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Distribution authorized to U.S. Gov't. agenciesonly; Test and Evaluation; JUL 1973. Otherrequests shall be referred to Naval ShipResearch and Development Center, Code 11,Bethesda MD 20034.

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NAVAL SHIP RESEARCH AHD DEVELOPMENT CENTER Bethssdo, Md. 20034

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ARCTIC SURFACE EFFECT VEHICLE PROGRAM

PREDICTION OF AXIAL AND CENTRIFUGAL FAN CHARACTERISTICS FOR LARGE SURFACE EFFECT VEHICLES

by John G. Purnell

i Sponsored by

ADVANCED RESEARCH PROJECTS AGENCY ARPA Order No. 1676 Program Code No. 1N10

Distribution limited to U. S. Government agencies only; Test and Evaluation; July 1973- Other requests for this document must be referred to Commander, Naval Ship Research and Development Center (Code 11), Bothesda, Maryland 20034.

PROPULSION AND AUXILIARY SYSTEMS DEPARTMENT

Annapolis

RESEARCH AND DEVELOPMENT REPORT

1 1

July 1973 ■ Report 3943

J Mr MÜ

A

J**K

The Naval Ship Research and Development Center ia a U. S. Navy center tat laboratory effort directed at achieving improved tea and air vehicles. It was formed in March 1967 by merging the David Taylor Model Basin at Carderoclc, Maryland with the Marine Engineering Laboratory at Annapolia, Maryland.

Naval Ship Research and Development Center

Bethesda, Md. 20034

MAJOR NSRDC ORGANIZATIONAL COMPONENTS

ORIGINATOR

NSRDC

COMMANDER „ 00

TECHNICAL DIRECTOR

OFHCER-iN- CHARGE CARDEROCK j

OS

OFFlCER-IN-CHARGE ANNAPOLIS

04

SYSTEMS DEVELOPMENT DEPARTMENT

SHIP PERFORMANCE DEPARTMENT

AVIATION AND SURFACE EFFECTS

DEPARTMENT 16

STRUCTURES DEPARTMENT

COMPILATION

AND MATHEMATICS DEPARTMENT

11

SHIP ACOUSTICS DEPARTMENT

19

PROPULSION AND * AUXILIARY SYSTEMS

DEPARTMENT 27

MATERIALS CENTRAL

INSTRUMENTATION

a DEPARTMENT 79

l

■mnsHH

mi m,

u

I I . DEPARTMENT OF THE NAVY

NAVAL SHIP RESEARCH AND DEVELOPMENT CENTER

BETHESDA.MD. 20034

1 -

PREDICTION OF AXIAL AND CENTRIFUGAL FAN CHARACTERISTICS FOR LARGE SURFACE EFFECT VEHICLES

by John G. Purnell

This research was supf/orted ry the Advanced Research Projects Agency of ths Department of Defense and was monitored by the Arctic SEV Program Office, Systems Development Department.

Distribution limited to U. S. Government agencies only; Test and Evaluation; July 1973- Other requests for this document must be referred to Commander, Naval Ship Research and Development Center (Code 11), Bethesda, Maryland 20024.

July 1975 27-404 Report 3943

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ABSTRACT

Two digital computer programs have been formulated for predicting performance charac- teristics of centrifugal and axial fans which may be used to provide lift air for large sur- face effect vehicles. Pressure rise and flow characteristics of forwardly curved, radial, and backwardly curved centrifugal fans can be evaluated. Axial fans having either inlet flow prerotators or exit flow straighteners can also be handled in the program. Sample results are presented to illustrate the method of calculation and the nature of the results.

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ADMINISTRATIVE INFORMATION

This study was conducted for the Arctic Surface Effect Vehicle Program Office of NSRDC through support provided by the Defense Advance Research Projects Agency of the Department of Defense. This work was done in the Gas Turbine Branch of the Power Systems Division, Propulsion and Auxiliary Systems Depart- ment of this laboratory under Work Unit 1-1150-272-15.

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*§* TABLE OF CONTENTS

Page

ABSTRACT iii ADMINISTRATIVE INFORMATION iv NOMENCLATURE VÜ INTRODUCTION 1

Prediction of Centrifugal Fan Characteristics 2 Flow Through the Centrifugal Fan 2 Euler Line 4 Effects of a Finite Number of Blades 6 Effects of Nonuniform Discharge Velocity 8 impeller Loss 11 Inlet Losses 12 Leakage Flow 14 Recirculation Loss 14 Outlet Losses 15 Efficiency 17 Comparison of Experimental and predicted Results 19 Limitations on Centrifugal Fan prediction Program 26

AXIAL FAN CHARACTERISTICS PREDICTION 27 Preliminary Design 28 Detailed Design 39 Prerotator Design 59 Impeller Design 41 Sfcraightener Design 43 Off-Design Performance Prediction 44 Comparison of Predicted Results 46 Limitations of the Axial Fan Prediction Program 49

CONCLUSIONS 55 RECOMMENDATIONS 53 TECHNICAL REFERENCES 54 APPENDIXES

Appendix A - Centrifugal Fan Characteristic Prediction Program (6 pages)

Appendix B - Axial Lift Fan Characteristic Prediction Program (10 pages)

Appendix C - Centrifugal Fan Weight Estimate (3 pages) INITIAL DISTRIBUTION

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NOMENCLATURE

CENTRIFUGAL FAN (EQUATIONS 1 THROUGH 40)

English

a - Effective radius of interblade circulation, ft

A - Area, ft3

b

cd

d

9c

k

Blade height, ft

Discharge coefficient

Diameter, ft

Characteristic roughness size, ft

Acceleration of gravity, ft/sec2

Gravitational constant, It^-ft/lbf-sec3

Loss coefficient

P - Pressure, lbf/ft3

AP - Pressure loss, lbf/vt3

Q - Volume flow, ft3/sec

r - Radius, ft

Rj-, - Blade height ratio, b1/bg

Rd - Diameter ratio, d1/d2

U - impeller speed, ft/sec

V - Velocity, ft/sec

w - Weight flow, lt^/sec

W - Weight, lbg,

z - Number of blades.

27-404

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Greek

g - Blade angle (measured from tangent), degrees

ß_ - Preswirl angle, degrees

6 - Inlet clearance, ft

r\ - Efficiency

p - Density, lbm/ft3

Y - Pressure coefficient

AY - Pressure coefficient

0 - Flow coefficient

uu - Rotational speed, rad/sec,

Subscripts and Superscripts

D - Diffuser

e _ inlet eye

E - Modified Euler line

imp - Impeller

in ~ inlet

leak - Leakage

m - Radial condition

max - Maximum

min - Minimum

out - Outlet

Ji

i

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I L.i r - Relative velocity

RC - Recirculation loss

S - Preswirl angle

static - Static conditions

total - Total conditions

u - Tangential velocity component

u' - Corrected tangential velocity component

V - Velocity pressure

0 - Impeller inlet

1 - Impeller blade inlet

2 - Impeller blade outlet

3 - Downstream of impeller outlet

oo _ Theoretical Euler line equation.

AXIAL FAN (EQUATIONS 41 THROUGH 95)

English

A - Area, ft3

c _ Blade chord, ft

CD .

CL -

D -

gc "

j -

n

Drag coefficient

Lift coefficient

Diameter, ft

Gravitational constant, lt^-ft/lbf-sec3

Number of blade sections

- Fan speed, rpm

i

27-404 IX

1 i

N - Number of blades

p _ Pressure, lbf/fts

Q - Airflow rate, ft3/sec

r - Radius, ft

s - Blade pitch (spacing), ft

V - Velocity, ft/sec

X - Diameter ratio, D^/Dtip

CL/

CD - Lift-to-drag ratio

Djj/Dtip - Hub-to-tip ratio, XH = DH/Dt£p

... i

Greek

a - Angle of attack, degrees

fc> - Blade angle of impeller, degrees

Y - Angle which relative velocity makes with the plane of rotation, degrees

6 - Angle which relative velocity makes with the axis of rotation, degrees

6 - Swirl coefficient

r\ - Efficiency

6 - Camber angle, degrees

p - Air density, lbm/ft

a - Solidity, c/s

0 - Flow coefficient

Y - Pressure coefficient

AY - Pressure drop coefficient

uur - Tangential velocity component, ft/sec.

27-404 J ^^______ am -= ■ ■. ■- .'■ -----

memx&.mämim

Subscripts and Superscripts

an - Annulus

ax - Axial direction

D - Diffuser

des - Design cond: .tion

duct - Duct

H Hub

i - Blade section

imp - Impeller

j - Total number of blade sections

m - Midspan of blade

o _ Zero lift condition

p - Prerotator

PR - Profile

S - Straightener

sec - Secondary

St - Stall

T - Total

th - Theoretical

tip _ Blade tip

* - Optimum condition

1 - Impeller inlet condition

2 - Impeller outlet condition,

i^maH

27-404

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INTRODUCTION

Cushion air fan characteristics play an important part in the speed/range performance, as well as the riding quality of a surface effect vehicle (SEV). The most desirable fan character- istic is one having as flat a slope as possible, that is, a small change in pressure output for a large change in fan output flow rate at a given fan speed. The flatter the fan characteristic, the smoother the riding characteristics of the SEV.

At this time, only axial and centrifugal fans appear to have future application to large SEV craft.1 This is due mainly to their high efficiencies but also to their low-to-moderate weight and size, and their proven feasibility and reliability. Centrifugal fans with backwardly curved blades have been used extensively in the relatively small SEVs that have been built to date. Axial fans have seen a very limited application on present SEVs, mainly due to the cost advantage of the simpler centrifugal fan, which may not be a decisive factor on larger craft.

In this report, digital computer programs are outlined for predicting fan characteristic curves for centrifugal and axial fans. One objective of these programs was to provide the fan performance prediction in a relatively uncomplicated manner so as to enhance their usefulness. A reasonably high accuracy can be achieved with the programs which mainly require only the geo- metric details of the fan to make the performance prediction. The centrifugal fan prediction program is based largely on the work of Osborne3 and Shipway.3 Additional modifications to account for nonuniform discharge velocities and recirculation losses were added. The centrifugal program will predict fan performance for a forwardly curved, radial, or backwardly curved centrifugal fan. The axial fan prediction program was the result of work pre- sented by Wallis4 and Shipway.5 The axial program predicts per- formance for an axial fan having either exit flow straighteners or inlet flow prerotator using either isolated or cascade airfoil data.

With these programs, it is possible to predict the perfor- mance of a given axial or centrifugal fan with a reasonable degree of accuracy. Also, these programs will be used to study the effects of certain variables on the fan characteristic curve in order to determine what most significantly affects the fan char- acteristic slope.

1 Superscripts refer to similarly numbered entries in the Technical References at the end of the text.

27 -404

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A printout of the present centrifugal and axial fan charac- teristic prediction programs with sample data are shown in appendixes A and B, respectively. Also, separate nomenclatures are used for the axial and centrifugal fan, and no attempt has been made to unify them since the similar expressions can have a totally different form for the different fans. Appendix C pre- sents the details of the centrifugal fan weight estimation proce- dure.

i

PREDICTION OF CENTRIFUGAL FAN CHARACTERISTICS

The following method outlines a means of predicting centrif- ugal fan characteristic curves for squirrel-cage-type fans which are commonly used in SEVs. The prediction method follows similar methods presented by Osborne3 and Shipway3 but several modifica- tions have been made. These modifications include mainly a cor- rection for nonuniform discharge velocities suggested in Shepherd6

and Wislicenus,7 and a recirculation pressure loss proposed by Galvas.8 The characteristic pressure-flow curve is derived in both dimensional and nondimensional form h-2 .onsidering the theo- retical Euler line equation and substracting the various losses from it. The method requires only the following fan geometry and system parameters to predict results:

• Inlet and exit blade diameter.

• Inlet and exit blade heights.

• Inlet and exit blade angles.

• Inlet eye diameter.

• Number of blades.

• Exit flow area.

• Tip speed.

A comparison of predicted and experimental characteristics for a HEBA/B-type centrifugal fan is made, and the effects of varying this fan geometry on the characteristic curve is studied.

r'LOW THROUGH THE CENTRIFUGAL FAN

By conservation of mass for steady incompressible flow, the inlet flow to the fan will equal the flow out of the fan. How- ever, the flow through the impeller is usually greater than the inlet flow because of a leakage flow between the impeller and

27-404 Ji

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[ 1

! ■

casing which recirculates through the fan and is a function of the static pressure differential between the impeller inlet and outlet. Thus, referring to figure 1:

'Jin = Q out

Qimp ■ Qin + Qleak * Qout + Qleak

(1)

(2)

Mil

QLEAK

Mil

c, -

OUT °IMP

1

T

-d|-

-d2.

»2 1 1

Figure 1 Geometry of a Centrifugal Fan

27-404

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Therefore, in the analysis of the fan and its losses, the impel- ler should be based on equation (2) while the analysis of the inlet and outlet should be based on equation (1). It should be noted that even when Qin and Qout equal zero, Qimp can be greater than zero. The method of calculating Q^eak will be shown later.

i ,j

I v

EULER LINE

The Euler line describes the maximum theoretical pressure flow line for the centrifugal fan. it considers the fan to have an infinite number of blades of infinitesimal thickness so that the entire airflow through the fan follows the blade contour exactly, thus producing the maximum pressure rise assuming no sources of loss are present. Figure 2 shows an outlet and inlet velocity diagram for a centrifugal fan impeller.

Item (a) - Outlet Velocity Diagram Item (b)

Inlet Velocity Diagram with Preswirl

FOR ZERO PRESWIRL()8S=0)

Figure 2 Centrifugal Fan Velocity Diagrams

In item (a) of figure 2, the tangential component of the absolute outlet velocity Va is Vu , while the radial component is Vm and the relative velocity is Vr . The maximum work that can be done on the air will be equal to the energy in the air leaving the impeller, where, for radial inflow:

maximum work ■ Pco Qimp W V u. u. (3)

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I

where W is a weight flow rate of air. In terms of pressure rise rather than energy, equation (3) may be written as:

gc us a (4)

Using figure 1 and item (a) of figure 2, the following expression for Vu is obtained:

u9

5 i !

Vua - Us - vms cot ßa

where

3 2 (5a)

vm. " imp

"d2bS (5b)

Thus, the theoretical Euler line equation becomes

P_ = u; P U0 Q s ^imp

g„ 3 g„ Trd„b„ 3c ^c 2 2 cot ß (6)

The calculations carried out in terms of physical variables may be converted to dimensionless form by the use of two princi- pal dimensionless variables:

pressure coefficient f - pressure

-2- U* 9c '

(7)

27-404

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flow coefficient 0 = flow

(8)

* J

i ■ -

The pressure coefficient characterizes the dynamic condition of the flow and represents the pressure divided by the velocity pressure corresponding to the impeller tip velocity.9 The flow coefficient expresses the kinematic conditions of the flow and represents the ratio of the axial velocity of the flow based on the fan diameter to the tip velocity of the fan impeller.9 Hence, using the above expressions, equation (6) becomes (in nondimen- sional form):

Y. = 1 - 0imn -St cot ß imp TTb„

(9)

where 0imp is based on Qimp of equation (2).

EFFECTS OF A FINITE NUMBER OF BLADES

The Euler line equation was derived by assuming the air exits the fan at exactly the trailing-edge blade angle. However, this is true only in the case of an infinite number of blades. This is particularly important for the impeller channel of a centrifugal machine where even for ideal flow (that is, without friction, turbulence, and separation), effects combine to modify the expression for the theoretical Euler line equation.

One cause of deviation of flow from the theoretical ideal is interblade circulation. Stodolai0 has suggested that it is the inertia effects of the fluid particles between adjacent blades of a radial flow impeller that must be considered. Due to their inertia, some particles tend to retain their orientation with respect to fixed axes, the result being a circulatory motion relative to the channel. This is similar to a container of fluid whirled with an anguiar velocity of w at the end of an arm, as shown in figure J>, where a particle of fluid, A, tends to remain stationary. However, relative to a point on the container, B, point A appears to be rotating in a direction opposite but equal in magnitude to that of tie arm. At any radius "a" within the container, the particle has a relative velocity of -aou.

27-404

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Figure 3 interblade Circulation

Assuming that the impeller channel flow behaves similarly and that this motion is superimposed on the outward flow between the blades, the effect is to reduce the value of the tangential veloc ity Vu to Vu2', where Vu' = Vu - aw. The effective radius of the area between the blades is difficult to assess, but is gen- erally taken as half of the perpendicular distance between the blade tangents at the impeller periphery,9 that is:

TTda sin 0. a = —a £- 2z (10)

where z is the number of blades,

Since,

OJ = Ha. £Hi

3 2

a* = *dP sin e? . £üi 2z d„

n sin p *-". • (11)

27-^04

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and

*■.'" V

n sin ß. u. Ue (12)

The net result of interblade circulation is to reduce the theo- retical pressure based on the theoretical ideal velocity diagram. However, this reduction of output potential is the result of the behavior of an ideal fluid and does not represent a loss in terms of fluid and rotor energies because the impeller is not called upon to supply this additional energy. The significance of the interblade circulation correction is that by increasing the number of fan blades for a given fan, while maintaining constant tip speed, diameters, and blade angles, higher pressure outputs are possible since the flow more closely follows the blade profile •angles; thus, the theoretical Euler line equation is more closely approached since interblade circulation effects are minimized.

L i

The reduction in theoretical Euler pressure due to inter- blade circulation is expressed by:

APb = -i. Ua aw 9c 8

„ __£. u? - sin ßa , g„ 3 z 2 (15a)

and nondimensionally:

A?, = H sin ß„ . (13b)

EFFECTS OF NONUNIFORM DISCHARGE VELOCITY

Another effect which causes the fan to deviate from the theoretical Euler line is that the radial velocity may not be uniform along the discharge of the impeller. The pressure pro- duced with a varying velocity is less than that produced with a uniform discharge velocity giving the same net flow rate. For a centrifugal fan having a linear variation of velocity across the depth of the channel, as shown in item (a) of figure 4, Shepherd6 showed that:

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1 !

i. i AP nd

= p Ufi Qimp

gc TTdsb S 3

(vmamax ~ vmamin) 4„f

12 V, m. cot ß. (14a)

and nondimensionally:

A? _ ^imp da nd =

rrb.

(v, m2max ~ msmi nV 12 Vm*

cot ß. (14b)

Item (a) Linear Profile

V,'-2MIN 'm2MAX

Item (b) Sinusoidal Profile

Figure 4 Nonuniform Discharge Velocity Distributions

For the case of a sinusoidal flow distribution, as shown in item (b) of figure 4, wislicenus7 showed that:

AP nd ■ P u

5 Qimp I""3 "I gc nd2b2 1$ ' J cot ß? , (15a)

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and nondimensionally: » y

0. d9 TTDg 8

- 1 cot ß. (15b)

Equations (15a) and (15b) also hold for a sinusoidal distribution in the peripheral direction around the impeller and the two velocity patterns may be superimposed giving a correction7 factor of [(rr2/8)2 - 1]. The causes of the nonuniform velocity distri- bution can be the manner in which the flow is turned from the axial to the radial direction in the inlet, as well as by real fluid effects such as friction and separation on the walls of the disk, shroud, and blades.

The net result of nonuniform discharge velocity is to reduce the maximum theoretical pressure predicted by the Euler line equation. However, like interblade circulation, this reduc- tion in output potential does not represent a loss because the impeller is not called upon to supply this additional output. Radial velocity distributions at centrifugal fan outlets, shown by Brotherhood,11 suggest that both linear and sinusoidal veloc- ity distributions' combined are generally present.

Although interblade circulation and nonuniform velocity distribution do not require or expend any energy, they do affect the fan efficiency since they represent lost potential which causes the theoretical Euler line to be modified downward. The modified Euler line equation on which efficiency is based now becomes:

PE = P» " APb - AP nd (16a)

and nondimensionally:

YE - *. - AYb - ATnd (16b)

Thus, minimizing interblade circulation and nonuniform velocity distribution effects should improve efficiency, since the theo- retical Euler line condition will be more closely approached.

27 -40*1 10

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UJ IMPELLER LOSS

A loss occurs in the impeller due to separation of the fluid stream during flow through the blade passage and is defined as:

APimp ~ yimp 1 _£ 2 g.

1 P (17)

The value of k-[mp is between 0.2 and O.J> for flat plate blades and on the order of 0.15 for aerofoil section blades.3' 3

Zero preswirl has been assumed in the calculations of Vj since APimp is very small at low flow rates and will not affect the final result, while at high flow rates preswirl is zero.2'3

By considering the inlet and outlet velocity diagrams of figure 2 and putting,

Qimp Vm = ——.— and v, 'm, TTd/b,

Qi mp m.

TTd8bS (18)

then equation (17) becomes:

AP. = KimP _£. Q* imp 2 gc

imp

- a

ndjbj sin ^ "daba sin ß. (19a)

and nondimensionally:

M. _ kimp /^imp d, vr—1 L_r I [PdPb sin p, sin ga I

(19b)

where Pd = d, /d, and Rb = b,/^.

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INLET LOSSES

The inlet loss is divided into two parts. First, air enters the impeller inlet section,usually through a reducing section, as shown in figure 1. The airflow must expand from the velocity at the inlet eye, Ve, to the axial velocity, VQ, at the impeller inlet (or exit of the reducing section) and be turned from axial to radial flow. The loss associated with the expansion may be expressed as:

AP in. 'in, _P_

9c vS (20)

Although the inlet conditions should be based on Qin, the calcu- lations may be simplified with minimal error by using Q^mv since the leakage condition is not known until the outlet conditions are known. Thus, equation (20) becomes:

AP in, - ^i^ _P_

2 9c

4* Q imp

TTV (21a)

and nondimensionally:

ini J- AYin, = -~ $ imp

Ü < TTde

2 (21b)

The value of kin ranges from 0.2 to O.5.3» 3

A second loss occurs as a result of expansion or contraction oi the air as it enters the blade passages. The loss also takes into account the effect of preswirl. British work0 suggests that for low flow rate where V0£Vr , the preswirl angle, ßs, is on the order of 45 degrees. At higher flow rates, where V0>Vr , the preswirl angle is zero. This loss is expressed by:

AP m.

kin_ p . .a

T"g7(V°-V (22)

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....... .. -..,

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. where kin_ lies between 0.5 and O.8.3,3 By substituting,

vo - 4* Q imp

rrdl (25)

and from the inlet velocity diagram of item (b), figure 2,

vrt - V Vmi + (Ul " V»i tan ßs)! (24)

Thus, equate a (22) becomes:

APin = 2ilk _£ " 2 gc

5-SiSB -«/ Vm" + (Ut - V tan ßa):

(25a)

In nondimensional form, this becomes:

*in Afin^ = Jp. 4 0 imp

Rd= TT

(1 + tan8 ps) . 2d, 0 2 '-imp tan ßs JL _ 3

+ *d HRbba

(25b)

The definitions of Rd, p^, Ay, and 0i , equation (18), and various relationships obtained from the inlet velocity diagram (item (b), figure 2) must be substituted into equation (25a) in order to obtain equation (25b).

27-404 13

■'-'- niiTfifirt-nrniM riiirtrfj-«i«-i«ii-i»MMrrifir«

■gypwawywBwp^ ■"" I^B^M.-S: ■TK,"-T-^; ::! .,.,,,, ■ .,,..,.... - . :.^r«^V^

;>;;?,.■-='.T.'-*'■:■■■ ■■■■,--■:■■■"■

■ ...„■■ ..;..- ■■■■...'. . ■ ■ ■:.-. >-: -! i ■ ■ ■ ■■ ■ ■■.■■; ■■■:—:■■ .■■ :--.-■!,:-.■ :;■.-. ■..■■:..-. ■ > -■■ ...;■■, ■-

LEAKAGE FLOW

Internal flow leakage occurs primarily between the impeller inlet and the casing inlet as shown in figure 1. Also, a leakage may occur around the drive shaft where it enters the casing, but this is far less serious than the inlet leakage and is not con- sidered. The leakage volume that flows back into the inlet from the impeller exit area may be treated as flow through an orifice, that is, the leakage volume may be written:

i....; i \

Qleak = cd nd

■ •/

2P static (26a)

where C<3 is a discharge coefficient on the order of 0.6, Pstatic is the static pressure increase across the fan impeller, and 6 is the clearance between impeller and casing. Written nondimen- sionally:

#leak = cd ~ TT 6 d3 a

^2? static (26b)

where Tstatic = PstaticA pAfc) ul• In general, the static pres- sure difference (Ps) is nearly equal to the fan total pressure (Ptotal)» due to tne static depression caused by the inlet veloc- ity pressure and, thus, Ptotal may b® used in place of Pstatic without significant error.

For the case of Qout = 0, a static pressure difference exists across the fan impeller. Thus, a leakage flow exists, and there is a flow through the impeller, though the flow downstream is zero.

;imp " Qleak' even

FECIRCULATION LOSS

The recirculacion pressure loss is due to the leakage flow reentering the intake and causing addi,'onal work to be done to overcome dissipation, turning, and mixi. T losses. Osborne3 and Shipway3 do not consider a recirculation loss, although Galvas8

does consider a somewhat similar loss. The recirculation loss appeared to be best expressed as a function of the leakage flow velocity where:

27-404 14 i

ii-nffriTii"** -*"*■* iriiiiir^"** ... .. iii.

'" ' '■ "' ■■■'.- '■- - .-•■■ ■ . ' ■ . ■ ." •

■ l jäW ■■:.:■':—■.>-'■

\

APPC ~ kleak 1 _p / Qleak\ 3

2 gc ^ 6^ ' (27)

where k-,eaj, appears to lie between 0.2 and 0„5 based on recalcu- lating data presented by Shipway3 used to compare to experimental data. Substituting equation (26a) in (27) yields:

ApFC = kleak cdS pstatic (28a)

and nondimensionally:

M*C - kleak Cd3 Ystat 1C (28b)

OUTLET LOSSES

There is almost always an increase of flow area from the blade passage to the volute casing which may range up to 2 1/2 times. Thus, there is a tendency for retardation of flow velocity with resultant eddy formation. This is expressed as an expansion-type loss by:

APout - W I-* CV,' - V3]2 .

c (29)

The coefficient k . will vary with deviation from design condi- tions, but at maximum efficiency it is probably on the order of O.4.2» 3 Also,

V3 « ^out

(50)

where V3 is the average velocity at some measuring station of area, A3, which may be at the volute casing exit. If V3 is mea- sured close to the fan outlet, the case where V3 = Va' is obtained, and hence APout = 0* From the outlet velocity diagrams, item (a) of figure 2 and figure J>, the following is obtained:

27-404 15

HitMliMM»M*^«V-Tm.-->W.»^a^|f.i^||MW^

'T*? '■-"^■.i-^- —

■■-»:v-^>.A'.^-,.i.--'.'-J~- . ... ,,irr>^^:,::-.^cW«Vi!'.™!»r.-^>*-^::':W-'-»'-<^'.-;'-*<^.'---- ■ ...■ ■ .■ ..-■■■-.

v.' = U, - QimP COt B 2 nd2b3

USTT sin ß. +1 Qimp

nds*3

, ,

(51)

Written nondimensionally, equation (29) becomes:

AY out

out 0jmp d5

TTb. cot ßs . JL_ sin ß2 j

<^)T #out da (52)

In many present SEV installations, the centrifugal fan is mounted directly in a large plenum rather than a volute. No attempt is made to recover the tangential component of velocity, such as by mounting exit turning vanes. In this case, the outlet pressure loss is due entirely to the dissipation of the tangen- tial component of velocity13 and is stated as:

P V*l AP , ■ — —3L out gr 2 (55a)

or nondimensionallyi

AT out M- 2 V Ü. (55b)

where V^ is obtained from equation (12)

27-404 16

»„J.^..M..,-:.,., ■,:,»,.■,..,>.>.-.>,..„.»,.,„»„»■ .,.. ::_:.,,.._,.:...-. . .fa . . - -| .._,_, ,„. .,.., 3^_|^J^ JJ^a^^..„ . . ^^._^-,»,„■. - .^-^ff:^, ^^g ftf - ■fjjghi'j- fftf || | | [flj

ic«?f».'.'*!i.l Ti» ■■>.-*>■ *. J^l ...-:.-•

EFFICIENCY

The efficiency of a fan is generally defined as the ratio of useful output power to the required input power to the impel- ler. The input power to the impeller is equal to the product of the impeller volume flow rate and the modified Euler line pres- sure of equations (17) or (18). Thus,

input power = Qimp* PE (54a)

or nondimensionally,

input power = 0imp* (54b)

The outlet power ;.s equal to the product of the outlet pressure times the outlet volume flow rate. The outlet volume flow rate is equal to the impeller volume flow rate minus the leakage flow rate, which flows back toward the fan inlet and is calculated from equations (26a) or (26b). The outlet pressure may be based en either the total or static pressure conditions. The total pressure condition is obtained from:

'total - PE - APimP - APini - AP - APRC - APQut , (35a)

and nondimensionally:

Ytotal - h ~ ^imp " ^in, - ^ina " AYPC - *W • (35*)

T>" static pressure condition is obtained from;

static - ptotal " APv ' (36a)

or

¥ B V -AY static Ttotal v ' (56b)

27-404 17

^f^JIP#WWt-*«-.P:'"*\l\W-fJ'-..':. !--;■,-- J:,

where &PV and AYV represent velocity pressure and 4 1

2 g„ (if static and total pr >ssure

are measured at f«.i exit), (57a)

. ;

.J

or

IP 3

2 gc (if static and total pressure are

measured downstream of fan);

(57b)

and nondimensionally:

(/ V V'

(if static and total pressure are measured at fan exit),

(58a)

or

A*v=IfV3

2 lua (if static and total pressure are

measured downstream of fan).

(58b)

The fan total efficiency may now be expressed as:

total

ptotal Qimp " Qleak „ total 0imp - #leak PE imp

YE 0. ^imp

(59a)

The static efficiency is expressed by:

P Q — 0 v (A — $ static imp leak static ^imp ^leak static

imp f. 0 imp

(59b)

27-404 18

ft'tiMMMrn—lfflrffl«'

■•■■,. ■■..■■,..,..- ■

. ■■■:.. I . : ■■■■' 3 ■.■-.■:-■■■■■- ■■;■:

The efficiency of an impeller and volute (or diffuser) will always be less than that of just the impeller. The difference will be determined by the efficiency of the volute, rw, where

T1D = PE " APout *E " AYout (40)

In some cases, fan characteristics which are presented by manu- facturers are based on measurements at the exit of the fan diffuser or volute. However, efficiencies quoted with these fan characteristics often do not include the outlet loss and represent only the higher fan impeller efficiency. Thus, when comparing experimental and predicted data it is important to know how the experimental data were obtained.

COMPARISON OF EXPERIMENTAL AND PREDICTED RESULTS

The fan characteristic prediction program was used to pre- dict experimental performance for a 60-inch outside diameter (OD) backwardly-curved, airfoil-bladed, HEBA/B centrifugal fan. The results are shown in figure 5 along with all the losses. Agree- ment between experimental and predicted value is quite good, but this depends to some extent on the selection of loss coefficients which requires either experience or experimental background to make proper selections. For the present case, the following loss coefficients were used:

k- imp = 0.15

kinj = 0.28

kina = 0.7

kleak = 0.3

K/-m*- = 0.4.

27-404 19

■■-.. :■-;.•■,,. . -, ..-. .- -:r- ■ .-.. ,-..-.. ■■■■-■■

10

NO. 60 HEBA/B DIAMETER«60 INCHES

VELOCITY PRESSURE,APV

LEAKAGE LOSS.OLEAK

-L _L J_ -L _L J_ J_ J_ 200 400 600 800 1000 1200 1400 1600 1800

AIRFLOW RATE, FT3/ SEC

Figure 5 Comparison of Predicted and Experimental Results

27-^04 20

Also, the following physical variables describe the HEBA/B cen- trifugal fan system:

vtip = 255 ft/s+

dj = 5.46 ft

d2 = 5.00 ft

bx = 1.62 ft

b2 = 1.18 ft

ß1 = 25 degrees

ßa = 50 degrees

z =12 blades

A3 = 21 fts (volute exit)

de = 0.9* dj

Cd = 0.6

Ö = 1/16 inch per foot of inside diameter (ID).

A sinusoidal nonuniform discharge velocity is assumed to be occurring at the impeller outlet since this helps simplify the calculations and does not appear to offer any significant error in results over assuming a linear profile or combination.

Of particular interest for SEVs is having a fan with as flat a characteristic as possible, that is, having a large change of flow rate for a small pressure change at a given fan speed. To see what effect the different variables have on the fan char- acteristic curve, most of the above variables for the HEBA/B centrifugal fan were varied above and below the actual values in the prediction program. Items (a) through (h) of figure 6 show the results where one variable at a time was varied with the resultant static pressure and efficiency being plotted against the outlet airflow rate.

+Abbreviations used in this text are from the GPO Style Manual, 1973» unless otherwise noted.

27-UQh 21

HMH ____

■ ■ .... ■■■ . ..-.. ■. ... ■.-■■■;---r'-^»-<-:* V"f -f ■■'.>■:■-■■ -.V.t....,,.,r.,„,.

/ 0.8 1 i i i i i i

y0.7

|o.e ■ s00^* s~-\ -

■/> -v^> - >■" 0.5 z a 0.4 o

t 03 u

;/ V \

-

y 0.2

Ho, M i

\ ©

i i i

\\ ® ®

i i i

1200 1600 2000 2400 2000

OUTLET AIRFLOW RATE,Q0uT.FT /SEC

Item (b) Effects of Outside Diameter

I - i

Item (a) Lffects of inside Diameter

* 0.8

o 07 < ts 06

p- > n« u z UJ 0.4 u U- u. 0.3 UJ

o 0? P t- 0 1 V)

0

70

t 60 N.

5

8 UJ

30

20

10

- T ■ 1 —r d2"

1 1

4J7FT R^ 0.830

1 !

b2/d,-0293

v © d2- S.00FT Ra-0 692 b2/d2-0236

NV5 "2* 3 83 FT Rj" 0.394

WEIGHT RATIO

© 0 73 * Wj

V <D *2

b2/dj «0.202-

- \\® li0* *2 -

- \ \\

-

- v\ -

-

1 1 —1

6*^ i i 1 I

400 800 1200 1600 2000 2400 2800

OUTLET AIRFLOW RATE.QQUT." '*K

27-404

Figure 6 Effects of Centrifugal Fan Parameters

22

...■„,..-...._-, ,,.„.,,.,..■. -«^^ ^ v ■ | „-,,,-T, 11,, | ! iia^^mTfflaMif^^»^"^****"--"'~~

. ...... ■■■ .. ,■,'--■ •:■: -. : ■. ■ ■ ■•-■ ...-...-.. ■ ■ ■ .:■■..■■■ .v.- ■■ ■■■.-■■ ■: .. ..■ .-....■■... :.-.;■■.:.-,,:.-. ■

0.8

i J u 07 t- <

0.6 p-

> 0.5

LÜ 0 4 O

1*. 0.3 Id

u 0.2

< 01 0)

0

70

—i r ii ii i

:^x -

0® i i i i i i i

KEY

© »i« 1.18 FT Rb'1.00

<D b|»l.62FT Rb'1.3? ® b|*IMPT Rb'l76

WEIGHT RATIO:

© 0.94 # W2

© *2

© 1.08 * W2

400 800 1200 1600 2000 2400

OUTLET AIRFLOW RATE, OQUT .FT3/SEC

2800

Item (d) Effects of Outside

Blade Height

0.S 111

0 0.2

1 0, n 0

70

(M 60 -,

r so-

3

20 -

Item (c) Effects of inside

Blade Height

i i r —p- -1 i KEY© b2"0.83FT b2/d2-O.I66

1

Rb-I95

. ©b2-I.IBFT bj/dj-0.256 Rb>I.S7

^—^^N/N® b2- 1 62FT b2/dz-0 324 Rb.IOO"

>. \ \ WEIGHT RATIO

\ \ \ © ° 9e * w2 -

\ \\® W* \ \ V^ l04 * *2

_

© ® ®

1 1 1 1 1 ' 400 800 1200 1600 ? ,00 2400 2600

OUTLET AIRFLOW RATE.0OUT.FT3/SEC

27-404

Figure 6 (Cont)

25

ll(lllil|-M«r,J",""-''J"'''"~' ----- Ii liMÜW "-"—"■-

.....

■ ■ ■.. ■ ■

/ 0.8 ~|ll 1 II 1

u 0.7 X" ^ 6; 0.6 " / A. *• ^»

>■ 0.5 N v ¥ \ til 0.4 - >&> O ^\ li. 0.3 - v\ tu YV. u o.z \\/«v

1 0.1

n I i i 1 1 1 1

70 —i r

KEY

© *|'20«

© 0I-2V

® /9|-S0«

WEIGHT RATIO

© 1.02 « \*2

® w2

® 0.98 * W2

_1_ _l_ _). 400 800 1200 1600 2000 2400 2CO0

OUTLET AIRFLOW RATE, Q0UT, FT3/SEC

Item (f) Effects of Exit

Blade Angle

60

S so-

40 -

SO

20

10 ■

Item (e) Effects of inlet

Blade Angle

L..J '

1 1 T 1 1 1

KEY

© J9.-40« ,;^*^^v © 0J- SO*

7 \V\ ® JB,"60«

1

\\\ WEIGHT RATIO -

\\\ © l04* w2 \\\ ® W* _ \ \ \ ® 0.97 * W2

\v\ -

© ® ®

1 1 1 1 1 1 .1 400 800 1200 1600 2000 2400 2800

OUTLET .vsrLOw RATE.QOUT,FT5/SEC

Figure 6 (Cont)

27-404 24

—-■---■- - - - •HMHSt „^u^i. ■ -■■-■-■^«^—^->* If III 1 £^UÜ^L- -.

?.,lJ.r.?,iT:,:^.._,.:..,^;„,:,r....

I 1 ; > 1 I

%

„4*m*!<mvMim»>mMmemmmm ■ s■ - ■■■■■- ■-■ '■■' ■■- '--■ ■

* «»h

o

70

<

40 k

30 h

20

T"" T- —r KEY > ' '

© Z-9BLA0ES

© 1' 12 BLADES

—I -

£"x\ ® Z • 15 BLADES -

/—*\\\ WEIGHT RATIO

^\X\ © 0.93 # W2

® *2 -

\\ ® 1.07 * W2

-

1 1 1

\\ © ®®

1 1 1 1 _ 400 800 1200 1600 2000 2400 2800

OUTLET AIRFLOW RATE ,Q0UT. FT J/SEC

Item (h) Effects of Outlet Area

«SOI

soh

20 h

10h

Item (g) Effect of Number

of Blades

1 r— —T ■ ■ —i —r- i

KEY

I "

© AJ-I3.89FT2

® Aj.2l.00FT2

V ® ..J'27.78FT2

~

- \. WEIGHT RATIO

^L © 1.0 * W2

-

. vV ® *2 -

- ^^ ® 1.0« W2

\

-

1 4 1 1 1 1 ' 400 800 1200 1600 2000 2400 2800

OUTLET AIRFLOW RATE , O^y ,FTS/SEC

Figure 6 (Cont)

27-404 25

-**""*—* ^~-^—^^^>—^^

■.■■V"'^--''--■

•- ■■■■■ ! ■■■ ■■■■:- ! ■■-. . - I ■- - ■ ■ ■

Included in the figures is an estimate of how the variable change affects basic fan impeller and hub weight as compared to the original HEBA/B fan noted as curve 2 in all figures. The rational for the weight estimates is snown in appendix C. Item (a) of figure 6 showed the most significant effect on characteristic slope. When the fan inside diameter approached the outside diameter, a significantly flatter char- acteristic resulted, although peak efficiency was reduced compared to the original fan. The fan static efficiency and pressure are both determined at the fan volute exit. Vari- ation of the other parameters in items (b) through (h) did not significantly affect the slope or peak efficiency but could affect the pressure flow output. In figure 7» both the inlet and exit blade heights were changed together. Increasing the fan blade height allows greater airflow through the fan at a slightly increased pressure and a slightly more favorable slope without signi- ficantly affecting peak effi- ciency.

0.8 ~\ 1 1 1 r

1 1 \ 1 1 r KEY ® bl*l20Fr b2*0.76FT Rb«l.58 t^^'OMT

® b|-l62FT b2'I.ISFT Rb«l.57 tjWj-OZäe "*" b|»2.03FT b2-l.60FT Rb»l.27 bg/dj-QSZO

WEIGHT RATIO:

© 0.91 * W2

® *2 ® 1.09 * W2

400 800 1200 1600 2000 2400 2800

OUTLET AIRFLOW RATE,Q0UT,FT3/SEC

Figure J Effects of Changing

Blade Height

LIMITATIONS ON CENTRIFUGAL FAN PREDICTION PROGRAM

It has been found that size affects efficiency when geomet- rically similar fans of different size are compared.*3 Increas- ing the fan diameter for a family of similar fans will cause the fan efficiency to increase due to a decrease in relative rough- ness (e/d), where e = characteristic roughness size. The

27-404 26

. ?mm

s^aw* ■ ■ '"" ■'* ■'• • : . ■ y ..■•;.:: '■ :- ' ■■■:.-' ..'-:':.'.; . ' ■ ,.--.■■... ^ ■ ■ '

characteristic roughness remains more or less constant in manu- facturing processes so that relative roughness (e/d) varies inversely as the fan diameter. The degree of modification for size effects is small compared to the accuracy limits of the above method and has been omitted to simplify the calculations.

Increasing the number of fan blades in the above program has the effect of improving output flow and pressure as well as efficiency, since interblade circulation effects are minimized to provide a higher modified Euler line. To avoid designs having too many or too few blades, the pitch-to-chord ratio of the fan is generally maintained between 0.5 and I.5.14

AXIAL FAN CHARACTERISTICS PREDICTION

The method of predicting axial flow lift fan characteristic curves was based on work by Wallis4 and Shipway.6 Using this method, axial fans could be designed with either prerotator or straightener vanes, as is usual with surface effect vehicles. The program requires the basic geometry of the fan and the characteristics of the desired airfoil blade to be used. Both isolated airfoil and cascade data can be used in the program, depending on the solidity value calculated for the fan.

The method for predicting axial fan characteristics is essentially divided into three sections:

• Preliminary design

9 Detailed design

• Off-design characteristics.

In the preliminary design, the fan efficiency and other variables based on given flow, pressure, and geometry are estimated. The detail design will specify the geometric details, such as inlet and exit angles of the fan blade and the prerotator or straight- ener blades. The off-design characteristics predict the varia- tion of fan pressure and efficiency with flow rate for a given fan speed.

27 -Ü04 27

----- m&m

.:■■■ WST.'SWW»-'.'->

. I PRELIMINARY DESIGN

The preliminary design is necessary to calculate and esti- mate some of the variables that will be needed in the later detailed design. The preliminary design estimates the total fan efficiency based on the following input design variables:

• Total pressure, PT

• Flow, Qdes

a Outside (or tip) diameter, Dt^p

• inside (or hub) diameter, DH, or hub-to-tip ratio, XH

• Tip speed, V"tip, or fan r/min, n.

Various combinations of the above variables can be tried at this point to determine the optimum fan design dictated normally by the highest efficiency. At the end of the preliminary design, the basic physical dimensions have been determined and a more refined design will be performed to detail the aerodynamic design of the fan.

The preliminary design procedure requires the five input variables above and proceeds to calculate total fan efficiency for a fan having one of two options:

• Prerotators (or inlet guide vanes)

• Straighteners (or exit guide vanes).

If prerotators are used, the case is denoted by having the straightener swirl coefficient equal to zero (es = 0). If straighteners are used, then the prerotator swirl coefficient is zero (e_ = 0). The swirl coefficient represents the ratio of the tangential velocity component to the axial velocity component at a given radius. The design method used does not cover the case of using both prerotators and straighteners at the same time.

The axial velocity through the fan for a given flow is cal- culated by:

I

1

i

!■ i

27-404 28

* " '■•"'" '"''

■ ■■■■■■■-r.yi-r-.-.-rt->■■;-?&.■*.*■

-..-,..., .:.-.,: um) fj^!m,^es«&<s^!tmimmrm«^if^

«

v. ax Dtip (41)

-%*)

where xH = DH/Dtip. The flow coefficient at the blade tip is determined by:

0t ip Dti| vtiP (42a)

at the hub,

0H = ^i£ (42b)

and at the midspan of the blade,

0m = vm 0+ ytip

fpH + Dtip

2 D tip

2 0 tip

1 + X H (42c)

The conditions at the tip, hub, and midspan of the blade, in general, represent the extremes and average conditions associa- ted with the fan. Thus, conditions at these three sections are important and each is required to be known to assure a proper axial fan design.

The theoretical total pressure coefficient is calculated in dimensionless terms by:

th * P

>7 iTvtip W)

27-404 29

■ -.■■ ■■■:';>v^V;,vir^;.:,. -*■■.,. .:-;'■..-/.'.*:-:.■' o.;"-': ^-^w?-.

For the fan design, it has been assumed that the total pressure rise and the axial velocity component remains constant along the blade length and that there is no radial component of flow. These assumptions fulfill the requirement for the free vortex flow that the fan design is based on.

ij

The impeller swirl coefficient, which is defined as the ratio of the tangential-to-axial velocity component, is obtained from:4»6

•imptip

* vtip2

TT Vax3 HT (1 - XH

3) Cth 0til (44a)

£imPm "" eimptip (1 + XH) (44b)

eimpH

e . imPtip (44c)

where r]T is the total fan efficiency and is assumed to be 0.8 for initial calculations. The swirl coefficient is an important variable in that it represents a measure of the torque of the impeller, in this case, and will be used in many subsequent equations.

The product of lift coefficient (CL) and solidity (a = C/S) at a section on the blade is given by:4

(CLa) = 2 e imp sin Vimp (*5)

where Y^mD is the angle between the resultant velocity through the fan impeller and the plane of rotation and is expressed by:4

27-404 50

'""■^••:T]Mf-T--"a*i-nf"ii - ■ t m

■■ ■-. ...... .. ■. ■.,.,. .■ .. .. -. ,...<: .-■■■■■ ■ . .,

.... ,.,,.........,,., ..«:~w ;.■.■.,..,..,..,-..-

imp = tan -i 40 (if straighteners

n(l - XH2) -2 <Hmp 0/ are USSd' £P = °) '

cr

Y. imp = taxi' 40 (if prerotators

"H

(46a)

n(l - X»> + 2 Gimp 0 are used, eg = 0)

(46b)

Figures 8 and 9 show the geometric and velocity vector details of the blades which are used for the above and following equa- tions. If equation (45) is to be solved at the hub, the appro- priate values of 0fj, eimp„, and Yimpu

at t^ie ^ub must ke used in the equations. Likewise, if the value at the midspan is desired, the values of 0m, ^imp^ to follow, the subscript

and ■H»

Yimpm means

must be used, values at the

in equations hub and the

subscript 'm1 means values at the midspan.

AXIS OF ROTATION

Ö«CAMBER ANGLE

S

S* 2rrr

N

PLANE OF ROTATION

Figure 8 Geometric Details of Blades

27-404 51

— -■ - - - ■■ -■-■——-■

■^■».„^^w ^.„-.„-^^..^.^^-^«^ - —"—-

■ ■.-■■:>«sffla'«9W*»«f^i»«vW«r»B**ia3r™iw;i" B»aqwi^waM^*fe^awW^w»wairwtf>»B

INLET VELOCITY

PREROTATOR

IMPELLER INLET

CONDITION

IMPELLER

AXIS OR ROTATION

IMPELLER OUTLET

CONDITION

P VAX

£ = f|MPfa

PLANE OF ROTATION I—^iMpr-l/2(^s -0P)r

c*jcr

k-wIMP'-*l

I STRAIGHTENER

OUTLET VELOCITY

S VAX

°IMpr« ROTATIONAL SPEED

OF IMPELLER AT RADIUS,r

Figure 9 Velocity Vectors for Fan System

27-404 32

:""--~ -'- -'- ^^^mta^temmami ^u^--:^-

i j With increasing static pressure rise across the fan impeller, there is a sharp increase in drag just prior to blade stalling. Maximum efficiency or optimum conditions should occur just before this rapid increase occurs. The following relationships4 express the optimum lift coefficient (CL*):

CT.* = 2

1 + TT(1 -XH»)

1 /n(l - *H3) +4 eimp 0\ \ ~ " 40 ~" /

1 .375

(if es = 0),

(*7a)

or

CT.* = 2

- ,.^ -V) -4 £imp** ~ "l 40

1 + "(i - xH

a)V 40

1 .375

(if £D= 0)

(47b)

The solidity at any blade section may then be obtained by divid- ing equation (45) by (47). Thus,

■(¥) (48)

The value of a at the blade hub should be checked to assure that it is within the design limits of CTH £ 1-5« If Ou exceeds 1.5. the preliminary design input variables should be changed (i.e., increasing V^ip and/or XJJ will decrease aH) and the calculations up to this point repeated.

The profile, secondary, and annulus losses associated with the impeller can now be calculated. The values are obtained at the midspan of the blade since they should represent the mean

27-404 35

Mesinatmihir-Nn « n^T^^i.TC'ra^>i:agMaMH^-^asww^;--'v^'1'' """■j: ■ ' '.■-■■■...^.■---«-uw-.=-™«fi**i-!'ä.^

loss for the impeller as a whol^. profile drag4»5 is:

The loss of efficiency due to

AY irappp DPR 0

»th sin3 YimD n(l -Xlr») '

W rimp

where Yimp is obtained from equation (46) and Copp is the pro- file drag coefficient. The loss of efficiency due to secondary losses is obtained by:4» 5

AY impsec 'sec 0 Y th

sinS YimD n(l - XHa) '

(50) imp

where CD is the secondary drag coefficient. Combining equa-

tions (49) and (50) yields:

^ imD + AYimr, CD + Cr imppp imPSec UPR l

'sec 0

'th sin3 Vimp n(l - XHs)

(51)

Shipway5 suggests that for this case the value of lift, -to-drag ratio can be set as constant for preliminary evaluation as,

+ C PR D

— C-W . J (52) sec

The magnitude of the annulus drag loss was assumed by Wallis4

not to vary greatly from fan to fan and hence he suggests:

27-404 54

— - —" 1 HiMililf IIIM^IiMMIMI ^m m ■■ - —

;■-■■ : ■ ■■■ ■-■ '■ -- '■ :- ;.:■>■..'■■'■':■;-■.■■:■■ ■:■-■■■ ■-■■-- - -■■■■■•:,"■ ■ -■■- ■■ .,:■ . ■ ' " f

I ! A* imPan

= 0.02 (for aerofoil-shaped blades)

= 0.03 (for constant thickness plate blades)

(53)

The fan impeller efficiency can then be determined by adding equations (51) and (53) or,

AYimppR A¥impsec

AYimpan ^imp = y + +

■th fth *th (54)

The loss in efficiency caused by prerotator or straightener vane pressure drop must be determined, if straighteners only are used,4

es = eimp and e = 0 , (55)

and also4

A*. CDs* 0

(2.18 - 1.43 es) sins YS TT(1 - X^) (for 0.5 * eg < 1.0),

or"

(56a)

AY« CDS* &

Tth 3 es sin3 Ys n(l - XH«) (for e < 0.5) ,

(56b)

where

Y = cot s \2 -(f) (57)

27-404 35

. , .. . ■•.---.■vy ■ ■ -: -■■■■■ ■ . ■.■■■■■-■.■■■■■■■ ■.■:-....-: . ■ ■ ,-..,..

The straightener and prerotator pressure loss are both calculated at the midspan of the blade. CD is the straightener drag coef- ficient. It is made up of the sum of the profile and secondary drag coefficients for the straightener blade. Wallis4 recommends the following drag coefficients be used:

i i j

u i • i

Cn = Cr\ + Cri us Us-PR us-sec (58a)

CD nn » 0.016 , US-PR (58b)

cD = 0.018 cT*3 . us-sec ijs

(58c)

The optimum lift coefficient used in equation (58c) is obtained from:4

<v = 2 1 +

n(l - Xir) - 4 Cc)ä A. 40

1 + n(l -XH8

)

40

1 .376

If only prerotators are used then,'

eD = Eimo and es = 0 ' (60)

and also,

Af£_ 0

iin* YD n(l - Xtf) (for 0.7 * e < 1.5) .

(61a)

27-404 36

,*w«*iäi^ä"a!WeM^i«*i33«iS :&!9*^H*^te"'--i;^';-'iv'^'- ■ '? "■ ^-.■."W PJ!iaBSWWMK*W*"

1 1 ? or

—E= 5 E-r-5 ' -/, v a\ (for eD < 0.7), 5 ep sm3 Y n( 1 - XH*) v P (;' Y th (61b)

where

cot"1^ (62)

The prerotator drag coefficient Cp is calculated exactly as in

equation (58). The optimum lift coefficient of equation (58c) now becomes,4

= 2

1 + n(l . xH*)

5$

n(l - XH3) + 4 ep0 1 +

40

1-375

(63)

The clearance losses can be avoided with proper sealing of the straightener or prerotator blades to the casing. Thus, the annulus drag component need not be considered since it will be small.

The pressure loss associated with the diffusion process can be obtained by assuming the diffusion efficiency. Provided flow separation is avoided, diffuser efficiencies of t)D = 0.8 are obtainable and will be assumed in the calculations. For an annular-type diffuser, as shown in figure 10, in which 6D = 3°, the diffusion pressure loss coefficient (ATD) is,4

where

AYD = (1 - Tfc) 1 - "imp Aduct

1T V ax 2 V*. • 3 c vtip

Aimp = Impeller annulus area

Aduct= Diffuser outlet or duct area.

27 -404 57

(64)

ÜfiHOi - --- amiM

■ ■. - . .......-..,. .

-

FAN IMPELLER

AIMRÖD ADUCT

2ÖD = 6°

Figure 10 Annular Diffuser

If the duct diameter of the fan unit remains constant, the loss coefficient becomes,4

L J 2 Vtip« (65)

The efficiency loss associated with the diffusion is obtained by dividing equation (64) or (65) by (43).

The fan total efficiency may now be determined from:

'T 'imp °'D ^ "*s

•th "th or

AY.

th (66)

If the nT calculated in equation (66) differs by more than ~5# from the value of nT, assumed initially in equation (44), repeat the calculation substituting the new value of r\ in equation (44) and repeating all calculations up to this point. If the iiT cal- culated is within 5# of the T>p assumed, then the initial design assumptions are reasonable and design calculations may continue.

27-404 38

.riswwEw.-^f'M««^?'^ * ' ~ ^^mmmamm

DETAILED DESIGN

At this point, the preliminary fan design is completed and the detailed fan design will be undertaken. Two design methods are available, the isolated airfoil method or the cascade design method. For solidity values below 0.7» the isolated airfoil data are used, while for solidity above 1.0 the cascade data are used, in between, either method may be used. Wallis4 also recommends that the straighteners or prerotators be designed by the cascade method only. For the design of all blade elements, free vortex flow is assumed, that is, constant axial velocity along the blades.

In designing the impeller blading, an airfoil section must be chosen such as one of the NACA profiles, in the detailed design, only the lift coefficient (CL) and the angle of attack (a) for the design point are required. When the detailed design is completed, the complete airfoil section characteristic data will be needed to calculate off-design performance.

PREROTATOR DESIGN

If prerotators are used, their design must be determined before the impeller design can be finalized. To define the blade shape, it is divided into an even number of segments of equal length. An even number of segments will also provide specifications of the blade at a midspan location which is required for the off-design characteristics. Thus,

D. = DH + (Dtip - DH)

j i=0

(67)

where j is an even number of blade sections and i denotes the diameter location from the hub to the tip of the blade. The ratio of section-to-tip diameter is expressed by:

X^ = DtiP

(for i = 0 to j) (68)

27-404 59

^a.„.^-„J,.,_J~„ •Trr"*nrrirhirit"riiif'iriHi ■""""—-"'-•-■"•—* .......—:.... ...„-.- m --- ■-■ jama

«taWMMfMa&UfStg '■ - ■- ....,.-.;..;■. .-■ «flBMBps»«*««^^

Likewise, the flow coefficient at each section diameter is expressed by:

0L = -UP- (for i = 0 to j) . (69)

The prerotator swirl coefficient is then

en. =, lmPtiP (for i = 0 to j) , 'Pi (70)

X4

and the relative velocity of the flow coming off the prerotator is at an angle (6p) with respect to the axis of rotation, defined by: k

5Pi = tan_1 (ePi) (for i = 0 to j) (71)

The solidity at each section for the prerotator is determined by:4

oD, = 2 (for , < 0.7) , Pi

(72a)

and

2 epi sin Yj - (for 0.7 * e

D, < 1.5) . (72b) Pi

and Wallis4 assumes that with prerotators, CT = 2 satisfies most cases.

The camber angle (see figure 8) of the prerotator blade at each section is obtained from:4

3Pi= 1 - 0.2/aD. <f0r i = ° t0 j) * (75)

.

27-404 40

i^f&mm^mmmM i ■ ini-nr. ■ ■ n r i ■ it—■■m.ii.i.fl^fli|^■■yTiilii|gir^^^^w—

us

B^&SJSEW"fe&)SääftJ«tt ■■-■■.: :-■■-■'- -.:■■■■ ■■-.,■.■;■-■■ '■-■■.<-'■-• ™«

The blade chord is equal to,

'Pi N (74)

where Np is the number of prerotator blades, in general, it is recommended that the number of prerotatcr or straightener blades be greater than the number of impeller blades.5»15 Strieker and Shank15 recommend that the number of straightener or prerotator blades be two more than the number of impeller blades for opti- mized noise considerations.

N = N = N. + 2 p s imp (75)

In order to facilitate manufacturing of the prerotator blades, the blade chord and/or the blade camber angle may be kept constant. The values of Cp and would be set at the values calculated for the midspan and new an.# 6D ■ # anc^ er>.

E* i c i JE* i coefficients must be calculated by using equations (74) , (73)» and (71)/ respectively.

IMPELLER DESIGN

The impeller design will depend on whether prerotators or straighteners are used. The impeller blade is broken into sec- tions along its diameter equal to those used for the prerotator or straightener section. Thus, equations (67)/ (68), and (69) apply for calculating D^, Xf, and 0^, respectively. If no pre- rotators are used, then ep^ equals zero for the design point on the impeller. However, if prerotators only are used, es- equals zero at the design point unless the prerotator blades were modi- fied to have constant Cp and/or 6p to facilitate manufacturing. In this case, there may be a swirl component coming off the blade at the design point and thus es- 4 0. The swirl coeffi- cient calculated for the modified prerotator must be subtracted from,

(GS + ep). = impti

iP

X; (76)

27-404 41

,ifiS!H*WWKV-i.'- ■ ■ ■■'■■•■: 'r-::^y-'-^.-7">y: ■ ^i»m»mt^ieBm»S*0l^^m>>^mPimsmm -,:■,,■■;-—,.- — .; ■' ■ ■■■-,■■■-■ .■:.-..■..-«..: :Krr^---^.r~yr-y.Jr^M,-:- . ■ ■

in order to determine es-, if the prerotator blade has not been modified, es^ equals zero at the design point.

The product of lift coefficient (CL) and solidity (aimpi) can be expressed by,4

CL CTimPi - 2 (es + ep)i sin Yimpi * (77)

"I ' I I I < * 1

where Yimp ^s snovm i° figure 9 ant^ determined by,4

Yimpi = tan -l 40i

TT(1 - XH2) - 2 (es - ep). 0± _ (78)

At this point, the lift coefficient (CL) is selected from the characteristic of the airfoil to be used. The angle of attack (a) at which it occurs is also noted. Then, dividing equation (77) by the value of CL selected, the solidity (aimpi) is deter- mined. The blade chord ie then obtained by,

TTDi aimPi

•impi N (79) imp

If the number of impeller blades (N£mp) is not specific, it may be approximated from the hub-to-tip ratio (XJJ) given by,16

6x N

H imp " (1 - xH)

(80)

The blade angle (ß•) is determined by,

Pi = (Yimpi + a) (81)

27-404 42

........ ■ ... . ... ... ■■....■ -.. ■ .;■■:-.■-;'. ■■:::, --. ; - '•'r;--'W^'v^''.^-.-*?^:.^J'-W-'V.i-.'--

I

STRAIGHTENER DESIGN

If the design includes the straight<*ners only, then e = 0 and thus,

'si = ■imptip

(82)

The solidity is obtained from:4

os± = £. (for eSi s 0.5) , 3

(83a)

or

aSJ = 2 €S. sin Ys.

1 (2.18 -1.43 csJ (for eSi > 0.5) (83b)

The camber angle of the blade is determined from:4

es, « 1 - 0.26

1 ' <7e.

(84)

where

6S. = tan"1 (es.) (85)

The straightener blade chord is

l si c. . = sl N, (86)

27-404 43

■ ..■-.■ ■ -.■-..,. . ■■■. ■ .-■ -.-.-:..-;■ ■■■■

. .. . , ■ ... .-.■ ■.:-■,• ■ ....-..-. .. ■■■..■■-.,.,■. :-,.■■ ,.,.■.. ...... ■.-.:■ ■.. . .•■.- • .; • ■■■■■■■ -. ■:.■■ .■■ .V.. 1 .■■.",.■.::■..'..;■:.' ■ ',, <?'!"■.-■.? V ■■.:..,.,

where Ns is the number of straightener blades as defined in equation (75)• As before, the values of cs and/or 6S can be kept constant at their midspan value to facilitate manufacturing. However, new os-, 6S-, and eSj values must be determined from

equations (86), (84), and (85)» respectively.

OFF-DESIGN PERFORMANCE PREDICTION

The off-design performance details the pressure-flow charac- teristics of the fan at a given speed for other than the design flow condition. The basic assumption of the off-design theory is that conditions at the midspan of the blades are representative of the fan as a whole. Depending on the solidity values calcula- ted earlier, it will be known whether isolated or cascade airfoil data should be used. The data required from the selected blade characteristic are the anglt of attack (a) and the corresponding lift coefficient (CL), and lift-to-drag ratio (CL/CQ). Several angles of attack on both sides of the design point should be selected to describe fully the fan characteristic curve.

The angle between the mean relative velocity to the impeller and the plane of rotation (Yj_mD) is defined by:

111

Y^ = (Pm " °0 • imp (37)

The angle is then used to calculate the swirl coefficients,4

(es + e ) = CL aimp

2 sin Yimp

cot YJ

1 + (Ci/CD)

(88)

The value of es or ep is obtained from the detailed design sec- tion for the midspan of the straightener or prerotator, depending on which is used. If straighteners are used, the value of ep is assumed to equal zero which means no preswirl is occurring prior to the impeller, which greatly simplifies the math involved without significantly affecting the results.4 However, if prerotators are used, es can be nonzero due to the swirl component coming off the impeller blades at off-design flows. This can easily be determined since ep would already be known. Thus, the flow coefficient can now be calculated at midspan from,4

27-404 44 j] 1J

rirWMWfti 1 »I.I.H. nn, .~~~.~~~.~,-r>t,ri,-| .n„-n, ||-|mnimjfrfi

0m = tan Y imp

"m [l +0.5* (es - ep) tan Y.mp]

(39)

Ths theoretical pressure coefficient will be,

2 (es + ep) V; ax th

0, m 2 vtip2 ^T

(90)

I

The fan system total efficiency can now be expressed by,

r|T = 0.98 - 0m

sin" Y imp + cot Y,-„„ CD/ imP

55-5 + cot Y. imp

-=- or

th Y th

(91)

where

*th

0m / £P \ CD prerotator loss - -—^^-J . -

or

(92a)

—— = straightener loss = Yth

0m. sins Ys CL

(92b)

27-404 45

jjjggj^|Mg|j|gj|jjg|j»|j^^

-i.i.v^^.. - „^ ;//--.^-;;;;.-ii^^v.^,v^3^,v..fi^.j'^-;:>v;l.:i^li^,:^.,1. fWaC^KffiJjtWBW)S9 ■ ■■■'".Viv.-'V.■-.'■:■.-.--.' «..v-rj-, : ...... ............... ..

The flow through the fan is calculated by,

n Dtip3

Q = —T^C1 -XH2) VtipXm0m (95)

|

The total pressure of the fan is,

PT = tip th

The horsepower required to operate the fan is

(94)

hp = Prp*Q

55e * TL (95)

COMPARISON OF PREDICTED RESULTS

Several saraple calculations were performed with the axial fan characteristic program that has just been summarized. The base preliminary design data were:

DUp = 4.5 ft

Dhub = 2.25 ft

Vtip = 400 ft/sec

pTdes =36.0 lb/ft3

Qdes = 125° ft3/sec.

27-404 46

LJ I

Oi ■ frfjltitrii tfk.. t^tmmäimäi&^äSäKm ■üHü mrnmrnm * — ■ ■ ---*

For the above data, the fan characteristics were predicted for the case with prerotators and with straighteners, as shown in figure 11. The figure shows that with prerotators, a flatter characteristic curve is obtained which is desirable for SEVf,. However, its peak efficiency is lower that for the case with straighteners. These data were determined from the characteris- tics of a RAF 6E blade section such as shown in figure 12.

60

50

u. 40 CO

UJ or w 30 UJ cc 0.

-I <

o 20 I-

z <

10

KEY

© WITH PREROTATORS

(D WITH STRAIGHTENERS

FAN TOTAL PRESSURE

-— FAN TOTAL EFFICIENCY

J. J_ 500 1000 1500 2000

AIRFLOW RATE, FT3/SEC

\ \

© CD

100

80

60

FAN TOTAL EFFICIENCY,0/»

40

20

2500

Figure 11 Comparison of Similar Fan Designs with

Prerotators and with Straighteners

27-404 47

mmm MMM

x&^~vw&mm$mmmim&&ifr - ■■■■■■ MHWWWS»«»^'-^«««^«»0««" ■ ■,'■■■> ^:-.; ..^■•/••^^"^^^«■i«*^ ^

80-

70

60

Q — O u ^j50 u

- »-

ÜJ o O »- u. < u. QL UJ o 40 <

- o u

a: a o _l i-

t 30

20

10

1 1 1 1 1

1.6 / \ / -

1.4 I V -

1.2 1 / \ V - 1.0

cL

0.8 -

0.6 -

0.4 -

0.2

^v^/CD

xy /ill 1 1 -5 0 5 10 15

ANGLE OF ATTACK.a,DEGREES

Figure 12 Characteristics of RAF 6E ßection

20

27-404 48 u - •- - •- •■- ! !■! l^lü^——* IIIIII iiiiiiniiiiiTWiiiilliiilli»"

taaaaitu

. ... -■ ■ :■ .-.,.- ■ .-• ■ ■ S " ■■' ■■■■■ ■" ■■-.■- ■ ■ . -. ■ «e j&g ■ ■■-- -■ ■ ■■ ■ .;

i 1 To determine the effect of blade characteristics on the resultant pressure-flow characteristics, a NACA blade profile whose data are shown in figure 1J> was used for the same base preliminary design data as the RAF 6E section. Items (a) and (b) of figure 14 show the comparative results for the two blade profiles with prerotators and with straighteners, respectively. The difference between the predicted results for the two blade profiles is significant. The NACA 65 series profile provides the flatter, more desirable pressure-flow characteristic for SEV use. However, its peak efficiency is slightly lower.

In the selection of the most suitable airfoil section for the impeller, three main properties of the section are important to examine.

• CL - The lift coefficient determines both the solid- ity of the impeller and the slope of the pressure-flow charac- teristic. High values of C^ are advantageous in providing both low solidity and low slope.

• CL/CD - The lift-to-drag ratio tends to give high efficiencies for high values of the ratio.

a st - c0 - The difference in angle of attack between stall and zero lift tend to yield increased operating range and reduced characteristic slope at high values of the difference.

The effects of fan diameter on the fan characteristics are shown in items (a) and (b) of figure 15 for an axial fan with prerotators and with straighteners, respectively. Increasing the tip diameter (or decreasing the hub-to-tip ratio) will decrease the slope of the fan characteristic and also lower peak fan total efficiency. The figures also include an estimate of how the basic axial fan weight will vary for the change in vari- ables compared to the base fan design of curve 2. The axial fan weight rational was obtained from reference 1.

LIMITATIONS OF THE AXIAL FAN PREDICTION PROGRAM

In the axial fan prediction program, the number of impeller blndes does not affect the fan performance other than to increase or decrease chord length. This is not absolutely true and exper- ience must be relied on not to choose too many or too few blades. This program is intended to be used in the range of incompres- sible flow for an axial fan having either straighteners or pre- rotators, but not both.

27-404

.

49

«MUMM

80

70

60

30

20

Q1-

.6-

.4-

1.3-

Q -i O u N. *

o 50 - £ i.o . w

o o < It.

u. Ul

< 40 - 8 °-8 f£ O u. o 1- _J

0.6-

0.4-

0.2-

0 5 10 15

ANGLE OF ATTACK, a,DEGREES

20

*-j

Figure 1J> Characteristics of NACA 65-(12)l0 Section

27-^04 50

ifrrnnitnifiiiMMitri'irrrT ---- ^^■^'-^■^^mtmmamtr wi- i ■■^*-*-<~~****flffl

$&$£*&«# J^^-W^^^:P^^^^«"^^'JV*;^^^'---

Item (a) Comparison of Two Blade profiles with Prerotators

60

50

CM

t 40

u

tu cc & -I

o 20

10

-100

'© KEY

® RAF 6E SECTION

(f) NACA 65 SERIES

FAN TOTAL PRESSURE FAN TOTAL EFFICIENCY

FAN TOTAL EFFICIENCY, %

500 1000 1500 2000

AIRFLOW RATE, FT3/SEC

2500

Item (b) Comparison of Two Blade Profiles with Straighteners

60

50

40

30

20

z < 10

KEY

® RAF 6E SECTION

© NACA 65 SERIES

— FAN TOTAL PRESSURE

FAN TOTAL EFFICIENCY

500 1000 1500 2000 AIRFLOW RATE, FT^/SEC

100

80

60

FAN TOTAL EFFICIENCY,*

40

-20

2500

Figure 14 Effects of Blade profile on Axial Fan Performance

27-404 51

. ■■,,.-:. ■'. •:':. :■■■:■'■•■ ..-.v.' ^»'^-^^'vL^."-^'-«***'*^ ~

Item (a) Effects of Tip Diameter and Prerotators

■u.t

60

50-

(M 40-

UJ a: 30 to in u a. a.

20

10

/© KEY

© DTIP = 5.0FT XH=0.450

© DTIP «4.5 FT XH «0.500

(D DT|p «4.0FT XH -0.562

FAN TOTAL PRESSURE

FAN TOTAL EFFICIENCY

WEIGHT RATIO © 1.07 W2

(|) W2 0.94*2

FAN TOTAL EFFICIENCY %

500 1000 1500 2000

AIRFLOW RATE, FT3/SEC

2500

Item (b) Effects of Tip Diameter and Straighteners

60r

50 -

I- u. 40 m _i

a. O </) 30

a. a.

< O 20

-£. <

10-

KEY

© DTIP »S.OFT XH«O.450 © DT|p '4.5FT XH»0.500

(I) DT|P ^.OFT XH »0.562 FAN TOTAL PRESSURE

— FAN TOTAL EFFICIENCY

WEIGHT RATIO

§I.07W2 W2

0.94W2

500 1000 1500 2000

AIRFLOW RATE, FT^/SEC

-100

FAN TOTAL EFFICIENCY,%

2500

Figure 15 Effects of Tip Diameter on Axial Fan Performance

27 -404 52

Tii^iTiiiMfiM^Mli

■.■'■■'■■■■'■. ■ ■ ■ ■-.■ ■■ ■ ■. ■■■ ■

The axial fan prediction program was not compared directly with experimental data due to the lack of suitable data for com- parison. Suitable experimental data require knowing what blade profile section was used, a fact which is not included in any obtainable experimental data to date. Shipway6 claims success in applying a very similar design method to an actual fan design,

CONCLUSIONS

The fan characteristic programs provide a relatively uncom- plicated means of predicting centrifugal and axial fan performance With these programs, such things as the effects of design changes on the performance and efficiency can be evaluated. On the basis of using these programs, the following general conclusions were drawn:

• Any modification to a fan which results in a flatter fan characteristic slope also tends to cause some reduction in peak fan-system efficiency.

• A significantly flatter fan characteristic slope for a centrifugal fan with backwardly curved blades can be obtained by allowing the fan inside diameter to approach the outside fan diameter, thus resulting in a narrower fan blade.

• An axial fan with straightener vanes is more effi- cient than a similar fan with prerotator vanes. However, an axial fan with prerotator vanes has a flatter fan characteristic slope than a similar fan with straightener vanes.

• The selection of the axial fan blade profile or blade characteristics can have a significant effect on the resulting fan characteristic slope.

• Decreasing axial fan hub-to-tip ratio or increasing tip diameter will cause a much flatter fan characteristic slope for similar conditions.

RECOMMENDATIONS

• The prediction programs should be compared against any suitable experimental data that can be obtained in order to evaluate the programs more completely and to understand the selection of suitable design variables for various cases.

27-404 5?

l^fm-ittWrWTifriiriM^ r. twWiff-'ii -^ih Hif fa- >-*^-;fr ■■■■- iwiiwiiiiwiiiif'V''•"■

• The effects of various parameters and combinations the'eof on the fan characteristic slope require more study.

• The effect of the number of fan blades on the per- formance of the fans should be evaluated separately in the pro- grams. Th i may perhaps be done best by expressing it as a frictiona" -pe of loss.

TECHNICAL REFERENCES

1 - Purnell, J. G., "Evaluation of potential Fan Concepts and the Lift Fan Requirements for Large SEV's," NSRDC/A Rept 27-182 (Aug 1972)

2 - Osborne, W. C. , Fans, London, England, pergamon Press (I966) 3 - Shipway, J. C., "Estimation of Head-Flow Curves for Centrif-

ugal Fans," National Physical Lab rept (Oct 1968) 4 - Wallis, R. A., Axial Flow Fans, London, England, Academic

Press (1961) 5 - Shipway, J. C., "Aerodynamic Design of Axial Lift Fans,"

National Physical Lab rept (July 1968) 6 - Shepherd, D. G., Principles of Turbomachinery, New York,

The MacMillan Co. (1956) 7 - Wislicenus, G. F., Fluid Mechanics of Turbomachinery, New

York, McGraw-Hill Book Co. (1947) 8 - Galvas, M. R., "Analytical Correlation of Centrifugal

Compressor Design Geometry for Maximum Efficiency with Specific Speed," NASA TN-D-6729 (Mar 1972)

9 - Csaky, T. G., "A Synthesis of Fan Design for Air Cushion Vehicles," NSRDC Rept 3599 (Oct 1972)

10 - Stodola, A., Steam and Gas Turbines, New York, McGraw-Hill Book Co. (1927) ~~

11 - Brotherhood, P., "Development of improved Fans for the Britten Norman CC2-001 Cushion craft," Royal Aircraft Establishment Tech Rept 66271 (Aug 1966)

12 - Shank, S. R., and J. S. Houston, "10-Ton SEV Obstacle Crossing Data Related tc Cushion System Dynamics," NSRDC/A Rept 27-229 (Aug 1972)

13 - Csanady, G. T., Theory of Turbomachines, New York, McGraw- Hill Book Co. (1964)

14 - Emery, J. C., et al, "Systematic Two-Dimensional Cascade Tests of NACA 65-Series Compressor Blades at Low Speeds," NASA Rept TR-I368 (1958)

15 - Strieker, J. G., and S. R. Shank, "Development of Noise-- Optimized, Mixed-Flow Pumps for Main Sea-Water and Proposed Hovering Systems," NSRDC/A Rept CI83 (Aug I969)

16 - Fan Engineering, 5th edition, Buffalo, New York, Buffalo Forge Co. (1966)

27-404

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APPENDIX A

CENTRIFUGAL FAN CHARACTERISTIC PREDICTION PROGRAM

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AXIAL LIFT FAN CHARACTERISTIC PREDICTION PROGRAM

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APPENDIX C

CENTRIFUGAL FAN WEIGHT ESTIMATE

aH

*H

t,

NOMENCLATURE

b^ - Inside blade height, ft

b0 - Outside blade height, ft

d^ - inside fan diameter, ft

d0 - Outside fan diameter, ft

- Hub diameter, ft

- Hub height, ft

- Base plate thickness, ft

- Upper shroud thickness, ft

- Average blade thickness, ft

- Base plate weight, lb

- Upper shroud weight, lb

- Blade weight, lb

- Hub weight, lb

WCF - Centrifugal fan weight, lb

z - Number of blades

- inlet blade angle, degrees

- Outlet blade angle, degrees

lavg

W

W

W

W

ß l

e0

o

1

2

h

27-404

- Fan material density, lb^/ft2

- Base plate

- Upper shroud

- Fan blades

- Hub.

C-l

^^^^^^^^^^^^^^^^^^^^^^

■ ■. ■ - :■■ ■ :■ ■ - ■■ .■-..-. : -

..,■■.■-• „_■.-• ,.-■.:', ■^v&ja.-,.:f. ■■:,.

The centrifugal fan weight is composed of four main parts as shown in figure 1-C.

I ■

Z»N0. OF BLADES

Figure 1-C Centrifugal Fan Basic Geometry

The base plate weight

w: = Pt| n£ol (i)

The upper shroud v-eight:

W, = npt„ _i o dQ - dt

+ (bi - bo)a

i/a

(2)

27-404 C-2

....... ..... ... ;' 1 ■.-.■. -. . -■ ■ ■-"., :. ■ ■. .. .: . ■-■■.-

:

The blade weight:

W3 = apt,

cos/90o.^±i2.

do - di bQ + b±

(5)

The hub weight:

W4 = ph. TTdH3

H CO

i i The basic centrifugal fan weight is obtained by adding equations (1) through (4). Thus,

wCF = Wj + W2 + W3 + W4 (5)

27-404 c-3

••«■•i»»1""

-su»erwaw»«W" *,.:; :i ^.T :■:-'■"-■ '"\;" •^•*—f^""*-■" """""rr-^.-- -.•««^-Wiv

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*Addressee.

27-404, July 1973

______________

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27-404, July 1973 a!

Security Classification Unclassified DOCUMENT CONTROL DATA -R&D

(Security classification of title, body ot abstract and indexing annotation must be entered when the overall report is classified)

1. ORIGINATING ACTIVITY (Corporate author)

Naval Ship Research and Development Center Annapolis, Maryland 21402

2«. REPORT SECURITY CLASSIFICATION

Unclassified 26. GROUP

3. REPORT TITLE

Prediction of Axial and Centrifugal Fan Characteristics for Large Surface Effect Vehicles

4. DESCRIPTIVE NOTES (Type of report and inclusive dates)

Research and Development 5- AUTHOR(S) (First name, middle initial, last name)

J. G. Purnell

6. REPORT DATE

July 1973 7a. TOTAL NO. OF PAGES

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16 Sa. CONTRACT OR GRANT NO.

b. PROJEC T NO.

9a. ORIGINATOR'S REPORT N'JMBER(S)

3943

Work Unit 1-1130-300-05 9b. OTHER REPORT NO(S> (Any other numbers that may be nssigned

this report)

27-404 !0. DISTRIBUTION STATEMENTr Distribution limited to U. S. Government agencies onl^ ; Test and Evaluation; July 1973- Other requests for this document must'be referred to Commander, Naval Ship Research and Development Center (Code 11), Bethesda, Maryland 20C34.

11. SUPPLEMENTARY NOTES 12. SPONSO RING Ml LI T AR V ACTIVITS

ARPA

13 ABSTRACT

Two digital computer programs have been formulated for predicting performance charac- teristics of centrifugal and axial fans which may be used to provide lift air for large sur- face effect vehicles, pressure rise and flow characteristics of forwardly curved, radial, and ba^'kwardly curved centrifugal fans can be evaluated. Axial fans having either inlet flow prerotators or exit flow straighteners can also be handled in the program. Sample results are presented to illustrate the method of calculation and the nature of the results.

(Author)

DD,?o1MJ473 S.'N 0101.807-680 1

(PAGE 1) Unclassified Security Classification

\ ' ■.■:.-■ ■; .^.* \;'-wl^'-,:fl^^-'W"^ .^i^-f r'.j-r.i^.-..v.: ~ — "^ffljKMJ

Security Classification Unclassified

KEY WORDS

Axial fans Centrifugal fans Fan characteristics Lift fans Fan performance

DD/r..1473 BACK, 'PAGE 2)

Unclassified Security Classification

-

I 1 •'

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