19942060.2008

This article was downloaded by: [120.164.45.33]On: 09 June 2015, At: 07:58Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: MortimerHouse, 37-41 Mortimer Street, London W1T 3JH, UK

Engineering Applications of Computational FluidMechanicsPublication details, including instructions for authors and subscription information:http://www.tandfonline.com/loi/tcfm20

A Study in The Use of CFD In The Design ofCentrifugal PumpsS. Yedidiahaa aaa 89 Oakridge Rd, West Orange, NJ 07052, USA E-Mail:Published online: 19 Nov 2014.

To cite this article: S. Yedidiah (2008) A Study in The Use of CFD In The Design of Centrifugal Pumps, EngineeringApplications of Computational Fluid Mechanics, 2:3, 331-343, DOI: 10.1080/19942060.2008.11015233

To link to this article: http://dx.doi.org/10.1080/19942060.2008.11015233

PLEASE SCROLL DOWN FOR ARTICLE

Taylor & Francis makes every effort to ensure the accuracy of all the information (the Content) containedin the publications on our platform. However, Taylor & Francis, our agents, and our licensors make norepresentations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose ofthe Content. Any opinions and views expressed in this publication are the opinions and views of the authors,and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be reliedupon and should be independently verified with primary sources of information. Taylor and Francis shallnot be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and otherliabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to orarising out of the use of the Content.

This article may be used for research, teaching, and private study purposes. Any substantial or systematicreproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in anyform to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions

Engineering Applications of Computational Fluid Mechanics Vol. 2, No. 3, pp. 331343 (2008)

A STUDY IN THE USE OF CFD IN THE DESIGN OF CENTRIFUGAL PUMPS

S. Yedidiah

89 Oakridge Rd, West Orange, NJ 07052, USA E-Mail: [email protected]

ABSTRACT: CFD has the potential of assisting an engineer in arriving at improved designs. However, to be effective, this requires a much closer cooperation and mutual understanding between the pump specialist and the expert in CFD, than it is presently in existence. This conclusion is based on actual case histories from past experience, as well as considerations of the physical meaning of certain mathematical expressions. The presented discussion relates, primarily, to the design of centrifugal pumps. However, there are strong indications that analogical situations exist also in other fields of fluids engineering.

Keywords: centrifugal pumps, CFD, flow pattern, impeller, volute, noise, pump design

1. INTRODUCTION

Successes in predicting the flow patterns within the passages of centrifugal pumps indicate that CFD might be capable of assisting a pump engineer in arriving at improved designs. Success, however, is still very elusive. This paper discusses the principal cause of that state of affair, and what can be done about it. For a predicted flow pattern to be of practical use, it has to inform the engineer whether it will allow the pump to perform at its best, whether there exists a different flow pattern which will allow the pump to perform even better, and what geometry of the waterways will generate such a flow pattern. The nearest which a predicted flow pattern came to answering some of the above questions is based on the assumption that the presence of vortices have an adverse effect on performance. This has been confirmed in practice (Yedidiah, 1996: p. 191). However, cases in which the presence of a pair of forced vortices has even improved the performance of a centrifugal pump are also known. Below we shall discuss such a case.

2. EFFECT OF A PAIR OF FORCED VORTICES AT THE PUMP INLET ON ITS PERFORMANCE

Prang and Oates (1971) presented results of tests, which were expected to shed light on the effect of the distribution of the inlet-velocities on the performance of a centrifugal pump. The objective of these tests was to determine the optimum

geometry of a side-inlet suction-nozzle (Fig. 1) of a centrifugal pump. Suction nozzles of different geometries have been prepared in transparent epoxy (Prang and Oates, 1971). The flow patterns within their passages were observed visually by introducing into the flowing liquid small amounts of glitter. In addition to the above, the distributions of the axial and of the tangential velocity components were measured at the outlet of these suction nozzles along the diameter M-M, as shown in Fig. 2. (During the performance tests, these outlets of the suction nozzles became the inlets to the tested pump). These distributions were taken at a number of discrete flow rates. For comparison, the distributions of the same velocity components were also taken at the same flow rates, when the pump was tested as an end-suction pump with a straight, concentric suction pipe. In the latter case, the measurements were taken along a vertical diameter, 5.5 upstream of the suction flange of the pump. Fig. 3 presents the results of these measurements for the side-suction inlet-nozzle shown in Fig. 2, as well as for the straight, concentric suction pipe. The measurements shown in Fig. 3 were taken at the flow rate of 56 m3/hour. After completing these observations and measurements, each of the experimental side-suction nozzles was assembled with the same 328 end-suction centrifugal pump, thus converting it into a side-suction unit. Afterwards, it was tested for performance. For comparison, the same pump was also tested as a straight end-suction pump with a straight, concentric suction pipe.

Received: 1 Dec. 2007; Revised: 5 Feb. 2008; Accepted: 4 Mar. 2008

331

Dow

nloa

ded

by [1

20.16

4.45.3

3] at

07:58

09 Ju

ne 20

15

Engineering Applications of Computational Fluid Mechanics Vol. 2, No. 3 (2008)

Fig. 1 Centrifugal pump with side-inlet suction

nozzle.

Velocitym/sec

RADIUS (inches)

Fig. 4 presents the results of the performance tests carried out with the suction-nozzle shown in Fig. 2, as well as with the end-suction pipe. It shows that the performance with the side-suction nozzle (which has produced a pair of forced vortices) is superior to its performance with the straight, end-suction pipe.

Fig. 2 Suction chamber used in the tests reported in

Fig. 3 and Fig. 4.

Fig. 3 Distribution of the axial and of the tangential

velocity components at the inlet of the tested pump at 56 m3/hr, when tested as a straight end-suction unit and with the suction chamber shown in Fig. 2.

At the first sight, these results seem to present an impossible-to-solve enigma. However, a closer look at the physical meaning of Eulers equations of motion of an inviscid incompressible liquid demonstrates that there is nothing mysterious about the test results shown in Fig. 4.

332

Dow

nloa

ded

by [1

20.16

4.45.3

3] at

07:58

09 Ju

ne 20

15


Fig. 4 Performance of the experimental pump, when

tested as a straight end-suction unit and as a side-inlet pump with the suction nozzle shown in Fig. 2.

3. THE PHYSICAL MEANING OF EULERS EQUATIONS

A translation of Eulers equations of motion into their physical meaning provides a feasible explanation of the cause of the test results shown in Fig. 4. These equations are frequently expressed in the following forms:

zV

yV

xV

xP

xxx

+

+

=

zyxx VVV1F

zV

yV

xV

yP

yyy

+

+

=

zyxy VVV1F (1)

zV

yV

xVP

zxz

+

+

=

zyxz VVVz1F

Let us have a look at the term x

Vx

xV .

As velocity means the derivative of distance with respect to time , therefore, the above term can be reduced to:

)T/xV( x =

TV

xV

Tx

xV xxx

=

=

xV (2) H m

This means that the studied term expresses acceleration (rate of change of velocity with respect to time). In a similar manner, it is possible to prove that all other terms on the right side of Eulers equations represent acceleration. To be more specific, each of these equations expresses an adaptation of Newtons Second Law of Motion to an inviscid, incompressible liquid. The accelerations in such a liquid are the result of the combined action of external forces plus the forces generated by the pressure gradients which exist within the acted-upon liquid. These pressure gradients are the generating forces (Yedidiah, 2004) which accelerate the liquid in the direction opposite to the direction in which these pressures are increasing. (This accounts for the minus sign of the terms which express the pressure gradients).

100 m3/hour

EFF

When applied to the flow through an impeller, these equations of motion tell us how the geometry and the motion of the impeller-passages will alter the velocity distributions of the incoming liquid. This has been confirmed by the experiments reported in Hureau et al. (1993). 100 m3/hourLet us have a look at the shroud-to-shroud distribution of the normal velocity components measured along the axis 10 (upstream of the inlet edges of the blades) and along the axis 6 (upstream of the outlet edges of the blades) of the tested impeller (Fig. 5). Figs. 6 and 7 show these distributions at two flow rates: at the design flow, and at 0.41 of that flow.

10

6

Fig. 5 Axes, along which the normal velocity

components shown in Figs. 6, 7 and 8 were measured.

333

Dow

nloa

ded

by [1

20.16

4.45.3

3] at

07:58

09 Ju

ne 20

15


Fig. 6 Shroud-to-shroud distribution of the normal

velocity components upstream of the inlet edges of the blades along axis 10 shown in Fig. 5 at optimum flow and at 0.41 of the optimum flow.


velocity components upstream of the outlet edges of the blades along axis 6 shown in Fig. 5 at optimum flow and at 0.41 of the optimum flow.


velocity components along axis 10 shown in Fig. 5 at different fractions of the optimum flow rate.

We note that at both flow rates, the geometry and the motion of the impeller-passages have a similar effect on the distribution of these velocity components: they have increased their relative magnitudes towards the suction-shroud, and reduced them towards the hub-shroud. However, due to the initial differences in these distributions, they have converted a fairly uniform distribution of the inlet velocities (at the design flow) into a very non-uniform one upstream of the outlet edge. Also, they have converted a very non-uniform distribution of the velocities at the inlet (at 0.41 of the design flow) into a fairly uniform one, upstream of the outlet edge.

nq 20Cn/U1 [ - ]

S/So [ % ]

It is possible that the improvements in performance shown in Fig. 4 are due to the fact that the presence of the pair of the forced vortices upstream of the impeller-eye have resulted in a more advantageous distribution at the outlet of the blades. Also, the advantages of that improvement in the velocity distribution at the impeller-outlet had a more beneficial effect on performance than the possible adverse effects of the presence of the pair of forced vortices which existed upstream of the blades.

Cn/U2 [ - ]

This is yet not all. A glance at Fig. 6 tells us that this colossal difference in the distribution of the inlet velocities was caused by recirculation. This effect, as has been explained in Yedidiah (1996 and 2005a), develops below a certain flow rate (compare Fig. 8). The flow rate, below which recirculation starts to develop, depends among others upon the geometry of the blades.

S/So [ % ]

4. EFFECTS OF BLADE GEOMETRY ON INLET RECIRCULATION

Fig. 9 shows the effects of reducing the projected area of those inlet-parts of the blades, which extend into the eye of the impeller. It shows that a reduction in the magnitude of that area also reduces the intensity and the flow rate at which recirculation sets in (Yedidiah, 2005a). The blades of that particular impeller were purely cylindrical. This makes it possible to establish a simplified qualitative model of the manner, in which the projected area of these parts of the blades is affecting recirculation.

nq 20Cn/U1 [ - ]

With reference to Fig. 10, let us consider the effect of a strip of radial width Ro and of length Lo, which extends into the impeller-eye. The volume of liquid directly affected by such a strip of the blades is equal to (Yedidiah, 2003):

S/So [ % ]

oouoobo RL)CU(Q = (3)

334

Dow

nloa

ded

by [1

20.16

4.45.3

3] at

07:58

09 Ju

ne 20

15


335

And the head added to that acted-upon volume of liquid is equal to (Yedidiah, 2003):

gCuo

oo Uh = (4)

Eq. (5) tells us that Ho increases with Qbo. The latter, as follows from Eq. (3), increases with the product (Lo Ro). This explains the effects shown in Fig. 9.

Consequently, the total head added to the total volume of the pumped liquid by that strip of the blade is equal to (Yedidiah, 2003):

q

bogQQCuooo UH = (5)

The above discussions demonstrate that when applying CFD to the study of the effects of the impeller-passages on the performance of a centrifugal pump, it is mandatory to take into account a significantly larger amount of parameters than those which are presently included in any known CFD programs. In particular, that recirculation is only one of the numerous factors which affect the flow through an impeller (Ref. 18). The above conclusion is also confirmed by the following case history.

This increase in the head of the liquid will generate a pressure gradient which will accelerate the liquid in the direction opposite to the direction in which the increase of that pressure takes place. The magnitude of that acceleration will, of course, increase with the increase in Ho.

Fig. 9 Effect of the blade parts which project into the eye of the impeller on recirculation.

H mm Hg

Q/Qopt

Fig. 10 A simplified model of the effect of a strip of a blade which projects into the eye of an impeller on the intensity of recirculation.

36r

63r

R bR a51

r

OrignialImpeller

Orignial Impeller

OriginalImpeller

Ro Ro

L o

Dow

nloa

ded

by [1

20.16

4.45.3

3] at

07:58

09 Ju

ne 20

15


5. EFFECT OF THE STRENGTH OF FORCED INLET-VORTICES ON THE NPSH REQUIREMENTS OF A PUMP

Fig. 11 presents the distribution of the axial and of the tangential velocity components at the outlet of two different side-suction nozzles (Prang and Oates, 1971). Both nozzles resembled the shape shown in Fig. 2. However, the radius R (Fig. 2) in shape C was larger, and its center was located nearer to the diameter M-M than in shape D. Both geometries produced a pair of forced vortices. However, the geometry D has produced stronger vortices than the geometry C at all flow rates. These differences, as can be seen in Fig. 12, had no effect on either the QH-curve or on the efficiencies of the tested pump. However, the suction nozzle which has generated stronger vortices has allowed the pump to operate at lower available NPSH-values. The reason for this effect is simply as follows.

Fig. 11 Distribution of the tangential and of the axial

velocity components at the outlet of two different side-inlet-suction nozzles (nozzle C and nozzle D) at two different flow rates.

Fig. 12 Performance of the same pump when tested

with suction nozzle C and suction nozzle D.

The impeller of the test pump used in Prang and Oates (1971) had purely radial blades, which projected only a short distance into the suction-eye. The pairs of the forced vortices have increased the pressures at the outermost radii of the pump inlet. This means, near the inlet-tips of the impeller blades. This is the location where cavitation is most likely to start at reduced available NPSH-values. Stronger vortices produce larger increases in pressure. Consequently, the stronger vortices made it possible for the pump to operate at lower available NPSH. CFD is a very powerful and versatile logical tool, which is capable of providing engineers with enormous assistance in arriving at better results. However, versatility implies that it can be used in many different ways, depending on the task it has to accomplish. To be of practical use, CFD has to be applied in a manner specifically adapted to handle the problem in question. This requires an in-depth knowledge and understanding of the problem(s) to be handled. The present explosion of information makes it prohibitive for the expert in CFD even to try to master the design of centrifugal pumps. Similarly, the pump specialist cannot afford to be distracted from his field of activity in order to attempt to master CFD. The only feasible solution to such a state of affair is teamwork. However, for

336

Dow

nloa

ded

by [1

20.16

4.45.3

3] at

07:58

09 Ju

ne 20

15


teamwork to be successful, each member of the team has to know and to understand what the others are doing. This includes the knowledge of how, where and when the use of CFD is the best choice for a given task. Below, we shall discuss two design problems, where CFD might be capable of providing extremely useful assistance to pump designers.

6. A DESIGN PROBLEM IN WHICH CFD MIGHT PROVE EXTREMELY USEFUL

When a liquid is flowing between the blades without separation, the law of continuity mandates that the flow should satisfy the following condition (Yedidiah, 2007) (see Fig. 13):

= ba fe dm dnwBdsCzR RB)2( (6) In Eq. (6), BR signifies the width of the impeller at any given radius R, ds signifies the length of an element of a given arc of radius R, Bd signifies the width of the impeller at the center of an inscribed circle of diameter d (Fig. 13).

Fig. 13 Schematic flow between impeller blades of a

centrifugal pump (hypothetical).

This means that the flow rate across any arc a-b of radius R is the same, as the flow rate across any normal line e-f. If we assume that the liquid is flowing through a set of congruent passages (Fig. 13) and that Cm is constant across any arc of a given radius R, Eq. (6) can be re-written as:

== fe d dnwBzRzQ mRCB)2( (7)

In a correctly designed impeller, the magnitude of the relative velocities w, within the passages created by the overlapping portions of the blades, is, in most cases, selected to vary linearly with the radius. In that case, Eq. (7) can be approximated by the following expression:

dBwCB)2( dcdmR =zR (8)

In Eq. (8), BR is the width of the impeller at any given radius R, wd is the calculated relative velocity at the center of any inscribed circle of diameter d, and Bdc is the width of the impeller at the center of the same inscribed circle. At the first sight, Eq. (8) seems to have no relevance to the actual pump performance. After all, in a real pump, the liquid never flows in congruent partial passages. Also, the magnitudes

are never the same across the total length of any arc a-b of a given radius R. Still, a study of how far the geometry of the passages deviates from the condition expressed by Eq. (8) provides the pump designer with useful information.

of Cm

Let us see what will happen when our original assumption that the magnitudes of Cm across any arc of a given radius R are identical is not correct. Let the actual magnitudes of Cm, within certain partial passages, be equal to Cm (1+c). For a given flow rate, this means that there may exist an equal number of passages, in which the magnitudes of Cm are equal to Cm (1c). The magnitudes of the relative velocities are equal to:

f b e a d

n

.SinwCm = This means that if Eq. (8) is satisfied in the case when Cm = constant along any given arc of radius R, it will also be valid in many other cases. In summary, this leads to the following conclusions.

R

If an examination of the passages reveals that Eq. (8) is satisfied along their total length, there exists a possibility that the flow through the passages will really be free of any major disturbances. However, if we shall find significant differences between the flow rates calculated by each side of Eq. (8), this signifies the probability of major disturbances or even reversals of flow.

B

In practice, certain deviations from the condition imposed by Eq. (8) are allowable or even desirable (Ref. 18: sub-section B-3). However, large differences between the flow rates calculated by means of each side of Eq. (8) will unavoidably lead to undesirable results. This conclusion has also been confirmed by the test results reported in Yu, Cua and Leo (2001).

337

Dow

nloa

ded

by [1

20.16

4.45.3

3] at

07:58

09 Ju

ne 20

15


Fig. 14 Effect of the width of the passages between

the overlapping portions of the blades on the flow of the liquid within an impeller (Yu, Cua and Leo, 2001).

Fig. 14 presents the distribution of the velocities within one of the impellers studied in Yu, Cua and Leo (2001). For the tested flow rate, the calculated correct distance between the blades at the inlet of the passages (Ref. 18: sub-section 30-2.1) is equal to the diameter of the circle inscribed (in Fig. 14) in one of the passages marked I. We see here that the distances between the blades at the inlets of the passage marked II are considerably larger than the calculated ones. This has generated huge zones of separation. It even gave rise to a significant reversal of flow back into the suction-eye of the impeller. In a radial-flow impeller, it is very easy to verify whether the geometry of the passages deviates too much from the condition expressed by Eq. (8). However, in a mixed-flow impeller, the task is much more complicated. In particular, in such an impeller, the distribution of the velocity components is usually drastically altered by the condition of radial equilibrium (Ref. 18: sub-section 16; Yedidiah, 2005b). Here, CFD has the potential of becoming the best or maybe even the only tool for optimizing the design. Of course, this is not the only problem which could be best handled with the aid of CFD. Below, we shall bring up a second case history in which only CFD is capable of making it possible to arrive at the optimum results.

7. IMPROVING THE EFFICIENCY OF A CERTAIN CLASS OF CENTRIFUGAL PUMPS

Decades ago, the author has developed a very successful method for designing sewage handling

pumps. From a commercial point of view, all pumps designed with the aid of that method are regarded as having the highest quality. However, when compared to the efficiencies attainable with conventional pumps of the same size and specific speed (Stepanoff, 1957: Fig. 5.1), there were significant differences between the attainable values and the results of tests (Yedidiah, 1997). Particularly, baffling were the extremely high efficiencies of the pump (Yedidiah, 1997: #6 in Table II). The expected peak efficiency for a conventional pump of that size and that specific speed is 84%. The test results (Fig. 15) for that pump show considerably higher magnitudes (over 89%). It took the author more than three decades to find an explanation for that mystery.

II

I I

II II

I I

2 1

1 m/s II 3 4

Quadrant 1 4

Impeller C

Hm

m3/hour

Fig. 15 Performance of a 5 sewage disposal pump, designed in 1958.

It has been demonstrated in Yedidiah (2003) and confirmed by results of tests discussed in Yedidiah (2001) that the head developed by a blade of an impeller can be expressed by the following equation:

)21(

))((CE 1n

nnq

nnvnqunvn

rRQ

RCEQQKCQ

+

+=

(9)

where nmun CotCUC = . The above equations imply that the head developed by an impeller-blade is determined by its geometry (not by its tip angles). This conclusion has also been corroborated by the results of independent tests carried out thousands of miles apart (Acosta and Bowerman, 1957; Saalfield, 1966). An impeller of a sewage disposal pump is provided with a pair of heavy blades, whose thickness varies along their total length. This

338

Dow

nloa

ded

by [1

20.16

4.45.3

3] at

07:58

09 Ju

ne 20

15


means that each side of a blade is determined by a different curve (Fig. 16). This fact, as is implied in Eqs. (9) and (10), causes each side of a blade to develop a different head. Calculations based on these equations have demonstrated that smaller differences between the heads developed by each side of the blades are always producing higher efficiencies (Yedidiah, 1997), as compared to what is expected from a conventional pump of the same size and specific speed.

Fig. 16 Typical shape of the impeller blades of a

sewage disposal pump.

The above findings provide us with a very important clue to improve the efficiencies of sewage disposal pumps. Also, with certain adaptations, they may become capable of assisting a pump designer in improving the efficiencies of any pump which is equipped with mixed-flow blades. However, the need to take into account many additional design parameters (as discussed in Ref. 18) makes it almost impossible to know if the solution is really the best possible one. Here, the use of CFD might be capable of providing extremely useful assistance. While CFD may be the only logical tool capable of optimizing certain design requirements of a centrifugal pump, it does not yet mean that its use will produce a pump which will perform better than any other existing ones. There exists a huge number and variety of factors which are capable of affecting the performance of a pump (Yedidiah, 1996 & 2006). Below, we shall discuss one of such factors.

8. EFFECT OF THE DISTANCE BETWEEN THE BASE-CIRCLE OF THE VOLUTE AND THE IMPELLER-RIM

Fig. 17 is a schematic presentation of the flow within a volute. When the distance between the impeller-rim and the base circle of the volute is equal to m, the liquid which is issued from the impeller at the angular position from the vertical centerline is barely capable to enter the discharge nozzle of the pump (Yedidiah, 2002). Now, let us see what will happen to the flow of the liquid which exits the impeller at the same angular position , if we shall reduce this distance m by, say, n. In that case, the liquid which exits the impeller at the same angular position would have been forced to re-enter the impeller at the position C (Fig. 17). This study implies that pumps of higher specific speeds need greater distances between the impeller-rim and the base circle of the volute (as the ratio between the meridian velocity components and the peripheral velocity components, at the impeller outlet, increases with specific speed). This has been confirmed in practice (Stepanoff, 1957: Fig. 7.8). However, the distance between the impeller-rim and the base circle of the volute is not the only parameter which affects the flow within an impeller. It is evident that each of the volute shapes shown in Fig. 19 will have a different effect on that distribution. This has been confirmed by the tests reported in Benra et al. (2007). Instead of a double volute, a diffuser ring has been used in those tests. The radial distance between the impeller-rim and the blades of the diffuser was very small. Nevertheless, these experiments have shown no effect of the circumferential position of the impeller blades in relation to the diffuser blades. The differences between the test results shown in Fig. 19 and the results reported in Benra et al. (2007) have a simple logical explanation. The discussion regarding Fig. 17 leads to the conclusion that the effects observed in Fig. 18 are primarily due to the spiral motion of the liquid within the casing. For such a spiral motion to develop, the casing has to be adequately wider than the outlet passages of the blades. In the pump tested in Benra et al. (2007) (a diffuser pump), the width of the casing was of the same order of magnitude as the outlet passages of the impeller (see Fig. 20). This explains the difference in the results of the tests shown in Fig. 18 and the results reported in Benra et al. (2007).

339

Dow

nloa

ded

by [1

20.16

4.45.3

3] at

07:58

09 Ju

ne 20

15


340

In an impeller with backward-curved blades, the returning liquid will usually penetrate only a short distance into the impeller passages before it will be expelled into the volute for a second time. In most cases, this means that the liquid will have to make at least one additional turn around the impeller before exiting the volute. In an impeller

with straight, radial blades, the liquid may even return all the way back into the impeller-eye. This has been confirmed by the experiments reported and discussed in Yedidiah (2002) and Yu, Cua and Leo (2001). This can be clearly seen in the impeller passages facing the tongues of the (double) volute in Fig. 18.

Fig. 17 Effect of the distance between the base circle of the volute and the impeller rim on the flow within an impeller (schematic).

Fig. 18 Effect of volute geometry on the flow within an impeller (Yu, Cua and Leo, 2001; Yedidiah, 2002).

n

C

m

Fig. 19 Some of the frequently used cross-sections of a volute.

(a) (b) (c)

VOLUTE DIFFUSOR

Fig. 20 Effect of casing geometry on the spiral motion of the liquid at the outlet of an impeller (schematic).

Dow

nloa

ded

by [1

20.16

4.45.3

3] at

07:58

09 Ju

ne 20

15


At present, we do not know of any method which is capable of determining the optimum relative distance between the impeller-rim and the base circle of a volute. Only CFD is offering logical tools which are capable of leading us to the desired solutions. The above study also illustrates the enormous amount of knowledge which is needed for arriving at a desired solution. At the present explosion of information, we cannot expect a single person to become an expert in more than one single area of engineering. The only obvious solution to that situation is teamwork. To arrive at meaningful useful solutions, there is a need for close cooperation and mutual understanding between experts in CFD and centrifugal pump specialists. Finally, an engineer also needs to keep in mind that the capability of a logical tool for solving a given problem does not always mean that its use is the best choice for the given task. This is illustrated by the following case history.

9. A CASE HISTORY IN WHICH THE USE OF CFD HAS PROVEN INFERIOR TO OTHER APPROACHES

An improved design tool means that it provides a faster, more reliable, and less expensive means for achieving the targeted objective(s). In many cases, only CFD might be able to satisfy the above requirements, particularly in situations where a significant amount of trial and error work is required. However, in practice, there exist many areas in which CFD offers very little advantage over other known design procedures. Such a case history is discussed below. Ballesteros-Tajadura et al. (2006) presented the results of a study in which CFD has been used in an attempt to reduce the noise generated by a centrifugal fan. This study has correctly predicted that the most intensive noise will occur at the passing frequency of the blades. The fact that the passing frequency of the blades is a major source of noise is known to the pump engineers for more than half a century (Yedidiah, 1996: 229231). What an engineer needs to know is whether the intensity of that noise will be within acceptable limits. The graphs presented in the published paper seemed to show a good agreement between the predicted and the tested intensities of noise. However, the author also presented tests results which showed that the predicted intensities were significantly different from the tested ones. This means that the approach used in Ballesteros-Tajadura et al. (2006)

can hardly be regarded as a reliable means for predicting the level of noise which a given design will develop. We can expect that experts in CFD will find a more reliable way for predicting the intensity of that noise in the future. In that case, it will be possible to predict the maximum noise levels of several different designs, and to select this one, which has been found capable to operate within the acceptable limits of noise. This, however, will not solve a different problem. To the best of the authors knowledge, it took a mainframe, high-speed computer 15 hours to arrive at the results presented in Ballesteros-Tajadura et al. (2006). If we shall add to this the time spent by the engineering and the auxiliary staff, and take into account that this has been spent on only one single design, we arrive at the conclusion that the use of CFD for predicting the levels of noise of a number of different designs is rather a very costly and time-consuming venture, considering that there is known a much simpler and by far less expensive way of reducing the noise generated at the passing frequency of the blades (Ref. 18: Figs. 11-17 and 11-18). The author has applied this method in 1965, long before CFD became a popular subject of study. This solution, while it can hardly be classified as being based on fluids dynamics, has proven to be so simple, effective and inexpensive that the author made it a standard feature of all his subsequent pump designs. Since the introduction of that design feature, the author has never again encountered any problem of excessive noise caused by the passing frequency of the blades.

10. CONCLUSIONS

Properly applied, CFD has the potential of providing the practicing engineers with enormous assistance in their quest for better designs. However, to know how, where and when the use of CFD is the best choice for a given task requires an in-depth knowledge and understanding of the problem(s) to be handled. At the present explosion of information, this requires close cooperation between the pump experts and the specialists in CFD. Such cooperation, however, can be effective only if each member of a team knows and understands what the others are doing. The presented discussion, as well as the studies in Yedidiah (2003, 2004, 2007 & Ref. 18), indicates that the needed mutual understanding between the pump experts and the specialists in CFD can be

341

Dow

nloa

ded

by [1

20.16

4.45.3

3] at

07:58

09 Ju

ne 20

15


significantly facilitated by considering the physical meaning of mathematical expressions.

NOTATION

B blade width mC meridian velocity component of the

liquid mavC average value of Cm, at any given radiusuC velocity component, in the direction of

U, of the liquid which has been directly affected by the blade

CE equivalent magnitude of Cu, related to the total flow of the pumped liquid

CU magnitude of Cu for the case when Cm = Cmav

E energy per unit of time (=power) g acceleration due to gravity H total head h head added to the liquid by a strip of a

moving blade K coefficient used in equations

L length of a blade element along the blade surface

oL length of a strip of a blade which projects into the eye of an impeller

n total length of a normal line which extends between two consecutive blades (Fig. 13)

sN specific speed: (m3/sec)0.5

(rev/min) / (m)0.75 Q flow rate of pumped liquid

qQ flow rate between two consecutive blades (=Q/Z)

bQ volume of liquid displaced by a strip of a moving blade

vQ volume displaced by a finite blade element R

R radius oS distance between the shrouds, measured

along the axis #10 respectively axis #6 (shown in Fig. 5)

S Distance from suction shroud, (relates to Figs 6, 7, and 8)

S length of an arc of a given radius R (relates to Fig. 13)

T time t pitch of blades U peripheral velocity of a blade V velocity of the liquid

Z,Y,X location, determined by Cartesian coordinates

zZ, number of blades b blade angle (=w+) w angle of relative velocity

angle of incidence density angular speed radians/sec efficiency blockage due to finite thickness of the

blades head coefficient = gH / U22 flow coefficient = Cm2 / U2 Subscripts 0 refers to the impeller-eye 1 refers to the leading edge of a moving

blade 2 refers to the outlet tip of a moving bladei refers to the inlet tip of a stationary

blade ou refers to the outlet tip of a stationary

blade av average value based on the magnitude

of Cmav b refers to a blade n refers to the n-th element of a blade n-1 refers to the preceding blade element R refers to the radius, at which the given

dimension was taken x,y,z refers to the directions of Cartesian

coordinates

REFERENCES

1. Acosta AJ, Bowerman RD (1957). An experimental study of centrifugal pump impellers. Trans. ASME J. of Fluids Eng. 81:18211838.

2. Ballesteros-Tajadura Rafael et al. (2006). Prediction of the aerodynamic noise generated by a centrifugal fan. ASME-Publication FEDSM2006-98507.

3. Benra FK et al. (2007). Measurement of the periodic flow field in a radial diffuser pump by the PIV method. ASME-Paper FEDSM2007-37400 [CD-ROM].

4. Hureau F et al. (1993). Study of internal recirculation in centrifugal impellers. ASME-Publication FED. Vol. 154, 151157.

5. Prang AJ, Oates DM (1971). Suction Chambers for In-line Centrifugal Pumps with Inducers. Worthington, Canada.

6. Saalfield K (1966). Einige neuere Gedanken zur Laufradberechnung von radialen und halbaxialen Kreiselpumpen (in German). KSB-Technicsche Berichte, KSB-Company, Frankenthal (Pfalz), Germany. Aug. 1966, 11.

342

Dow

nloa

ded

by [1

20.16

4.45.3

3] at

07:58

09 Ju

ne 20

15


343

7. Stepanoff AJ (1957). Centrifugal and Axial Flow Pumps. John Wiley & Sons, Inc., New York.

8. Yedidiah S (1996). Centrifugal Pump Users GuidebookProblems and Solutions. Chapman & Hall, New York. (At present: Springer Science and Business Media, Inc., Norwell, MA).

9. Yedidiah S (1997). How to design more efficient pumps. ASME Paper FEDSM97-3383.

10. Yedidiah S (2001). Practical applications of a recently developed method for calculating the head of a rotodynamic impeller. Proc. Inst. Mech. Eng. Vol. 215, Part A, 119131.

11. Yedidiah S (2002). Effect of pump geometry on the flow within a centrifugal impeller. Proc. Inst. Mech. Eng. Vol. 216, Part C, 11451149.

12. Yedidiah S (2003). An overview of methods of calculating the head of a rotodynamic impeller, and their practical significance. Proc. Inst. Mech. Eng. Vol. 217, Part E, 221232.

13. Yedidiah S (2004). A bridge between science and practical engineering. ASME Paper HT-FED2004-56011 [CD-ROM].

14. Yedidiah S (2005a). An updated study of recirculation at the inlet of a rotodynamic impeller. ASME-Paper FEDSM2005-77048.

15. Yedidiah S (2005b). Certain effects of blade-geometry and of inlet-recirculation on the distribution of the meridian velocities at the impeller-outlet. ASME-Paper FEDSM2005-77041 [CD-ROM].

16. Yedidiah S (2006). Translating equations into their physical meaning, as an effective tool of engineering. ASME-Paper FEDSM2006-980012 [CD-ROM].

17. Yedidiah S (2007). Application of CFD to the design of centrifugal pumps. ASME-Paper FEDSM2007-37349 [CD-ROM].

18. Yedidiah S. Centrifugal Pumps: Theory, Design, Use, Diagnostics, and Problem-solving (unpublished manuscript).

19. Yu SCM, Cua LP, Leo HL (2001). The angle-resolved velocity measurements in the impeller passages of a model biocentrifugal pump. Proc. Inst. Mech. Eng. Part C. Journal of Mechanical Engineering Science 215(5):547568.

Dow

nloa

ded

by [1

20.16

4.45.3

3] at

07:58

09 Ju

ne 20

15

List of FiguresFig. 1 Centrifugal pump with side-inlet suction nozzle.Fig. 2 Suction chamber used in the tests reported in Fig.3 and Fig.4.Fig. 3 Distribution of the axial and of the tangential velocity components at the inlet of the tested pump at 56 m3/hr, when tested as a straight end-suction unit and with the suction chamber shown in Fig.2.Fig. 4 Performance of the experimental pump, when tested as a straight end-suction unit and as a side-inlet pump with the suction nozzle shown in Fig.2.Fig. 5 Axes, along which the normal velocity components shown in Figs.6, 7 and 8 were measured.Fig. 6 Shroud-to-shroud distribution of the normal velocity components upstream of the inlet edges of the blades along axis 10 shown in Fig.5 at optimum flow and at 0.41 of the optimum flow.Fig. 7 Shroud-to-shroud distribution of the normal velocity components upstream of the outlet edges of the blades along axis 6 shown in Fig.5 at optimum flow and at 0.41 of the optimum flow.Fig. 8 Shroud-to-shroud distribution of the normal velocity components along axis 10 shown in Fig.5 at different fractions of the optimum flow rate.Fig. 9 Effect of the blade parts which project into the eye of the impeller on recirculation.Fig. 10 A simplified model of the effect of a strip of a blade which projects into the eye of an impeller on the intensity of recirculation. Fig. 11 Distribution of the tangential and of the axial velocity components at the outlet of two different side-inlet-suction nozzles (nozzle C and nozzle D) at two different flow rates.Fig. 12 Performance of the same pump when tested with suction nozzle C and suction nozzle D.Fig. 13 Schematic flow between impeller blades of a centrifugal pump (hypothetical).Fig. 14 Effect of the width of the passages between the overlapping portions of the blades on the flow of the liquid within an impeller (Yu, Cua and Leo, 2001).Fig. 15 Performance of a 5 sewage disposal pump, designed in 1958.Fig. 16 Typical shape of the impeller blades of a sewage disposal pump.Fig. 17 Effect of the distance between the base circle of the volute and the impeller rim on the flow within an impeller (schematic).Fig. 18 Effect of volute geometry on the flow within an impeller (Yu, Cua and Leo, 2001; Yedidiah, 2002).Fig. 19 Some of the frequently used cross-sections of a volute.Fig. 20 Effect of casing geometry on the spiral motion of the liquid at the outlet of an impeller (schematic).

1. INTRODUCTION2. EFFECT OF A PAIR OF FORCED VORTICES AT THE PUMP INLET ON ITS PERFORMANCE3. THE PHYSICAL MEANING OF EULERS EQUATIONS4. EFFECTS OF BLADE GEOMETRY ON INLET RECIRCULATION5. EFFECT OF THE STRENGTH OF FORCED INLET-VORTICES ON THE NPSH REQUIREMENTS OF A PUMP6. A DESIGN PROBLEM IN WHICH CFD MIGHT PROVE EXTREMELY USEFUL7. IMPROVING THE EFFICIENCY OF A CERTAIN CLASS OF CENTRIFUGAL PUMPS8. EFFECT OF THE DISTANCE BETWEEN THE BASE-CIRCLE OF THE VOLUTE AND THE IMPELLER-RIM9. A CASE HISTORY IN WHICH THE USE OF CFD HAS PROVEN INFERIOR TO OTHER APPROACHES10. CONCLUSIONSNOTATIONREFERENCES

19942060.2008

Documents