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Scientific Bulletin of the

Politehnica University of Timisoara

Transactions on Mechanics Special issue

The 6th International Conference on

Hydraulic Machinery and Hydrodynamics

Timisoara, Romania, October 21 - 22, 2004

THE PRINCIPLE OF NEGLECTING UPSTREAM REACTIONS

rpd . FY, Docent*

Department of Hydro- and Thermo-machinery

The University of Miskolc

*Corresponding author: Szent Dont u. 33. Pilisborosjen, 2097, Hungary

Tel.: (+36) 26 336931, Fax: (+36) 26 336931, E-mail: arpad.fay@axelero.hu

ABSTRACT

This paper presents a practical principle, which

states that in the case of modifying a flow boundary(e.g. adjusting a blade angle), upstream of the modi-fication the flow is affected to a very small extent,what is usually negligible, while the downstreameffect of the modification is large, usually notnegligible. This is not a new statement; in specialsituations many researchers used it. Nevertheless,the author felt that an analysis of well-knownexamples from this aspect may be useful both forresearch and for teaching.

Examples when this principle is applicable:Flow around a body placed into uniform flow

(plates, airfoils, etc.)Blade cascades in wind tunnelsTesting the hydraulic losses of pipe-like elements

(elbows, valves, etc.)Reactions of Kaplan turbine runner blades on

their inlet velocity conditionsThe problem of spontaneous swirl caused by

pump impellers on the approaching flowCases when this principlefailed:

The guide vane opening of a Kaplan turbine affectsthe flow in the spiral casing

The flow conditions in the pump volute affect the

flow in the impellerPump testing, with special considerations.

KEYWORDS

Hydro machines, hydraulics, flow losses

NOMENCLATURE

c [m/s] absolute velocity at the runner (Fig. 4)v

r

[m/s] velocity before modification (Fig.1, 2)v r

[m/s] velocity after modification (Fig.1)E [-] error term of modification, Eq. (1)

H [m] headQ [m3/s] discharge

Subscripts

1u peripheral direction, upstream of runner, Fig. 41m meridional direction, upstream of runner, Fig. 42u peripheral direction, downstream runner, Fig. 42m meridional direction, downstream runner, Fig. 41, 2 front and back side, Fig. 7small, opt, large small, optimal, large, Fig. 8

ABBREVIATION

IEC International Electrotechnical Commission

1. INTRODUCTIONIn hydro-machinery practice one is frequently faced

with flow boundary modifications. Some of theseare intentional (e.g. adjusting a blade angle), whilesome modifications are unwanted (e.g. facing witherroneous blade shapes). In such cases the principleof neglecting upstream reactions is a potential, usefultool. This is based on the fact that upstream of themodification the flow is only slightly affected.Whether a small change in the velocity is negligibleor not, depends on the accuracy requirements of thecalculation. In many practical cases, however, theupstream reaction of the modification proves to benegligible. This largely simplifies the analysis (e.g.the calculation of the changes in the characteristicscaused by the modification). Many researchers mayhave used this principle in the past. Nevertheless, itseems that focusing attention to its features, and tothe cases of its failures, may be useful.

2. INTRODUCTORY EXAMPLESTo formulate the principle in a more specific way,

some simple flow configurations are shown in Fig. 1.On the upper part of Fig. 1 a uniform flow is seen

above a plane. A frictional, turbulent (i.e. a real)

flow is considered. In the middle of Fig.1 the flowboundary is modified by a hump. The shape of the

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Figure 1. Uniform flow, modification of the flowboundary without and with flow separation

hump gives the impression that no flow separationtakes place on the hump. At point A (Fig. 1) whichis not too near to the hump, the parameter

v

vv

r

rr

=E (1)

based on the absolute values of the vectors, gives ameasure of the effect of the modification.

Looking at the flow configuration with this hump,one may have the feeling that the flow can be wellapproximated with incompressible, frictionless flow.Based on the usual training with such classical flows, itcan be stated that in this flow configuration presumablyE is small at Point A. With not too strict accuracyrequirements, E may benegligible.

Point A is upstream of the hump. Point B in Fig. 1,the mirror of A over the symmetry axis, is situateddownstream. Since the frictionless flow (in the middleof Fig. 1) is symmetrical,Eis the same for B as forA, and so it is similarly negligible at B.

The situation is, however, different on the lowerpart of Fig. 1. In this case the shape of the barrier

implies flow separation downstream the barrier.Vortices are shed, the flow character changed. Whileat point A the effect of the modification may still beneglected, at point B parameterE, calculated with theaverage (turbulent) velocities, might be quite large,and so in a large area downstream, in the wake andin its neighborhood, the effect of the modification isnot negligible.

In both modified flows of Fig. 1 the upstreamreaction of the boundary modification may beneglectedin a large area. This is what the principlestates. In contrast to this, it is also seen that the

downstream effect of the modification may not benegligible, due to flow separation.

3. BODIES IN WIND TUNNELSBlunt bodies placed into nominally uniform flows

of wind tunnels, such as the symmetric profile inFig. 2, have usually considerable wakes. The sameapplies for such bodies as for the barrier in Fig. 1.

Figure 2. Symmetric profile placed into uniform flowin wind tunnel, blade cascade in the wind tunnel

In the lower part of Fig. 2 a blade cascade isplaced into the wind tunnel. The flow upstream ofthe cascade changes only slightly. Downstream of

the cascade, however, the flow direction is largelyaffected. Thus, while the upstream reaction of the

blade cascade may be neglected, the downstreamreaction surely may not, since the aim of thecascade is just to create the flow deflection.

4. PIPE-LIKE ELEMENTS IN HYDRAULICS

In Fig. 3 a bend is shown in a pipeline. A mercurymanometer indicates that checking of its loss coeffi-cient is intended. It is known from practice that themanometer tapping should be placed away from the

bend. The necessary length upstream of the bendmay be rather small. The downstream length shouldbe, however, quite large, in order to allow smoothingout of the flow disturbance caused by the bend.These are in accordance with the above principle.

If the discharge in the pipe of Fig. 3 is intended tobe measured with an orifice plate, then the minimumstraight length of the orifice from the bend can betaken from the standards [1]. For example, using anorifice of diameter ratio 0.6, the zero additionaluncertainty length is: 7 diameters from the bend ifthe orifice is situated upstream of the bend, and 18

diameters if the orifice is situated downstream of it.

Figure 3. A bend in a pipeline, equipped with amanometer for loss measurement

With less strict requirements, using 0.5 % additionaluncertainty, these lengths are [1]: 3.5 diameters

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upstream, and 9 diameters downstream. Thus, theflow region, where the upstream reaction of the bendis negligible (as far as the application of an orifice isconcerned) depends on the accuracy requirement. Itis also seen from the numerical values that the down-stream reaction is much larger.

5. THE EFFECT OF KAPLAN RUNNERBLADES ON THE APPROACHING FLOW

In the past the author made velocity traversing tests[2], with 3-hole cylinders, upstream and downstreamof a Kaplan model runner, in a test configurationshown in Fig. 4.

Figure 4. Velocity traversing with 3-hole cylindersupstream and downstream of a Kaplan model

runner

It was important to make such tests in order to

check the design parameters of the runner blades. Atthe best efficiency point of the turbine the velocitydistributions of Fig. 5 were obtained. The velocitydistributions were measured in many operatingconditions of the turbine (covering the range ofmodel efficiency above 75 per cent).

In evaluating the vast amount of the test results itwas surprising to see that at the same opening of theguide vanes (as the opening of the best efficiency

point, for which Fig. 5 is valid), the proportions ofthe c1u, c1m distributions were the always the same,independently of the runner speed. The tests were

made with H = constant, but recalculating the veloci-ties with the similarity laws for Q = constant, justthe same velocities were obtained as in the upper

part of Fig. 5. Thus the speed of the runner did notaffect the velocity distributions upstream of therunner (within the test accuracy). Then the bladeangle was changed, and at the same opening andsame discharge, again the same velocities wereobtained at any speed. Then, the runner blades wereremoved, and the velocity traversing was made withthe bladeless turbine, and at the same opening thisresulted again the same velocity distributions. Thus

it was concluded that the Kaplan runner did not affectits upstream flow conditions. Neither the runner

speed, nor the blade angle affected the inflowconditions, and not even the presence of the blades.

Figure 5. Test results of the velocity traversing atthe best efficiency point of the Kaplan model turbine.

The opening of the guide vanes naturally affectsthe c1u, c1m distributions, but for a given modelturbine the opening is the only parameter whichaffects the proportions of these velocities.

A generalization of this conclusion may also beattempted. It seems that the usual blade shapes ofKaplan or bulb turbines (excluding extraordinarycases) do not affect their inlet flow conditions.

This conclusion largely simplifies both the designand the experimental work. Knowing this, one needs

to measure the upstream velocity distributions onlyat a few openings. From these, the inlet velocitytriangles can be determined, and these are valid forany blade shape, at any operating condition.

Thus, in this case the upstream reactions of theKaplan blades were negligible.

6. THE PROBLEM OF THE SPONTANEOUSSWIRL UPSTREAM OF PUMP IMPELLERS

In pump impeller design it is a crucial questionwhether spontaneous swirl (or prerotation) should

be assumed upstream of the impeller or not. Someof the designers have a philosophy that the impeller

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creates a spontaneous rotation upstream of the blades.The smaller the specific speed the larger the sponta-neous prerotation what they assume. Other designersuse zero prerotation upstream of the impeller.

Csanady [3] presented an elegant proof that rotatingblades cannot create spontaneous swirl. The basicidea follows from Fig. 6. Apply the moment of

momentum theorem for the fluid mass bounded bythe intake pipe and Sections 1 and 2. At Section 1the fluid enters without rotation. On the pipe wallthe fluid friction is very small, and its direction isaxial. Therefore the moment of the momentum overSection 2 should also be zero. (Some fluctuationsmay appear in the velocities at Section 2 due to the

passing blades but the average torque of the impulsiveforces should be zero.) This implies that the rotatingimpeller blades cannot create prerotation upstreamof the impeller.

Figure 6. Intake pipe section of a pump impeller

The test results, however, showed small butmeasurable prerotation upstream several radial-flow

impellers [4]. This contradiction between theoryand tests created a puzzle for the author for a longtime, solved at last by the following considerations:Upstream of the pump impeller the clearance flow

enters into the inlet pipe with considerable rotation,and carries a moment of momentum into the inlet

pipe. Mixing with the main flow this creates someprerotation.

When the pump operates at a very small discharge, below a certain limit value a backflow appearsflowing from the impeller into the inlet pipe at its

periphery. This rotating backflow brings a momentof momentum into the inlet pipe, where mixingwith the main flow creates considerable prerotation.

The limit discharge of the backflow is usuallysmall. In most cases the backflow region is found

below the normal operating range of the pump. Abovethe limit value only the clearance flow causes pre-rotation. Cs. Fay [5] and Lnzmann [6] discussed ofhow different clearance geometries affected the pumpcharacteristics. Their results are in accordance withthis concept of the prerotation.

As a theoretical exercise, let us assume that the

pump operates in the normal discharge range (without backflow) and the clearance flow is zero. (With

special geometry the clearance flow can be reduceddramatically.) Then no prerotation occurs. Thus therotating impeller blades does not create spontaneous

swirl upstream of the impeller. The prerotation, if itappears, is due to other reasons.

It is seen again that the upstream reaction of therotating impeller blades is negligible, like for the

turbine blades above. The prerotation, when it occurs,is caused by the downstream effect of the clearanceflow, and by the downstream effect of the backflow.

Figure 7. Flow boundaries of a Kaplan spiral casing

7. THE GUIDE VANE OPENING AFFECTS THEFLOW IN A KAPLAN SPIRAL CASING

One of the cases when the upstream reaction isnot negligible concerns Kaplan turbines.

In Fig. 7 a semi-spiral casing of a model turbine isshown. At one of its sections a mercury manometerindicates the intention to make index test by theWinter-Kennedy method [7]. This method assumesthat the discharge is proportional to the square rootof the differential pressure. However, it is known [8],that this is not satisfied for any section of the spiralcasing. Following the recommendations of the IECmodel test code [8], several sections were preparedon the model turbine for the pressure measurements.As expected, it was found that the pressure differentialsdepended not only on the discharge but also on theopening of the guide vanes. Thus, it was concludedthat the upstream effect of the guide vanes cannot beneglected.At design point the discharge from the spiral into the

stay-vane row is rather uniform (along the periphery).

Thus, at equal arcs the same flow enters: Q2 = Q1,(Fig. 7). However, at an opening away from the design

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value, experimental evidence shows that these dis-charges are not equal: Q2Q1. This is due certainlyto the fact that the flow resistance of the guide vanesvaries along the periphery.

Therefore the flow velocities at the casing wall,and also the pressure differentials at the varioussections are a function, besides of the discharge,also of the guide vane opening. Fortunately, for theturbine tested, the required proportionality was nearlysatisfied at one of the sections, and this section wassuitable for the Winter-Kennedy method.

It may be concluded that the guide vane openinglargely affected the flow in the spiral casing, thoughit is situated upstream, and this effect was notnegligible if the application of the Winter-Kennedymethod was in view.

8. THE FLOW CONDITIONS IN THE VOLUTE

AFFECTS THE FLOW IN A PUMP IMPELLERAnother case, when the upstream reaction is notnegligible, is the effect of the flow conditions of a

pump volute on the flow in the pump impeller.

Figure 8. A volute pump and its characteristics atconstant speed

When the volute pump of Fig. 8 operates at itsoptimum point (Q = Qopt), assuming proper volutedesign, at points A,B,C, and D (Fig. 8) the pressuresare more or less the same. This uniform pressuredistribution assures uniform discharge from theimpeller into the volute.

In design, the spiral is regarded sometimes as asingle vane of a vaned diffuser. When operating atlarge discharge (Q = Qlarge, Fig. 8), the attack angle

of the tongue is larger than its optimum value.Therefore the pressure at A is larger than at C. Thismeans on one hand that the discharge from theimpeller is not uniform, and on the other hand that aradial force arises on the impeller.

Similar statement can be made for the operation atsmall discharge (Q = Qsmall) but the direction of the

pressure differential and the radial force is opposite.The author has seen a case in the past when this

radial force was large enough to destroy thebearings of the pump. Thus, in this case, the flowconditions in the volute affected the flow conditions

in the impeller, and so the upstream reaction of thevolute was not negligible at all.

Figure 9. Pump testing

9. PUMP TESTING

In pump testing (Fig. 9), when the valve body isadjusted to a new position, then the pump works ata new operating point on its characteristics. Thus, in

this case the upstream effect of the valve may not beneglected. However, in the pipe between the pumpand the valve the upstream effect of the valve issmall. The proportions of the velocity distribution atthe discharge flange of the pump are affected onlyslightly. It is only the pressure level variation whichaffects the pump. If a booster pump were applied to

produce the same pressure variation at the suctionflange of the pump, then the original flow conditionsare essentially restored in the pump (unless cavitationdisturbs the picture). Thus, in this case there exists ameans to compensate for the pressure variation, andthe principle of neglecting upstream reactions is still

valid.

10. CONCLUSIONIn many flows several structural elements can be

distinguished, and the fluid passes through theseelements in a sequence. The surface between neigh-

boring elements is called here as interface. Themodification of the flow conditions is produced inthis paper mainly by a change in the flow boundary(Sections 2 to 7 and 9). However, one example is

shown here, when not the boundary but the flowangle changed at the interface (Section 8).Several practical examples are shown when the

upstream reactions may be neglected(Sections 3 to 6).Some of the fundamental technical tasks are included.It is particularly important that rotating blades donot affect their inflow conditions.

There are, however, warning examples when theupstream reactions may not be neglected (Sections7 to 9). It seems that the size and the shape of theinterface matters. In the examples when the principleis applicable (Sections 4 to 6) the interface is a simple

circle, while when the principle fails (Sections 7 and 8)

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the interface is a large circumferential surface. InSection 9, for the first sight the principle fails, butwith some manipulation the validity of the principlemay be assured.

The main conclusion of this paper is that theprinciple of neglecting upstream reactions may beused in many cases simplifying both the theory and

the experimental work. However, the application ofthe principle should be verified in each case either

by tests or by estimates.

REFERENCES

1.International Standard, ISO 5167-1 (1991) Meas-urement of fluid flow by means of pressuredifferential devices Part 1: Orifice plates, nozzlesand Venturi tubes inserted in circular cross-section conduits running full. Publ. by ISO.

2.Fay A. A. (1969) Explanation of the difference in

the moment of momentum of axial-flow impellersor runners and the shaft torque of axial-flowturbomachines. Ganz Mavag Publications No. 42.Budapest, pp 89-95.

3.Csanady G.T. (1964) Theory of Turbomachines,McGraw-Hill Book Company, New York, SanFrancisco, Toronto, London. LCCC Number: 63-21475, 23456789-MP-10987, 14877

4.Hajd S. (1957) Prerotation upstream radial-flow pump impellers (in Hungarian), Ph.D. thesis,Hungarian Academy of Sciences

5.Fay Cs. (1995) The clearance geometry of pumpimpellers affects their cavitation performance,Proceedings of the 10th Conference on FluidMachinery Budapest. Ed. Szab ., Budapest, byGTE, Paper 23, pp 187-190

6.Lnzmann K. (1988) Untersuchungen an Kreisel-pumppen mit Schrgspalt. Pumpentagung Karlsruhe1988, Section B4

7.International Standard, IEC 41 (1991) Fieldacceptance tests to determine the hydraulic

performance of hydraulic turbines, storage pumps

and pump turbines. Publ. by IEC8.International Standard, IEC 60193 (1999) Hydraulicturbines, storage pumps and pump-turbines Modelacceptance tests. Publ. by IEC