the performance of an axial-flow pump

874

THE PERFORMANCE OF AN AXIAL-FLOW PUMP By E. A. Spencer, B.Sc. (Eng.), Ph.D. (Associate Member)*

Tests were made on an 11-inch diameter axial-flow propeller pump with impeller and guide blades designed for free vortex conditions, using as a basis the modified aerofoil theory. The best overall efficiency obtained was 82 per cent. Apart from head-flow and efficiency characteristics, measurements were made of velocities and yaw angles within the pump at the design flow of 6 cusecs. and these showed where departures from the theoretical assumptions occurred.

Head-flow characteristics were obtained for various impeller blade-tip clearances from 0.015 to 0.060 inch (0.6 to 2.4 per cent blade height) and it was deduced that secondary flows were not confined to the tip region alone, but extended across the whole annulus.

The pump was on an open circuit, so that cavita+on tests were limited. Nevertheless, methods of increasing the resistance to cavitation susceptibility are considered.

I t was concluded that despite the fact that some of the assumptions made in the theory are invalid, this method of design may be used with confidence for pumps in the specific speed range of approximately 8,000.

INTRODUCTION THE AXIAL-FLOW PROPELLER PUMP has a range of applications, where large quantities of water are to be pumped against low heads. Examples are in drainage, de-watering docks, circulating cooling water in power stations and for sewage disposal. In the past thirty years, there have been considerable developments in their design and construction. These pumps are now manufactured in a wide range of sizes, usually between 4 and 72 inches diameter, and specific speeds, ranging from 6,000 to 15,000.

The tendency in the early days was to follow centrifugal pump design methods and base the blading design on velocity mangles, obtained from the simple Euler theory. Empirical modifications were used to take into account the deviations from the theory found in practice. For instance, the theory gives no indication of the length, or number, or shape of the blades between inlet and outlet fluid directions.

Numachi (1929)t applied aerofoil theory to the design of propeller pumps, using modifications of the general aerodynamic theory which had been developed considerably earlier by others. It was assumed that the actual blade was replaced by a series of aerofoil sections, each layer being independent from those adjacent. An aerofoil of any arbitrary shape will experience a VXng force when suitably placed in a velocity field, and if this force can be predicted,

The M S . of this paper was first received at the Institution on 10th October 1955. For a report of the meeting, in London, at which this paper was presented, see p . 908. * Senior Scientific Oficer, Fluid Mechanics Division, Mechanical Engineering Research Laboratov, East Kilbride. t An alphabetzcal list of references is grven in Appendix II .

then the pressure developed by the blade element can be calculated. With the steady accumulation of data on aerofoil characteristics, ofien including the effect of Reynolds number, the use of this method of pump design became increasingly practical. OBrien and Folsom (1939) give details of the method and apply it to the design of a pump for a specific duty.

The impeller blades impart a rotational spin, or whirl, to the fluid. Since the ratio of whirl velocity head/total head developed by the pump is relatively high, it is of major importance that this energy be regained and utilized. To do this a stationary blade system must also be employed and the same difficulties apply if the simple Euler theory is used. In a de Laval pump (Anon 1933) outlet guide blades were used, but these were merely axial-deflecting plates before the discharge bend and recovery of pressure head must have been small.

Stationary blade rows may be either upstream or downstream of the impeller. In the former case, the fluid is given an initial whirl in the opposite direction to the rotation of the impeller and this is removed when the fluid passes through the impeller. In the latter case, the outlet guide blades straighten the flow after it leaves the impeller. Numachi (1929) showed that for the same rotational speed, head and flow, inlet guiding was basically less efficient than the use of straighteners. More recently Marples (1954) concluded from experiments on a fan with upstream blades, that the angle setting of the guides was more critical and the efficiency curve was very peaked.

Patterson (1944) describes the use of axially symmetrical straighteners for ducted fans which, for small whirls, act

at Seoul National University on April 9, 2015pme.sagepub.comDownloaded from

THE PERFORMANCE OF AN AXIAL-FLOW PUMP

independently of the amount of rotation behind the fan. In general, however, the straightener blade row will only produce maximum recovery at the design conditions. Away from those conditions, there will be entry losses and usually underguiding.

In the experiments now described, a set of inlet guide blades was used in conjunction with the straightener row after the impeller. These inlet blades were thin symmetrical aerofoil sections, mounted axially to ensure good entry conditions to the impeller. The flow direction upstream of the impeller was axial and the whirl produced by the impeller was removed in the downstream blade row.

Notation a C

ck CL. g H N P

P I

POP r

U v,

S

W

B

Y 4 *

Mean axial velocity of fluid through pump annulus. Chord length of blade element at radius r. Cavitation number. Aerofoil section lift coefficient. Gravitational acceleration. Head developed by pump. Number of blades. Static pressure in undisturbed stream ahead of

Maximum suction pressure on blade surface. Water vapour pressure. Radius. Blade spacing at radius I(= 2nrlnr>. Tip speed of impeller blades. Relative fluid velocity across blades at radius r. Fluid whirl velocity component after impeller at

Blade angle between chord line and rotational direction

Ratio of lift/drag coefficients on aerofoil section. Flow coefficient (= a/U). Head coefficient (= 2gH/U2).

impeller.

radius r.

at radius r.

1 cusec. = 374 gal. per min.

EXPERIMENTAL APPARATUS The blades were tested in a self-contained open circuit with a flow path of about 40 feet (Fig. 17). Water was pumped from an open cylindrical tank of approximately 250 gallons capacity and discharged through a control valve and 11-inch diameter piping. The return pipe to the tank was always run drowned to prevent air bubbles being carried into the circuit. Power was supplied to the pump from a 25-h.p. electric dynamometer, having a speed range from 1,050 to 1,400 r.p.m.

Details of the pump are shown in Figs. 18 and 19. The upper-half casing could be removed to provide access to the blading. The impeller and guide blades were enclosed in t inch liners, machined to 11-inch internal diameter. Clearances between the propeller blade tips and the liner were measured with feeler gauges. The blades, made from free-cutting brass, were copy machined from a master and hand finished to templates. The profile was finished to a tolerance of 0.005 inch.

Fig. 17. Axial-flow Pump Test Circuit

To obtain good entry conditions to the pump unit, the intake from the tank was screened and a 15-deg. contraction installed before the straight length into the pump. Fig. 19 shows the transition to the 6-inch hub diameter and the position of the inlet guide blades.

INSTRUMENTATION The shaft speed was measured with a tachometer. The torque output from the driving motor, which was mounted on trunnions, was measured with brake weights, on a lever arm of 1 ft. 9 in., and read to 2 02.

The overall pressure rise was taken between tappings on the suction side 8 inches upstream from the pump, and on the discharge side 18 inches downstream from the straightener blades. Differential pressure readings were observed on a mercury manometer which could be read to 0.02 inch.

The flow was measured with two +-inch diameter Pitot tubes of a N.P.L.-type, installed in the upper pipeline 8 diameters from the bend. Turning vanes were welded in the two vertical bends and two he-mesh screens were mounted at the beginning of the straight length to obtain

Fig. 18. Experimental Axial-flow Pump


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\ \ \ / J /// n

Fig. 19. Plan View of Experimental Pump

a uniform velocity dismibution. The distribution was measured on two diameters at right angles and correlated with the Pitot tube readings at the three-quarter radius points. The values of integrated flow agreed within 1 per cent with that from an orifice plate. The three-quarter radius readings were used normally to determine the flow, check calibrations being carried out occasionally.

Apart from the measurements described above, flow conditions within the pump were determined at three stations. Two of these were immediately upstream and downstream from the impeller and the third was 10 inches past the straightener blades. Flow angles were found with a small claw-type yaw meter and stream velocities with a swan- necked Pitot tube. The accuracy was about f l deg. on angle and about 1 per cent on velocity.

BLADING DESIGN In applying the aerodynamic theory, various simplifying assumptions have been made. The mutual independence of blade layers has been mentioned, and for free-vortex- blading constant efficiency and constant head are assumed for all sections. This is to preserve radial-pressure equilibrium. The theory is a combination of momentum actuator disk theory and blade element theory. A number of authors, von Mises (1945), Keller and others (1937), and Numachi (1929), have described these in detail. Both Patterson (1944) and OBrien and Folsom (1939) give applications to the design of fans and pumps. These references were used as the basis for the deign of a set of propeller and straightener blades for the present investigation.

The hub and tip diameters for the experimental pump were fixed at 6 and 11 inches, giving a hub/tip ratio of 0-56. At the design flow of 6 cusec., based on the mean axial velocity in the annulus in front of the impeller, the calculated

head was 16 feet. With a speed of 1,300 r.p.m., the specific speed of the pump was therefore 7,700. The impeller tip speed was 62.4 feet per second. The number of blades was chosen as 4 to give reasonable chord lengths.

Calculations were made to determine blade angle and chord length at +inch intervals across the 25inch blade. Between these successive radii the blade was smoothly graded so that there were no abrupt changes in geometry. Calculated blade efficiency at design flow varied between 93 and 97 per cent from tip to hub. This resulted since the lift coefficient chosen for the tip was smaller than at the hub and, consequently, the dragllift ratio, on which the blade efficiency mainly depends, was greater.

The aerofoil section used was the Royal Air Force R.A.F. 6, Section E, tested by Williams, Brown, and Smyth (1937) at various Reynolds numbers. It exhibited good performance characteristics and the flat undersurface eased manufacture. Fig. 20 shows a frontal view of the impeller abd sections through the blade. The projected blade area was 71.5 per cent. Further details are given in Tables 3 and 4.

The straightener blades, six in number, were designed with constant chord length. A thinner section, National

Table 3. Details of Propeller Blades

Aerofoil 1 Chord, inches Blade angle, I deg. R.A.F. 6E 28.7 R.A.F. 6E 1 2::; I 23.5

4.25 R.A.F. 6E 5-12 19.6 4.75 R.A.F. 6E 1 5.22 16.6 5-25 I R.A.F. 6E 1 5.29 I 14.3

The blade angle is measured from the rotational diredon.


THE PERFORMANCE OF AN AXIAL-PLOW PUMP a77

Advisory Council for Aeronautics (N.A.C.A.) 6306, tested by Jacobs, Ward, and Pinkerton (1933), was chosen for these blades.

Table 4 . Details of Straightener Blades

Radius, inches 1 Aerofoil Chord, inches Blade angle, i deg. 66.4 1 71.0 3.25 1 N.A.C.A. 6306 3.75 N.A.C.A. 6306

4.25 N.A.C.A. 6306 5.00 74.3 4.75 (N.A.C.A. N.A.C.A. 63061 6306 5.25 1 77.0 79.1

EXPERIMENTAL RESULTS

Tests were run over the dynamometer speed range from 1,050 to 1,350 r.p.m. with the blades mounted in their design setting and with a tip clearance of 0.015 inch. It was not possible, however, to detect any Reynolds number effects and, thereafter, tests were normally made at a speed of about 1,300 r.p.m.

SECTION 5 AA

Two parameters widely used in presenting performance curves are the non-dimensional head and flow coefficients :

These coefficients make it possible to compare the characteristics of fans and pumps on the same dimensionless basis. Scales of equivalent head and flow at 1,300 r.p.m. are given in the graphs.

Overall Pump Performance A typical performance curve for the pump is given in Fig. 21. The efficiency plotted is the gross efficiency which includes mechanical friction losses as well as hydraulic losses. The loss in the gland packing where the shaft entered the pump was measured with the pump running in air, without blades. An average of 0.7 h.p. was absorbed at 1,300 r.p.m.; this varied, depending on the tightness of the tallowed hemp packing, By subtracting this from the brake horsepower, it may be deduced that the hydraulic efficiency at the best point was about 86 per cent, and the loss incurred in the straightener and the passages through the pump was about 8 per cent. This would be improved with less rapid diffusion.

At the duty flow of 6 cusecs., overall efficiency was just over 79 per cent, 1+ per cent below the maximum. This was not unexpected since the blade sections were not designed to work at the best possible liftldrag ratios. The ratios of x SECTION BB

Fig. 20. Experimental Impeller Blades

0 0.05 0.10 0.15 0.20 0.25 0'10 FLOW COEFFICIENT, 4

L i I I L , , , ,

0 1 2 3 4 5 6 7 8 FLOW AT 1.300 R.P.PI.-CUSEC.

Fig. 21. Perfmame Characterktics of Pump


878 E. A. SPENCER

head and brake horsepower at zero and normal flow were 2.22 and 1-67, values which are within the ranges given by Stepanoff (1948).

At flows below 4 cusec. there was violent hammering in the pump caused by the blades cavitating.

Attempts have been made to estimate the semi-theoretical head-flow curves of propeller pumps. Stepanoff (1948) gives a universal diagram from which such a curve can be predicted, based on the Euler head and the angle made by the mean line of the blade at the trailing edge. Empirical factors are, however, introduced. Pattantyus (1949) suggests that the zero lift angle of the blade section should be used to estimate the maximum flow, Fig. 22. Since it is assumed that the blade, as a whole, reacts similarly to the section at the mean radius, it is doubtfid if these methods can give more than a very rough guide to the behaviour of an individual pump.

The anticipated performance of each individual blade section can be obtained by a reiterative method similar to that used in the original design. Fig. 22 shows the type of

Fig. 22. Theoretical Performunce Curves

---- Based on aerofoil theory for hub and tip of impeller Based on Pattantyus. blade.

result obtained. It is, however, certain that at flows away from. the normal, the free-vortex pattern does not persist and with radial flows the axial-velocity distribution does not remain constant. The overall performance cannot then be deduced with any accuracy. Within about 10 per cent from the design point, however, averaging the individual curves enables a fairly accurate prediction to be made.

At very low flows near the shut-off point, the fluid will tend to rotate as a forced vortex, but there will be recirculation and back flow at the hub, Kit0 (1936).

The inflexion on the curve of the hub section occurs when the aerofoil section reaches stalling conditions. Separation appears and blade losses will increase rapidly. Although the blade Reynolds numbers at design flow were above 1 x 106, the inflexion occurs at considerably lower flows, and the behaviour of most aerofoil sections has not been determined for Reynolds numbers less than 5 x 105. In general, it may be said that stalling occurs at lower angles of attack as the Reynolds number is reduced. Since the pump cavitated before this dip in the head-flow curve, theoretical analysis is impossible on existing knowledge.

Flow Conditions Inside the Pump Measurements were made at the three stations inside the pump for the duty flow of 6 cusec. A traverse to determine the yaw angle downstream from the straightener blades, at their design setting (Fig. 23), showed that there was a deviation from the axial direction of over +20 deg. The angle, measured from the axial direction, was counted positive if the flow inclined towards the direction of rotation of the runner. This represented a residual whirl velocity

-20 ' I I I I I I 2 3 4 5 6

RADIUS-INCHES

Fig. 23. Yaw Angle fisfribation Past Straightener Blades Design setting. ---- -4 deg.

head of about 0-2 foot. When the blade setting was changed by -4 deg., thus increasing the angle of attack, the flow direction was almost axial. There was a slight improvement on the head-flow curve and on efficiency (82 per cent maximum), so that, thereafter, the blades were left at this new setting.

No pre-rotation was found in front of the impeller, the angle variation across the annulus being less than 1 deg. When the local velocities, illustrated in Fig. 24, were integrated, the quantity determined agreed within 2 per cent of that measured in the upper pipeline by the standard Pitot tubes. The mean annular axial velocity was increased by the restriction of the inlet guide blades. There was a marked boundary-layer at the casing wall and Scoles and Patterson (1945) have suggested that such a configuration should be taken into consideration when designing blade systems. It is probable that a slight improvement would be obtained if the boundary-layer could be predicted correctly and due allowance made in the pump design.

In passing through the impeller the axial-velocity dismbution was further distorted. The reduction in velocity at the tip may be attributed to the secondary flows in the clearance between the blade tips and the casing. The yaw angles at both hub and tip were much higher than anticipated, though the actual velocities were reasonably close to the design over most of the annulus.

The lift coefficients on the blade surface can be compared with the predicted values, since


THE PERFORMANCE OF AN AXIAL-FLOW PUMP am

1 - -n--X----xl--~ 1

I

880 E. A. SPENCER

maximum flow at zero head would be common although this point could not be confirmed without a booster pump in the circuit. The best efiiaency point with the two-bladed runner was about 4 per cent less than that for the other two tests. Schmidt shows an efEciency drop of this order between the projected area ratios of 35.8 and 71.5 per cent, the ratios for the 2 and 4 blades here.

When the modified aerofoil theory was applied to the

I I I I I I I I I I ! I

04 0.15 0.20 0.25 .\ 0.30 0.35 FLOW COEFFICIENT, I$

t 3 4 5 6 7 6 4

FLOW-CUSEC AT 1.300 R.P.M.

Fig. 270 and b. Performance Curves for Two, Three, and Four-bladed Impeller ---- Two blades. ------- Three blades.

Four blades. Shaded area shows zone of cavitation.

prediction of the head developed at design flow for the reduced number of blades, the velocity mangles were found to alter r a d i d y from the four-bladed design. The head distribution across the blades was no longer constant, and for two blades integration gave a value below that found experimentally. For three blades, agreement was within a few per cent. The use of the aerofoil theory, therefore, though limited, does give a rough approximation to the facts. This is an advantage when compared to the Euler theory which cannot give any indication of the effect of blade number.

With reduced numbers of blades, audible cavitation occurred at flows nearer the design point. This may be expected since the blades will be additionally loaded. If cavitation is feared in an installation, the number of blades should be increased, although possibly th is may mean some sacrifice in efficiency.

Impeller Blade Tip Clearance The effect of changes of clearance between the impeller blades and the casing was studied by systematically increasing the clearance. The blades were not removed from the impeller boss during these tests, the whole assembly being machined as one unit. The previous tests had been made with a clearance of 0.015 inch, or 0.6 per cent of the blade height. Successive tests were now carried out with intervals of approximately 0.006 inch. At 0.060 inch (2.4 per cent) the effects on performance were very marked and the tests were discontinued as limits of practical usage had been reached.

0.12 0.16 0.20 0.24 FLOW COEFFICIENT. d . .

L I 4 5 6 7 8

FLOW AT 1.300 R.P.M.-CUSEC.

Fk. 28. Characteristic of Pump with Increasing Impeller Blade Tip Clearance

Tip clearance, 0.015 inch. Tip clearance, 0.022 inch. --- Tip clearance, 0.028 inch. - - - - Tip clearance, 0.034 inch. --- Tip clearance, 0.039 inch. Tip clearance, 0.043 inch. - - - - - Tip clearance, 0.052 inch. Tip clearance, 0.060 inch.

Shaded area shows zone of cavitation.

---_

------- ----

The related series of tests are plotted in Fig. 28. The effect on the head-flow curves was more marked at low flows than at flows above the normal. This change must be caused by the leakage flow across the blade tips although secondary effects are discussed later. This leakage flow depends upon the pressure Werence between the two sides of the blade, and will be smaller at the higher discharge rates where the pressure developed in the pump is less. The 1.8 per cent increase in clearance resulted in a drop in head of 15 per cent at the design flow.

The efficiency also decreased with increasing clearance, Fig. 29. The initial improvement in efficiency may have been a spurious effect from mechanical friction losses, and further tests would be needed to confirm that an optimum best efEciency exists for a non-zero clearance.

The characteristic curve of a pump was discussed earlier in relation to the aerofoil characteristics of the blade


THE PERFORMANCE OF AN AXIAL-FLOW PUMP 88 1

I I I I I I I I

I I I I I I

I I

F&. 29. Effect of Impeller Tip Clearance at Desip Flow The tip cIearance is shown as a percentage of the blade height.

elements. Theoretically a dip in the head-flow curve would be expected when the blades were stalled. This idlexion is found to a varying degree in all the published curves of propeller pumps. The present tests suggest that there may be a relation between the amount of the dip and the tip clearance.

The yaw angle of the flow after the impeller was measured for each clearance, only the extreme values being shown in Fig. 30. The change was, however, progressive throughout

3.0 3.5 4.0 4.5 5.0 5.5

F&. 30. Variation of Yaw Angle after Impeller Blades with Increasing Tip Clearatue at Design Flow - x- Tip clearance, 0.015 inch. -- o - - Tip clearance, 0.060 inch.

RADIUS-INCHES

the series. Pivoting about a point near the centre of the blade, the fluid angle increased over the outer half, and decreased over the inner half for increasing clearance, instead of a reduced axial-velocity component being confined to a limited area adjacent to the tip; this means that the whole annulus was affected by the clearance flow. Impeller and straightener blades were thus working under conditions increasingly removed from the uniformity necessary for free-vortex flow.

Finally, it was noticed that at higher clearances, audible cavitation occurred at flows nearer to the design flow. It is likely that with the change in flow co-ation the blades were more highly loaded at the outer radii although at the tip itself the lift coefficient would be reduced.

Cavitation Performance Propeller pumps are more susceptible to cavitation than centrifugal pumps, and the improvement of this feature presents one of the main problems of design. The low pressures result from a combination of the static pressure level and high velocities.

The flow coefficient, #, is usually between 0.15 and 0.4 for axial-flow pumps. The use of higher values, up to 1.0, will, according to Patterson (1944), improve efficiency. Above 1.0 the maximum possible blade efficiency slowly decreases again. Higher values of # may be achieved either by lowering the speed or by increasing the axial velocity. The latter heightens the risk of cavitation while the former, beneficial for cavitation, will require a larger driving unit for the same output, with higher all round costs. The balance between all the considerations is a delicate one.

A non-dimensional parameter, C,, is used to express the local conditions in terms of the undisturbed stream.

Ch=--$ P-P . . . . (8) - 2g

It is assumed that the inception of cavitation occurs when at some point the pressure equals the water vapour pressure, pq. The undisturbed stream static pressure can be deter- mmed fairly accurately. The positive submergence in the present experiments was 3 feet at the pump centre-line. The static pressure just upstream from the impeller at the highest tip position, which also takes account of upstream friction losses and the velocity head, was 31.6 feet above water vapour pressure. An aerofoil usually has a fairly high suction pressure on

the upper surface at normal angles of attack, and the peak of the pressure distribution moves towards the leading edge as the angle is increased. Meiderer (1949) and others give as a general guide

* (9) . . . or2 PI = 0*7CL . - g where p, is the maximum pressure drop on the blade surface. This is measured below the average pressure over the section.

OBrien and Folsom (1939) found, by analysing aerofoil pressure-distribution data, that normal sections fall within the band drawn in Fig. 31a. Very little information is available, however, on actual cavitation tests on hydrofoils. Daily (1949) tested a National Advisory Council for Aero- nautics (N.A.C.A.) 4412 section and, more recently, Numachi and Murai (1952) made a study of hydrofoils in cascade, the spacing/chord ratio being 1-24. Tests on a Clark Y section 8 per cent thick which has a similar geometry to the Royal Air Force (R.A.F.) 6E, although thinner, gave results very close to the Pfleiderer equation for 0-2

882 E. A SPENCER

I I 1 1 0 0.4 0 4 1.1 1.6

LIFT COEFFICIENT, CL

F3. 31a. Cavitation P d m a n c e of Free Aerofods Pfleiderer p, = 0.7G. ") . ( g ----

--tf-t O'Brien and Folsom. - - - - - - - Daily (experiments on N.A.C.A. 4412). tbe blade tip since the relative velocities are highest there, and these are squared in the expression. When the discharge is reduced, the angle of attack between the fluid velocity vector and the blade will increase. The lift coefficient therefore increases and, fiom equation (9), the pressure drop increases and cavitation again OCNS. In that case the inception point need not necessarily be at the blade tip.

The available reserve pressure at entrance to the runner- blade tip was 31.6 feet and hence for th is pump, from

z, 31.6 = C, = function C, . v,

The proposed design valves of O'Brien and Folsom were calculated using this equation. The Pfleiderer equation is also plotted in Fig. 31b, using equation (9) and substituting p , equal to 31.6 feet. It may be anticipated that when the

equation (8),

. (10)

I I I I

. . LIFT COEFFICIENT, CL

F3.31b. Comparison of Experimental Values at Normal Flow with Free Aerofoil Data at Same Submergence

+ 5.25 inches radius. - - - Eypcrimentalvalues: { o 3-25 inches radius. - - - PBeidcrer. O'Brien and Foleom-proposed design values.

conditions give a point above this line there wi l l be an area on the blade surface below the water vapour pressure.

The experimentally determined values of lift and velocity are plotted at the duty flow of 6 cusecs. The blade tip is seen to be already in a pressure region where cavitation is expected, but is very close to the values proposed by O'Britn and Folsom (1939) as design Criteria. The pump was tested up to 120 per cent of the normal flow without audible cavitation and down to nearly 70 per cent before cavitation set in. Under these conditions the whole blade will have been working in the region beyond the Pfleiderer m e .

Spannhake (1948) points out that in a pump the pressure is increasing between inlet and outlet from the impeller. The point of minimum pressure, therefore, is in a region where the stream pressure is higher than that at the entrance. This will delay the onset of cavitation at the higher flow rates, but should not greatly affect the onset at reduced flows where the angle of attack is increased.

It has been assumed that cavitation occurs as soon as the water vapour pressure is reached anywhere. If, however, the fluid passes through the low-pressure region in a very short time interval, cavitation may be delayed until a larger pro- portion of the blade section is at the low pressure. Although the onset of the cavitation zones marked in the figures was quite sudden, nevertheless, reduced cavitation will probably take place at flows nearer the design point. This is despite the fact that the performance curves were apparently stable. Visual observation is essential for the study of incipient cavitation. Numachi and Murai (1952) showed that vibra- tion danger did not occur at normal angles of attack until nearly the whole hydrofoil section was cavitating.

Warren (1953) has developed sections that are theoretically more resistant to cavitation than the normal aerofoil sections. They differ from the low-drag acrofoils derived by rhe N.A.C.A., mainly in having sharp leading edges which result in flatter pressure dismbutions. Numachi and Murai (1952) have tested similar sections under cavitating conditions. Whilst performance is good at the design setting, some sacrifice in efficiency must be accepted at off-design conditions.

The secondary flows associated with the blade-tip clearance may cause another form of cavitation phenomenon. Vortices are shed from the blade tips which have low pressures at the core and, if sufficiently strong, these will induce cavitation. Damage to the blade may be expected if the bubbles impinge on the undersurface of the blade which is at a higher pressure. Since the strength of the vortex may be expected to change with clearance, the pattern of cavitation performance would alter from this cause.

CONCLUSIONS The performance of a small axial-flow propeller pump has been examined and it has been shown that reasonable efficiencies can be achieved using a design method based on modified aerofoil theory and free-vortex conditions. Aero- dynamic theory, moreover, assists in the analysis of conditions near the design point and allows rough predictions to be made on how the pump will behave in altered


THE PERFORMANCE ON AN AXIAL-FLOW PUMP 883

circumstances. This is despite the fact that some of the assumptions of the theoretical approach have been proved to be untenable in practice. It may be concluded that some of the effects from such non-ideal conditions cancel each OthlX.

It is apparent that efficiencies may be M e t improved by the use of low-drag blade sections and by Carrying out annular cascade tests where the effects of hub and casing can be taken into consideration. The use of hydrofoil sections specifically designed to haw flatter pressure distributions wil l reduce the cavitation susceptibility of this type of pump. Whilst tests in idealized pumps, where the analysis is confined to blading performance, are valuable, the overall performance of the pump unit as a whole is of major importance. This includes intake and diffuser design.

ACKNOWLEDGEMENTS

The author wishes to acknowledge his indebtedness to Professor Lloyd-Evans of University College, London, under whose guidance this investigation was carried out and to the swff of the Engineering Faculty for their assistance in making and assembling the apparatus. This report is published by permission of the Direaor,

Mechanical Engineering Research Laboratory.

APPENDIX I1

R E F E R E N C E S

ANON. 1933 Et&em~, VOL 135, NO. 3498, P. 99, De LaVal Propeller Pump.

DAILY, J. W. 1949 Trans. A.S.MB., voL 71, No. 3, p. 269, Cavitation Characteristics and Infinite-aspect-ratio Charec- teristics of Hydrofoil Section.

JACOBS, E. N., WARD, fc B., and PINKERTON, R. M. 1933 National Advisory Committee for Ammutics Technical Report 460, The Characteristics of 78 Related Aerofoil Sections from Tests in the VariableDensity Water Tunnel.

KELLER, C., MARXS, L. S., and W a n , J. R 1937 The Theory and Performance of Axial-flow Fans (McGtpw-Hill Publish- ing Co., New York and London).

KIro, S.

MARPLESa J.

1936 Tokyo Imperial University Eng. JI., vol. 20, No. 12, p. 283, Experimental Study on a Propeller Pump.

1954 Thesis, National College of Heating, Ventilat- ing, Refrigerating and Fan Engineering, A Modified A p proach to the Design of Low Pressure and Medium PreSpurr Axial-flow Fans.

NUMACHI, F. 1929 Tohoku University Technical Repom, vol. 8, p. 411, Aerofoil Theory of Propeller Turbines and Pumps.

1952 A.S.M.E. Paper No. 52, A-87, Tohoku University Reports of Inst. of High Speed Mechanics, voL 2, Cavitation Tests on Hydrofoil Pro& Suitable for Arrangement in Cascade (First Report).

The Design of Propeller Pumps and Fans (Publications m Engineering. University of California).

PATTANNUSa G. 1949 Miiegyetemi KOzlemenyek, Budapest No. 1, p. 51, Approximative Design of the Charactrristic Curve of Mal-flow (Propeller) Pumps from the Velocity

PATTERSON, G. N. 1944 Australian Council for hronaudcs, Report ACA-7, Ducted Fans: Design for High Efficiency.

PPLBIDERW, C. 1949 p. 344, Die Kreiselpumpen f7ir Fluasig- keiten und Gase, third edition (Springer, Berlin).

SCHLIMBACH, A. 1935 vol. 4, No. 2, p. 51, Mitt. aua dem Forsch., G. H. H. Konzem, Der M.A.N.-Schrauber- schaufler.

SCHMIDT, H. F. 1928 Jl. Am. SOC. Naval Eng., voL 49, p. 1, Some Screw Propeller Experiments with Particular Reference to Pumps and Blowers.

SCOLBS, J. F., and PATTERSON, G. N. 1945 Australian Council for Aeronautics, Report ACA-14, Wind Tunnel Tests on Duaed Contra-rotating Fans.

SPANNHAKE, W. 1948 David W. Taylor Model Basin, Navy Dept., Miscellaneous Publications, Regular Series No. 621, Analysis of Modem Propeller Pump Design.

STEPANOFF, A. J. 1948 Centrifugal and Axial-flow Pumps, Theory, Design, and Application (Wiley, New York; Chapman and Hall> London).

Co., New York and London). WARREN, C. H. E. 1953 A e r ~ ~ u t i c a l Research Council, Repons

and Memoranda, No. 2836, A Theoretical Approach to the Design of Hydrofoils.

1935 Die Stromung um die Schaufeln von Turbo- maschinen (Barth, Leipzig).

nautical Research Council, Repom and Memoranda, No. 1771, Tests of Four Airscrew Sections in the Compressed Air Tunnel.

NUMAW, F., and MURAI, H.

OBRIBN, Me P . y and FOLSOM, R. G. 1939 VOL 4, NO. 1, p. !,

Diagralll.

vON MISS, R. 1945 Theory of Flight (McGraw-Hill Publishing

W ~ G , F.

WILLIAMS, D. He, BROWN, A. F., and SMYTH, B. 1937 A-


834

Discussion Mr. H. ADDISON, O.B.E., M.Sc. (Member), in opening the discussion, said that, although the papers were both valuable in themselves, comparison between the two st i l l further heightened their value, for there were such great differences in apparatus and in results. In one set of experiments air had been used, and in the other, use had been made of water. The rotors were of different shapes, as could be seen by comparing Figs. 2 and 20. Outlet guide blades had been provided for the water rotor, but not for the air rotor. Then there was a contrast between a free vortex type of distribution of velocities and a less formal type. Never- theless, the findings had been said to apply equally well to axial-flow fans and pumps with water or air.

That being so, he wondered whether the authors believed that their tests proved that one of the rotors was in any sense superior to the other. In brief, which was better in a broad general sense, a rotor such as in Fig. 2 with narrow blades and a small hub diameter, or the rotor in Fig. 20 with a broad blade and a large hub diameter. The rotor used by Dr. Hutton for air had been of a special kind that would give certain stipulated characteristics, but nevertheless he would be interested to hear whether that rotor in itself had any superiority.

The experimental results did not appear to include any direct observations of radial velocity components. In fact, although Dr. Huttons paper was specifically concerned with three-dimensional motion, direct values of axial components only had been given. The tangential or whirl components had to be inferred or conjectured, and there appeared to be no measured values of radial components. It might be that the radial components were found only inside the rotating impeller, where they could not be measured, but perhaps they might have been measured in the adjacent field of flow, where measuring appliances could be inserted. If such observations could have been made, they might have thrown light on the conditions prevailing at very low flow rates.

From Fig. 3, showing the axial-f(ow distribution, it could be seen that at a flow coefficient of 0.2the axial velocity at the hub had already fallen to zero, so presumably at still lower flow rates there would be a reversal of direction there : back flow and recirculation would occur, as mentioned on p. 878. He wondered whether the authors had actually observed that secondary circulation, wbich would manifest itself by an outward velocity component on the upstream side of the rotor.

It was interesting to find from Fig. 23 that the pump was

so sensitive to the sening of the outlet guide blades. Ap- parently a change in blade setting of only 4 deg. increased the pump efficiency by 2 per cent. He would therefore like to ask whether any measurements had been made to assess the efficiency of the guide-blade ring, which was regarded as an energy converter : namely, what was the ratio between the pressure rise in the diffuser and the energy corresponding to the whirl velocity at rotor exit.

According to Dr. Spencer, in the guide-blade apparatus there was a reconversion amounting to 10, 20, or 30 per cent, but he understood that that had been merely an estimated value.

Then, if the guide-blades had been removed altogether, the performance of the pump rotor might then have been directly compared with that of the fan rotor shown in Fig. 2. He thought it had been known that in centrifugal pumps the performance of a rotor by itself was quite different to what it was when there was a diffuser or a ring of guide-blades surrounding the centrifugal pump impeller. He would ask whether the same applied to axial-flow impellers. On the question of tip clearance, the two papers seemed

to be wholly in agreement. Their findings, too, agreed with what some pump manufacturers had discovered a number of years earlier by actual full-scale experience. Some early types of axial-flow pumps were disappointing because the importance of close clearances between casing and blade tip had not been fully realized; yet in the historical sense it was interesting to know also that in some of the early types of axial-flow pumps there was a continuous shroud, which would help to reduce tip clearance. Doubtless the losses due to friction of the rotating crown were excessive and so the crown was cut away; and as was now known, there was no continuous rim.

From Dr. Spencers explanation it appeared that increased tip clearance would have one possible counter- vailing advantage in getting a more predictable shape of head-discharge curve. There would not be the hysteresis loop as shown in Fig. 8, yet with the water pump, on p. 878, there seemed to be no way of avoiding violent hammering at low discharge rates.

The hysteresis question or the zone of instability in the characteristic was awkward in practice, and he would like to ask whether the authors could show any way by which those disturbances could be eliminated. An interesting point in comparing two papers by Werent

authors was to observe variations in terminology. For example, there were three different terms to describe the


AXIAL-FLOW IMPELLERS AND PUMPS 885

angle between the direction of the absolute velocity axid the axial component: whirl angle, swirl angle, and yaw angle. In addition, the outlet guide blades of the pump were sometimes spoken of as straightener blades.

Those who might choose another term were fortified by noticing that the straightener blades did not always straighten the flow. Fig. 23 showed an example of that, and so perhaps guide blades might after all be a more acceptable term.

It might be useful to have those divergencies of usage exposed, because the question of terminology was now under study by the British Standards Institution, whose guidance might help to achieve more uniformity.

Mr. A. D. S. CARTER, B.Sc. (Member), said that he found the papers fascinating because they dealt with the case of rather widely pitched blades. He would approach the problem from the aspect of the gas-turbine axial-compressor, with which the blades were more closely pitched.

In the impeller testing by Dr. Hutton, the diameter ratio had been also slightly lower than would be used even in aircraft compressors ; and also, of course, the blade sections were constant radially, whereas the axial-compressor blade would have substantially different sections from root to tip.

That led to the question of the difference between these two methods of approach. He wished that Dr. Hutton had given the overall performance of his impeller, because it was not clear from Fig. 11 just what comparisons were being made. He was not sure, for example, how far stalling of the blades-particularly those long blades, with the constant but twisted section-would affect the slope of the test curve. There would be an appreciable change in blade efficiency with flow coefficient, and that would be represented as a change in slope of the pressure-rise curve.

He also wished that Dr. Hutton had produced the overall pressure-rise and efficiency curves, because there were many curves of that nature available. Almost anything could be proved from looking at the detailed curves for different radii. He did not necessarily disagree with the findings of Dr. Hutton, but it would have helped in giving an opportunity for more detailed calculations.

He himself had found similar effects-i.e. that the slope of the test curve was much less than that of the calculated one shown, for example, quite clearly in Fig. l lb . In fact, an analysis of his own made some years earlier of many multi-stage axial-compressor results had led him to the belief that there must be both an allowance-it might have to be an empirical one-in the fluid angles from the blade, and in addition a work-done factor, as they called it, or, in the nomenclature of the papers, a slip factor. In other words, he did not think that either of those methods taken in- dividually would give the right answer. Both had to be combined.

In regard to Fig. 13, he would like to ask the author whether in using the method which he had developed he had used the cascade outlet angles to get the axial velocity from the radial equilibrium theory. He would like to know whether he had used the outlet angles from cascade theory

and a constant total energy radially, or whether he had used the measured rate of dismbution of total energy in doing his calculations from whence he could apply the aerofoil theory.

He was somewhat disturbed as to just how much tip clearance effects were affected by stalling. As a rough and ready rule, in orthodox multi-stage axial-compressors tip clearances of up to about 2 per cent were assumed to have practically no effect. That was largely in agreement with the m e shown by Dr. Hutton, but not in agreement with the curves shown by Dr. Spencer, which showed a rapid fall-e.g. Fig. 29-41 efficiency for clearances of much more than about 1-13 per cent. He was referring to the mean value of the staging in a multi-stage compressor, and there was a very significant increase in boundary layer through the compressors, whereas in the single-stage tests there was just the inlet boundary layer to be contended with.

In some tests they had made on a multi-stage axial- compressor in which they had been actually comparing tip clearance and radial clearance, the conclusion arrived at had been that, provided the blades were not stalling in the region of the tip clearances, there was very little effect-for instance, between clearance and shrouding; but if, on the other hand, the blades were stalling in that region, there was quite a marked difference between tip clearance and shrouding.

That led him to wonder just how much the results could be generally adopted. It might account for some of the difference between the two authors results. He considered that care should be exercised in generalizing.

He would like to have seen a test on, perhaps, a twisted blade-not free vortex-for comparison with the stalling occurring at the other end of the blade.

He would like to know whether Dr. Hutton had weighed the advantages between water and air as a medium for carrying out those tests. They themselves had dealt in air, but they had come to the conclusion that water would be a much more convenient medium to use and were beginning test work on it when they had heard that Dr. Hutton had decided to use air.

Mr. S. P. HAWES, B.Sc. (Eng.), Wh.Sc. (Associate Member), said that the two papers provided plenty of new data for a study and reassessment of design methods. They were particularly useful to manufacturers who usually had little opportunity to carry out such detailed and fundamental tests.

Considering, for example, one fundamental conception- that of radial equilibrium, which mathematically was given

by $ = ,-sufficient information was given in Figs. 6, 7, and 14 to check whether that occurred at station 2 on the fan discharge at 4 = 0.3.

In actual fact, the calculated slope, based on w2/r, of the pressure against radius curve was appreciably less than that obtained by measurement and given in Fig. 7. He would be interested to know the reason for that, especially in view of

WZ


886 DISCUSSION

the fact that the station 2 traverse section had been chosen because conditions had apparently stabilized and, moreover, the integrated flow and aerodynamic torque agreed well with the measured flow and dynamometer torque.

The effect shown of tip clearance on the distribution of flow and work within the impeller was most interesting to a designer. However, the curves showing the effect of varying tip clearance on performance and efficiency were misleading because it was suspected that the head and flow coefficients had been based on the nominal uncropped diameter and not on the actual impeller diameter.

Thus in Fig. 10, which gave the results for a 4 of 0.3 when tip clearance effects were not very severe, most of the reduction in head shown would have occurred with constant tip clearance simply by reduction of the impeller size. On the other hand, had the results for a 4 of 0.2 been available, the more severe tip clearance effects would probably have made any indication of optimum efficiency disappear.

Finally, the suggestion of the lack of agreement with wind- tunnel data of the lift against incidence curves in Fig. 15 was due mainly to the difficulty in calculating the true incidence for the operating impeller blade sections.

Mr. R. H. YOUNG, B.Sc. (Eng.) (Manber), said that however much chance might have entered into it, it was indeed fortunate that investigations had been made in parallel of the behaviour of a fan and a pump having sufficient similarity of blade profile and Reynolds number, and sufficient divergence in hub ratio and blade form, to demonstrate at the same time the close relationship between aerodynamics and hydraulic engineering, and the widely Wering performance of two axial-flow impellers.

While a detailed comparison of the performance of the two machines would take into account the differences in hub ratio and solidity and the presence or absence of guide vanes and hub fairings, it would appear reasonable to use the recorded results for some direct comparisons between impellers designed for free vortex whirl conditions and those designed for a whirl distribution far removed from the free vortex pattern.

It would seem that the design of the pump impeller used by Dr. Spencer had been based on the assumption that at all radii the deviation of the fluid leaving the blades was zero or, alternatively, was smal l and constant. Fig. 30, which recorded the yaw angle or whirl angle after the impeller, showed that on test the whirl was far removed from the fiee vortex pattern. For instance, the yaw angle at 4.5 inches radius should, theoretically, be around 37 deg., while at 5.5 inches the angle should be 33 deg. 30 min. approximately. Measured values of whirl velocity plotted against radii would apparently give a similar concave curve and would agree in general form with the measured lifl coefficient curve (Fig. 25a).

Dr. Huttons investigations on the impeller which had no claims to a free vortex design showed a strikingly similar concavity between hub and tip in the whirl angle for 4 = 0.20 (Fig. 6). For the higher flow coefficient the concavity was less marked but, even at 4 = 0.30, the ratio

of whirl velocity to axial velocity when plotted against radius (Fig. 14) showed the same marked concavity.

Perhaps the most striking similarity was in regard to the rapid rise in all cases in whirl angle and whirl velocity as the blade tips were approached. He would like to ask the authors whether they could throw some light on that phenomenon, bearing in mind that those rises were not accompanied by commensurate rises in measured pressure development around the tips, as confinned by the curves in Fig. 7. No doubt the boundary layer in the vicinity of the duct walls might have some bearing on the matter, but it would seem hardly feasible that that was the sole reason for the non-linear whirl distribution in the case of the faired medium hub-ratio impeller investigated by Dr. Spencer.

The results suggested that there might be some justifica- tion for a procedure sometimes adopted for medium hub- ratio fan designs, whereby the blade chords and blade angles were calculated for hub and tip sections on the basis of free vortex whirl distribution, and intermediate blade angles and chords were developed from those. To take the most simple case, a blade of most constant chord from hub to tip would have blade angles at all radii in linear progression. Compared with the impellers covered by the authors, the procedure outlined would give increased blade angles at intermediate radii and possibly a better velocity distribution. However, if the ideal condition of two-dimensional flow was to be approached, it would be necessary to allow for a greater deviation at the hub than at the tips where, for an efficient design, the angle of incidence should be lower.

On the question of blade Reynolds number, there appeared to be some disparity between the statements made by the two authors in regard to the availability of aerofoil data for Reynolds numbers less than 5.0~ 105. Wbile the behaviour of RAF6 aerofoils at a Reynolds number as low as 0.5 x l@ might have been estimated by Dr. Hutton, the National College for Heating, Ventilating, Reftigeration and Fan Engineering had taken tests in a two-dimensional flow wind tunnel on RAF6 aerofoil of 14 per cent thickness ratio at a = 2.0 x 105. There had been very little difference as regards coefficient of lift or stalling angle compared with published data for Reynolds numbers 1 to 2 x 106. The total drag at zero incidence and at stall had appeared to be d e c t e d by Reynolds number-r, at least, the figures obtained had agreed closely with the published data for the higher Reynolds numbers-but, over the normal working range of incidence, the increase m total drag with reduction in Reynolds number had been marked. The experiments, however, had been somewhat incomplete as the true Reynolds number or Jacobs number had not been accurately established.

Mr. J. B. SCIVIER, B.Sc. (Eng.) (Mder), said that he would like to confine his remarks to Dr. Spencers paper. In particular, in regard to cavitation, Fig. 32 showed cavitation over the blade tips of an axial-flow pump rotor. The rotor in question had been 10 inches diameter, having four blades set at a tip angle of 17 deg. The pump had been running at a speed of 1,450 r.p.m. and it had been in a circuit with a


AXILPLOW IMPELLERS AND PUMPS 007

Venturi meter and open tank, to which the pump delivered and from which it had taken its suction, with a positive head on the suction of about 3 feet. A perspex casing had been fitted to the pump so that

cavitation could be observed, and the rotor had been of the variable-pitch type. Since the perspex casing had been of cylindrical form, the rotor periphery had been machined for the smallest blade angle available, which had been 8 deg. Hence with the blades set at 17 deg. there had been an increased clearance, particularly at the nose and tail end of the blades. Photographs had been taken of each blade with a high-speed camera and the flash synchronized with the Shaft.

a 12.25 feet head.

b 20.5 feet head.

Fig. 32. Leakage Cavitation

Fig. 32a showed the pump running at a speed of 1,450 r.p.m. and generating a head of 12-25 feet. That was just beyond the best efficiency point of the pump, the head at the best efficiency being approximately 15 feet. Cavitation over the tip of the blade could be clearly seen at that operating condition, and cavitation had increased with increasing head until the condition shown in Fig. 32b had been reached at a generated head of 20.5 feet.

Fig. 32b w a s particularly interesting as it showed that not only had the cavitation increased considerably at the higher

head, but that it was also collapsing and subsequently reforming farther along the flow passage.

It would appear that with that particular rotor cavitation was always present, although not necessarily audible. There had been cavitation around the nose of the blade extending from the tip to the hub on the low-pressure side. That could be seen only with a mirror, and it had not been possible to photograph it. H e noted that the author had &ed out tests with a

bossltip ratio of 0.56, and he would like to ask him whether any work had been carried out to analyse the effect of varying that ratio.

It could be shown that N,= 3 2 7 K J 1 2 z / K v m . . (11)

where K = U/z/H, K , = VlU, 7 was hubltip ratio, V was mean axial velocity through the rotor, U was peripheral velocity of the rotor, and H the generated head.

Fig. 33. Chart fm Determination of Axial-floev Pump Rotor Details

Fig. 33 showed the variation of specific speed against blade angle for various values of hub/tip ratio. That series of curves had been obtained by taking a large number of test results of axial-flow pumps having rotors ranging from 10 to 33 inches diameter, and values K and K , had been found for various blade angles.

In preparing the diagram, it had been assumed that the average values of K and 1;6 for the different blade angles taken from test results were approximately correct, and the values of K and K , were assumed to be independent of the hub/tip ratio. All the pumps in question had had blades of one family of air foils and, in addition, the hubltip ratio of the pumps had varied between 0.41 minimum and 0.51 maximum.

The rest of the chart shown in Fig. 33 enabled the various rotor details such as blade angle, hub/tip ratio, and


888 DISCUSSION

diameter to be obtained quickly, together -with speed of rotation, for any given duty.

As already stated, the chart had been produced by averaging the results of a large number of tests, but it should be regarded as only approximate and then true only for the pamcular air foil in question. The chart did not show the effect on efficiency of the interrelationship of those various factors, particularly the hub/tip ratio.

The specific speeds for the various pumps tested, calculated in accordance with equation (1 l), were in close agreement with the specific speeds obtained from the test curves.

He would like to ask the author whether he had done any work in connexion with the variation of the hub/tip ratio.

Mr. B. B. DALY, B.Sc., A.M.I.E.E., said that as a fan designer, he would comment on Dr. Huttons paper. He was interested in the necessity of taking readings two blade chords downstream in order to obtain freedom from radial flow. He would like to ask the author whether that had been two blade chords measured axially or measured along the helical streamlines.

He had always wondered why compressor designers placed their stator rows so very close to their rotor rows. To have the leading edge of the following row constantly impinging upon a succession of wakes and probably up- setting the flow instantaneously each time, seemed to be a poor arrangement.

He had found that the placing of the stator vanes about

two chords axially downstream of the rotor blades quietened the operation very much indeed, although he had been unable to detect any improvement in efficiency.

Commenting upon the value of such a method as Dr. Huttons of predicting performance when departing from the simple free-vortex constant axial-flow regime, it was most useful to escape from the tyranny of that very simple theory, because it certainly gave useful improvements in some of the characteristics-in particular, he had found, in noise level and in sharpness of stall-because the tip of the impeller was affected by both the tip gap and by the fact that it was churning through a comparatively stationary boundary layer, both of which made the flow anything but what a reasonable theory would predict; to reduce the amount of work done in the tip region of the blade and increase that in the central region, and even in the hub region, which was not as bad as the tip region so fax as losses were concerned, was generally advantageous.

He wondered whether the author or others had tried, in the region which was perhaps the outer fifth of blade height which was so much affected by the tip, a really drastic local reduction of the pitch angle of the impeller, so that the extreme tip was more or less feathering through the boundary layer instead of trying to advance it. There would be serious weaknesses in the blade geometry, for instance, there would be inward facing sections of impeller, introduc- ing radial components. That could perhaps be overcome by having a very large number of very narrow wings, which would mean that the twist was much less drastic when approaching the tip.

Communications M. G. DESMUR (Paris) wrote, in regard to the paper by Dr. Hutton, that the experiments described by the author were of peculiar interest. Modem axial-flow fans had recently been designed to be self-contained in cooling towers, their tips frequently being of diameter 1, 2, 4, and even 6 metres. An analysis of flow patterns inside and out- side the wheel were consequently of great importance.

Fig. 34 showed that the meridional velocity was far from being uniform at the impeller outlet and that it was not located on concentric cylinders. These anomalies could be elucidated.

Allowance should be made for the effects of friction at the tip and hub diameters when designing aerofoils. The relative velocity v was decreased to some extent, the velocity triangles were altered, and experimental work had shown a certain increase in the head generated near the periphery and the hub. That phenomenon could be suppressed by reducing the chord length of the blade at the tip and the hub. In addition, to ensure radial pressure equilibrium, every

cylindrical section of the impeller should provide the same work and should act simultaneously without producing

any secondary flow along the height of the blade. The design of each aerofoil therefore should meet the following conditions :

(1) The difference D2wz-DIwI must be of the same value for all aerofoils. In other words, the difference in

w I Fig. 34. Noa-uniform Meridwnal Velocity at Impeller Outlet



circulation between the inlet and the outlet must be a

The velocity triangles should be drawn correctly (em, meridional velocity, being the actual velocity). Angles f12 at the trailing edge should be calculated, account being taken of the effect of the cascade.

It could be demonstrated (Kovh and Desmur 1953)* that requirement (1) was satisfied by

Comtant.

r f sin 6, . z . c . err, - = c for any streamline

where 6, was taken as = ,6, +8, outlet angle of blade, z was the number of blades, v,, the mean relative velocity (Fig. 34), j, the angle between the vector of mean relative velocity and peripheral velocity,

A

5 lift in cascade -- E - lift as free aerofoil = f f , 9). s was themean blade pitch and c the chord length of blade.

(2) The local pressure of adjacent streamlines should not produce a permanent deflexion of the meridional Velocity. If it did, the velocity triangles would be altered. The individual streamlines would no longer produce the same head, and eddies would develop. The vectors by which they were represented would assume the same direction as v, with resulting energy losses.

(3) The lift coefficient of adjacent streamlines should not be too different. In other words, the variation in lift coeficient should be smoothly graded. The former condition was self-explanatory. The two

latter requirements would be satisfied if the lines of constant energy were perpendicular to the meridional streamlines. A slight deflexion of the meridional velocity would represent no drawback if compensated at the trailing edge.

Those conditions being satisfied, it was possible to obtain a flow without deflexion of the meridional streamlines or energy losses due to secondary eddies.

Experimental work he had carried out some years earlier with an axial-flow fan designed to meet the foregoing requirements had shown a constant meridional velocity everywhere except near the tip and the hub. The total head (account being taken of the deflected velocity) had represented exactly the same value all along the blade height, except for the tip and the hub, its value being somewhat lesser at the periphery and somewhat greater at the hub. Clearance through the tip and hub friction accounted for those differences.

It was not purposeless to note that the theoretical head- flow curve never was a straight line from zero delivery to zero theoretical head. It set out from 1,5 -- 2, but it was always located under Eulers straight line. The only straight portion of it was in the vicinity of the design point, and that was most helpful in forecasting the head-flow curve near the design point (Fig. 35).

In regard to the paper by Dr. Spencer he wrote that an analysis of tests carried out within a research programme * de Kovdts, A., and Desmur, G. I953 Pompes, ventilateurs, com-

presseurs centrifuges et axiaw (Dunod, Paris).

DESIGN POINT I

Fig. 35. Head-Flow Curve

was always valuable provided that boththe experimental apparatus and the instrumentation were suited to such purposes.

The design submitted of impeller and straightener blades was judicious. In applying the aerodynamic theory, constant efficiency and constant head had been assumed for all sections of the blading. That preserved radial pressure equilibrium, but it should be stated that the hydraulic efficiency HIH, was not constant from the tip to the hub (as stated in the paper). The velocity triangles therefore were changed. In addition, there certainly had been an increment in the mean axial velocity by the effect of the blade thickness. It seemed to him that the allowance made for frictional drag near the tip and the hub was not sufficient. Figs. 24 and 25a showed clearly that the increase in C, corresponding to the increase of w near the tip and the hub.

He considered that aerofoil R.A.F. 6E, although it exhibited easier manufacture and good performance characteristics, was not perfectly suited to avoid cavitation. The R.A.F. 6E was a conventional aerofoil showing a rapid increase of v, on its curved face, and he, basing his remarks on a rather rough calculation, believed that the inlet angle near the tip was about half of the theoretical

meridional inlet velocity value corresponding to tgp1 =

It might, however, have been the designers intent to secure a negative incidence at the tip.

The values of f12 at the trailing edge (18 deg. at tip and 36 deg. at hub), were consistent with the values calculated by a more general rule, described by himself and his co- author (Kovdts and Desmur 1953), = /?=+go, where the angle assumed by the mean line (skeleton) at the trailing edge to plane of rotation

U

was the angle formed by the vector of mean relative velocity (Fig. 34) to peripheral velocity, c the chord length, s the mean peripheral pitch of blades, z the number of

blades, - = ratio E lift in cascade 6 lift as free aerofoil - 2


aw COMMUNICATIONS

p1 the angle formed by the inlet relative velocity and the peripheral velocity, g' / f was not the Weinig factor. It had been experimentally determined by himself and his co- author through a great number of tests carried out with

A prediction of the head-flow line of an axial-flow pump based on the assumption that blades as a whole reacted similarly to the section at the mean radius indeed gave nothing but a very rough guide as to the behaviour of an individual pump. For flow coefficients away from the normal, the free vortex pattern certainly did not persist and, with effects of back and radial flows, the overall performance could not be deduced with accuracy.

However, as the theoretical head variation + against 4 was a fairly straight fine within 10 per cent from the design point, it was possible to predict the head-flow curve near that point, calculation being made by means of the mean velocity triangle.

The change in the hydraulic efficiency was practically zero near its maximum value. The intersection of both tangents through the theoretical head-flow and the head- flow lines at the design point therefore had to be on the axis of 4. That remark gave a practical means to draw the tangent to the +h against 4 curve (Fig. 35).

It should be pointed out that it would be a mistake to deduce the hydraulic efficiency at points other than the design point from the b.h.p. by subtracting the mechanical losses.

The energy losses due to back flows must be subtracted from the b.h.p. and, so far as he hew, that analysis was not possible in the case of axial-flow pumps, whilst it was feasible with a very reasonable accuracy for radial impellers from zero delivery to zero head points.

As he had previously mentioned, allowance had to be made for the effect of the boundary layer near the hub and the casing wall. The radial motion of the boundary layer on all sides of the blades apparently had little effect on overall performance, whilst the fluid fiction produced a decrease in the meridional velocity near the tip and the hub. The aerofoil design had to be modified to avoid back flow, for instance by diminishing the chord length.

The author had pointed out that the cascade effects had not been taken into consideration for the impeller. That procedure seemed to be justified, since the ratio ['/g varied from 1.03 at the tip to 1.02 near the hub. On the other hand, the dect of f ' / [ upon the design of the straightener must not be overlooked.

It seemed obvious that the best value ofp (efficiency) was obtained when the blade surface was the minimum permis- sible with good performance.

It was possible to demonstrate (Koldts and Desmur 1953) that the product of zc, ( z being the number of blades, c the chord length), would assume the minimum value when :

various values of SIC and 81+&/2.

where 72 was the outlet circulation, 71 the inlet circulation, 6' the lift coefficient for free aerofoil, F/Cthe ratio lift in cascadellift for free aerofoil, and orOD the mean relative velocity, above defined (Fig. 34).

The efects of changes in the clearance between the impeller blades and the casing had shown that the importance of the clearance value for the head-flow and elKcienq- flow curves. The optimum value of the clearance was about 1 llOOO of the outer diameter. The assumption that the inception of cavitation occurred when at some point the pressure equalled the water vapour pressure had been sufficiently proved to be accurate through the experiments carried out by T h o t (1934)* and Daily (1949)t.

The p , value of the maximum pressure drop on the blade surface given by Pfleiderer and other authors: p, = 0.7%. (w,2/2g) was useful as a general guide but had the defect of concealing the mechanism of depression. In fact, the maximum depression under the blade was the sum of two terms, of which the former, dpl = (w2/2g), was to be found just at the impeller eye, whereas the latter, dp2, was due to the acceleration of v, along the streamline. It had to be pointed out that any given aerofoil might give the same c, value whether it was rounded or sharp-headed.

If v, was the relative velocity just before the leading edge, at the top of the eye diameter, and KO, the maximum relative velocity along the blade, the maximum pressure drop due to the acceleration of v, was equal to

". 2 _. 2

where k = k'2- 1.

leading edge) or 0.3 (blunt leading edge).

it would be found that

It was found that the mean value of K was 0.2 (sharp

Substituting 0-3, 0.4 for c, (tip) in Pfleiderer's e q d o n ,

Those values were consistent with experimental results. Briefly, the author's method of design might be used

with confidence for pumps in the specific range of approximately 8,000. The efficiency might be increased if the effects of the boundary layer at the tip and the hub were taken into consideration.

The resistance to conditions generating cavitation might be increased by designing aerofoils according to the method described by himself and his co-author. In fact, the curva- ture of the vanes (sharp-edged), should be chosen such that the direction of the leading edge matched the direction of the relative velocity w.

How to design an aerofoil could be seen from Fig. 36: A straight line should be drawn from the leading edge, the * T h t , A. I934 Bulletin des Inglru'eurs Civils de France, MaG

ruin, ' P M n e s dz la cuvitarion'. f Daky, 3. W. 1949 Trans. A.S.M.E., volt 71,

Characterisria and I*te Aspcct Rano C actemstxu of an Hydrofoil Section'.

LS9, *'c-


AxlAGPLOW IMPELLERS AND PUMPS 891

Fig. 36. Deszgn of an Aerofoil

angle with u being equal to & (inlet angle), with length 3 the chord length. From the latter point a second straight line should be drawn, the angle with w direction, p2, being = j3co+60, with length 3 the chord length. Those lines would be tangents to the aerofoil at leading and trailing edges respectively. A parabolic curve should then be drawn tangent to the same lines at the leading and trailing edges. That curve would give the aerofoil skeleton. The trust centre would not be located at the intersection of the straight lines but approximately at 0.6 of the chord length from the trailing edge upon the skeleton. On both sides of the skeleton e/2 should be measured, e being the blade thickness, as given, for example, in aerofoil catalogues.

Mr. AND& DE KOVATS (New York) wrote that the experiment made by Dr. Hutton was very interesting since few similar measurements had been made on forced vortex- type axial-flow impellers. It seemed the flow tended to realize a pressure equilibrium by changing the axial velocity. That could be expected. The increase of the swirl angle adjacent to the tip area was the consequence of the low axial velocity due to the friction on the wall. It might be less in pumps because of the lower viscosity of the water.

It could be seen from Fig. 1 that there were no straightener vanes downstream of the impeller. Straightener vanes would have changed the flow pattern, and he sup- posed that the shape of the axial velocity curve would be steeper if influenced by straightener vanes.

He agreed completely with the author that the aerofoil theory allowing for change in axial velocity was the best calculating method known.

It was regrettable that efficiency values had not been given. Testing a pump with different impellers, but all at the same head and flow, and with the impellers and straightener vanes made with different vortex patterns, going from the constant pitch to the free vortex pattern, had shown that the latter had the best efficiency if designed by the corrected aerofoil theory. For pumps he had not found any advantage in the forced-vortex type.

In regard to the paper by Dr. Spencer, it seemed that

the straightener blades of the test pump had been over- loaded. Lift coefficients of 1.2 to 1.4 were generally in or near the zone where separation losses occurred. The blade angle should be 71 deg. at 3.25 inches radius and 83 deg. at 5.25 inches radius calculated by the aerofoil theory. That seemed to be in accordance with the test result shown in Fig. 23. More or longer straightener blades would have been better, but the improvement could not be more than some & per cent of the efficiency. Apart from that detail the pump was of a correct design, and, therefore, he believed that the test results were of general interest.

He himself had designed a propeller pump, 25 years earlier, with a head coefficient of 1+4 = 0.24 and a flow coefficient of + = 0.225. The 13-inch diameter impeller had had 4 blades and a hub/tip ratio of 0.55.

At that time very little had been published about propeller pumps, therefore, he had calculated the blades by the simple aerofoil theory using the profiles tested by the Gottingen Institute.

The pump had given a slightly lower head and had had an overall efficiency of 79 per cent. Then he had measured the yaw angle and velocities in five sections. The data had been very erratic. He had altered the chord, and the blade- angles until there had been good radial pressure equilibrium, and until the head and capacity had corresponded to the design point. The efficiency had increased to 82 per cent. The h a l blade angles, the chordradius ratio had been very close to those described in the paper and the performance characteristic had been nearly identical with those shown in Fig. 21.

Some years earlier he had had to design a pump with identical head and flow coefficients. He had tried the slip theory but the calculations had shown that it would not give good results. Finally the impeller had been made by a modified aerofoil theory. The pump had given the same results as the earlier pump made by the partially experimental method. Some improvement could be reached by using a bell instead of a suction pipe, eliminating the axial velocity reduction in the area adjacent to the tip.

He believed that not much improvement could be expected for low head coefficient pumps except for those of bigger size which had efficiencies of 84-86 per cent.

Professor MARIO WICI (Padova, Italy) wrote that he fully agreed with Dr. Huttons statement that the generalized application of two-dimensional design methods by axial- flow pumps was restricted and that particularly for predicting pump performances at flow rates less than the design values.

By visualization of flow, in various experimental pump models, he had found, in his long laboratory practice, that the secondary flow associated with changes in radial distribution of the velocities and the tip-vortices might considerably affect flow conditions al l over the pump annulus. Those effects were somewhat influenced by tip clearances, but only when the clearance ratios became greater than about 1 per cent, us stated in Dr. Huttons analysis. Where three-dimensional flow conditions were involved, it seemed


892 COMMUNICATIONS

appropriate to introduce some modified two-dimensional theory and design and to develop new methods on a com- promise, according to the authors proposal. The authors study was a real advance in that direction, but some further work and experimental evidence was surely needed, in order to ascertain completely the importance and the in3uence of three-dimensional effects on pump performance by different impellers and diffuser bladings and for various specific-speed ranges.

Dr. Spencers work in establishing valuable information about overall performance of an axial-flow pump in the investigated specific-speed range and by various numbers of blades and by various blade tip clearances (from 0.6 to 2.4 per cent blade height) was of remarkable interest.

He fully agreed with the authors results and conclusions. He had himself had occasion, some eight or nine years earlier, in his research laboratory, to investigate by different axial-flow and Kaplan pumps the influence of blade tip clearances with a varied number of impeller blades (3,4, and 5 blades), on both an open and a closed circuit. One of them had been an axial-flow pump with a spiral casing, four thin symmetrical inlet guide-blades, an experimental impeller with 230 and 115 mm. (about 9& and 4 g inches) tip and hub diameters, five straightener blades and 300 mm. (about 11% inches) volute delivery diameter. Its blading-height had been 57.5 mm. The specific speed of the pump at the operating point had been

n4 = n . QO.5 . H-0.75 = 175 The best overall pump efficiency had been obtained with

a tip clearance of 0.5 mm.; the optimum tip clearance had been found to be 0.87.

With other investigated experimental axial-flow pumps or pump models with a bending-casing, the optimum tip- clearance per centage values had reached from 0.7 to 0.85.

The effect of the number of impeller blades on axial- flow pump performance curves as determined by the authors, was somewhat in agreement with his own results. With reduction of the number of blades audible cavitation had occurred at flow-rates nearer the operating point, but all through his own research work in that field he had obtained the highest efficiency values with three-blade impellers. That had perhaps been due to the method he had used in calculating and designing the bladings of his experimental axial-flow pumps. That had been a somewhat intermediate method between the conventional cascade (two-dimensional) and a three-dimensional flow motion method with an approximate consideration of the secondary flows associated with the change in axial velocities and their radial distribution along the pump blading.

Dr. Spencer was correct in acknowledging that an analysis of overall performance of the entire pump unit, which included intake, impeller, and diffuser, was of major practical importance to one confined only to the blading performance.

Professor F. NUMACHI (Japan) wrote that Dr. Hutton had done valuable work in obtaining results on the impeller of

small hub tip diameter ratio and of large specific speed; it was also very useful that he had found the optimum value to lie in e = 1-2 per cent as to the effect of tip clearance, which was usually subject to discussion at the design stage. But, as to the result in which tip clearance was shown as giving an extremely great effect on the characteristics of blade sections (Fig. 15, etc.), a problem remained for researchers to solve in regard to how it worked in a usual type of impeller, having smaller pitchchord ratios of blade elements.

Kahane (1948) Bowen and others (1951) and Goga (Goga 1955)* had already pointed out that there was an agreement between the theoretical and the eXrjerimental result of performance when mean axial velocity was taken in three-dimensional design of impellers (by cascade theory). It followed that change of axial velocity was duly to be considered also in the case of three-dimensional design by aerofoil theory, papers on which, however, had not been made known except by Ikui (1956)t. In that paper, which had been read only a short time before the authors paper, the whirl distribution of impeller treated had also not been of the free-vortex type.

In comparing slip theory and cascade theory with his so-called modified theory, the author had limited the former to two-dimensional scale, the propriety of which he would question. . Further, he would point out that in the two-dimensional

slip theory to be used for comparison, when residual whirl component eu at the exit of impeller was considered, the value of + obtained by that theory agreed with the experimental result to the same degree as the result of the authors modified aerofoil theory, i.e. static pressure rise obtained merely by the impeller was :

012-022

2g H = -

Expressed non-dimensionally gave, in place of equation (l), the expression

The slip factor h by Wislicenus being introduced, +ca = 1-(+2 cot Pz)2++12-+22

- {l-dl-#m)

neglecting the axial velocity change (+12-+22). The results calculated by that expression had been drawn

into Fig. lla, b and c and was shown in Fig. 37$. It should be remembered that Howell had aimed at the

case where the range of pitch chord ratio = 0.64.2 and had not considered the application to the case where the range was 1.3-3.0 as in the impeller of the authors

Gaga, A . 1955 Tram. Japan Sac. Mech. Eng., 001. 21?p. 358, Theory of All 50 per cent Reaction, Uniform Axial Velocrty Type Axial Flow Compressor. Ikui, T . 1956 Memoirs of Faculty of Engineering, Kmhu University, vol. 16, No. I , Axial-Flow-Fans and Compressors of Solid Vortex Blading, read at the General Meeting of Japan SOC. Mech. Eng., in Tokyo, on 1st April 1956. H . Murai, Assistant Professor of the Instrtute of High Speed Mechanics, worked out the &vation of the expression and the illustrations.



original cascade theory which he had quoted in comparison with his own. In regard to Dr. Spencers paper he considered it very

useful to designers that the author had made clear the effect of tip clearance on the overall aciency and head coefficient. Measurement had been made at downstream from the bend pipe in the experiment, but he himself did not think the true pump pedormance could be observed at that head.

With respect to increasing the resistance to cavitation susceptibility, the author had quoted the sections of Warren (1953) as well as Numachi and Murai (1952). But, he would point out that adequate sections (Numachi and Abe 1952, 1953)* could be obtained by interference theory taking account of the suitability (Numachi andothers 1953)t of pressure distribution on the section surface, and theoretically developed sections such as those by Warren should be preliminarily verified by cavitation tests for them to be of use in cavitation characteristics.

Mr. A. PFENNINGER (Zurich) wrote that, in regard to Dr. Spencers paper, he would first refer to his own paper (Pfenninger 1953)$ in which were reported some investigations on model runners of various specific speed for axial pumps and the test results illustrated. Since calculation of a good propeller called for observance of the aerofoil theory,

Numachi, F., and Abe, S. 1952 Reports Institute High Speed Mechanics, Second Report, vol. 2, p . 21; 1953 Fourth Report, vol. 3, p . 139, Cavitation Tests on Hydrofoil Profiles Suitable for Arrangement in Cascade. + Numachi, F., Murai, H., Abe, S., and Chida, 3. 1953 Report Institute High Speed Mechanics, Third Report, vol. 3, p . 99, Comparative Study of Suitable Types of Pressure Distributron Prescribed for the Calculation of Cascade Profiles.

$ Pfenninger, A . 1953 Hydraulic Installations, Propeller Pumps (Escher Wyss News, Zurich).

0 0.2 0.4 0.6 0.8 1.0 1.2 FLOW COEFFICIENT. 42

a Near hub, x = 0.44.

0.2 0.4 0.6 FLOW COEFFICIENT, 42

b Near tip, x = 0.78.

0 0.2 FLOW COEFFICIENT.

c near tip,^ =

0.6 b*

0.98.

Fig. 37. Comparisons of Theoretical and Measured Head-Flow Curves for Sections Along the Blade X Aerofoil theory. 0 Experiment. ---- Numachi slip theory.

I


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knowledge was necessary of the behaviour of the chosen blade profile in the cascade. The measurement results were shown for the separate blades as also in the cascade. In view of the fact that the guide apparatus also had a considerable influence on the characteristics, particular atten- tion had been paid to its design. Axial-flow wheels also called for a satisfactory and well-ordered inflow of the water to the impeller, which factor had also been investigated on the basis of separate tests carried out with air. The final shape of the inlet found in that manner had then been confirmed as correct by hydraulic tests, whereby an improvement in efficiency had resulted as compared with the normal bend.

Dr. RAMADAN SADEK, M.Eng. (Associate Member), wrote that Dr. Hutton had stated that for constant inlet incidence i, the deviation angle at any particular blade section was un- affected by tip clearance; i.e. for widely different three- dimensional conditions, the relative flow always left the blade at the same angle. That did not agree with his own computation.

Considering Fig. 6, for + = 0.20 and the two extreme tip clearances, the whirl angle downstream of the rotor, at x = 0.5, ranged from 52.7 deg. for e = 0.5 per cent to 33.5 deg. for e = 4.5 per cent. Using th

the performance of an axial-flow pump

Documents

design flow

axialflow pump

method of pump design

method of design

design of propeller

modified aerofoil theory

blading design

aerofoil characteristics