BNL 50362(Propulsion Systems and Energy Conversion - TID-4500)

ROTATING FLUIDIZED BED REACTORFOR

SPACE NUCLEAR PROPULSION

Annual Report:Design Studies and Experimental Results,

June 1971 - June 1972

JJLK.C.R.J.

September 1972

CONTRIBUTORS

HENDRIE

HOFFMAN

ISLERH. LUDEWtG

A.J. MANNING

E. SUUBERGF.T.C.J.

MILES

RASEMAN

-NOTICE-Thls report was prepared as an account of worksponsored by the United States Government, Neitherthe United States nor the United States Atomic EnergyCommission, nor any of their employees, nor any oftheir contractors, subcontractors, or their employees,makes any warranty, express or Emptied, or assumes anylegal liability or responsibility for the accuracy, com-pleteness or usefulness of any information, apparatus,product or process disclosed, or represents that its usewould not infringe privately owned rights.

ENGINEERING DIVISION, DEPARTMENT OF APPLIED SCIENCEBROOKHAVEN NATIONAL LABORATORY, ASSOCIATED UNIVERSITIES, INC.

UPTON, NEW YORK 11973

prepared for

SPACE NUCLEAR SYSTEMS OFFICEa joint office of the

UNITED STATES ATOMIC ENERGY COMMISSIONand the

NATIONAL AERONAUTICS AND SPACE ADMINISTRATIONWASHINGTON, D.C. 20545

underNASA AGREEMENT NO. 13254

NOTICE

This report was prepared as an account of work sponsored by the United StatesGovernment. Neither the United States nor the United States Atomic Energy Com-mission, nor any of their employees, nor any of their contractors, subcontractors, ortheir employees, makes any warranty, express or implied, or assumes any legal liabilityor responsibility for the accuracy, completeness or usefulness of any information,apparatus, product or process disclosed, or represents that its use would not infringeprivately owned rights.

Printed in the United States of AmericaAvailable from

National Technical Information ServiceU.S. Department of Commerce

5285 Port Royal RoadSpringfield, Virginia 22151

Price: Printed Copy 83.00; Microfiche 80.95

November 1972 500 copies

ACKNOWLEDGMENTS

The authors wish to acknowledge the guidance they re-

ceived from Norman Gerstein and David J. Miller of the

Space Nuclear Systems Office, U. S. Atomic Energy Commission.

- iii -

CONTENTS

Page

I. Summary 1

II. Introduction 2

III. Background and History 4

IV. Progress During Report Period 7

A. Analytical 7

1. Critical Mass 8

2. 90,000-N Thrust Engine Operating 17

Conditions

B. Experimental 32

1. System 32

2. Pressure and Flow Measurements 33

3. Experimental Results 36

4. Heat Transfer 39

V. Future Program 45

VI. Nomenclature 46

VII. References 48

- iv -

LIST OF TABLES

Table Page

I Energy Group Structure 11

II Thrust/Weight Ratios, Throat Diameter 220.08 m

III Thrust/Weight Ratios, Throat Diameter 230.08 m

IV Thrust/Weight Ratios, Throat Diameter 240.10 m

V Thrust/Weight Ratios, Throat Diameter 250.15 m

VI Thrust/Weight Ratios, Throat Diameter 260.15 m

- v -

LIST OF FIGURES

Figure Page

1 Two-dimensional reactor model. 9

2 Spatial variation of neutron flux. 14

3 Neutron spectra at various positions. 15

4 Variation of cavity L/D with reflec- 16tor volume - 235y fuel.

5 Variation of thrust-to-weight ratio 28with nozzle diameter for selectedfuel.

6 Schematic of rotating fluidized bed 34apparatus.

7 Correlation of Galileo number versus 38Reynolds number for minimum fluidiza-tion.

8 Zenz and Othmer correlation showing 40experimental data.

9 Correlation of fluidization data for 41500-n glass beads (specific gravity= 2.5).

10 Expansion of bed with increasing gas 42flow: 500-n glass beads, specificgravity = 2.5, 2,000 rpm, unexpandedbed 5/8 in. thick (1.59 cm); (a)5,000 scfm, (b) 6,500 scfm, (c)7,300 scfm, and (d) 8,000 scfm.

- vi -

I. SUMMARY

The suitability of the rotating fluidized bed re-

actor concept for nuclear rocket propulsion systems is being

investigated. A low thrust (90,000 N) rocket engine was

optimized with details of the critical mass determination and

engine operating conditions included. The investigation of

the fluid mechanics of a rotating fluidized bed system was con-

tinued. A correlation is given to predict minimum fluidiza-

tion Reynolds numbers based on particle, fluid, and rotative

properties.

"• 1 •-

II. INTRODUCTION

The rotating fluidized bed reactor was initially pro-

posed for rocket propulsion by L. P. Hatch, W. H. Regan, and

(1 2)J. R. Powell at Brookhaven National Laboratory in 1960. '

The fuel in this system is in the form of small diameter

particles that are retained by centrifugal force in a rotat-

ing cylindrical structure to form an annular core. The use

of small fluidized particles for the reactor fuel offers the

following specific advantages:

1. The large surface-to-volume ratio of the fuel

and the high fuel-to-coolant heat transfer coef-

ficient permit very high rates of heat transfer

with a minimum temperature difference between

the fuel and gas stream.

2. Since the primary structure remains cool, design

requirements are dictated by high temperature

stability of the fuel rather than structural

factors which are limiting in conventional solid

fuel element nuclear propulsion systems.

3. The volume and mass of material that must be

handled in loading and unloading fuel is less

M o mm

than that handled in comparable solid fuel

element systems and refueling of the core is

simplified.

4. The fuel particles are retained by the core by

centrifugal force and the fuel ioss problems

characteristic of gas core concepts

are minimized.

Thus, the rotating fluidized bed reactor promises to

avoid many of the problems that limit the performance and

suitability of solid fuel elements and gas core systems.

High gas temperatures and a high specific impulse can be

achieved, with the limit dependent on fuel particle melting

and sintering properties.

- 3 -

III. BACKGROUND AMD HISTORY

For many years fluidized bed techniques have been uti-

lized by the chemical process industries. Superior tempera-

ture control, heat transfer, and continuity of operation have

resulted in certain applications. Studies of the character-

istics of powder suspensions (100 to 500 (i) showed that a

dense concentration of solids could be maintained in a highly

turbulent state by a proper combination of gas velocity and

particle size of the powder. The solids appear to be buoyed

up by the upflowing gas and thus exhibit a "fluid" behavior.

The effective slippage between gas and solids is so great

that a powder of small enough particle size to exhibit

a free-fall velocity of the order of 0.03 m/sec (0.1 ft/sec)

can be maintained as an air-suspended bed at a superficial

gas velocity of the order of 0.3 m/sec (1 ft/sec). The be-

havior of the agitated solids indicates excellent contact

between gas and solids, with a modest pressure drop equal to

the weight of the bed.

Early fluidized bed studies were carried out with liquid

flow, which resulted in uniform dispersion of the material.

Moreover, unless the liquid is in highly turbulent motion,

the top of the bed will be flat and will remain essentially

_ 4 _

stationary as long as the velocity and the viscosity of the

liquid remain the same. In the gas fluidized system, how-

ever, there is a definite tendency for bubbles to form and

for a portion of the gas to pass through the bed in the form

of bubbles. Whether the original bubbles pass all the way

through the bed, or the bubbles collapse and new ones form,

is not known, but the latter is probably a safe assump-

tion. The question that arises in nuclear reactor design

considerations is how much of the gas passes through the

bed without contacting a sufficient number of particles to

maintain efficient heat transfer. To some extent heat would

transfer in the form of radiation, but the main mechanism is

convective transfer.

Preliminary studies were performed at Brookhaven

from 1962 to 1S66 with rotating beds of glass particles

fluidized with air to demonstrate the principles involved and

to provide a basis for the definition of a development pro-

gram. A rotating fluidized bed test rig with a 25.4-cm

(10-in.)-diameter by 2.54-cm (1-in.)-long bed was operated

with various bed depths at 138, 500, and 3,450 g. As

expected, no loss of the simulated fuel occurred during these

experiments and the beds did not show any instabilities.

- 5 -

Experiments were planned to determine the bed dynamics

of a fluidized bed with a length-to-diameter ratio of 1.0.

Design work was completed on a rig that would hold a 25.4-cm

(10-in.)-diameter by 25.4-cm (10-in.)-long bed. Construc-

tion of this rig was initiated in 1966 and several com-

ponents including the rotating fluidized bed assembly were

completed before work was stopped for lack of funding.

Additional experiments were performed to determine

particle-to-fluid heat transfer coefficients in beds fluid-

ized at high mass velocities. Although these experiments

2 o,

were performed in 1-g systems, the results indicated that

heat transfer coefficients were well in excess of 5.68 kW/m'-oK

(1000 Btu/hr-ft -° F ) , a value used in preliminary calcula-

tions for the rotating fluidized bed reactor system.

Work was resumed at Brookhaven National Laboratory

(4)under the guidance of the present sponsors during 1970.

The analytical results and experimental work confirmed the

suitability of this reactor concept for consideration in

future nuclear rocket propulsion systems.

- 6 -

IV. PROGRESS DURING THE REPORT PERIOD

A. Analytical

The primary analytical effort during the past

fiscal year has been devoted to optimizing a low-thrust

(90,000 N) rocket engine. The effort was motivated by an

increased interest in smaller nuclear rocket engines. The

(4)previously outlined program was altered to include the

smaller engine.

Early investigations ' indicated that the

first two reactors to be considered were not suitable in

this thrust range and new configurations had to be designed.

At such low thrust levels the reflector weight dominates the

total weight and there is thus a great incentive to reduce

the reflector weight. A reduction in reflector weight, and

hence its thickness, increases the neutron leakage. The

loss of neutrons may be compensated for by reducing the

nozzle area and thus the loss due to streaming. However,

a nozzle of reduced area implies a higher chamber pres-

sure to maintain the desired thrust level. The increased

chamber pressure increases the weight of the containment

vessels and turbopump. Thus a reduction in the reflector

weight implies an increase in the weight of the remainder

- 7 -

of the system, and vice versa. An optimum throat area can

be found which minimizes the weight for a given thrust level.

In designing the new critical configuration, one

of the chief points of departure from the previous analysis

was the reduction of the void fraction in the fuel bed. Ex-

perimental studies have suggested that the bed can be ex-

pected to be essentially settled at its largest radius and

fluidized only at the inner radius. This reduction in void

fraction has made it possible to increase the fuel loading

by a large fraction over the loading in the previously con-

sidered reactors, with a resultant reduction in reactor size

and reflector thickness.

Details of the critical mass determinations will

be outlined next, followed by an analysis of the operating

conditions of a 90,000-N (20,230-lb f) thrust rocket en-

gine.

1. Critical Mass Determination

The critical mass was calculated with use of

the two-dimensional representation shown in Fig. I. How-

ever, before computations could be carried out, appropri-

ate few-group cross sections had to be determined. Few-

group or macro-group cross sections were obtained by

- 8 -

BeREFLECTOR(10% VOIDS)

Fig. 1 Two-dimensional reactormodel.

-9-

assuming a one-dimensional model with many energy groups.

In this way an accurate representation of the neutron energy

spectrum can be determined in the various regions of the re-

actor. This spectrum can then be used to collapse the large

number of micro-groups in the one-dimensional calculations

to macro-groups to be used in two-dimensional calculations.

Only a radial variation was allowed for in the one-dimen-

sional model, thus the cavity, fuel bed, frit, and reflector

were assumed to be coaxial cylinders. In this way the

spatial variation of the spectrum from the cavity containing

hot hydrogen to the reflector composed of beryllium and hydro-

gen can be accounted for. Furthermore, the diffusion cool-

ing effects in the spectrum, due to the neutron leakage out

of the reflector, are incorporated.

The one-dimensional calculations were further

divided into two separate calculations, one for neutrons

above the thermal cutoff and another for those below the cut-

off. In this case the thermal cutoff was assumed to be

2.15 eV? Table I shows the macro- and micro-group structure.

The epithermal (above the cutoff) range was treated by using

(8)the ABBN cross-section set and the diffusion theory code

1-DX. It was decided that diffusion theory would be adequate

- 10 -

Table I

Energy Group Structure

I-

Micro-GroupNumber

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

Macro-GroupNumber

1

1

1

1

1

1

1

I

1

1

2

2

2

2

2

3

3

3

UpperEnergy

10.5 MeV

6.5

4.0 "

2.5

1.4

0.8

0.4

0.2

100 keV

46.5

21.5

10.0

4.65 "

2.15 »

1000 eV

465

215

100

Micro-GroupNumber

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

Macro-GroupNumber

3

3

4

4

5

5

5

5

5

5

5

5

5

5

5

5

5

5

Upper Energy,eV

46.5

21.5

10.0

4.65

2.15

1.62

1.24

0-911

0.633

0.512

0.405

0.356

0.310

0.276

0.243

0.213

0.184

0.158

Micro-GroupNumber

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

Macro-GroupNumber

5

5

5

5

5

5

5

5

5

5

5

5

5

5

5

5

Upper Energy,eV

0.134

0.112

0.0933

0.0820

0.0731

0.0648

0.0569

0.0496

0.0428

0.0364

0.0306

0.0205

0.0124

0.00633

0.00228

0.000405

in this range since the flux gradients would not be very

steep. Pour macro-group cross sections were obtained from

these calculations for the epithermal range. In the thermal

range a great deal of care had to be taken, since the gradi-

ent in the neutron flux from the reflector to the fuel

region is very steep, the Bragg scattering of beryllium had

to be accounted for, and the reactor is highly thermal. For

these reasons, the one-dimensional calculations were carried out

by using thirty thermal groups, with up and down scattering

among all groups and the DSN code ANISN. From such a

computation, cross sections for a single thermal group were

extracted. The thermal cross sections were based on ENDF/B

(Evaluated Nuclear Data File) data and processed through the

FLANGE-II^1X' code to make it acceptable to ANISN. In the

case of beryllium, isotropic and linearly anisotropic scatter-

ing was allowed for. Finally, a variation in temperature

was allowed for in the thermal group calculation by generat-

ing hydrogen scattering matrices at temperatures

ranging from 2400s K (4321*1*) in the cavity to 255° K (951° R)

in the reflector, with a steep temperature rise in the

fuel bed. The increased hydrogen temperature in the fuel

bed and cavity hardens the neutron spectrum

from the beryllium reflector.

- 12 -

Results of the one-dimensional calculation in

233the thermal range are shown in Figs. 2 and 3 for the U

fuel reactor. Figure 2 shows the spatial variation of the

neutron flux for 0.765 and 0.053 eV. The discontinuity in the

0.053 eV curve occurs at the point where the bed changes

from settled to fluidized. Figure 3 shows the neutron energy

spectrum in the cavity, fuel, and reflector. From these

curves the progressive softening of the spectrum is evident

as one moves out from the cavity to the reflector.

Criticality determinations of the actual rocket

reactor were carried out with use of the two-dimensional DSN code

(12)DOT. All the two-dimensional calculations were made

by using the five macro-group cross sections obtained from

the one-dimensional calculations and four angular quadratures.

Before a final geometrical shape for the reactor was decided

on, the effect of changing the length/diameter (o.d. of bed)

ratio of a critical reactor cavity was investigated. Fig-

ure 4 shows the variation of the L/D ratio rfith reflector

235volume for a U-fueled reactor. A broad minimum is seen

to exist between L/D values of 1.0 and 2.0.

The critical reactors computed by using the above

formalism and assuming the fuel bed to be 50% settled and 50%

fluidized are as follows:

- 13 -

10,-2

I0"3

10

CAVITY .FUEL

10"

FRIT REFLECTORj I l l

4 8 12 16 20 24 28 32 36 40 44 48 52RADIUS-cm

Fig. 2 Spatial variation of neutronflux.

- 1 4 -

10"

CAVITY

aa:

X REFLECTOR

zoo:

IO"e

I0"7

15 16 17 18 19LETHARGY-u

Fig. 3 Neutron spectra at variouspositions.

- 1 5 -

— 40

2.5

Fig. 4 Variation of cavity L/D withreflector v o l u m e — u fuel.

-16-

^33(a) For the " U-fueled reactor

d = throat diameter = 0.18 m (0.59 ft)

d = bed internal diameter = 0.24 m (0.79 ft)

t = radial reflector thickness = 0.16 m (0.52 ft)

t = axial reflector thickness = 0.25 m (0.82 ft)

t = fuel bed thickness = 0.10 m (0.33 ft)

h = cavity height = 0.44 m (1.44 ft)

h = overall height of reactor = 1.04 m (3.41 ft)

m = critical mass of fuel =140.0 kg (309 lb m)

235(b) For the U-fueled system

<j = throat diameter = 0.18 m (0.59 ft)

d = bed internal diameter = 0.48 m (1.57 ft)

t = radial reflector thickness = 0.21 m (0.69 ft)

t = axial reflector thickness = 0.25 m 0.82 ft)

t3 = fuel bed thickness = 0.10 m (0.33 ft)

h = cavity height = 0.747 m (2.45 ft)

h = overall reflector height = 1.35 m (4.43 ft)

m = critical mass of fuel =420.0 kg (926 lb m)

2. 90,000-N Thrust Engine Operating Conditions

The above two reactors will now be optimized,

using techniques similar to those outlined in Reference 5,

to deliver a thrust of 90,000 N (20,230 lb f) at the highest

- 17 -

thrust/weight ratio. As in previous analyses, ' the

total weight of an engine will be assumed to be composed of

(a) Fixed weight (fuel, reflector, rotating gear),

(b) nozzle and controls,

(c) pressure vessel, and

(d) turbopump.

Weights for the last three items are based on

a model proposed by Johnson and Smith. The fixed weight

was determined by the criticality calculations.

The procedure outlined in Reference 5 was ex-

panded to account for the fuel bed in a more realistic manner.

It will be seen that fuel particle size, and hence thermal

stress, will be a major limiting factor of the performance in

the case of a small reactor. The size of the particle pre-

dicted depends, to a large extent, on the model used relating

particle diameter and the superficial velocity of the bed.

The fuel bed was considered to have

two distinct regions, one fluidized and one settled. Since

the bed fluidizes at the inside edge first, with the boundary

between the fluidized and the settled region moving out with

increasing flow rate and a given rotational speed, a model

to simulate e two-region bed was used. In order to maintain

- 18 -

consistency between the models used for the criticality

study and the pressure drop determination, it will be as-

sumed that the bed is half fluidized and half settled.

A correlation for the minimum fluidization con-

dition for a fluidized bed, which describes the experimentally

(14)obtained results accurately, is given by

Re*,T* - C(33.7)2 + 0.0408 Ga]'2 - 33.7, (1)

where

Re = D V -£- = D V X,

p e |af p e

P(P -P)

D V D Vp e |af p e

, 3

Ga = D 3g — f — - D g Y,

D = particle diameter,P

V = superficial velocity,

g = gravitational force,

p = fluid density,

p = particle density, and

M- = fluid viscosity.

The subscript MF refers to minimum fluidization conditions.

It can be shown that

- 19 -

V X (D V X + 67.4)e p e

g = B 220.0408 D Y

P

Thus, given the superficial velocity and a

particle diameter the gravitational force required for

fluidization can be determined. Hence, the pressure drop

across the fiuidized section of the bed can be computed.

The correlation relating pressure drop to

particle size and superficial velocity for the settled see-ds)

tion of the bed is given by *

Ap TlSCLJl^l 1 L G2 (l-£) (3)

L Re J D G 2 p 32.17P

where

e = void fraction for packed bed,

L = thickness for packed section, and

6 = mass flow rate.

The total pressure drop across the bed is the sum

of the pressure drop values computed by using Eqs. (2) and (3).

From Eqs. (2) and (3) it can be seen that the

value of g, and hence the bed pressure drop, increases with

increasing V and decreasing D . Minimizing the bed pressure

drop is an important goal in maximizing the thrust/weight

- 20 -

ratio, since a high value of bed pressure drop increases the

turbopump weight and pressure vessel weight. In order to

decrease V for a given reactor, the propellant flow rate

has to be reduced; however, to maintain a constant thrust

level, the cavity pressure must be increased. It is thus

seen that the sum of the cavity pressure and the bed pres-

sure drop must be minimized. In minimizing this combined

pressure, it is important to take into account the correspond-

ing particle diameter, since the bed pressure drop decreases

with increasing particle size. Although this decrease in

bed pressure drop is very desirable, increasing particle

size is not, since the thermal stresses rise very rapidly

2

with diameter (stress « D ). For this study it was decided

to limit the particle diameter to 500 n and the thermal stress

to 55 MN/m2 (8,000 psi) .The larger values of V resulting from a throat

e233

diameter of 0.18 m (0.59 ft) in the case of the small U-

fueled reactor led to unacceptably high pressure drop and/or

particle diameters. It was thus decided to reduce the throat

diameter. Tables II to VI show the thrust/weight ratio for

values of throat diameter varying from 0.08 to 0.15 m (0.26

to 0.49 ft). In this way, D was reduced to an acceptable

- 21 -

Table II

Thrust/Weight Ratios for

Throat Diameter = 0.08 m, Constant Bed Pressure Drop (CAP) = 4.38 MJ/mZ (700 psia),

and Constant Particle Diameter (CPD) = 300 microns

to

i

CavityPressure

psia

250.0

500.0

750-0

1000-0

1250.0

1500.0

MJ/m2

1.72

3.45

5.17

6.89

8.62

10.34

Thrust

lb fxlO3

3.51

7.02

10.52

14.03

.17.54

21.05

kN

15,61

31.23

46.80

62.41

78.02

93.64

Thrust/Weightat CfP

lbf/lbn

1.27

2.47

3.59

4.64

5.57

6.40

i N/kg

12.45

24.22

35.21

45.50

r4.62

62.76

Thrust/Weightat CPD

lb f/lb m

1.33

2.55

3.67

4.71

5.63

6.42

H/kg

13.04

25.01

35.99

46.19

55.21

62.96

Particle Diameterat CAP

microns

149.0

173.0

200.0

229.0

261.0

293.0

Bed Pressure Dropat CPD

psia

219.0

312.0

404.0

496.0

589.0

681.0

MN/m

1 . 5 1

2.15

2.79

3.42

4.06

4.70

Table III

Thrust/Weight Ratios for

Throat Diameter = 0.08 m, Constant Bed Pressure Drop (CAP) = 2.07 MN/m (300 psia),

and Constant Particle Diameter (CPD) = 500 microns

I

to

CavityPressure

psia MN/m

ThrustThrust/Weight Thrust/Weight Particle Diameter Bed Pressure Drop

at C*P at CPD at CAP at CPD

lb fxlO kN 1b f/lb m N/kg 1b f/lbm H/kg microns psia MN/m

250 .0

500 .0

750 .0

1000 .0

1250 .0

1500 .0

1

3

5

6

8

10

.72

.45

.17

.89

.62

.34

3

7

10

14

17

21

.51

.02

.52

.03

.54

.05

15

31

46

62

78

93

.61

.23

.60

.41

.02

.64

1.32

2.58

3.70

4.78

5.79

6.66

12.94

25.30

36.28

46.88

56.78

65.31

1

2

3

4

5

6

.34

.55

.73

.80

.77

.61

13.14

25.01

36.58

47.03

56.58

64.82

247.0

308.0

378.0

453.0

533.0

616.0

101.0

157.0

211.0

267.0

323.0

378.0

0.69

1.08

1.45

1.84

2.27

2.61

Table IV

Thrust/Weight Ratios for

Throat Diameter = 0.10 m, Constant Bed Pressure Drop (C£P) = 4.83 MN/m (700 psia)t

and Constant Particle Diameter (CPD) = 300 microns

to

CavityPressure

psia

250.0

500.0

750.0

1000.0

1250.0

1500.0

MN/m

1.72

3.45

5.17

6.89

8.62

10.34

Thrust

lb fxl0J

5.49

10.97

16.46

21.94

27.43

32.91

kN

24.

48.

73.

97.

122.

146.

42

79

22

59

01

.39

Thrust/Weightat CtP

lb f/lbn

1.97

3.81

5.54

7.06

8.41

9.61

i N/kg

19.32

37.36

54.33

69.23

82.47

94.24

Thrust/Weightat CPD

lb f/lb m

2.01

3.83

5.46

6.79

7.90

8.82

N/kg

19.71

37.56

53.54

66.59

77.47

86.49

particle Diameterat CflP

microns

215.0

283.0

361.0

444.0

531.0

621.0

Bed Pressureat CPD

psia

424.0

649.0

875.0

1101.0

1326.0

1552.0

Drop

MN/m2

2.92

4.47

6.03

7.59

9.14

10.70

Table V

Thrust/Weight Ratios for

Throat Diameter = 0.15 in, Constant Bed Pressure Drop (C*P) - 4.83 MN/m2 (700 psia),

and Constant Particle Diameter (CPD) * 300 microns

CavityPressure

psia MN/m

250.0 1-72

500.0 3.45

750,0 5.17

Thrust

lbfxlO3

12.39

24.78

37.17

kN

5 5 .

110.

165.

11

23

34

Thrust/Weightat c/P

lb f / lb m N/kg

4.41 43.25

8.49 83.26

11.96 117.29

Thrust/Weightat CPD

1b f/lbm N/kg

4.11 40.31

6.92 67.86

8.66 84.93

Particle Diameterat CtP

microns

587.0

1037.0

1505.0

Bed pressureat CPD

psia

587.0

1034.0

1505.0

Drop

MN/m

4.05

7.13

10.38

Table VI

I

Thrust/Weight Ratios for

Throat Diameter - 0.15 m, Constant Bed Pressure Drop (O*P) > 10.34 MN/m (1500 psia) ,

and Constant Particle Diameter (CPD) = 500 microns

CavityPressure

psia MN/ 2m

Thrust

Ib fxlO3 kN

Thrust/Weightat CAP

1b f/lbm N/kg

Thrust/Weightat CPD

BJ f/lbm N/kg

Particle Diameterat O'P

microns

Bed Pressureat CPD

psia

Drop

MN/m

250

500

750

.0

.0

.0

1

3

5

.72

.45

.17

12

24

37

.39

.78

.17

55

110

Io5

.11

.23

.34

4

7

10

.14

.77

.91

40.60

76.20

106.99

4

7

10

.36

.79

.12

42

76

99

.76

.39

.24

314

509

722

.0

.0

.0

845

1530

2215

.0

.0

.0

5

10

15

.S3

.55

.27

value, but the cavity pressure had to be increased to de-

liver 90,000 N (20,230 lb f) of thrust.

From these tables it can be seen that for the

smallest throat diameter, 0.08 m (0.26 ft), the thrust/weight

ratio is comparatively low because of the high chamber pres-

sures required. In contrast, for the largest throat diameter

considered, 0.15 m (0.49 ft), the best thrust/weight ratio

for 90,000 N (20,230 lb f) cannot be considered practical,

since the particle diameter and hence thermal stress is too

large. The variation of thrust/weight ratio as a function

of throat diameter and particle size is shown in Fig. 5, for

a thrust of 90,000 N (20,230 1b f) .

The curves in Fig. 5 include the optimizations

discussed in Reference 6 concerning the trade-off between

reflector weight and the weight of the remainder of the sys-

tem. However, they also include the effect of different

particle size, not included in previous discussions. They

all have the characteristic shape discussed previously.

Increasing the throat diameter improves the performance

initially, because of a reduction in cavity pressure, which re-

duces the pump and pressure vessel weight. However, larger

throat diameters require increasingly heavier reflectors,

~ 27 -

inch5 6

65 —

60 -

- 6

t -I(0

5

55 -

50 -

1 1 1

—

1 1 1

1 1

N. 500 fi

>v 400ft

\ 300/t

\

\ 200/i

1 1 1

— 5

0.08 0.10 0.12 0.14 0.15THROAT DIAMETER-m

0.18

Pig. 5 Variation of thrust-to-weightratio with nozzle diameterfor selected fuel.

-28-

which reduce the performance levels. Furthermore, it can

be seen that larger fuel particle diameters correspond to

improved performance levels since they result in lower fuel

bed pressure drops, as pointed out above.

It is interesting to note that, for the fluid-

ized section of the bed, for a constant particle diameter D and

a constant thrust, V X is a constant and thus the Reynolds

number is a constant, regardless of throat diameter. Prom

Eq. (1) it can be seen that this implies a unique Galileo

number, also independent of throat diameter. With D constant,

Y must be constant since Y varies directly as p, the fluid

density, which decreases with decreasing cavity pressure,

Therefore, g increases with decreasing cavity pressure, in-

creasing the bed pressure drop. It is thrs seen that for

the same reactor operating at the same thrust level with the

same size particles the bed pressure drop for lower cavity

pressures is larger than for higher cavity pressures. The

same general conclusion applies to the settled section of

the bed, since G, the mass flow rate, remains constant with

thrust and since the density, p, decreases with decreasing

cavity pressure, it can be seen from Eq. (3) that Ap increases.

This explains the rapid drop-off of the curves for 200- and 300-|j

- 29 -

diameter particles for larger throat diameters. For larger

particle diameters the bed pressure drop is comparatively

small and this effect is not as important. It should be

pointed out that in this analysis the bed temperature was

assumed uniform and a variable temperature model for the bed

seems necessary to include variation in propellent properties.

Finally, a reactor operating with 500-n-diam-

eter particles under the conditions necessary to produce

90,000 N (20,230 lb f) thrust sustains a particle thermal

2stress of «12.9 MN/m (1,870 psi) and the 200-(J-diameter

2particle sustains a stress of 2.1 MN/m (300 psi). Although

the stress level at 90,000 N (20,230 lb f) thrust is ac-

ceptable, increases in thrust increase the stress level

proportionately.

235In the case of U-fueled reactor the

above problems are largely avoided since the reactor is large

enough to have a comparatively small value of V . Thus,

assuming a particle of 400 n in diameter, a low bed pressure

drop is assured and with a throat of 0.18 m (0.59 ft) a

2relatively low cavity pressure of approximately 2.1 MN/m

(300 psia) is required to deliver 90,000 N (20,230 lbf) thrust.

The corresponding thrust/weight ratio is 33.3 N/kg (3.41b f/lb m)

- 30 -

All the above analyses were carried out at

2,367°K (4,250°R); the same methods and conclusions apply

to a cavity temperature of 3,400°K (6,12O°R).

The following conclusions may be drawn from

this study

1. Prom the four reactors studied, it is evident

that although the rocket engine would be able

to operate over a large range of thrust, it is

worthwhile to optimize it for a thrust range

of interest.

2. In addition to the problems posed by optimizing

the reflector weight and the remainder of the

system weight by adjusting the throat diameter,

it has been found that the particle stress plays

a limiting role on performance.

3. For comparatively low thrust rocket engines

233U seems to have an overwhelming advantage over

235

U-fueled engines from a performance point of

view. This conclusion is based on a thrust/weight

ratio of 65.7 N A g (6.7 1b f/ lb m) for a ""JU-

fueled engine and 33.3 NAg (3.4lb f/ib m) for a

U-fueled engine.

- 31 -

B. Experimental

During this period an active experimental program was

centered on the fluid mechanics of a rotating fluidized

bed system. Experiments involved the measurement of pres-

sure drop across a fluidized bed as a function of flow rate.

A correlation was developed to predirt minimum fluidization

Reynolds numbers (and hence, necessary flow rates) based

on particle, fluid, and rotative properties.

1. System

The equipment remains much the same as reported

(4)previously, with some important modifications. Work

being conducted currently should increase the allowable

nitrogen flow rate in the bed to a maximum of about

34,000 STP m /h (20,000 scfm). This will permit fluidiza-

tion of particles under higher rotative speeds than pre-

viously possible.

The frit (the porous support structure for

the bed which contains the particles during rotation with

low gas flow) was replaced twice during the year. The

latest model (manufactured by the Bendix Filter Division)

is seamless, which eliminates the concern over potential flow-

- 32 -

pattern disturbance by the seams in the two previous models.

It was formed by winding continuous wire on a mandrel and

subsequently furnace sintering the cylinder. During wind-

ing, successively larger diameter wire was used to increase

the porosity of the supporting layers and thereby reduce

the pressure drop across them. This is important, as the

pressure drop across this frit was roughly three times

greater than that across the previous frits. However, the

structural strength was much improved.

Although experimental work on higher density

material was hampered by lack of uniform spherical copper

particles of 100-n size (specific gravity = 8.9), a source

of such particles was recently found. The data from the

previously examined glass beads (specific gravity = 2.5,

4.49) and the new copper particles should bracket the range

of density of the UC, ZrC fuel (specific graveity «6.5).

2. Pressure and Flow Measurements

The same techniques were applied during

this reporting period as during the last. To obtain the

pressure drop across the bed itself by using the mea-

sured pressures P and P. (see Fig. 6), the pressure

drop across the frit and the pressure due to free

- 33 -

rm

Ito

ffv

Hi COH-TJ

c trH-fl)

N rP.OCO' H:8.a> o•o n-•a PIP- f t<% p-fl> 3(TlQCIB

expansion of the gas after it leaves the bed must be deter-

mined. Their effect can then be factored out to give

P^-P , the bed pressure drop. Because of the presence of

the bed, it is not possible to insert pitot tubes to mea-

sure P and P directly.

Several computer programs were devised to per-

form the above calculations. P_ was determined from the

equation

2 2P - P 2

1 2 a T n G + B T —

where

p ,c - - ̂ sured pressure and mass flow rate, respectively,

L = frit thickness,

a,B = constants,

T = absolute temperature,

(if = viscosity, and

g = gravitational constant.

Once P was established, the apparatus was run without a bed

2 2to obtain a table of P - P = f (elevation, wall distance

and flow rate).

With these data, another computer program, fed

data on temperature, P., P4# bed weight, flow rate, and

- 35 -

rotational speed, calculated all desired quantities: pres-

sure drop per unit bed thickness, Re, Ga, and C .

For a more complete description of experimental

(4)techniques, see previous annual report.

3. Experimental Results

Extensive testing was carried out with 100 to

500 u glass spheres having specific gravities of 2.5 or 4.5. The

full range of attainable rotational speeds was examined, up

to 5,000 rpm. For the present apparatus, the following

rotational speeds develop the indicated g forces

G ravitationalrpm force

1,000 142

2,000 568

3,000 1,278

4,000 2,272

5,000 3,550

Among the more important results to arise

from the experimental program is verification of a ccrrela-

(14)tion due to Wen and Yu. This correlation is extremely

useful in predicting the point of minimum fluidization, and

- 36 -

hence the minimum flow rate required to fluidize a given

system. The correlation is obtained by plotting the

Galileo number (Ga) as a function of the Reynolds number

(Re), where

Dl P<PPGa =

andG D

where

p,H,G = the fluid density, viscosity, and mass flow

rate per unit area, respectively,

D ,p = the particle diameter and density, and

g = the gravitational acceleration.

The theoretical correlation presented in

Reference 14 and the actual experimental results are plotted

in Fig. 7. These data are in good agreement with the

theoretical model, for which the equation is

2 JiR®MJ? = E (33.7) + 0.0408 Ga] - 33.7.

Another interesting, although somewhat less use-

ful correlation, is presented by Zenz and Othmer. It in-

1/3 2 1/3volves plotting the quantity (Re/C ) ' vs. (C /Re ) ' ,

- 37 -

108

I 0 7

I 0 6

I 0 5

104

1—

: oo•A

r

•

-

i i i i n i | 1—i i i i nij i i—i

lOO/i gloss500ft glass500/t high density glossiOOft high density gloss

Jo7y

D /

0 /

i i Vi 111 i I I I I I I I I i i i

i i i i u| r

+ /

/

—i—1111II

/

i i

11

1 •

ni

L ij

.nl

-

L.,1

1 1 1

1 | 1 1 1 1 1

1

1 1 1 1 1 1 1

!0 102

Re

10' I04

Fit;. 7 Correlation of Galileo numberversus Reynolds number forminimum fluidization.

-38-

where C_ is the drag coefficient defined by

where all symbols have been defined earlier. Figure 8 shows

the theoretical correlation and experimental data points.

The fit is good, although the void fraction predicted appears

low.

The point of minimum fluidization is defined as

the point at which the pressure drop across the bed becomes

roughly independent of flow rate. Typical plots are shown

in Fig. 9. The pressure drop across a fluidized bed should

be independent of flow rate and simply equal to the weight

of the bed. The effect of increasing flow rate on bed

thickness is shown in Fig. JO. The four pictures are from runs

in which the only variable was gas flow rate and are re-

presented in Fig. 9 by the vertical half-moon data points.

4. Heat Transfer

Heat transfer studies were begun on a 1-g bed but

were discontinued when difficulties were encountered in trying

to obtain useful correlations. Instead, various proposals

for measuring heat transfer coefficients in high-g beds were

examined. The process of selecting such an experiment con-

tinues .

- 39 -

100 * I I I I I I I I i I I I I I I 1 1

0 lOO/i glass

O 500ju. glass+ 500/L high density glassA lOO/i high density glass

10 -

FROM ZENZ S OTHMER

0.0110 100

(Cn R e 2 ) " 31000

Fig. 8 Zenz and Othraer correlationshowing experimental data.

- 4 0 -

0

(SCFM)

2000 4000 6000 8000 10000| I | I "| | 1 1 1

• 1000 RPM 0.95 cm (3/8 in.) BED

A 1500 RPM 0.95 cm (3/8 in.) BEDO 2000 RPM 0.95 cm (3/8 in.) BED yj.f) 2000 RPM 1.59 cm (5/8 in.) BED ^ ©% 2000 RPM 2.54 cm ( I in.) BED

I 6

S / " H20--Q

UJ(£V)<nin

^ 110

0 50 100 150 200 250 300GAS FLOW (STP m /̂min)

Fig. 9 Correlation of fluidizationdata for 500 |J glass beads(specific gravity = 2.5).

- 4 1 -

toI

&

2u lb 1UlOO

01oMi3

0

" " • ^

- 0

woo010Ml

•*

SI

0.

&*"00

ooo01nMi3•

w1(D&

tf(D&

00

•

gO

Ul

n

•Si-

ooo01

n

0)tov

0)a01

H

01V

H-MlH-

n4fu<:H-

* ^

II

M

Ul-

to

ooo

«3

mP

H-0

0Ml

0"

3

K(I)PI01

5-

PI01

Hi

05••

UlooX-

The v?.«lue of the heat transfer coefficient

should, by all indications, be excellent. As an example,

for hydrogen gas at high temperatures and pressures (as in

rocket applications) the thermal conductivity k « 2 x 10 cal/sec-

cm-°K («48 Btu/hr-ft-6F). If the particles are 400 \i (13.1

—4x 10 ft) and the particle Reynolds number is 100, then,

employing the correlation presented by Sen Gupta and Thodos '

for packed beds,

= 2.06 Re°' 4 2 5Pr 1 / 3

If e (void fraction) = 0.4 and Pr « 1, then

Nu = *f = (5.15) (10 2) 0- 4 2 5 = 36.4,

Therefore,

h = 1.33 x 10 4 Btu/hr-ft2-6F.

The results for fluidized beds are similarly encouraging, with

the important difference that the Nusselt number in a fluidized

bed tends to be flow rate independent, as hypothesized by

Chang and Wen and demonstrated by Lindauer.

Chang and Wen present the following correla-

tion with which Lindauer obtained fair agreement:

Nu = 2 + 0.79 Ga1'4 Pr1'3 ,

where Ga is the Galileo number, defined as before. The

- 43 -

reason for the discrepancy between the predicted correlation

and experiment is that the drag force was as "anted independent

of void fraction, which is not the case.

Since it has been predicted that the actual

rotating bed reactor will be a partially settled - partially

fluidized device (because of the variation of Ga and Re with

radius), it will be necessary to examine the heat transfer

correlations for both packed and fluidized bed experi-

mentally.

- 44 -

V. FUTURE PROGRAM

The experimental effort for next year will include the

acquisition of fluidization data at higher gas flow rates.

The experimental apparatus has been revised to operate at

gas flow rates approximately double those previously avail-

able. Data will be obtained with use of 100- and 500-n copper

(specific gravity = 8.9) and glass particles (specific

gravity = 2.5 to 4.5). Pluidization behavior and flow

patterns will be investigated for a smaller nozzle to

rotating bed diameter ratio. The behavior of thicker beds,

up to a ratio of 0.2 bed thickness to rotating bed diameter,

will be investigated.

The analytical effort will include the estimation of

power distribution and temperature profiles. During the

first half of the year, active liaison will be maintained

with the Aerospace Systems Laboratory at Princeton University.

- 45 -

VI. NOMENCLATURE

Btu = British thermal unit

cm = centimeter

C = drag coefficient

D = particle diameter

E = energy, eV

G = mass flow rate

g = gravitational constant

Ga = Galileo number

h = heat transfer coefficient

I = specific impulse

L = thickness of packed section of bed

lb f = pound force

lb m -- pound mass

MN = meganewton

N = newton

Nu = Nusselt number

Pr = Prandtl number

psi = 1b f/in.2

2psia = lb f/in. absolute

psig = lb f/in. gage

u = lethargy, At *&J^

s,sec = second

- 46 -

scf = standard cubic feet

scfm = standard cubic feet per minute

STP = standard temperature and pressure

V = superficial fluid velocity

°R = degrees Rankine

e = void fraction

M. = micron

|i = fluid viscosity

p = fluid density

p = particle densityP

a = tangential thermal stress

A = pressure dropP

- 47 -

VII. REFERENCES

1. Hatch, L. P., Regan, W. H., and Powell, R. J., Pluidized

solids as a nuclear fuel for rocket propulsion, pre-

sented at Amer. Rocket Soc. Semiannu. Meet., Los

Angeles, May 1960.

2. Hatch, L. P., Regan, W. H., and Powell, J. R., Fluidized

bed for rocket propulsion, Nucleonics 18. No. 12, 102-3

(1960).

3. Lindauer, G. C., Tichler, P., and Hatch, L. P., Experi-

mental Studies on High-Gravity Rotating Fluidized Beds,

BNL 50013 (T-435), Sept. 1966.

4. Rotating Fluidized Bed Reactor for Space Nuclear Propul-

sion. Annual Report: Design Studies and Experimental

Results, June 1970 - June 1971. BNL 50321 (UC-33),

Brookhaven National Laboratory, Aug. 1971.

5. Ludewig, H., Design parameters for a rotating bed re-

actor-powered rocket engine, Trans. Amer. Nucl. Soc. 15.

8 (1972).

6. Ludewig, H., Preliminary considerations of a 90,000 N

thrust engine, Memo to C. J. Raseman. Brookhaven

National Laboratory, Dec. 1971.

7. Ludewig, H. and Chernick, J., Physics parameters of the

Hatch reactor, Trans. Amer. Nucl. Soc. 14, 11 (1971).

- 48 -

8. Abagyn, L. P. et al.. Group Constants for Nuclear Re-

actor Calculations, Consultants Bureau, Ne^ York 1964.

9. Hardie, R. W. and Little W. W. Jr., 1DZ; A One-

Dimensional Diffusion Code for Generating Effective

Nuclear Cross Sections, BNWL-954, Battelle Memorial

Institute, Mar. 1969.

10. Engle, W. W. Jr., A One-Dimensional Discrete Ordinates

Transport Code with Anisotropic Scattering, K-16S3,

Union Carbide Corporation, Oak Ridge National Laboratory,

Mar. 1967.

11. Honeck, H. C. and Finch, D. R., FLANGE-II, A Code to

Process Thermal Neutron Data From an ENDF/B Tape, DP-1273,

Oct. 1971.

12. Mynatt, F. R., A User's Manual for DOT, K-1694 Union

Carbide Corporation, Oak Ridge National Laboratory, to

be published.

13. Johnson, P. G. and Smith, R. L., An Optimization of

Power-Plant Parameters for Orbital-Launch Nuclear

Rockets, NASA-TN-D-675, 1961.

14. Wen, C. Y. and Yu, Y. H., Mechanics of fluidization,

Chem. Eng. Progr. Symp. Ser. No. 67, Vol. 62., 100 (1966).

15. Eckeot, E. R. G. and Drake, R. M., Heat and Mass Trans-

fer. McGraw-Hill, New York, 1959.

- 49 -

16.. Zenz, F. A. and Othmer, D. F., Fluidization and Fluid

Particle Systems, Reinhold, New York, 1960.

17. Sen Gupta, A. and Thodos, G., A.I.Ch.E. J. .9, 751 (1963)

18. Sen Gupta, A. and Thodos, G., Ind. Enq. Chem. Fundam. 3.

218 (1S64).

19. Chang, T. M. and Wen, C. Y., Chem. Enq. Proqr. Symp.

Ser. No. 67, Vol. 62, 111 (1966).

20. Lindauer, G. C., A.I.Ch.E J. L3, 1181 (1967).

- 50 -