefficient q~l = Cl/Ul:
-k 11 125[ 2.2JnqI 0.418 %-
3.2 Selection of the impeller eye diameter
-+
n [nss j
= l 5210"93 £01 / ns--'T/
[27J
+
(inducers)
40%
(Sa)
(6a)
For any specific application with given Q, n, NPSH a and hub diameter d n a suitable range of impeller eye diameters or suction specific speeds can be determined in the following way: (i) calculate Ul, c 1 and '4)1 for different eye diameters (ii) determine nss from Eq. (5); from nss calculate NPSH3, Eq. (1) (iii) calculate recommended NPSHA from Eq. (TI.1) in table 1 (iv) determine actual margin FNPSH = NPSHA/NPSH3 (v) plot data as function of u 1 or d 1. The result is shown in Fig. 4 for a process pump with n =2950 rpm; QBEP = 230 m3/h; HBEp = 81 m; NPSHA = 6.5 m; d n = 45 mm; FF = 1.0; FR = 1.2 (design for partload operation). Figure 4 shows: • As d I or u 1 increases, the suction specific speed increases and NPSH 3 decreases. • Consequently the actual margin FNPSH,actuaI increases while both cavitation coefficients ~A and ~3 decrease because of the rising tip speed u 1. Any selection with FNPSH,actuaI < 1.0 has to be discarded, since the pump would operate with more than 3% cavitation induced head drop • The eye diameter should be selected such that the intended NPSH-margins - for example according to Eq. (TI.1) in table 1 - can be approximately obtained. If the actual NPSH-margin becomes appreciable lower than the values stipulated by Eq. (TI.1) either an impeller with a higher nss or a pump with a lower speed (lower nq in this case) should be selected. • Interestingly the NPSHi,recommended from Eq. (TI.1) shows a minimum in the curve NPSHA,recommended = f(ul ): at first NPSHg,recommendeddecreases since NPSH 3 falls with a larger eye, but eventually the NPSHa,recommended rises again because of the growing tip speed u 1. Since hydraulic
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.......................................................
excitation forces increase with ul 2 the optimum selection should be found to , the left of the mathematical minimum. • The recommended NPSH A from Eq. (T1.2) in table 1 decreases continuously with increasing u l, since it is a multiplier on NPSH 3. This approach to determine an NPSHmargin is thus not appropriate when large variations of the nss are involved. • In the present example the optimum selection would be found in the range o f u l = 21 to 23 m/s and nss = 230 to 265 giving recommended safety margins between fNPSH = 1.38 to 1.6. The risk of cavitation erosion increases exponentially with the tip speed u 1. The higher u l the shorter the allowable cavity length. For u 1 > 75 m/s the pump must be operated virtually without any cavitation which means that NPSH g > NPSH i is required. For such cases the impeller must be designed for low cavitation inception and this calls for the smallest possible inlet diameter and suction specific speed compatible with maximum flow requirements. For applications with u 1 > 50 m/s the suction specific speeds is typically limited to nss = 160 to 180. If the cavity length is known or estimated as a function of NPSH A, the Impeller life and erosion rate can be estimated by the methods given in [7] and [12]. The impeller tip speed can then be optimised with respect to m i n i m u m erosion by a procedure similar to the one used in Fig. 4.
Conclusions Progress in pump technology during the past 30 years includes new concepts for the design of high nss impellers with low incidence and lower inlet diameters as used formerly. The failure statistics compiled on pumps designed in the late 1960s with high incidence and exaggerated impeller eye may not be considered relevant any more for this new generation of impellers. At NPSH 3 the cavities formed on the leading edge extend into the impeller throat. Margins on the NPSH 3 are needed to reduce the extent of cavitation to acceptable levels to avoid loss in performance, excessive noise,
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eye diameter optimisation
eye diameter optlm=sation
i
|
450
0.5
~--
sigma-A
0.4
nss
400 /
sigma-3
;':
350
/
/
/
0.3 300
l
/
0.2
250 0.1
•
?L
20O
0.0 15
20
25
30
,V
150
35
15
20
ul (m/s)
25
30
35
ul (m/s) impeller eye diameter optimisation
impeller eye diameter optimisation 14 12
to
g8 ~6
,~.
~ i
~,,~~ - , ~
4
~
2
-e--NPSH-3 ~ NPSH-A •-~--NPSH-A, Re¢[8] -~-NPSH.-A,Re¢[7] J,=
2.6 j
2.4 2.2 2.0
1.8
•
/
~.o
,~,~ _ ~
1.4 1.2 1.0
!
o
2.8
I
>~/
/.
--4~-- F-NPSH,actual
0.8
•
F-NPSH,Rec[7]
0.6
15
20
25 ul (m/s)
30
35
15
20
25
30
35
ul (m/s)
Figure 4. Optimisation of impeller eye diameter and suction specific speed for a given NPSHA with respect t o NPSH - margin
vibrations and erosion. Such margins should increase with the impeller tip speed, they depend on the liquid pumped, flow rate and the pump inlet conditions. Table 1 provides a method to define such margins in a logical way. Following this concept it is found that for a given NPSH a there exists an optimum suction specific speed.
Notation Alq b2 c d1 dli dn FF FN~ H FR fq
g H 1L iI
impeller inlet throat area (if trapezoidal: Alq = a 1 b 1) impeller exit width absolute velocity impeller inlet (or eye) diameter at outer streamline impeller blade inlet dia meter at inner streamline hub diameter fluid factor (table 1) NPSH safety margin: FNPSH = NPSHA/NPSH 3 risk factor (table 1) impeller eyes per impeller: single-entry fq = 1; doubleentry fq = 2 acceleration due to gravity (g = 9,81 m/s 2, rounded) head per stage Impeller life incidence at impeller leading edge: i 1 =
blade angle - flow angle blockage caused by hub: kn k n = 1 - dn2/dl 2 cavity length measured from Lcav leading edge NPSH net positive suction head NPSH A net positive suction head available NPSH i net positive suction head of cavitation inception NPSHR net positive suction head required according to a specific cavitation criterion, usually NPSH R = NPSH3 NPSHx net positive suction head required for operation with x-percent head drop ( x = 0 , 1, or 3 %) rotational speed n (revolutions per minute) specific speed nq nq = q (qBEP/G)0'5/HBEp 0 " 7 5 (min" , m-J/s, m) suction specific speed nss nss =
P0 p Pv Q q*
n (QBEP/fq)O'5/NPSH3,BEp0'75 (min d, m3/s, m) power at Q = 0 (at coupling) static pressure vapour pressure flow rate, volumetric flow flow rate referred to flow rate at best efficiency point:
WORLD PUMPS
January2001 3 3
Rm u1
u2
wI
Wlq
ZLa ZLe z~t 13
[31 ]31B Ae
)~c, ~-w p
qh
q* = Q/QBE.p tensile strength of impeller material circumferential velocity at tip of impeller eye: u 1 = n d I n/60 circumferential velocity at tip of impeller outlet: u 2 = n d 2 n/60 relative velocity at impeller inlet (outer streamline) average velocity in impeller throat area: Wlq = Q/(zka Alq) number of impeller blades number of diffuser vanes number of stages angle between relative velocity vector and the negative direction of circumferential velocity flow angle at impeller inlet blade angle at impeller inlet metal loss due to cavitation (location of strongest attack) coefficient for N P S H calculation, Eq. (2) density cavitation coefficient (subscript as NPSH): = 2 g NPSH/ul 2 inlet flow coefficient: (Pl = Clm/Ula
Subscripts, abbreviations 1 a BEP
DS m max rain o Ref RB Rez SF SS s u
impeller blade leading edge (tip or outer streamline) at outer streamline best efficiency point (operation at maximum efficiency) pressure side meridional component maximum minimum shut-off operation (Q = O) reference value onset of recirculation recirculation shockless flow (zero incidence) suction side suction nozzle circumferential component
References 1 Hallam JL: Centrifugal pumps: Which suction specific speeds are acceptable?. J of Hydrocarbon Processing, April 1982, 195-197 2 Fraser WH: Recirculation in centrifugal pumps. ASME Winter Annual Meeting 1981, 65-86 Bloch H: How to buy a better pump. J of
34
WORLD PUMPS
January2001
Hydrocarbon Processing, January 1982, 81-87 3 Makay E, Szamody O: Survey of feedpump outages. EPRI FP-754, Final report RP 641, 1978 4 Giilich JF, Bolleter U et al.: Feedpump operation and design guidelines. EPRI Report TR-102102, June 1993 6 Hergt P et al.: The suction performance of centrifugal pumps possibilities and limits of improvements. Proc. 13th Intl Pump Users Symp, Houston, 1996, 13-25 7 Gtilich JF: Kreiselpumpen. Ein Handbuch fiir Entwicklung, Anlagenplanung und Betrieb. Springer, Berlin, 1999. ISBN 3-540-56987-1 8 Budris AR: The shortcomings of using pump suction specific speed alone to avoid suction recirculation problems. 10th Intl Pump Users Symp, Houston, 1993, 91-95 9 G/ilich JF, Egger R: Partload flow and hydraulic stability of centrifugal pumps. EPR1 RP 1884-10, TR-100219, March 1992. 10 Stofel B, Hergt P: Zur Problematik der spezifischen Saugzahl als BeurteilungsmaBstab for die Betriebssicherheit einer Kreiselpumpe. Pumpentagung Karlsruhe 1988, Section B8 11 WeiB K: Experimentelle Untersuchungen zur TeillaststrOmung bei Kreiselpumpen. Diss. TH Darmstadt, 1995 12 Gtilich JF: Guidelines for prevention of cavitation in centrifugal feedpumps. EPRI RP 1884-10, GS-6398, Nov. 1989 13 Avellan E Karimi A: Dynamics of vortex cavitation involved in the erosion of hydraulic machinery. Proc. 7th Conf. on Liquid and solid erosion impact. Cambridge 1987 14 Gtilich JF: Similarity characteristics for suction capacity and bubble propagation of pumps. Technical Review Sulzer, 2/1980 15 Gtilich JE Pace S: Quantitative prediction of cavitation erosion in centrifugal pumps. IAHR Syrup Montreal, Sept. 1986, Paper 42 16 Sloteman DE Cooper P, Graf E: Design of high-energy pump impellers to avoid cavitation instabilities and damage. EPRI Power Plant Pump Symp. "Fampa 1991 17 Hergt P: Design approach for feedpump suction impellers. EPRI Power Plant Pump Symp. Tampa 1991 18 Schiavello B et al.: Improvement of cavitation performance and impeller life in high energy boiler feedpumps. IAHR-Symp. Trondheim 1988 19 Cooper P et al.: Elimination of cavitation-related instabilities and damage in high-energy pump impellers. 8th Pump User's Syrup. Houston 1991 20 Schiavello B: Field cases due to various cavitation damage mechanisms. EPR1 Power Plant Pump Symp. Tampa 1991 21 Stoffel B, Jager R: Experimental investigations in respect to the relevance of
suction specific speed for the performance and reliability of centrifugal pumps. Proc. 13th lntl Pump Users Symp, Houston, 1996, 13-25 22 Hirschi R: Prediction par mod~lisation numerique tridimensionelle des effects de la cavitation ~ poche dans les turbomachines hydrauliques. Diss. EPF Lausanne, 1998 23 Gtilich JF: MOglichkeiten und Grenzen der Vorausberechnung von Kavitationssch~iden in Kreiselpumpen. Forsch Ingenieurwes 63 (1997) H1/2, 27-39 24 Gtilich JF et al.: Pump vibrations excited by cavitation. 4th Congress on Fluid Machinery for the Oil & Petrochemical and related Industries. The Hague, May 1990. 25 Gtilich JF et al.: Cavitation noise and erosion in jet cavitation test devices and pumps. Second ASME Pumping Machinery Symp., I993 26 Gtilich JF: Diagnosis of cavitation in centrifugal pumps. Technical Review Sulzer No 1, 1992. 27 Giilich JE Bolleter U: Pressure pulsations in centrifugal pumps. ASME J Vibr Acoustics 114 (1992) 272-279 28 Hergt P: Hydraulic design of rotodynamic pumps. In: Hydraulic Design of Hydraulic Machinery. Rada Krishna (Hrsg), Avebury, Aldershot, 1997 29 Worster DM and Worster C: Calculation of 3D-flows in impellers and its use in improving cavitation performance in centrifugal pumps. 2nd Conf on Cavitation, 1983, Paper IMechE C203/83 30 Cooper P: Pump Hydraulics Advanced. Short Course 8. 13th Intl Pump Users Syrup, Houston, 1996 31 Krieger P: Spezielle Profilierung an Laufr~idern von Kreiselpumpen zur Senkung von NPSHi. VGB Kraftwerkstechnik 72 (1992), Nr 5 32 Spring H: Critique of three boilerfeed pump suction impellers. ASME Pumping Machinery Symp., FED 81 (1989) 31-39 33 Stoffel B: Experimentelle Untersuchungen zur r~iumlichen und zeitlichen Stmktur der Teillast-Rezirkulation bei Kreiselpumpen. Forsch Ingenieurwes 55 (1989) 149-152 34 Sulzer Centrifugal Pump Handbook. 2nd ed, Elsevier Advanced Technology, Oxford, 1997 35 Schiavello B: Minimum continuous flow as related to suction recirculation and cavitation in pumps. Norwegian Society of Charted Engineers, Course No 84303, Pumps Offshore, Geilo, Norway, 1988 36 Schiavello B: Cavitation and recirculation troubleshooting methodology. lOth Intl Pump Users Symp, Houston, 1993 37 Hydraulic Institute guideline HI 9.6.1 - 1998 38 Wesche W: Experimentelle Untersuchungen am Leitrad einer radialen Kreiselpumpe. Diss. TU Braunschweig, 1989
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B
1. H i s t o r y Statistical evaluations of failures with centrifugal pumps showed a trend that the frequency of failures increased above a suction specific speed of nss = 213 (about 11000 in USunits) [1]. This finding was explained by reasoning that high values of the suction specific speed need unnecessary large impeller eye diameters which cause impeller inlet recirculation to start at high flow rates. Strong suction recirculation could thus become responsible for cavitation damage and/or high excitation fi3rces causing noise and vibration, premature wear and all sorts of component failures - in particular on bearings and shaft seals. The analysis involved 480 process pumps observed over a period from 1976 to 1981. It can be assumed that these pumps had been installed on average at least 5 years before the observation period reported. Since process pumps usually are standardised machines (and developing a pump range takes some time) it is concluded that the pumps were designed in the mid to the late 1960s, if not earlier. These failure statistics [1] were extremely useful in drawing the attention of both pump users and manufacturers to a serious lack in product reliability. However, a thorough analysis of the root causes of the failures and the necessary remedies should have followed this work. Unfortunately such an analysis was not included in that report nor in subsequent publications. During the same period studies of partload recirculation at impeller inlet and outlet were published [2], in which the
28
WORLD
PUMPS
onset of impeller inlet recirculation was related to just one parameter - an average impeller blade inlet angle - and in a further simplification to the suction specific speed. The onset of inlet recirculation was plotted against the suction specific speed nss with the hub-to-tip diameter ratio v = dn/d 1 as parameter. This seemingly provided pump users with a procedure to "predict" the onset of inlet recirculation from the NPSH 3 at the BEP without knowing any specifics of the pump at all. Poor mechanical design and pump concepts of doubtful reliability - such as two-stage overhung or double-entry overhung impellers - contributed to the frustration of pump operators in that period [3]. In the late 1970s also a serious accumulation of power plant pump failures were reported in the USA [4], which triggered a comprehensive research project, sponsored by EPRI, on pump hydraulics, partload flow phenomena, cavitation, hydraulic excitation forces and rotordynamics, [5]. The problems reported in [1] and [3] occurred in the hydrocarbon industry, where hundreds of small to medium size pumps are required to ensure the reliable operation of complex plants. Since it is costly to do an in-depth technical analysis of every pump required for installations of that scale, the pump buyer likes simple criteria to assess the adequacy of the pumps offered to him. Based on the above studies part of the hydrocarbon processing industry elected to limit the suction specific speed to nss = 213 (US-units: 11000) with the object to improve pump reliability in their installations. Hydrocarbons are not very aggressive with respect to cavitation erosion; it can therefore be assumed that this limit mainly focuses on hydraulic excitation caused by impeller inlet recirculation rather than on cavitation erosion. There is indeed a general tendency that the onset of impeller inlet recirculation, with the associated excitation forces, increases with the impeller inlet diameter - or to be more precise - with the ratio dl/d u of the impeller eye diameters at outer streamline and inner streamline. This means that the onset of inlet recirculation increases, tendency-wise, with the specific speed nq and with the suction specific speed nss. Unfortunately there is no simple relationship between these parameters; and a reliable method to predict the onset and intensity of inlet recirculation has not yet been published. A large number of the pump failures reported in [1] may therefore be attributed to poor design, wrong material selection, poor quality and/or unsuitable pump selection. Typical examples might be: application of a singlevolute, where a double volute would have been appropriate to reduce bearing loads and shaft deflection; insufficient
0262 1762/01/$ - see front matter © 2001 Elsevier Science Ltd. All rights reserved
FEATURE *
shaft stiffness causing shaft seal failure due to high vibration amplitudes; excessive casting tolerances leading to high ~ynchronous excitation due to hydraulic unbalance; insufficient rotor damping due to inappropriate labyrinth design; insufficient bearing capacity; too small a gap between impeller and volute cutwater or diffuser vanes causing pressure pulsations and component failure. Any pump failure caused by such design insufficiencies may easily be interpreted as being caused by excitation from partload recirculation - which may have occurred, but was "excessive" only with respect to weak components and would have gone unnoticed with an appropriate design. The development of high energy boiler feed and injection pumps as well as rocket fuel pumps has triggered substantial efforts in pump research during the past 30 years; as a result there is today a much better understanding of the mechanisms and avoiding strategies of impeller inlet and outlet recircu[ation, cavitation damage, hydraulic excitation forces and vibrations. As discussed in detail below a new concept for the design of suction impellers with flat pressure distributions has emerged from that effort, from which process pumps have benefited as well as high energy pumps. At the time when the failure statistics were established, pumps with large impeller eye were designed with large incidence and very spiky pressure distributions - hydraulic design rules which must be considered today as obsolete and inadequate. While it is recognised that the pump buyer needs some simple engineering methods to assess the suitability of the pump selected; such methods must permit, however, to take full advantage of what present-day pump technology can offer to provide the most economic and reliable solution. Several investigators have stressed the fact that inlet recirculation and cavitation damage depend on a large number of design and operational parameters and that the use of the n~-criterion is an over-simplification which does n o t ensure safe operation, e.g. [8] to [10], [21], [35], [36]. In [8] inlet tip speed ul, type of pump, specific gravity and vane overlap were introduced as additional criteria, but the data and recommendations are essentially applicable f o r avoiding cavitation damage to cast iron impellers operating with marginal NPSHA.
2. Suction specific speed as cavitation criterion Consider an impeller blade moving with the velocity wl relative to the fluid. Due to high local velocities around the blade leading edge the static pressure decreases (Bemoulli's law) resulting in a pressure distribution with a pronounced minimum Pmin as sketched in Fig. 1. When the static pressure drops down to the vapour pressure (as imposed by the fluid temperature) a small portion of the liquid evaporates creating a vapour pocket or "cavity". Downstream of the leading edge, where the local pressure increases above the vapour pressure, the bubbles condense violently in a water-hammer-like manner; they "implode" and can damage the impeller, if the hydraulic cavitation intensity exceeds the cavitation resistance of the material. For a given pump at a given speed and flow rate the suction pressure necessary to avoid cavitation completely
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is expressed by the "incipient net positive suction head" NPSH i. If the available NPSHA exceeds the NPSHi (Pmin > Pv) there is no cavitation; but as NPSHA decreases successively below NPSH i (i.e. Pmin < Pv) cavities of increasing length are created. If the cavity length reaches the impeller throat area (sometimes even earlier), performance is impaired and the head created by the impeller drops. Cavitation is thus a phenomenon which develops gradually as the suction pressure (or NPSHA) is lowered. W h e n referring to "cavitation" it is therefore necessary to specify exactly what extent of cavitation is meant. This may be expressed by the following "cavitation criteria": • NPSHi: visual cavitation inception; i.e. first cavitation bubbles are visible • NPSHx: the cavitation causes a drop in x percent of the head developed by the suction impeller; x = 0, 1 or 3% • NPSHFc: full cavitation or head break down ("choking flow") representing the maximum flow limit, which is reached when the curves of NPSHA = f(Q) and NPSHFc = f(Q) intersect. • NPSH required for a specified amount of cavitation erosion, impeller life or increase in noise. These cavitation criteria, or the extent of cavitation, depend for a given pump on the flow rate and the rotor speed, which determine the relative velocity w 1 and the incidence i 1 ~ ]~IB - [31 (difference between blade and flow angle), which in turn generate the pressure distribution around the leading edge. The pressure distribution - and therefore the extent of cavitation - depends on the inlet flow distribution, i.e. the geometry of the inlet of the pump as well as suction pipe layout, and on the geometry of the impeller: blade profile, blade angles and 3D-contours of blades, shroud and hub. The only practical means to predict the pressure distribution as per Fig. 1 are numerical flow calculations; no simple procedure of adequate accuracy is available. In the industry a head drop of 3% is mostly used as a cavitation criterion and is represented as NPSH 3 = f(Q) on the performance curves provided by pump manufacturers. Some pump users also request the NPSH curves for zero and/or one percent head drop NPSH 0 or NPSH 1. Near BEP the NPSH ratio between cavitation inception and 3% head drop typically is NPSHi/NPSH 3 =
&
Total pressure static pressure
t/(P/2~c,2
I[-' , pDS[////~ ~
cavity
~pss without cavitation
pmi(wi n thout
cavitation)
Figure 1. Pressure distribution at blade leading edge, Pss = pressure on suction side of blade.
WORLD P U M P S
January2001
1.0 0.9
q*= 1; nss = 209 q* =0.67; nss=209 q" = 1; case 5.3, concept L q* = 0.78; case 5.3, concept L q* = 1, c a s e 5.1, concept H q* = 1, case 5.1, concept L NSPH0
•
0.8 0.7
•
0.6 la
4
0.5 car 0.4
•
"•0
/T
4•
•
e
0.3 C[••~• \,
0.2 0.1 0.0 1
2
3
FNPSH 4
5
II Figure l(a). Cavity l e n g t h as f u n c t i o n o f NPSH m a r g i n FNPSH = NPSHA/NPSH 3
4 to 6 (with special leading edge profiles also down to 2), while the ratio NPSH0/NPSH 3 = 1.1 to 1.3 [6]; in [4] N P S H 0 / N P S H 3 = 1.5 is proposed. It is important to note that the cavity length at N P S H 3 is of a size similar to the blade pitch at the impeller inlet, i.e. Lea,, ~ rt dl/ZLa. Even at N P S H 0 and N P S H 1 the impeller operates with extended cavitation. This fact is well illustrated by Fig. l(a) which shows measured cavity lengths plotted against the ratio FNPSH = NPSHA/NPSH 3 for different impellers and flow rates. The points where head drop starts are marked as N P S H 0. The intersection
NPSH A = NPSH3+
U2
0.05+2
of the curves with the x-axis gives the points of cavitation inception. As discussed above all these data and features depend on the pressure distribution and can vary in a wide range depending on the impeller geometry. Fig. l(a) gives an impression of the variations encountered. In order to reduce the risk of noise, vibrations or cavitation erosion, a safety margin between NPSHA and NPSH 3 is required in most pump applications. 20 years ago - when [I] to [4] were published - this requirement was less widely accepted than it is today. The NPSH-margin necessary to avoid damage, noise and vibrations depends on the eye tip speed u 1, type of pump (approach flow), type of fluid, impeller material and impeller geometry. Guidelines as to the margin are given in Table 1 (abbreviated and adapted from [7]). Table 1 l~rovides a consistent method to define N P S H margins as a continuous function of the tip speed u 1 which can be considered as the single most significant parametercontrolling cavitation erosion and vibration phenomena induced by inlet recirculation. The coefficients used in the method can be easily adapted to define more or less
U1
FtypeFF Fq. Eq. (T1.1)
URe f = 100 m/s.
Use only for
u 1 < 65 mls and NPSH A < NPSH i
Fq. =1+2q* (l-q*) 2
Fluid factors
I FF
water w i t h t < 200 °C seawater, corrosive fluids hydrocarbons
I 1.0 _> 1.15 1 0.75
Pump type factors
I Ftype
axial inlet, smooth approach f l o w radial inlet (multi-stage and double-entry pumps) unfavourable approach f l o w conditions
I 1.0 t 1.05 >_1.1
FNPSH-
30
WORLD I~UMPS
January2001
NPSH A = G._A_~_ NPSH3 (~3
FNPS.= 1.16 NPS,H3 l T M Nt-'UM Ref]
Eq. (T1.2)
conservative margins or to reflect the special features of various pump types and applications. A recent guideline from the Hydraulic Institute [37] recommends N P S H margins in terms of "low", "high" and "very high suction energy level" (SEL). The limit between low and high SEL is given by a graph which can be approximated by an impeller inlet tip speed H1,SE L = URef (nss,Ref /nss) 1"26with Ul,Re~ = 18 m/s and nss,Ref = 243 (12500 in US units). Recommended N P S H margins are low SEL: FNPSH= 1.1 to 1.3; high SEL: FNpsu = 1.3 to 2.0 and very high SEL: FNpSH = 2 to 2.5. No limit is specified between "high" and "very high" SEL. Another drawback is the step change between the different SEL. The guideline states that pumps operating with high SEL may still be susceptible to elevated noise levels and erosive damage to the impeller. The suction specific speed nss is a parameter which allows to compare geometric dissimilar pumps in terms of their suction capability:
nss = n
NPSH3,BEp 0'75
(1)
2g NPSH R ~-
2
(la)
LI t
The suction specific speed nss is thus defined with the flow rate per impeller eye at the best efficiency point (BEP) and the NPSH3,BE p i.e. the N P S H required for a specific pump to operate with exactly 3% head drop of the first stage in the case of a multi-stage pump. The nss is no criterion whatsoever for either cavitation inception, N P S H 0, NPSH 3 or the risk of cavitation erosion. By definition the suction specific speed has nothing to do with impeller inlet recirculation or hydraulic excitation forces. Nor does the nss say anything about pump reliability - even under cavitation performance. Only the safety margin FNPSH can give some clue as to the reliability and this only with respect to cavitation induced noise, vibration or damage. Another useful parameter is the cavitation coefficient c defined by Eq. (1 a) as the ratio of the required N PSH (for any of the cavitation criteria
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FEATURE •
C
mentioned above) to the impeller eye tip speed squared. It allows to assess the quality of the hydraulic design; for ,example: cavitation inception at ~i = 0.6 at BEP would represent a sophisticated blading while % = 2 would mean usually a poor hydraulic design of the impeller inlet (which may - or may not - imply trouble). To use the NPSH 3 as a cavitation criterion on performance curves is a matter of convenience only, because this value can be determined with some accuracy on the test bed, while the determination of the NPSH 0 leaves more room for individual interpretation, and measuring the NPSH i would require special test rigs, where the impeller inlet can be observed by means of a stroboscope. At high flow, q* > 1, the NPSH 3 = f(Q) is significant since the rise of this curve describes approximately the flow limit of the pump (NPSH 3 and NPSHFc being then close).
3. Design of impellers for high suction specific speed 3.1 Design concepts There are essentially two concepts that can be used to design an impeller with high nss: ( 1) A conventional design, concept "H", using a high incidence at the impeller inlet to increase the throat area. (2) A modern design able to achieve a high suction specific speed with low incidence, concept "L". The appreciation of the differences between these two design methods is the key to the evaluation of the suitability of pumps with high n~s. The features of these concepts are discussed in the following: Concept H: The impeller is designed to "swallow" the high vapour volume created by extensive cavitation. This is accomplished by providing a large impeller eye and large blade inlet angles in order to increase the impeller throat area. Excessive flow deceleration created by the oversized throat induces premature partload recirculation of high intensity. The blade leading edge profile used to be either wedge-like or even of constant blade thickness with a semicircular leading edge; the latter giving o i > 2. The large blade angles lead to high incidence even at BEP flow. This creates a sharp low-pressure spike, a zone of flow separation downstream of the leading edge filled by a cavity of considerable thickness, a high cavity volume, and strong pressure gradients in the zone where the cavitation bubbles implode (see Figs. 2 and 3). The thick cavity leads to the shedding of cavitation vortices which contribute strongly to the risk of cavitation erosion [13]. The potential for cavitation damage and surge is high because of the energy stored in the large cavity volume. Cavitation inception starts at high NPSH a (typically ~i = 1.5 to 2.5) because of the high incidence and non-optimum leading edge profiles. Concept L: During the 1970s the head per stage of large boiler feedpumps increased to levels of 600 to 800 m, with impeller eye tip speeds reaching u| up to 80 m/s. Severe cavitation damage was then observed on impellers designed according to the old rules (i.e. concept "H"). Superior impellers where developed subsequently by means of stroboscopic cavity observations and modifying, by trial
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~
Concept,,L"
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Wl
.
.
.
Wl
Wl
Wl
thick cavity, separated flow, vortices
-
thin sheet cavitation
![ _ _ Figure 2. Blade shapesof concepts "H" versus"L" a) U Cu
b)
1
o,s ! !
I ps~t
0,6 --unfa ourabl
0,4 0,2
avoura le
0 0
~
0,2
n
0,4
0,6
0,8
Lsch
:
Lseh
a) work transfer; b) pressuredistribution.
and error, leading edge profiles and blade angles until cavity length and volume were reduced sufficiently to achieve an acceptable impeller life. Later, advances in computing allowed the calculation of blade pressure distributions and thus optimisation of the impeller inlet through a reduction of the low pressure spikes. In the 1980s computer programs essentially used non-viscous flow models allowing only to calculate the single-phase pressure distributions, which were useful to optimise cavitation inception but failed to catch developed cavitation [29] [31]. Recently it has even become possible to calculate the development of a cavity and to estimate performance impairment [22]. The impeller designs emerging from these development feature a low blade loading u c u near the leading edge and consequently a flat pressure distribution to minimise the low-pressure spike, Fig. 3. Cavitation inception can be as low as (~i 0.5 tO 0.7. This is achieved by an aerofoil-like leading edge profile designed to be as insensitive as possible to a variation of incidence (hence flow rate). The leading edge is far advanced into the axial portion of the impeller eye (see Fig. 6) in order to obtain a small blade loading in the zone where bubbles are likely to implode (small driving pressure differential for bubble implosion). The increase of the blade angle from the leading edge to the impeller throat needs careful attention to get a sufficient suction capacity at flow rates above BEE but to avoid excessive local deceleration of the flow. Typically the cavity starts downstream of the leading edge, it increases rapidly in length once cavitation starts, but the cavity volume is very small since the cavity forms a thin transparent =
WORLD PUMPS
January2001
L. . . . . . . . . . . .
sheet. Because of the weak pressure gradient and the low cavity volume the risk of cavitation erosion, cavitation noise and surge is much lower than with design concept "H". At the author's company concept "H" was gradually abandoned from the early 1970s when a second generation of suction impellers for "advanced class" boiler feedpumps with a head per stage of 1200 m was being developed. Development efforts at that time led to suction impellers with very low cavitation inception above 60% of BEP flow [14]. The physical mechanisms behind concept L were recognised since the early 1980s when methods were also developed for the quantitative prediction of cavitation damage [15 and 12], and since then this knowledge has been applied systematically to the development of suction impellers. More recent publications show that major manufacturers now design impellers for high tip speeds essentially according to concept "L" with flat pressure distributions [16], [17] and [28] to [32]. Problems with impellers designed with high incidence and their elimination by applying in essence concept "L" were reported for example in [16] and [18] to [20].
other words there is a definite relationship between suction specific speed and impeller eye diameter as expressed by Eq. (5) for radial and semi-axial impellers and Eq. (6) for inducers. Equations (3) to (6) are derived from test data in [7]. Typically such test data show a very large scatter and can thus describe only a general trend. Graphs in [6] show similar trends as expressed by Eqs. (4) and (5).
12,5~n ,/nq "[0.19 nss = (p10,455 [ " ~ J
52 n s s - £011.075
Traditionally the NPSH required is expressed by Eq. (2) in which the coefficient 5Lc represents the acceleration of the fluid and inlet losses, while ;Lw is the blade coefficient describing the low pressure zone around the blade leading edge, Fig. 1.
C2 W2 NPSH=X c ~lm +;Lw -1 2g 2g
(2)
For pumps with an axial inlet we may set Xc = 1.05 to 1.15; for radial inlet bends 5% = 1.25 to 1.5 depending on the design. Different cavitation criteria - such as inception, zero, one and three percent head drop or full cavitation require different values of the blade coefficient i.e. Xw,i; )Vw,0;)Vw,1; )Vw,3 or Xw,FC. Furthermore Xw depends on the leading edge profile, inlet flow distribution and flow rate. Most significantly all of the blade coefficients k w depend on the stagger angle of the blades 131B,a or the flow coefficient q)l = tan ~l,a (approaching flow without prerotation); for inception and 3 % head drop Eqs. (3) and (4) give an idea of these relationships. Xw, i = 3(tanJ31B,a) 0'9 (3)
Xw,3 = 0,3(tan ~l,a) 0'53 (4) Unfortunately many publications leave the reader with the impression that k w can be considered as constant - in fact the "classical" concept of optimising the impeller eye diameter through a plot of NPSH = f(dl) fails when using such data as represented by Eq. (3) and (4)! Since the coefficient Xw decreases with decreasing flow coefficient (or increasing impeller eye diameter for given flow rate and speed) the NPSH required decreases with increasing dl; in
32
WORLD P U M P S
January2001
(inducers)
15 %ofor nq < 170
(5)
(6)
Equation (5) covers more than 50 single- and multi-stage pumps in the range of nq = 10 to 160 with a standard deviation of + 15 %. If one wants to design an impeller (or inducer) for a selected suction specific speed, Eqs. (5) and (6) may be solved for the flow coefficient q~l = Cl/Ul:
-k 11 125[ 2.2JnqI 0.418 %-
3.2 Selection of the impeller eye diameter
-+
n [nss j
= l 5210"93 £01 / ns--'T/
[27J
+
(inducers)
40%
(Sa)
(6a)
For any specific application with given Q, n, NPSH a and hub diameter d n a suitable range of impeller eye diameters or suction specific speeds can be determined in the following way: (i) calculate Ul, c 1 and '4)1 for different eye diameters (ii) determine nss from Eq. (5); from nss calculate NPSH3, Eq. (1) (iii) calculate recommended NPSHA from Eq. (TI.1) in table 1 (iv) determine actual margin FNPSH = NPSHA/NPSH3 (v) plot data as function of u 1 or d 1. The result is shown in Fig. 4 for a process pump with n =2950 rpm; QBEP = 230 m3/h; HBEp = 81 m; NPSHA = 6.5 m; d n = 45 mm; FF = 1.0; FR = 1.2 (design for partload operation). Figure 4 shows: • As d I or u 1 increases, the suction specific speed increases and NPSH 3 decreases. • Consequently the actual margin FNPSH,actuaI increases while both cavitation coefficients ~A and ~3 decrease because of the rising tip speed u 1. Any selection with FNPSH,actuaI < 1.0 has to be discarded, since the pump would operate with more than 3% cavitation induced head drop • The eye diameter should be selected such that the intended NPSH-margins - for example according to Eq. (TI.1) in table 1 - can be approximately obtained. If the actual NPSH-margin becomes appreciable lower than the values stipulated by Eq. (TI.1) either an impeller with a higher nss or a pump with a lower speed (lower nq in this case) should be selected. • Interestingly the NPSHi,recommended from Eq. (TI.1) shows a minimum in the curve NPSHA,recommended = f(ul ): at first NPSHg,recommendeddecreases since NPSH 3 falls with a larger eye, but eventually the NPSHa,recommended rises again because of the growing tip speed u 1. Since hydraulic
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excitation forces increase with ul 2 the optimum selection should be found to , the left of the mathematical minimum. • The recommended NPSH A from Eq. (T1.2) in table 1 decreases continuously with increasing u l, since it is a multiplier on NPSH 3. This approach to determine an NPSHmargin is thus not appropriate when large variations of the nss are involved. • In the present example the optimum selection would be found in the range o f u l = 21 to 23 m/s and nss = 230 to 265 giving recommended safety margins between fNPSH = 1.38 to 1.6. The risk of cavitation erosion increases exponentially with the tip speed u 1. The higher u l the shorter the allowable cavity length. For u 1 > 75 m/s the pump must be operated virtually without any cavitation which means that NPSH g > NPSH i is required. For such cases the impeller must be designed for low cavitation inception and this calls for the smallest possible inlet diameter and suction specific speed compatible with maximum flow requirements. For applications with u 1 > 50 m/s the suction specific speeds is typically limited to nss = 160 to 180. If the cavity length is known or estimated as a function of NPSH A, the Impeller life and erosion rate can be estimated by the methods given in [7] and [12]. The impeller tip speed can then be optimised with respect to m i n i m u m erosion by a procedure similar to the one used in Fig. 4.
Conclusions Progress in pump technology during the past 30 years includes new concepts for the design of high nss impellers with low incidence and lower inlet diameters as used formerly. The failure statistics compiled on pumps designed in the late 1960s with high incidence and exaggerated impeller eye may not be considered relevant any more for this new generation of impellers. At NPSH 3 the cavities formed on the leading edge extend into the impeller throat. Margins on the NPSH 3 are needed to reduce the extent of cavitation to acceptable levels to avoid loss in performance, excessive noise,
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eye diameter optimisation
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i
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450
0.5
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350
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20
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ul (m/s) impeller eye diameter optimisation
impeller eye diameter optimisation 14 12
to
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,~.
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-e--NPSH-3 ~ NPSH-A •-~--NPSH-A, Re¢[8] -~-NPSH.-A,Re¢[7] J,=
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Figure 4. Optimisation of impeller eye diameter and suction specific speed for a given NPSHA with respect t o NPSH - margin
vibrations and erosion. Such margins should increase with the impeller tip speed, they depend on the liquid pumped, flow rate and the pump inlet conditions. Table 1 provides a method to define such margins in a logical way. Following this concept it is found that for a given NPSH a there exists an optimum suction specific speed.
Notation Alq b2 c d1 dli dn FF FN~ H FR fq
g H 1L iI
impeller inlet throat area (if trapezoidal: Alq = a 1 b 1) impeller exit width absolute velocity impeller inlet (or eye) diameter at outer streamline impeller blade inlet dia meter at inner streamline hub diameter fluid factor (table 1) NPSH safety margin: FNPSH = NPSHA/NPSH 3 risk factor (table 1) impeller eyes per impeller: single-entry fq = 1; doubleentry fq = 2 acceleration due to gravity (g = 9,81 m/s 2, rounded) head per stage Impeller life incidence at impeller leading edge: i 1 =
blade angle - flow angle blockage caused by hub: kn k n = 1 - dn2/dl 2 cavity length measured from Lcav leading edge NPSH net positive suction head NPSH A net positive suction head available NPSH i net positive suction head of cavitation inception NPSHR net positive suction head required according to a specific cavitation criterion, usually NPSH R = NPSH3 NPSHx net positive suction head required for operation with x-percent head drop ( x = 0 , 1, or 3 %) rotational speed n (revolutions per minute) specific speed nq nq = q (qBEP/G)0'5/HBEp 0 " 7 5 (min" , m-J/s, m) suction specific speed nss nss =
P0 p Pv Q q*
n (QBEP/fq)O'5/NPSH3,BEp0'75 (min d, m3/s, m) power at Q = 0 (at coupling) static pressure vapour pressure flow rate, volumetric flow flow rate referred to flow rate at best efficiency point:
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January2001 3 3
Rm u1
u2
wI
Wlq
ZLa ZLe z~t 13
[31 ]31B Ae
)~c, ~-w p
qh
q* = Q/QBE.p tensile strength of impeller material circumferential velocity at tip of impeller eye: u 1 = n d I n/60 circumferential velocity at tip of impeller outlet: u 2 = n d 2 n/60 relative velocity at impeller inlet (outer streamline) average velocity in impeller throat area: Wlq = Q/(zka Alq) number of impeller blades number of diffuser vanes number of stages angle between relative velocity vector and the negative direction of circumferential velocity flow angle at impeller inlet blade angle at impeller inlet metal loss due to cavitation (location of strongest attack) coefficient for N P S H calculation, Eq. (2) density cavitation coefficient (subscript as NPSH): = 2 g NPSH/ul 2 inlet flow coefficient: (Pl = Clm/Ula
Subscripts, abbreviations 1 a BEP
DS m max rain o Ref RB Rez SF SS s u
impeller blade leading edge (tip or outer streamline) at outer streamline best efficiency point (operation at maximum efficiency) pressure side meridional component maximum minimum shut-off operation (Q = O) reference value onset of recirculation recirculation shockless flow (zero incidence) suction side suction nozzle circumferential component
References 1 Hallam JL: Centrifugal pumps: Which suction specific speeds are acceptable?. J of Hydrocarbon Processing, April 1982, 195-197 2 Fraser WH: Recirculation in centrifugal pumps. ASME Winter Annual Meeting 1981, 65-86 Bloch H: How to buy a better pump. J of
34
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Hydrocarbon Processing, January 1982, 81-87 3 Makay E, Szamody O: Survey of feedpump outages. EPRI FP-754, Final report RP 641, 1978 4 Giilich JF, Bolleter U et al.: Feedpump operation and design guidelines. EPRI Report TR-102102, June 1993 6 Hergt P et al.: The suction performance of centrifugal pumps possibilities and limits of improvements. Proc. 13th Intl Pump Users Symp, Houston, 1996, 13-25 7 Gtilich JF: Kreiselpumpen. Ein Handbuch fiir Entwicklung, Anlagenplanung und Betrieb. Springer, Berlin, 1999. ISBN 3-540-56987-1 8 Budris AR: The shortcomings of using pump suction specific speed alone to avoid suction recirculation problems. 10th Intl Pump Users Symp, Houston, 1993, 91-95 9 G/ilich JF, Egger R: Partload flow and hydraulic stability of centrifugal pumps. EPR1 RP 1884-10, TR-100219, March 1992. 10 Stofel B, Hergt P: Zur Problematik der spezifischen Saugzahl als BeurteilungsmaBstab for die Betriebssicherheit einer Kreiselpumpe. Pumpentagung Karlsruhe 1988, Section B8 11 WeiB K: Experimentelle Untersuchungen zur TeillaststrOmung bei Kreiselpumpen. Diss. TH Darmstadt, 1995 12 Gtilich JF: Guidelines for prevention of cavitation in centrifugal feedpumps. EPRI RP 1884-10, GS-6398, Nov. 1989 13 Avellan E Karimi A: Dynamics of vortex cavitation involved in the erosion of hydraulic machinery. Proc. 7th Conf. on Liquid and solid erosion impact. Cambridge 1987 14 Gtilich JF: Similarity characteristics for suction capacity and bubble propagation of pumps. Technical Review Sulzer, 2/1980 15 Gtilich JE Pace S: Quantitative prediction of cavitation erosion in centrifugal pumps. IAHR Syrup Montreal, Sept. 1986, Paper 42 16 Sloteman DE Cooper P, Graf E: Design of high-energy pump impellers to avoid cavitation instabilities and damage. EPRI Power Plant Pump Symp. "Fampa 1991 17 Hergt P: Design approach for feedpump suction impellers. EPRI Power Plant Pump Symp. Tampa 1991 18 Schiavello B et al.: Improvement of cavitation performance and impeller life in high energy boiler feedpumps. IAHR-Symp. Trondheim 1988 19 Cooper P et al.: Elimination of cavitation-related instabilities and damage in high-energy pump impellers. 8th Pump User's Syrup. Houston 1991 20 Schiavello B: Field cases due to various cavitation damage mechanisms. EPR1 Power Plant Pump Symp. Tampa 1991 21 Stoffel B, Jager R: Experimental investigations in respect to the relevance of
suction specific speed for the performance and reliability of centrifugal pumps. Proc. 13th lntl Pump Users Symp, Houston, 1996, 13-25 22 Hirschi R: Prediction par mod~lisation numerique tridimensionelle des effects de la cavitation ~ poche dans les turbomachines hydrauliques. Diss. EPF Lausanne, 1998 23 Gtilich JF: MOglichkeiten und Grenzen der Vorausberechnung von Kavitationssch~iden in Kreiselpumpen. Forsch Ingenieurwes 63 (1997) H1/2, 27-39 24 Gtilich JF et al.: Pump vibrations excited by cavitation. 4th Congress on Fluid Machinery for the Oil & Petrochemical and related Industries. The Hague, May 1990. 25 Gtilich JF et al.: Cavitation noise and erosion in jet cavitation test devices and pumps. Second ASME Pumping Machinery Symp., I993 26 Gtilich JF: Diagnosis of cavitation in centrifugal pumps. Technical Review Sulzer No 1, 1992. 27 Giilich JE Bolleter U: Pressure pulsations in centrifugal pumps. ASME J Vibr Acoustics 114 (1992) 272-279 28 Hergt P: Hydraulic design of rotodynamic pumps. In: Hydraulic Design of Hydraulic Machinery. Rada Krishna (Hrsg), Avebury, Aldershot, 1997 29 Worster DM and Worster C: Calculation of 3D-flows in impellers and its use in improving cavitation performance in centrifugal pumps. 2nd Conf on Cavitation, 1983, Paper IMechE C203/83 30 Cooper P: Pump Hydraulics Advanced. Short Course 8. 13th Intl Pump Users Syrup, Houston, 1996 31 Krieger P: Spezielle Profilierung an Laufr~idern von Kreiselpumpen zur Senkung von NPSHi. VGB Kraftwerkstechnik 72 (1992), Nr 5 32 Spring H: Critique of three boilerfeed pump suction impellers. ASME Pumping Machinery Symp., FED 81 (1989) 31-39 33 Stoffel B: Experimentelle Untersuchungen zur r~iumlichen und zeitlichen Stmktur der Teillast-Rezirkulation bei Kreiselpumpen. Forsch Ingenieurwes 55 (1989) 149-152 34 Sulzer Centrifugal Pump Handbook. 2nd ed, Elsevier Advanced Technology, Oxford, 1997 35 Schiavello B: Minimum continuous flow as related to suction recirculation and cavitation in pumps. Norwegian Society of Charted Engineers, Course No 84303, Pumps Offshore, Geilo, Norway, 1988 36 Schiavello B: Cavitation and recirculation troubleshooting methodology. lOth Intl Pump Users Symp, Houston, 1993 37 Hydraulic Institute guideline HI 9.6.1 - 1998 38 Wesche W: Experimentelle Untersuchungen am Leitrad einer radialen Kreiselpumpe. Diss. TU Braunschweig, 1989
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