Energy Convers. Mgmt Vol. 33, No. 2, pp. 89-97, 1992 0196-8904/92 $5.00+0.00 Printed in Great Britain. All rights reserved Copyright 1992 Pergamon Press pie

THE EFFECT OF TIP CLEARANCE ON THE PERFORMANCE OF AN AXIAL FLOW FAN

S. J. VENTER | and D. G. KROGER~ IBureau for Mechanical Engineering, and 2Department of Mechanical Engineering, University of

Stellenbosch, 7600 Stellenbosch, Republic of South Africa

(Received 1 September 1990; received for publication 16 April 1991)

AImraet--The effect of a change in clearance between the blade tip and the fan casing on the overall performance of an axial flow fan is investigated. A new approach, which accounts for the installation effect of a fan in its normal operating range, is employed. In the proposed method, changes in fan static pressure, volumetric flow rate and fan static efficiency are all evaluated, whereas normally the effect of tip clearance is presented only on fan static pressure and fan static efficiency for constant volumetric flow rates. The proposed method of evaluation is illustrated by applying it to experimental data generated in a standardized fan test facility. The hub to casing ratio of the fan investigated is 1:6.7. The test code used is BS 848: 1980: Type A, which is valid for a free inlet, free outlet installation. It is concluded that the tip clearance effects are dependent on the type of fan rotor, the size of the rotor, as well as the type of installation in which the fan is used.

Air cooled heat exchanger axial flow fan Blade clearance tion Fan characteristics Fan efficiency Fan losses Installation effect System effect Tip clearance Tip gap

Blade gap Fan Fan appliea- Fan performance Flow losses

Tip leakage

NOMENCLATURE

A ffi Area (m 2) c -- Constant of straight line correlation

D = Fan diameter (m) k ffi Pressure loss coefficient in terms of volume flow K--Pressure loss coefficient in terms of velocity m -- Gradient of straight line correlation N = Fan rotational speed (rpm) P -- Fan shaft power consumption (W) p = Pressure 0NT/m 2)

P,F = Fan static pressure (N/m 2) s ffi Local tip clearance gap (m) T = Torque input to the fan (Nm) V = Volume flow rate (m3/s) v = Velocity (m/s)

Greek letters = Flow coefficient -- Expansibility factor

A ffi Differential t/ffi Efficiency (%)

q.F = Fan static efficiency (%) p ffi Density (kg/m 3)

Subscripts 1 = Initial point of integration 2 = End point of integration

avg = Average bell = Inlet bellmouth

d -- Dynamic F ffi Fan

red -- Reduced values ref-- Reference values

s = Static sett -- Settling chamber sF -- Fan static

~ro whom all correspondence should be addressed.

89

90 VENTER and KROGER: AXIAL FLOW FAN PERFORMANCE

INTRODUCTION

The objective of this report is to present a method of evaluating the effect of tip clearance on the performance of axial flow fans. A typical example of the application of these fans is in air cooled heat exchangers, used extensively in chemical and industrial plants, as well as in electrical power generation units. It is shown that the power consumption of these fans can be reduced by ensuring that the gap between blade tip and casing is small.

A number of authors have investigated the effect of tip clearance on the performance of axial flow fans. The majority of these publications are concerned with shrouded axial flow fans incorporating flow enhancement devices such as preswirlers and multiple stages (notably those by Eck [1], Balje [2] and Wallis [3]). The publications most applicable to the type of fan investigated in this report are those by Monroe [4], Marcinowski [5] and Stork [6].

Monroe presented his data as a percentage loss in fan total pressure and fan total efficiency plotted as functions of the actual tip clearance. The results obtained in this study are presented as ratios of reduced fan static pressure and fan static efficiency relative to the reference values of the above, respectively. The preference for fan static pressure over fan total pressure for exhaust fans is in accordance with the proposals of authors such as Wallis [3]. The tip clearance is divided by fan casing diameter to present it as a dimensionless parameter. This is notably different from the ratio between tip clearance and blade span used by Wallis [3]. The blade span of the axial flow fan used in this work is not as well defined as those having multiple stages. Also, the velocity profiles at the fan outlet exhibit some reverse flow regimes in the vicinity of the hub. These factors combine to ensure that the tip clearance ratio should be referred to the casing diameter for fans exhausting directly into the free atmosphere. This is in accordance with the work by Marcinowski [5] and Stork [6].

APPARATUS AND EXPERIMENT

A schematic diagram of the fan test facility is presented as Fig. 1. It consists of a calibrated inlet bellmouth (1), followed by a flow throttling device of the louvre type (3), with egg-grate flow straighteners installed both upstream and downstream of the louvres (2 and 4). The auxiliary fan (5) is used to overcome the resistance inherent in the test facility. This makes it possible to test fans down to atmospheric inlet pressures. The egg-grate flow straightener (6), immediately downstream of the auxiliary fan, removes the rotational flow components introduced by the rotor

Z~Pbe I~ / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / IIJII.IlJJ lJJIIIIJJIllL

, ~ , ~ Tse~i"

I I I ,

I I I I I I I I I

I t t Anset , - - I I I

I I I l i . . . . I i .

. i t I I I . . | ~t t I I Iq .,.I I

"I l l I "J i , / / / / / / " / / / /2 / / / / )~ ' / / /} / / / / / / / / / / " / / / / / , : / / / / / /~

J /

| . I !

%\ / I

I

" / / / / / / / / / / / / / / / / / , " / /

Fig. I. Schematic of the standard fan test facility--type A.

VENTER and KROGER: AXIAL FLOW FAN PERFORMANCE 91

into the main air stream. The concentric flow dampers (7) at the inlet of the settling chamber (8), enhance the flow distribution before it passes through the set of stainless steel mesh streens (9). The test fan (10) is installed in a casing at the outlet of the settling chamber. The drive unit (11) consists of a hydraulic motor, a calibrated torque transducer and a rotational speed indicator. The complete test facility is calibrated to ensure that it conforms to the requirements of the British fan test code BS 848:1980:Type A [7].

The 8-bladed axial flow test fan or ventilator (referred to as V) has a huh diameter of 230 mm. It is installed in a casing with a fixed outlet diameter of 1542 mm. The inlet casing of the fan consists of an elliptical nozzle or bell inlet.

According to BS 848 [7], the volumetric flow rate through the calibrated inlet bellmouth is given by

~d~l, v = ~E- W- i " - - " (1)

The fan static pressure is obtained by measuring the static pressure inside the settling chamber, i.e.

Ap,F = -- (Ap,.,, + p~,,,) (2)

where I / vV

p, , . . = (3)

The corresponding shaft power consumption of the fan is determined from the measured input torque to, and the rotational speed of, the fan

[2nN'~ P = T~-~- ) (4 )

while the fan static efficiency is determined from

Ap,F V ~,F = - - (5)

P

The tip clearance is varied between 3 and 10.5 mm, resulting in corresponding tip clearance to casing diameter ratios, s/D, of between 1.9 x I0 -3 and 6.8 x I0 -3. The results of these tests are shown graphically in Figs 2-4.

Z

O.

0,,

U

u)

c- O

la.

3,50

300

250

200

150

100

50

B$ 848 : lg80 : Type A ~ , V - type fan : 8 bladed

Diameter -- 1542 mm Ap . 0.8184/V 2 Blade angle - 16 deg

," Denaity - 1.2 kg/rn a

Speed - 750 rpm .~ . ~ -

np ~lea~o / " ,: ...',,~',.,, o

- - *- 4.5 mm "~'"% - -~- 6.0 turn b~'~l~,~ . - . . - . - =n

--,-- 9.atom "':,,.~,%, ----e- 10.5 mm ~ ~'~

, , , , , , , . . , , , , , , , _ _ , . _ , . ,

4 6 8 10 12 14 16 18 20 22 24. 26 28

Volumetr ic flow rate . V , mm/a

30

Fig. 2. Tip clearance effects: Ap,r vs V.

ECM 33/2--.-B

92 VENTER and KROGER: AXIAL FLOW FAN PERFORMANCE

70

60

~=50

u 40 e-

30

20 c o

h

10

TIp cleoranae

a 3.0 mm - - e - 4.5 mm - '~- ' - 6.0 turn ----v--- 7.5 mm " -+- 9.0 mm

~ . .mm.

, I , I , I , I , I , I , I 0 I , I , ~1 ~ ~t I

6 8 10 12 14 16 18 20 22 24 26 28

Vo lumetr ic f low ra te . V . m3/s

!

3O

Fig. 3. Tip clearance effects: fan static efficiency.

ANALYS IS

In practice, the implications of different blade tip clearances on the performance of a fan are of interest to the designer of fan systems. Monroe [4], for instance, investigated the drop in pressure and efficiency at constant volumetric flow rates. This method is not representative of the reduction in fan performance if the same fan is installed in the same system with different tip clearances. An arbitrary system resistance line (through the point of maximum efficiency) is used to illustrate the argument (refer to Figs 2 and 5 with a system resistance Ap = 0.8184 V2).

9000

Tip clearance BS 848 : 1980 : Type A 8500

a ' 3.0 mm V- type fan : 8 bladed

8000 - -e - 4.5 mm Diameter == 1542 mm

- -~- - 6.0 mm Blade angle - 16 deg - -0 - - - 7.5 mm

~'. 7500 - -+ - 9.0 mm Density - 1.2 kg / rn ~

c =- 10.5 mm Speed == 750 rpm 0 = 7000 O.

6500

o 8ooo

~ 5500 ~= 5ooo I t .

4500

4000 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Vo lumetr i c f low ra te , V , m3/s

Fig. 4. Tip clearance effects: fan power consumption.

VENTER and KROGER: AXIAL FLOW FAN PERFORMANCE 93

350

, 300

z - 250

n

- 200

M 150

0 .6o

Ioo

0

b. 5O

0 I O0 200

Vo lumetr i c f low ra te . V 2 , mS/s 2

i i

BS 848 : 1980 : T Iee A

M- r ipe fort : 8 bloded

Diameter , , 1542 mm

D.~'~ '~.~ Blode *,ngle - 16 deg

" .~-4~. . - : .~ . .~~ / Density - 1.2 kg/m a

. . 3.0 m~ "--: : . "--.~..~ - - ~" 4.5 mm ~ ~." -'." - -~- - 6.0 mm "--< ~v- - 7.5 mm - -+- 9.0 mm

a- 10.5 mm

t I I I I I , I , I , I ,

150 250 300 350 400 450

Fig. 5. Tip clearance effects: Ape vs V 2.

The new approach, discussed in this paper, is based on the assumption that the fan static pressure curves for different tip clearances can be approximated by Ap, v ffi m V 2 + c. Figure 5 illustrates the reasoning behind such an approximation. A distinction is made between parallel and non-parallel fan static pressure curves presented on graphs similar to Fig, 5. Parallel curves all have the same gradient, m, whilst non-parallel curves each have a unique gradient (m,~ and m~).

The reference conditions are defined as the prevaifing operating conditions of a fan with a tip clearance of 3 nun and the reduced conditions as the prevailing conditions for any other tip clearance in excess of the 3 mra reference setting.

Classically, the system flow losses are assumed to be directly proportional to the square of the velocity or volume flow rate through the system [8, 9]. The definition of pressure loss coefficients states that

1 2 Ap = pv = k v 2 (6)

where the effective loss coefficient based on the volume flow rate k = Kp/2A 2 and V ffi vA. The reduction in fan performance is indicated by fan static pressure and volumetric flow rate

ratios. These ratios are defined as:

Fan static pressure ratio ffi (Ap,F),~ (7) (Ap,e)~f

Volumetric flow rate ratio = V.~ v f" (8)

In the application of fan characteristic curves to specific systems, the operating point is determined by obtaining the intercept between the increase in pressure due to the fan (fan static pressure) and the resistance of the system. This means that the following relationship exists between volumetric flow rate and fan static pressure at the operating point for the reference curve:

(Ap,F)ref ---- Ap~f ---- k V~f. (9)

Similarly, for a reduced curve,

= kvL (lO)

94 VENTER and KROGER: AXIAL FLOW FAN PERFORMANCE

thus

V~f /(ap,r).~ (11)

The direct relationship between fan static pressure and volumetric flow rate loss ratios for the same system reduces the number of calculations required to predict the effect of tip clearance on the fan performance. A more general definition of the loss ratios can be formulated by determining an average value, valid for systems having pressure loss coefficients in the practical range of application of the fan (say k ranges between k~ and k~). The average fan static pressure ratio for this range is equated as

F(ap,,.q _ - k2 (12) L~J,, , fk, dk

Equation (12) reduces to the following (see Appendix): for non-parallel curves:

(m,,a-m,,f~ (k,-m.~l=fV.~ Y [(aP")"l -~'~[1+ ~:k , , / x ln for parallel curves:

~ J a v g Cref k~ Vrgd/ "

(13)

(14)

RESULTS AND DISCUSSION

Figures 2-4 summarize the data pertaining to tip clearance effects with all the relevant derivations included in the Appendix. From the Appendix it is apparent that the final graphs representing the effect of tip clearance (Figs 6 and 7) are applicable to a range of volume flow rates (between 10 and 22 m3/s). This corresponds to a range of effective loss coefficients, k, of between 0.17 and 2.32. The effect of tip clearance on both fan static pressure and volumetric flow rate is linearly related

1.00

0.98 0

8 ~ o.gs

0.94 0

E 0.92

> "~ 0.90 t- O

0.sa

m 0.86

0.84. 0.0

B$ 84-8 : 1980 : T~e A ~

Diameter == 1542 mm I ~ "e. Blade angle - 16 de 9 I ~ "~ ~. Oen,Wty - 12 kg/m~ ] \ Speed ~

-7 - I \ -- e - Volumetr_ic_ flow rate J "1~

uonro= [4] - pr,=,ure roUo I \

1.0 2_0 5.0 4.0 5.0 6.0 7.0 8.0

Dlmenalonles8 tip clearance , D [x lO00]

Fig. 6. The effect of tip clearance on fan static pressure and volume flow.

VENTER and KROGER: AXIAL FLOW FAN PERFORMANCE 95

1.00

0.95

~ ~ 0.90

0 -~ 0.85 0

0 ~ o.8o "6

0.75 0

== 0.70 c- o u. 0.65

0.60 1.0

o

Cl Ill C l ~

BS 84.8 : 1980 : T)l~e A

Number of blades =, 8 OlameLer ,= 1542 mm

Blade angle - 16 deg Densi ty =, 1.2 kg /m a

Speed == 750 rpm

.O

a 16.08 m3/s . max. q Monroe [ ' ,] Marclnowsk! 1 [5 ] Ivlarclnowskl 2 [5 ] o s~.ork [6]

,V,

I I i I I I I I I I I l I

2.0 3.0 4.0 5.0 6.0 7.0

D lmens lon less 'Jp c learance . D [x1000]

8.0

Fig. 7. The effect of tip clearance on fan static efficiency.

to the clearance itself, provided that the system losses can be represented by Ap = kV 2. It is independent of the resistance of the system in which the fan is operating if the characteristic curves in Fig. 5 are parallel.

Unfortunately, the fan static efficiency is not only related to the fan static pressure and volumetric flow rate through the system, but also to the power input to the fan. This makes it intractable to use a single graph to present the effect of tip clearance for a range of systems having different loss coefficients. The effect of tip clearance on fan static efficiency is referred to a tip clearance of 3 mm for a range of volumetric flow rates. Figure 7 highlights the fact that tip clearance effects on fan efficiencies cannot be presented as a single graph for a specific fan. The effect is dependent upon the required differential pressure of a specific fan application (or system resistance).

The VDI fan test code [10] suggests that the tip clearance effect is related to the boundary layer thickness and the pressure differential across the fan rotor. In concludes that the tip clearance effect for a full scale unit results in larger reductions in fan performance than their scaled counterparts measured for a smaller model of the actual unit. This means that the reduction in performance of the scale model due to an increase in tip clearance, presented in Figs 6 and 7, underestimates the actual reductions in performance expected in larger scale units. The same argument is extended to the type of duct system in which the fan rotor is installed. The boundary layer thickness at the inlet to a fan installed in a ducted system is larger than the same for a fan with an elliptical inlet from free atmosphere. The rate of boundary layer growth for accelerating flow (associated with elliptical inlets) is less than for the flow between two parallel duct walls (associated with ducted fan inlets).

The relative boundary layer thickness is smaller in a full scale unit than in a scale model (provided that their entrance lengths are geometrically similar). The tip clearance ratio of the full scale unit is required to be smaller than the corresponding ratio for the scale model to ensure the same operating conditions in both cases. Thus, the tip clearance ratio for the full scale model which results in the same fan static efficiency as measured for the small scale model, is presented by:

a-- = (15)

where the primes refer to the full scale unit and the normal symbols to the measured results from the smaller scale model.

96 VENTER and KROGER: AXIAL FLOW FAN PERFORMANCE

Table 1. The effect of tip clearance on pressure and volume flow ratios

Tip Tip clearance Pressure Volume clearance ratio Gradient Abscissa ratio ratio s (ram) (s/D x 1000) m c c~/c~ c~/c~f

3.0 1.9 -0.4552 326.04 1.000 1.000 4.5 2.9 -0.4552 316.88 0.972 0.986 6.0 3.9 -0.4552 308.61 0.947 0.973 7.5 4.9 -0.4552 302.29 0.927 0.963 9.0 5.8 -0.4552 291.49 0.894 0.946

10.5 6.8 -0.4552 283.97 0.871 0.933

Equation (15) is derived from the boundary layer thickness growth relationships for a fiat plate. In the case of negligible inlet lengths (as for fans having inlet shrouds) equation (15) needs careful consideration because the boundary layer growth is limited due to accelerating flow in the inlet shroud.

The previous two paragraphs give some indication of the sensitivity of the tip clearance effect on different types of fan rotors and installations and should be taken into account when evaluating the data presented by other authors. Although not all the vital information is available for each relevant publication, a general comparison of results can be made. The pressure and volumetric flow rate data of this report is of the same order as that of Monroe [4], as is shown in Figs 6 and 7. Monroe's data is not representative of an axial flow fan installed in a system for which only the tip clearance is adjusted. Stork [6] presented their data in tabular form. Data for the worst possible cases are selected from their tables (maximum values for the drop in fan static pressure and efficiency). These are presented as data points on Figs 6 and 7. Unfortunately, no details are available as to the type of test facility or the boundary layer thickness used by Stork. Marcinowski [5] investigated the influence of tip clearance on two different fans for which two markedly different results are obtained (Fig. 7). He only stated the influence of tip clearance on fan efficiency. Results from his second set of data (for profiled and twisted blades) correlate well with the findings of this study, but a change in tip clearance results in lower efficiency ratio values for his first set of data (for untwisted steel blades). This accentuates the sensitivity of tip clearance effects on the type of fan model under investigation.

CONCLUSIONS

A new approach is proposed to present the effect of tip clearance on the performance of an axial flow fan. The resistance of the system in which the fan is installed is assumed to be Ap -- kV ~. The method gives the effect of tip clearance, not only on the fan static pressure and fan static efficiency, but also on the volumetric flow rate through the system. The experimental results, obtained for an 8-bladed V-type fan in a 1542 mm dia casing, can be approximated by straight lines through the reduction ratio in relevant parameters (see Figs 6 and 7).

Additional types of axial flow fans need to be investigated before more general comments on the effect of tip clearance on axial flow fans can be made.

REFERENCES

1. B. Eck, Fans--Design and Operation of Centrifugal, Axial-flow and Cross-flow Fans. Pergamon Press, Frankfurt (1973). 2. O. E. Balje, Turbomachines--A Guide to Design, Selection and Theory. Wiley, New York (1981). 3. R. A. Wallis, Axial Flow Fans and Duets. Wiley, New York (1983). 4. R. C. Monroe, Improving cooling tower fan system efficiencies. Combustion (May 1979). 5. H. Marcinowski, The influence of impeller gap in free discharging axial-flow fans without guide wheel. Voith-Forsch.

Konstruktion, No. 3 (1958) (Referenced by [1] and [11]). 6. Ventilatoren Stork Hengelo, General applications for E-type fans, V.691181, 73-08 (1973). 7. British Standards Institution, Fans for general purposes, Part 1. Methods of testing performance. BS 848 (1980). 8. R. Jorgensen (Ed.), Fan Engineering, 6th edn. Buffalo Forge, New York (1961). 9. W. C. Osborne, Fans, International Series on Heating, Ventilation and Refrigeration, Vol. 1. Pergamon Press, Oxford

(1977). 10. Verein Deutscher Ingenieure, VDI-Richtlinien-Abnahme- und Leistungsversuche an Ventilatoren, VDI 2044, Berlin

(1966). 11. General Electric, Fans--axial flow. Fluid flow division, Section 409.3 (April 1983).

VENTER and KROGER: AXIAL FLOW FAN PERFORMANCE 97

APPENDIX

Determination of Flow and Pressure Ratios A case study is performed to determine the pressure and volumetric flow rate ratios for a reduction in fan performance

due to a specific tip clearance. The fan static pressure curve for the reference case is given by

(ApsF)re f = rarefy 2 + Cre f (AI)

and for the reduced fan static pressure curve for the specific tip clearance by

(AP,v)~d = m.~V 2 + Cry. (A2)

Note that the gradients for these two cases have unique values m~ and m.~. The following two equations for the operating points of each system are derived from equations (9) and (10).

Ap~ = k V2f (A3)

Aped = k V 2 . (A4)

These two pressures are eliminated by substituting equations (I 8) and (19) respectively into equations (16) and (17), resulting in

2 _ 2 (AS) k Vre f -- mref Vre f + Cref

thus

V 2 - c~f (A6) ref - k - - ere f'

The same method can be used to derive the relationship for the reduced fan static pressure

c.~ (A7) V~d=k --m,.d" The fan static pressure ratio follows from equation (7):

mrcdCv~

(Apw)~ m~dV2+C~d k_m------~ "+e~

(~PsF)ref mref V2 + Cref mrefCref

k - m~ - - + c~

kcred

k - m~

kcref

k -- era

-m 5 = Cra\k - m-----~/

The average fan static pressure ratio is determined by solving equation (12).

F(,,p,F). 1 _J,, (,,,,,.),., = Jk, c.f\k - rn .~/

c.~ k 2 - m~ _~I (k2 -k , )+m~a-m~r) ln (k~- -~) l

(AS)

k 2 - k I

=c'F , + (m' - " ' l ln(k - m' l. (A9) c~ L \ k 2 - k, // \k , - m.~] J

In the event that all characteristics presented in Fig. 5 are parallel to each other, the gradients of the reference and reduced characteristic are equal, i.e. ere f = ere d . This assumption is incorporated into equation (24) which simplifies to

[ (Ap,F).. 1 =c . (AIO) (Ap,~),~fj,, l c~f

for parallel characteristic curves.