ML19341C519

Chapter 3 to Univ of Tx Triga Mark I RSAR, Reactor.

ML19341C519
Person / Time
Site:	05000192
Issue date:	01/31/1981
From:	TEXAS, UNIV. OF, AUSTIN, TX
To:
References
NUDOCS 8103030684
Download: ML19341C519 (86)

Text

o e i

%. J

3. REACTOR 3.1. DESIGN BASES The reactor design bases are predicated on the maximum operational capability for the fuci elements and configuration described in this report.

The TRIGA reactor system has three major areas which are used to define the reactor design bases:

1. Fuel temperature

2. Prompt negative temperature coefficient

3. Reactor power Of these three only one, fuel temperature, is a real limitation.

A summary is presented below of the conclusions obtained from the reactor design bases described in this section.

Fuel Temperature The fuel temperature is a limit in both stendy-state and pulse mode operation. This limit stems from the out-gassing of hydrogen from U-ZrH X

f uel and the subsequent stress produced in the fuel element clad material.

The strength of the clad as a function of temperature can set the upper limit on the fue.1 temperature. A fuel temperature limit of 1150*C for U-ZrH s een se - prec u e oss clad integrity.

1.65 prompt Negative Te.nperature Coef ficient The basic parameter which provides the TRICA system with a large safety factor in steady-state operation and under transient conditions is 3-1 til () 3() ) 0(sEhF#L l l

l

the prompt negative temperature coefficient which is rather constant with temperature (N1.0 x 10~ 6k/k'C), as described later. This coefficient is a function of the fuel composition and core geometry.

Reactor Power Fuel and clad temperature limit the operation of the reactor. However, it is more convenient to set a power level limit which is based on tempera-ture. The design bases analysis indicates that operation at 1700 kW (with a 63-element core and 90*F inlet water temperature) uith natural convective flow will not allow film boiling, and therefore high fuel and clad tempera-tures which could cause loss of clad integ*ity could not occur.

3.1.1. Reactor Fue- "mperature The basic safety limit for the TRIGA reactor system is the fuel tempet-ature; this applies for both the steady-state and pulsed mode of operation.

Two limiting temperatures are of interest, depending on the type of TRIGA fuel used. The TRIGA fuel which is considered low hydride, that with an H/Zr ratio of less than 1.5, has a lower temperature limit than fuel with a higher H/Zr ratio. Figure 3-1 indicates that the higher hydride composi-tions are single phase and are not subject to the large volume changes ass o~-

ciated with the phase transformations at approximately 530*C in the lower hydrides. Also, it has been noted (Ref. 1) that the higher hydrides lack any significant thermal diffusion of hydrogen. These two facts preclude concomitant volume changes. The important properties of delta phase U-ZrH are given in Table 3-1.

Among the chemical pruperties of U-ZrH and ZrH, che reaction rate of

, the hydride with water is of particular interest. Since the hydriding reaction is exothermic, water will react more readily with zirconium than with zirconium hydride systems. Zirconium it frequently used in contact 3-2 l

l l

l

950; i a e i i i  : 1 I 8 A' -

750 "

Ze(B) Zr(B) -

+ ,..**

8-HYDR.OE P

i] MO a

D Zr.(a) *

& h @)

N (a)

• h.550

• 1 ,

450 Zr (a) + 8 -HYDROE (cubic) , .--oe

. (tetrogonal) 330 .  : -

g , a+8

• o ' ' ' ' ' '

3 I

. O O2 04 06 08 to 12 L4 L6 18 20 HYDROGEN CONTENT (H/Zr)

Fig. 3-1. Phase diagram of the zirconium-hydrogen system i

I I

e e

4 3-3

TABLE 3-1 PHYSICAL PROPERTIES OF DELTA PHASE U-ZrH Thermal conductivity (93* - 650*C) 13 Btu /hr-ft *F Elastic modulus: 20*C 9.1 x 10 psi 650"C 6 6 x 10 p,1 Ultimate tensile strength (to 650*C) 24,000 psi Compressive strength (20*C) 60,000 psi compressive yield (20*C) 35,000 psi Heat of formation (6H* 298) 37.72 kcal/g-mole with water in reactors, and the zirconium-water reaction is not a safety hazard. Experiments carried out at General Atomic show that the zirconium hydride systems have a relatively low chemical reactivity with respect to

+

water and to air. These tests have involved the quenching with water of both powders and solid specimens of U-ZrH after heating to as high as 850*C, and of solid U-Zr alloy after heating to as high as 1200*C. Tests have also been rade to determine the extent to which fission products are removed from the surfaces of the fuel elements at room temperature. Results prove that, 4

because of the high resistance to leaching, a large fraction of the fission products is retained in even completely unclad U-ZrH fuel.

For the rest of the discussion of fuel temperatures, we will concern ourselves with the higher hydride (H/Zr > 1.5) TRICA fuel clad with 0.020-in.-

thlet 304 stainless steel, or a cladding material equivalent an strength at the temperatures discussed.

At room temperature the hydride is ceramic-like and shows little duc-tility. However, at the elevated temperatures of interest for pulsing, the material is found to be more ductile. The effect of very large thermal stress on hydride fuel bodies has been observed in hot cell observations to cause relatively widely spaced cracks which tend to be either radial or normal to the central axis and do not interfere with radial heat flow.

3-4

Since the ser,ments tend to be orthogonal, their relative positions appear to be quite stable.

The limiting effect of fuel temperature then is the hydrogen gas over-pressure. Figure 3-2 relates equilibrium hydrogen pressure over the fuel as a function of temperature for material with three different H/Zr ratios.

The hydrogen gas overpressure is not in itself detrimental but if.the stress produced by the gas pcessure within the fuel can exceeds the ultimate strength of the clad material, a rupture of the fuel clad could occur.

While the final conditions of fuel temperature and hydrogen pressure in which such an occurrence could come about are of interest, the mechanisms in obtaining temperatures and pressures of concern are different in the pulsing and steady-state mode of operation, and each mechanism will be discussed independently of the other. (Steady-state operation is discussed elsewhere in this section.)

In this discussion it will be a sumed that the fuel consists of U-ZrH 1.65

, with the uranium being 8.5 ut % and further that the cladding can is 0.020 in.

(0.05 cm) 304 stainless steel with an inside diameter of 1.43 in. (3.63 cm) .

These fuel parameters have been chosen since they represent the nominal specifications for TRIGA fuel elements.

Figure 3-3 shows the characteristic of 304 SS with regard to yield and ultimate strengths as a function of temperature.

In detarmining the stress applied to the cladding f rom the internal hydrogen gas pressore the equation S = PR/t (1) l j

~

applies where i

S = stress in psi, P = internal pressure in psi, 3-5

.- 3 10 ZrH l.7 ZrH l.6

2. /

E

$ 10 2 _

i g .. ZrH g,$

e n.

~

!. 5 E

g j 5 -

l

/

E 10 I -

d -

i 8

w _

i

/ / DATA FROM GA-8129

/ / AND NAA-SR-9374

0 ' ' ' ' ' '

10 600 700 800 900 1000 1100 1200 1300 TEMPERATURE ( *C) l

• l rig. 3-2. Equilibrium hydrogen pressures over Zrli versus temperature 3-6

10 5

~

ULTIMATE TENSILE 0.2% YlELD C

E 4

m 10 -

. O -

E m

REFERENCE:

CARPENTER AND CRUCIBLE STEEL 3 ' I i i i i 10 100 4 500 600 700 800 900 1000 1100 TEMPERATURE ( C)

Fig. 3-3. Strength of type 304 stainless steel as a function of temperature 3-7 l

.S ,

r = radius of the cladding can in inches, t = vall thickness of the clad in inches.

Then for the cladding we have approximately S = 36.7P ,

(2) or the stress applied to the clad is approximately 36.7 times the internal pressure.

It is of interest to relate the strength of the clad material at its operating temperature to the stress applied to the clad from the int'ernal gas pressure associated with the fuel temperature. Figure 3-4 gives infor-mation as to the ultimate clad strength as a function of temperature and also describes the stress applied to the clad as a result of hydrogen disso-

. clation for fuel having a H/Zr ratio of 1.65 as a function of temperature.

The following discussion relates the clad temperature and the maximun fuel temperature during a short time after a pulse.

The radial temperature distribution in the fuel element immediately following a pulse is very similar to the power distribution shown in Fig. 3-5.

This initial steep thermal gradient at the fuel surface results in some heat transfer during the time of the pulse so that the true peak temperature does not quite reach the adiabatic peak temperature. A large temperature gradient is also impressed upon the clad which can result in a high heat flux from the clad into the water. If the heat flux is sufficiently high, film boiling may occur and form an insulating j :ket of steam around the fuel elements per-mitting the clad temperature to tend to approach the fuel temperature.

Evidence has been obtained experimentally which shows that film boiling has occurred occasionally for some fuel elements in the Advanced TRIGA Prototype Reactor located at General Atomic (Ref. 2). The consequence of this film

. boiling was discoloration of the clad surface.

i 3-8

5 10 ULTinATE STREllGTH 304 55 ZrH '

l.65

! 10 -

C.

E M

u b;

3 10 -

~

2 10 _ ,

i , 1 , ,

500 600 700 800 900 1000 1100 TEMPERATURE (*C)

Fig. 3-4. Strength and applied stress resulting from equilibrium hydrogen dissociation pressure as a function of temperature 3-9

. 8 0

i 7 0

i 6 t

' . n 0 e m

e l

e l

e i 5 u

' . f 0 H r

Z

) -

. U N n I

i

(

i 4 n

. 0 SU o i

t u

I D b A i R r

. t s

i 3 i

. d 0 r e

w o

p l

i 2 a i

d 0 a R

5 3

i 1 g

0 i F

O 3 2 1 0 9 8 1 1 1 1

0 0 nee wLo

Thermal transient calculations made using the RAT

• computer code show

~

that if film boiling occurs after a pulse it may take place either at the time of maximum heat flux from the clad (before the volk temperature of the coolant has changed appreciably), or it may take place at a much later time when the bulk temperature of the coolant has approached the saturation tem-perature (resulting in a markedly reduced threshold for film boiling). Data obtained by Johnson et al. (Ref. 3) for transient heating of tibbons in 100*F water, showed burnout fluxes of 0.9 to 2 x 10 Btu /ft -hr for e-folding periods from 5 to 90 milliseconds. On the other hand, sufficient bulk heating of the coolant channeled between fuel elements can take place in several tenths of a second to lower the departure from nucleate boiling (DNB) 6 point to approximately 0.4 x 10 Btu /ft -hr. It is shown, on the basis of the following analysis, that the second mode is the most likely; i.e., when film boiling occurs it takes place under essentially steady-state conditions at local water temperatures near saturation.

A value for the temperature that may be reached by the clad if film boiling occurs was obtained in the following manner. A transient thermal calculation was performed using the radial and axial power distributions in Figs. 3-5 and 3-o, respectively, under the assumption that the thermal resis-tance at the fuel-clad interface was nonexistent. A boiling heat transfer model, as shown in Fig. 3-7, was used in order to obtain an upper limit for the clad temperature rise. The model used the data of McAdams (Ref. 44 for the subcooled boiling and the work of Sparrow and Cess (Ref. 5) for the film boiling regime. A conservative estimate was obtained for the minimum heat flux in film boiling by using the correlations of Speigler et al. (Ref. 6),

Zuber (Ref. 7), and Rohsenow and Choi (Ref. 8) to find the minimum tempera-ture point at which film boiling could occur. This calculation gave an upper limit of 760*C clad temperature for a peak initial fuel temperature of 1000*C, as shown in Fig. 3-8. Fuel temperature distributions for this

. case are shown in Fig. 3-9 and the heat flux into the water from the clad is shown in Fig. 3-10. In this limiting case, DNB occurred only 13 milliseconds

. af ter the pulse (conservatively assuming a steady-state DNB correlation).

• RAT is a 2D transient heat transport code developed to account for fluid flow and temperature-dependent material properties.

3-11

l I

II I I I l l l l 1.0 -

s i

0.9 -

4 m

O 0.8 -

u. ,

Y_.

0.7 -

j I

. 0.6 - -

i 0.5 l ' I I I I I 0 1 2 3 4 5 6 7 8 AXIAL DISTANCE FROM.MID-PLANE OF FUEL' ELEMENT (IN.) .

Fig. 3-6. Axial. power distribution in a fuel element assumed for thermal analysis '

l

i 6

10 i i i i i l

i Il i i i i f^s _

\

~

' ~

\ CURVE BASED ON

\ DATA 0F ELLION

^ N N ]0 5 _ s _

w \

u. -

g -

' N /

s N

s ~ __ ,e -

3 co v

x 3

w CURVE USED r IN ANALYSIS 5

I 104 -

3 i i i i l , i i i l , , , ,

10 2 3 4 10 10 10 10 Tg -T SAT ( F)

Fig. b7. Subcooled boiling heat transfer for water 9

3-13

I I I i I i i 1800 -

1700 -

ELAPSED TIME FROM END OF PULSE 1600 - '

C. 0 SEC

~

1.0 SEC E

R 1500 -

Y a G W 5

1400 -

N -

10 SEC - 1300 -

1200 - 100 SEC _

(

l I I I I I I o Gi 0.2 0.3 0.4 0.5 0.6 0.8 0.7 RADIUS (IN.)

Fig. 3-9. Fuel body temperatures at midplane of well-bonded U-Zrli element after pulse j

to 6 i i i i i i

i, i i i ij i i i i i i i ONSET OF i g f - PEAK HEAT FLUX i) ~

~

NUCLEATE I -

_ B0lLING n

g -

Y e ..

E 105 -

g -

O ~

ONSET OF STABLE x -

FILM BOILING _

3 6 ,

w '

~

u m i ,4 __

.L m

y -

u l e _

S 103 ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' '

O.001 0.01 0.1 1.0 10 100 ttArsED TIME FROM END OF PULSE (SEC)

Fig. 3-10. Surface heat flux at midplane of well-bonded U-Zrli element af ter pulse

f Subsequently, experimental transition and film boiling data were found to have been reported by Ellion (Ref. 9) for water conditions similar to those for the TRIGA system. The Ellion data show the minimum heat flux, used in the limiting calculation described above, was conservative by a factor of 5.

An appropriate correction was made which resulted in a more realistic esti-mate of 470*C as the maximum clad temperature expected if film boiling occurs. This result is in agreement with experimental evidence obtained for clad temperatures of 400* to 500*C for TRIGA Mark F fuel elements which have been operated under film boiling conditions (Ref. 10).

The preceding analysis assessing the maximum clad temperatures associated with film boiling assumed no thermal resistance at fuel-clad interface.

Measurements of fuel temperatures as a function of steady-state power level provide evidence that af ter operating at high fuel temperatures, a permanent gap is produced between the fuel body and the clad by fuel expansion. This gap exists at all temperature below the maximum operating temperature. (See, for example, Fig. 16 in Ref. 10.) The gap thickness varies with fuel tem-perature and clad temperature so that cooling of the fuel or overheating of I

the clad tends to widen the gap and decrease the heat transfer rate. Addi-tional thermal resistance due to oxide and other films on the fuel and clad surfaces is expected. Experimental and theoretical studies of thermal con-tact resistance have been reported (Refs 1-13) which provide insight into the mechanisms involved. They do not, hosaver, permit quantitative predic-tion of this application because the basic data required for input are pre-sently not fully known. Instead, several transient thermal computations were made using the RAT code. Each of these was made with an assumed value for the effective gap conductance, in order to determine the effective gap coefficient for which departure.from nucleate boiling is incipient. These results were then compared with the 1.ncipient film boiling conditions of -

the 1000*C peak fuel temperature case.

For convenience, the calculations were made using the same initial tem-perature diatribution as was used for the preceding calculation. The calcu-lations assumed a coolant flow velocity of 1 ft per second, which is within the range of flow velocities computed for natural convection under various 3-17

steady-state conditions for these reactors. The calculations did not use a complete boiling curve heat transfer model, but instead, included a convec-tion cooled region (no boiling) and a subcooled nucleate boiling region without employing an upper DNB limit. The results were analyzed by inspection using the extended steady-state correlation of Bernath (Ref.14) which has been reported by Spano (Ref. 15) to give agreement with SPERT II burnout results within the experimental uncertainties in flow rate.

The transient thermal calculations were performed using effective gap 2

conductances (hgap) of 500, 375, and 250 Btu /hr-ft *F. The resulting wall temperature distributions were inspected to determine the axial wall position and time af ter the pulse which gave the closest approach between the local computed surface heat flux and the DNB heat flux according to Bernath. The axici distribution of the computed and critical heat fluxes for each of the three cases at the time of closest approach is given in Figs. 3-11, 3-12, and 3-13. If the minimum approach to DNB is correcte! to TRIGA Mark F conditions and cross-plotted, an estimate of the effective gap conductance of 450 Btu /hr-ft *F is obtained for incipient burnout so that the case using 500 is thought to be representative of standard TRICA fuel.

The surf ace heat flux at the midplane of the element is shown in Fig.

3-14 with gap conductance as a parameter. It may be observed that the maximum heat flux is approximately proportional to the heat transfer coeffi-cient of the gap, and the time lag after the pulse for which the peak occurs Js also increased by about the same factor. The closest approach to DNB in these calculations did not necessarily occur at these times and places, however, as ir.diented on the curves of Figc. 3-11, 3-12, and 3-13. The initial DNB point occurred near the core outlet for a local heat flux of about 340,000 Btu /hr-f t *F according to the more conservative Bernath cor 21ation at a local water temperature approaching saturation.

This analysis indicates that after operation of the reactor at steady-state power levels of 1 MW(t), or af ter pulsing to give equivalent fuel temperatures, the heat flux through the clad is reduced and therefore reduces the likelihood of reaching a regime where there is a departure from nucicate boiling.

3-18

. 7 i i i i i

~

f ELAPSED TlHE FROM

[ , 6 _

END OF PULSE - 0.247 SEC E

S en. 5 - ACTUAL HEAT FLUX -

2 x

5 d f4 _ CRITICAL liEAT FLUX _

E E

. 3 7 8 9 10 11 12 13

. DISTANCE FROM BOTTOM OF FUEL (IN.)

Fig. 3-11 Surface heat flux distribution for standard non-gapped fuel element after pulse, h = 500 Eap w

3-19

u , . . . s 8 1 i I i i i I

, 7- -

^

CRITICAL HEAT FLUX .

l N i t-T 6 - -

e I

N o

E T

5 -

o

~

m ACTUAL HEAT FLUX i x

! O X  !

o a 4 -

I E w -

I 3

_ ELAPSED TIME FROM _

END OF PULSE IS t l 0.314 SEC i I i 2 -- -

I I I I I I I 7 8 9 10 11 12 13 15 DISTANCE FROM BOTTOM OF FUEL (IN.)

Fig. 3-12. Surface heat flux distribution for standard non-gapped fuel element after pulse, h = 375 l

?

_ - - ___ _ - --~ _ m - , , , _ _ . . _

8 r i i i

. i 7 ~

CRITICAL HEAT FLUX

[

[6 -

a E

E m,5 -

~

sn

'o~ ELAPSED TIME FROM END 4 x 4 -

OF PULSE IS 0.440 SEC -

x 3

u.

~

G3 -

$ ACTUAL HEAT FLUX 2 -

i i i i i i i i 7 8 9 10 11 12 13 14 15 DISTANCE FROM BOTTOM OF FUEL (IN.)

Fig. 3-13. Surface heat flux distribution for standard non-gapped fuel element after pulse, h p

= 250 3-21

)

106 , , , i i i g i i EFFECTIVE HEAT TRANSFER

- COEFFICIENT IN GAP, -

BTU /HR-FT2 ..F 500 375 250 N 105 _ ._

t _ _

E a

5

~

d y - -

. U U

ce a

o+g _ _

FLOW VELOCITY = 1 FT/SEC .-

GAP THERMAL RESISTANCES ARE

_ REPRESENTATIVE OF CONDITIONS AT _

END OF PULSE (f.E. TIME = ZERO) 10 3 I I i 1 ! I I I I 0.01 0.1 1.0 ELAPSED TIME FROM END OF PULSE (SEC)

Fig. 3-14. Surface heat flux at midplane versus time af ter pulse for standard non-gapped fuel element l

l l

3-22

i From the foregoing analysis, a maximum temperature for the clad during a pulse which gives a peak adiabatic fuel temperature of 1000*C is conserva-tively estimated to be 470*C.

As can be seen from Fig. 3-3, the ultimate strength of the clad at a temperature of 470*C is 59,000 psi. If the stress produced by the hydrogen overpressure in the can is less than 59.000 psi, the fuel element will not undergo loss of containment. Referring to Fig. 3-4, and considering U-ZrH 1 65 fuel with a peak temperature of 1000*C, one finds the stress on the clad to be 12,600 psi. Further studies show that the hydrogen pressure which would result from a trancient for which the peak fuel temperature is 1150*C would not produce a stress in the clad in excess of its ultimate strength. TRIGA fuel with a hydrogen to zirconium ratio of at least 1.65 has been pulsed to temperatures of about 1150*C without damage to the clad (Ref. 16).

There are several reasons why the gas pressure should be less for thc transient conditions than the equilibrium condition values would predict.

For example, the gas diffusion rates are finite; surface cooling is believed to be. caused by endothermic gas emission which tends to lower the diffusion constant at the surface; reabsorption takes place concurrently on the cooler hydride surfaces away from the hot spot; there is evidence for a low perme-ability oxide film on the fuel surface; and, as stated before, some local heat transfer does take place during the pulse time to cause a less than adiabatic true surface temperature.

To assess the effect of the finite diffusion rate and the rehydriding at the coc!er surfaces, the following analysis is presented.

As hydrogen is released from the hot fuel regions, it is taken up in the cooler regions and the equilibrium that is obtained is characteristic

, of some temperature lower than the maximum. To evaluate this reduced pressure, we will use dif fusion theory to calculate the rate at which hydrogen is evolved and reabsorbed at the fuel surface.

a 3-23 l

Ordinary diffusion theory provides an expression for describing the

. tine-dependent loss of gas from a cylinder:

E-c 7 4 ([ Dt c -e 2 exp -

2

, (3) g r n=1 n _ 0 _

where c, c , c = the average, the initial, and the final gas concentration f

in the cylinder, respectively.

( = the roots of the equation J '

O D = the ditfusion coefficient for the gas in the cylinder, t = time, r = the ratlius of the cy U nder.

9 Setting the term on the right-hand side of Eq. 3 equal to e, one can rewrite

. Eq. 3 as:

, c/c = c g/c + (1 - c g/c )e , (4) and the derivative in time is given by d(2/c,) ~

de dt ~ "f # 1}E *

(S)

This represents the fractional release rate of hydrogen from the cylinder, f(t). The derivative of the series in the right-hand side of Eq. 3 was approximated by bdt= - (7.339e-8.3h + 29.88e' ) de/dt , (6) where c = Dt/r 0 3-24 I

1 The diffusion coefficient for hydrogen in zirconium hydride in which the 11/Zr ratio is between 1.56 and 1.86 is given by

-1 00/R(T+273)

D = 0.25e ,

(7) where R = the gas constant, T = the zirconium hydride temperature in *C.

Equation 3 describes the escape of gas from a cylinder through diffusion until some final concentration is achieved. Actually, in the closed system 1

considered here, not only does the hydrogen diffuse into the fuel-clad gap, but also it diffuses back into the fuel in the regions of lower fuel temper-ature. (It also diffuses through the clad at a rate dependent on the clad temperature. Although this tends to reduce the hydrogen pressure, it is not considered in this analysis.) When the diffusion rates are equal, an equili-brium condition will exist. To account for this, Eq. 5 was modified by sub-stituting for the concentration ratios the ratio of the hydrogen pressure in

, the gap, P , to the equilibrium hydrogen pressure, P . Thus, Eq. 5 is rewritten as d (c /c')

f(t) =

dt = (1 - P (t)/P ) f ,

(8) where the hydrogen pressure,h P (t), is a function of time and P, is the I

equilibrium hydrogen pressure over the zirconium hydride which is a function of the fuel temperature.

V The rate of change of the internal hydrogen pressure, in psi, inside the fuel element cladding is dP 14.7 f(t)n h 22.4 T+273 dt '

6.02 x 10 \ g/\ /

3-25

where n = the number of molecules of 2H in the fuel, T = the gas temperature ('C).

f(t) = the fractional loss rate from Eq. 8, v = the free volume inside the fuel clad (liters).

As the atom density of hydrogen in Zril 22 3 s about 6.0 x M atoms /cm l.65 and the fuel volume is 400 cm , o h is 1.2 x 10' molecules (H ). The free 2

volume is assumed to consist of a cylindrical volume, at the top of the element, 1/8-in. high with a diameter of 1.43 in. for a total of 3.3 cm , 3 Also, the temperature of the hydrogen in the gap was assumed to be the tem-perature of the clad. The effect of changing these two assumptions was tested by calculations in which the gap volume was decreased by 90% and the temperature of the hydrogen in the gap was set equal to the maximum fuel temperature. Neither of these changes resulted in maximum pressures differ-ent from those base-1 on the original assumptions although the initial rate of pressure increase was greater. For these conditions P = 7.29 x 103 (T + 273) f(t) dt .

(10)

The fuel temperature used in Eq. 7 to evaluate the diffusion coefficient is expressed as T(z) = T O '

(11)

T(z) = T0+(m - 0 *" (* ~

• I 1 '

where T,= the peak fuel temperature ('C),

TO= the clad temperature (*C),

z = the axial distance expressed as a f raction of the fuel length, t = the time after step increase in power.

3-26

It was assumed that the fuel temperature was invariant with radius. The hydrogen pressure over the zirconium hydride surface when equilibrium pre-vails is strongly temperature-dependent as shown in Fig. 3-2 and, for Zril l.65, can be expressed by Pe = 2.07 x 10'e *

(12)

The coef ficietits have been derived f rom data developed by Johnson. The rate at which hydrogen is released (or reabsorbed) takes the form

~P* (z) - Ph (t) g(t,z) =

3, g f(t,z) , 03)

_ e .

where f(t,z) = the derivative given in Eq. 8 with respect to time evaluated at the axial position z, Ph (t) = the hydrogen pressure in the gap at time t, Pg (z) = the equilibrium hydrogen pressure at the Zrli temperature at position z.

The internal hydrogen pressure is then Ph (t) = 7.29 x 10 (TO+

0 0 This equation was approximated by P,,( t ) = 7.29 x 10 (T0+ * ~

P

~ ~

, x f(t ,z ) Azat ,

where the internal summation is over the fuel element length increments and the exterr.a1 sumation is over time.

3-27

r

' For the case in which the maximum fuel temperature is 1150'C, the equilibrium hydrogen pressure in ZrH is 2000 psi. Calculations indicate, 1.65 however, that the internal pressure increases to a peak at about 0.3 sec, at which time the pressure is about one-fif th of the equilibrium vrlue or about 400 psi. After this time, the pressure slowly decreases as the hydrogen continues to be redistributed along the length of the element from the hot regions to the cooler regions.

Calculations have also been made for step increases in power to peak fuel temperatu es greater than 1150*C.

Over a 200'C range, the time to the peak i

pressure and the fraction of the equilibrium pressure value achieved were approximately the same as for the 1150*C case. Thus, if the clad remains below about 500*C, the internal pressure that would produce the yield stress in the clad (35,000 psi) is about 1000 psi and the corresponding equilibrium hydrogen pressure could be five times greater or about 5000 psi. This pressure corresponds to a maximum fuel temperature of about 1250*C in ZrH 1.65*

Similarly, an internal pressure of 1600 psi would produce a stress equal to

. the ultimate clad strength (over 59,000 psi). This corresponds to an equili-brium hydrogen pressure of 5 x 1600 or 8000 pai and a fuel temperature of about 1300*C.

Measurements of hydrogen pressure in TRIGA fuel elements during steady-state operation have not been made. However, measurements have been made during transient operations and compared with the results of an analysis similar to that described here. These measurements indicated that in a pulse in which the maximum temperature in the fuel was greater than 1000*C i

the maximum pressure was only about 6% of t'ie equilibrium value evaluated at the peak temperature. Calculations of the pressure resulting from such a pulse using the methods described above gave calculated pressure values about' three timen greater than the measured values.

An instantaneous increase in fuel temperature will produce the most

, severe pressure conditions. b"nen a peak fuel temperature of 1150*C is reached by increasing the power over a finite period of time, the resulting 3-28

pressure will be no greater than that for the step change in power analyzed above. As the temperature rise times become long compared with the diffusion time of hydrogen, the pressure will become increasingly less than for the case of a step change in power. The reason for this is that the pressure in the clad element results from the hot fuel dehydriding faster than the cooler fuel rehydrides (takes up the excess hydrogen to reach an equilibrium with the hydrogen overpressure in the can). The slower the rise to peak tempera-ture, the lower the pressure because of the additional time available for rehydriding.

The foregoing analysis gives a strong indication that the clad will not be ruptured if fuel temperatures are never greater than in the range of 1200*C to 1250*C, providing that the clad temperature is less than about 500*C. However, a conservative safety limit of 1150*C has been chosen for this condition. As a result, at this safety limit temperatatre the pressure is about a factor of 4 lower than would he necessary for clad failure. This factor of 4 is more than adequate to account for uncertainties in clad strength and manufacturing tolerances.

Under any condition in which the clad temperature increases above 500*C, the temperature safety limit must be decreased as the clad material loses strength at elevated temperatures. To establish chis limit, it is assumed that the fuel and the clad are at the same temperature. There are no con-ceivable circumstances that could give rise to a situation in which the clad temperature was higher than the fuel temperature.

In Fig. 3-4 there is plotted the stress imposed on the clad by the equili-brium hydrogen pressure as a function of the fuel temperature, again assuming a clad radius of 0.73 in, and a thickness of 0.02 in. Also shovn is the ultimate strength of 304 stainless steel at the same temperatures. The use

. of these data for establishing the safety limit is justified as (1) the method used to measure ultimate strength requires the impasition of the stress over a longer time than would be imposed for accident conditions and (2) the stress is not applied biaxially in the ultimate strength measurements as it l 3-29 i

l l _ _

~

is in the fuel clad. The point at which the two curves in Fig. 3-4 intersect is the safety limit, that is, 970*C. At that temperature the equilibrium hydroge pressure would impose a stress on the clad equal to the ultimate strength of the clad.

The same argument about the redistribution of the hydrogen within the fuci presented earlier is valid for this case also. In addition, at elevated temperatures the clad becomes quite permeable to hydrogen. Thus, not only will hydrogen redistribute itself within the fuel to reduce the pressure, but also some hydrogen will escape from the system entirely.

The use of the ultimate strengch of the cJad material in the establish-nent of the safety limit under these conditions is justified because of the transient nature of such m -idents. Although the high clad temperatures imply sharply reduced ' tansfer rates to the surroundings (and conse-

, quently longer cooline, times), only slight reductions in the fuel temperature are necessary to reduce the stress sharply. A 50*C decrease in temperature from 970*C to 920*C will reduce the stress by a factor of 2.

As a safety limit, the peak adiabatic fuel temperature to be allowed during transient conditions is considered to be 1150*C for U-ZrH 1.65' 3.1.2. Prompt Negative Temperature Coefficient The basic parameter which allows the TRIGA reactor system to operate safely with large step insertions of reactivity is the prompt negative tem-perature coeftitient associated with the TRIGA fuel and core design. This temperature coefficient (a) also allows a greater freedom in steady-state operation as the effect of accidental reactivity changes occurring from experimental devices in the core is greatly reduced.

l General Atomic, the designer of the reactor, has developed techniques to i

, calculate the temperature coefficient accurately end therefore predict the transient behavior of the reactor. This temperature coefficient arises pri-marily from a change in the disadvantage factor resulting from the heating 3-30 1

i - '

of the uranium-zirconium-hydride fuel-moderator elements. The coefficient is prompt because the fuel is intimately mixed with a large portion of the moderator and thus fuel and solid moderator temperatures rise sLmultaneously.

A quantitative calculation of the temperature coefficient requires a know-ledge of the energy-dependent distribution of thermal neutron flux in the reactor.

The basic physical processes which occur when the fuel-moderator elements are heated can be described as follows: the rise in temperature of the hydride incr. ,ses the probability that a thernal neutron in the fuel element will gain energy from an excited state of an oscillating hydrogen atom in the lattice. As the neutrons gain energy from the ZrII, their mean free path is increased appreciably. This is shown qualitatively in Fig. 3-15. Since the average chord length in the fuel element is comparable with a mean free path, the probcbility of escape from the fuel element before capture is increasad.

In the water the neutrons are rapidly rethermalized so that the capture and escape probabilities are relatively insensitive to the energy with which the neutron enters the water. The heating of the moderator mixed with the fuel thus causes the spectrum to harden more in the fuel than in the water. As a result, there is a temperature-dependent disadvantage f actor for the unit cell in the core which decreases the ratio of absorptions in the fuel to total-cell absorptions as the fuel element temperature is increased. This brings about a shif t in the core neutron balance, giving a J ass of reactivity.

The temperature coefficient then, depends on spatial variations of the thermal neutron spectrum over distances of the order of a mean free path with large changes of mean free path occurring because of the energy change in a single collision. A quantitative description of these processes requires a knowledge of the differential slow neutron energy transfer cross section in water and zirconium hydride, the energy dependence of the transport cross

, section of hydrogen as bound in water and zirconium hydride, the energy dependence of the capture and fission cross sections of all relevant mate-rials, and a multigroup transport theory reactor description which allows for the coupling of groups by speeding up as well as by slowing down.

3-31

10 0 i

4 80 -

400*C m mTR H

U w

o.

e 60 - 23*C o

a: n.

w b3

" m+

o w 40 -

mp 24 m_

<w

• E 20 0 ' ' ' ' ' ' ' ' '

o.oi o.: i.o NEUTRON ENERGY (eV)

Fig. 3-15. Transport cross section for hydrogen in zirconium hydride and average spectra in TRIGA ZrH fuel element for 23*C and 400*C fuel 9

3.1.2.1. Codes Used for Calculations. Calculational work on the temperature coef ficient made use of a group of codes developed by General Atomic:

GCC-3 (Ref.17), GAZE-2 (Ref.18), and GAMBLE-5 (Ref.19), as well as DTF-IV (Ref. 20), an 5 multi-group transport code written at Los Alamos.

Neutron cross sections for caergies above thermal (>1 eV) were generated by the GGC-3 code. In this esde, fine group cross sections (N100 groups),

stored on tape for all commonly used isotopes, are averaged over a space independent flux derived by solution of the Bj equations for each discrete reactor region composition. This code and its related cross-section library predict the age of each of the common moderating materials to within a few percent of the experimentally determined values and use the resonance inte-gral work of Adler, Ilinman, and Nordheim (Ref. 21) to generate cross sections for resonance materials which are properly averaged over the region spectrum.

Thermal cross sections were obtained in essentially the same manner using the GCC-3 code. Ilowever, scattering kernels were used to describe properly the interactions of the neutrons with the chemically bound moderator atoms.

s The bound hydrogen kernels used for hydrogen in the water were generated by the TilERMIDOR code (Ref. 22) using the thermalization work of Nelkin (Ref. 23). Early thermalization work by McReynolds et al. (Ref. 24) on zirconium hydride has been greatly extended at General Atomic (Ref. 25),

and work by Pa ks resulted in the SLPMIT (Ref. 26) code, which was used to generate the kernels for hydrogen as bound in Zrl!. These scattering models have been used to predict adequately the water and hydride (temperature- i dependent) spectra as measured at the General Atomic linear accelerator as shown in Figs. 3-16 and 3-17 (Ref. 27).

3.1.2.2. Zril Model . Qualitatively, the scattering of slow neutrons by zirconium hydride can be described by a model in which the hydrogen atom motion is treated as an isotropic harmonic oscillator with energy transfer quantized in multiples of NO.14 eV. More precisely, the SUMMIT model uses a frequency spectrum with two branches - one for the optical modes for energy transfer with the bound proton, and the other for the acoustical modes for energy transfer with the lattice as a whole. The optical modes are repre-sented as a broad frequency band centered at 0.14 eV, and whose width is 3-33

a ,w.. -_.n.. -- - - . _ . _ = _ . - - -- . - - . . .

i I

I

, 5 T I I g I 5 I ig i i I I g i y a s s g i a g

. T.316 0C

. . . . .. es,t

,om. sone n..e. .so r.t..is,,t,n_ews sue J.T8080

_ ..--..-....,n _

/,. - s a .a w. -

_~~ .n . o.m f /- ,

105 _

.... _..o.o.n n, a r.o .= =- - .

j /./T = ,s 232*C

_ j o m-- '.t.

N m

t-f

/

f

/ e'

/ .- ' T = 150*C i - -lY."'?' "" '" "*""

z -

/

e7 3%

3 /

10 4 / .*

3 -- f / -, T = 3 0 *C \

) E -

/ #

4 _ -f /  %.

/ a~'.

E

/ / .: ..

m / ..

E / '... .

~-

lO3 ~ .

K

!e -

s. .

s. _

~.

io2

' ' ' 'I ' ' ' 'l ' ' l ' ' ' 'l 10' 0.0 01 0.01 0.1 1.0 10.0 10 0 NEUTRON ENERGY (EV)

Fig. 3-16. A comparison of theoretical and experimental neutron spectra in if30 using free hydrogen and bound hydrogen models for the calculation 1

1 1

3-34 t.

10 6 -

- '"i i i ' ' " T's > ' ' ' ' " Ti ' ' ' ""t -

ERATURE

! 5

10 ,

150 C -

4 10 U  : '. *  :

H) - .

2 _

a s., -

s 3

x _

316 C f '.. , . -

W lO* :- r* .

s- .

- = -

to N.~

x - -

s.,

G - 468 C

/

g

+ 2

+

10 ,

, ~ ., -

i

~

se -

+

j ,

ZrH.75 l BORON POISONED *  %

! 3

• 10  :

3.4 B ARNS/ HYDROGEN ATOM *

. .-2

***** DATA

• 1 ,

} EINSTEIN OSClLLATOR

~ MODEL INCLUDING ACOUSTICAL

[

TR A NSITIONS *

+

• 10 0 ' " " " ' ' ' "'

' ~ '

-''"2' ' ' ' "

0.0 01 0.01 0.1 1.0 10.0 NEUTRON ENERGY (EV)

Fig. 3-17. Experimental and theoretical neutron spectra from 2rll, ,$ n1 ming tlw cUcct of temperature variation 3-35

adjusted to fit the cross-section data of Woods et al. (Ref. 28). The low frequency acoustical modes are assumed to have a Debye spectrum with a cutoff of 0.02 eV and a weight determined by an effective mass of 360.

This structare then allows a neutron to slow down by the transition in energy units of 40.14 eV as long as its energy is above 0.14 eV. Below 0.14 eV the neutron can still lose energy by the inefficient process of exciting acoustic Debye-type modes in which the hydrogen atoms move in phase with the zirconium atoms, which in turn move in phase with one another.

These modes therefore, correspond to the motion of a group of atoms whose mass is much greater than that of hydrogen, and indeed even greater than the mass of zirconium. Because of the large effective mass, these modes are very inefficient for thermalizing neutrons, but for neutron energies below 0.14 eV they provide the only mechanism for neutron slowing down within the ZrH.

(In a TRICA core, the water also provides for neutron thermalization below 0.14 eV.) In addition, in the ZrH it is possible for a neutron to gain one or more energy units of s0.14 eV in one or several scatterings, from excited Einstein oscillators. Since the number of excited oscillators present in a ZrH lattice increases with temperature, this process of neutron speeding up is strongly temperature-dependent and plays an important role in the behavior of ZrH moderated reactors.

3.1.2.3. Calculations. Calculations of the temperature coefficient were done in the following steps:

1. Multigroup cross sections were generated by the GCC-3 code for a homogen4 zed unit cell. Separate cross-section sets were generated for each fuel elcment temperature by use of the temperature-dependent hydride kernels (water at room temperature was used for all prompt coef ficient calculations) ar.d Doppler broadening of the U-238

. resonance integral to reflect the proper temperature.

2. A value for k. was computed for each fuel element temperature by transport cell calculations, using the jP approximation. Comparisons 3-36

have shown4 S and8 S results to be nearly identical. Group-dependent disadvantage factors were calculated for each cell region (fuel, clad, and water) where the disadvantage factor is defined as 0 (region)/ eg (cell).

3. The thermal group disadvantage factors were used as input for a second CGC-3 calculation where cross sections for a homogenized c' ore were generated which gave the same neutron balance (nf hermal) as the thermal group portion of the discrete cell calculation.

4. The cross sections for an equivalent homogenized core were used in a full reactor calculation to determine the contribution to the tempera-ture coefficient due to the increased leakage of thermal neutrons into the reficctor with increasing hydride temperature. This calculation still requires several thermal groups, but transport effects are no longer of major concern. Thus, reactivity calculations as a function of fuel element temperature have been done on the entire reactor with the use of diffusion theory codes.

"Results from the above calculations indicate that more than 50% of the temperature coefficient for a standard TRIGA core comes from the temperature-dependent disadvantage factor or " cell effect," rnd %20% each from Doppler

' broadening of the U-238 resonances and temperature-dependent Icakage from the core. These effects produce a temperature coefficient of %-1.0 x 10~ /*C, which is rather constant with temperature. The temperature coefficient is shown in Fig. 3-18 for the high-hydride core of this TRIGA.

3.1.3. Steady-State Reactor power The following evaluation has been made for a TRIGA system operating with cooling from natural convection flow around the fuel elements. This analysis n:2.stigates the limits to which such a system may be operated.

k 3-37

. - . ~

-14 h STAINLESS STEEL CLAD 2, 8.5 WT-% U-ZrH ,so i CORE

-12 -

9 25 e _io _

t--

z W

U E -8 u.

w

. o O

. w -6 -

m o

D m

E -4 -

2 w

F-

$ -2 -

2 o

m O.

I I I I I O

O 200 400 600 800 1000 /200 TEMPERATURE ( C)

Fig. 3-18. TRIGA prompt negative temperature coefficient versus average fuel temperature 3-38 l

i

The analysis was conducted by considering the hydraulic characteristics

, of the flow channel from which the heat rejection rate is maximum. The geometrical data for this channel are given in Table 3-2.

The heat generation rate in the fuel element is distributed axially in a cosine distribution chopped at the end such that the peak-to-average ratio is 1.25 to 1.3. It is further assumed that there are 63 fuel ele-ments in the core.

TABLE 3-2 11YDRAULIC FLOW PARAMETERS Flow area (f t /elem.) 0.00580 Wetted perimeter (ft/elem.) 0.3861 Ilydraulic diameter (f t) 0.0601 Fuel elenent diameter (f t) 0.1229 Fuel surface area (f t ) 0.4826 The driving force is supplied by the buoyancy of the heated water in the core. Countering this force are the contraction and expansion losses at the entrance and exits to the channel, and the acceleration and potential energy losses and friction losses in the cooling channel itself.

Figure 3-19 illustrates schematically the natural convection system established by the fuel elements bounding one flow channel in the core. The system shown is general and does not represent any specific configuration.

Steady-state flow is governed by the equation

• n apt +AP e +OEt + Ap u Ej " *t "o '

j=1

• All symbols in Eqs. 16 through 45 are defined in the list of nomen-

, clature at the end of Section 3.1.3.8.

3-39 l

~

CHAllNEL SURFACE TO VOLUME RATIO, S/V CALCULATED FLOW AREA, Af FROM GIVEll HEATED PERIMETER, P DIMENSI0fiS EQUIVALENT DIAMETER, De -

f.

/ \

FREE SURFACE OF POOL y VIEW A-A /

n\/n 1-z = zt

• A A z =z n+ [- - - - -

' N H

Apu P I+o Pan.b k = n+1 j=n P  : T sat

!I z

POOL AT CONSTANT

" = q"(z) TEMPERATURE, T g

GIVEll) j=1 k=1

/

z71 App, CROSS FLO4, OR FLOW BETWEEN z=0 ADJACENT CHANNELS,

_ q" epi 2 IS IG'10 RED WA7EV-Y/7b ap;

]N COOLANT INLET HOLE OF AREA A i EL-0581 Fig. 3-19. General system configuration 3-40

where the left-hand member represents the pressure drops through the flow channel due to entrance, exit, friction, acceleration, and gravity losses and the right-hand member represents the driving pressure due to the static head in the pool. The pressure drops through the flow channel are dependent on the flow rate while the available static driving pressure is fixed for a known core height and pool temperature. The analysis, therefore, becomes an iterative one in which the left-hand side of Eq. 16 is evaluated on the basis of an assumed flow rate and compared with the known right-hand side until equality is achieved. The method has been programmed for digital computer solution. The methods of evaluating each of the op terms in Eq. 16 for known power distribution and flow geometry and assumed flow rates are discussed below.

3.1.3.1. Apt, Entrance Loss. The entrance loss, Apg, may be evaluated in the usual way as a fraction of the velocity head in the lower grid plate hole:

+K v Ap g = (Ki g

1 2 2 2

2g A g where N = the number of channels which receive their flow from a singic hole in the lower grid plate, K

g = the loss factor for the entrance to the hole in the lower grid I

plate. For even slight rounding of the entrance, K g will be no greater than 0.30. I K = the loss factor covering transfer of the flow from the hole in the 2

Inver grid plate to the coolant channels. In most cases this can be satisfactorily approximated as a sudden expansion using K = 1.0.

3.1.3.2. Ape, Exit Loss. The exit loss is expressed in terms of a coeffi-cient K, which is the fraction of the velocity head in the flow channel which is not recovered:

Ap ~ N *

(10) e 2g A g 3-41

The term v gj is the specific volume at the highest axial station along the

. heated length of the core. It is evaluated from the temperature Tg3 which is obtained from an overall heat balance:

q

~ + (

Tn+1 o '

where q =P q"(z) dz .

(20)'

• 1 3.1.3.3. apt Loss Through Portion of Channel Adjacent to Lower Reflector.

The flow is isothermal at the bulk pool temperature so that f v, A zt y W2 + y0*t op g = .

(21) 2; D,Af o f is evaluated from the Moody chart (assuming smooth surface) on the basis of a Reynolds number which is D y

=

R W .

(22) e A v f

3.1.3.4. Apu, Loss Through Portion of Channel Adjacent to Upper Reflector.

The flow is isothermal at T g where T g is determined by Eqs. 19 and 20:

1 v Az

" " "W2 , Az u Ap" = .

(23) 2g D A f

"n f min again evaluated from the Moody chart (assuming smooth surface) on the basis of a Reynolds number which is D" v R

= "W .

(24)

^f "n .

. 3-42

3.1.3.5. Apj, Losa Through Each Increment of the 'hannel Adjacent to the Fueled Portion of the Elements. For the present, let us assume that the entire heated portion of the channel is in subcooled boiling. This implies that the wall temperatures calculated from subcooled boiling correlations are lower than those calculated for convection alone and that the liquid is below its saturation temperature at all locations. The pressure drop through an factement is given by v -v f v az "kt1 *k)' g2,_D j "1 y 24 az 3pn -(n+1) 2 2 v

. 25) gA 2g A g g D e "j (acceleration) (friction) (gravity) 3.1.3.6. Acceleration Term. v denotes the mean specific volume and is larger than the liquid specific volume, because of the vapor voidage:

v = v/(1 - a) .

(26) a is the void fraction or the fraction of a channel cross section which is occupied by vapor, a may be calculated from the vapor volume (in. vapor /in.

heating surface) and the flow channel geometry. Denoting the vapor volume as C, a - ((S/V) (27) where S/V 19 the surface to volume ratio of the coolant channel. The param-eter C is dependent on the surface heat flux, the subcooling of liquid and the velocity of the liquid. It can be evaluated only by experiment. Data -

given by Jordan and Leppert (Ref. 29) were used to estimate (; thcee data are plotted in Fige. 3-20 and 3-21. Most of this represents a flow velocity of 4 ft/sec and appears to be the only available data applicabie under the

thermal conditions encountered in TRIGA-type reactors. Extrapolations from these data are maa'e for flow velocities different from 4 ft/sec. The 4

3-43

. . . . _ . . . . . _ . . _ _ _ _ . = . _ _ . . - . .

. --.___..__.m_.._.. _

__ . . _ _ . _ _ _ . . = _ _ _ _ _ _ , _ , _ . __ _ ._m..

I i

. 10*I i i g , ,  ;

SUBC00LINJ, (T *U*I I sat i

48'r 10 2 .

78'r '

i0s r 3

- . i i

v '

. A 6

s, -

i ac 2

s  !

10*3 -

. PRES $URE = 16.4 PSIA i

. 1 Fl.0W VELOCITY

• 4 FT/SEC t 10' l I , I l l O 2 4 6 8 to 12 14 HEAT FLUE, q" ( B1U/iO FT 2 X 10-5j Fig. 3-20. Experimentally determined vapor volumes for subcooled boiling in a narrow vertical annulus i

3-44 i

n

.- .m- ,-,_ve. < - . - . - - . 1 - ~ , . -.,..,- . . - i , ,, - - -

O.\ \  %  %  %  % s o

~

4 4

/

/

e

. e

• }

O b f

,6 4 /

O,v s s  %

e h Nw h h

/# se' %

1 Fig. 3-21. Cross-plot of Fig. 3-20 for use in calculations 3-45

,-. - . _ ._ ~ - - . _- . - -

extrapolations were based on a small amount of data given for flow velocities l,

other_than 4 ft/sec. The liquid temperature at a station, T k, may be calcu-f lated from

'[

k P

q"(Z)dZ I

T = +T .

(28) k WC o T, -- and pq " are known. Therefore, from T,, - Tg and q ", ne finds (

k (Fig. 3-21).

l j Since a =( (S/V) and v is a function of T , v, may be evaluated from Eq. 26.

, 3.1.3.7. Friction Term. v mj denotes a linear average of the mean specific volumes at the upper and lower boundaries of an increment. The approximate-mean value is assumed to apply o rer the entire increment so that v +v "k "k+1

{

V,3 2 (29) f j

bj is a friction factor which may be applied locally to. calculate the frfetion pressure drop over the increment in subcooled boiling. Jordan and 1

Leppert develop the correlation i

i 8h 8 q" o

i f =8S = =

(30)

- b t p CV p CV (T - T) w l

[ -

and provide experimental verification near atmospheric pressure in the range

<S < 5 x 10 -3 4

-3 1.5 x 10 .

This is simply an extension of Reynolds' analogy 4

3-4F I

1

- - . w-- ..m_. ,, y e v-w , .v., gm- m. re .e v - ,- r -_ - - -- - - -

to the case of subcooled boiling. The equation of continuity is used to write Eq. 30 as 8 q" A g

~

WC (T ( }

w - T) b which may be evaluated if T is known. For subcooled boiling, the heat transfer is usually defined by an experimentally determined correlation of q" vs (T -T ) which has been obtained over a given range of flow velocity and pressure. McAdams (Ref. 30) gives such a correlation for pressures between 2 and 6 atmospheres and flow velocities between 1 and 12 ft/sec.

This correlation will be used to determine T y for use in Eq. 31.

Approximate mean values are assumed to apply over the entire increment so that n

f ~ '

8A f

N k q"g

• b WC T -T +T -T , ( 2) j

, k w k Wk +1 and T -T =

4(qk ") + *IN m)

(33)

J where 4 (q") is the correlation of McAdams previously cited.

3.1.3.8. Gravity Term. v calculated from Eq. 29 is used to evaluate the gravity term.

As implied in Section 3.1.3.5, each increment must be checked to deter-mine whether heat is being transferred by subcooled boiling or by convection.

Twis evaluated at the lower boundary of the increment on the basis of both the correlation from McAdams for subcooled boiling and a standard correlation

. for convection (Dittus-Boelter). If the T calculated w from convection corre-lations is less than that obtained for subcooled boiling, boiling is assumed 3-47

not to be present in the increnent. Equation 25 still applies, but since there is no boiling and hence no vapor void, v becomes y and f becomes f .

b In the foregoing analysis an assumption was made that all of the vapor formed on the surface of the fuel element detaches and adds to the fluid buoyancy. This is not a conservative assumption. The position where vapor bubbles first leave the heated surface is obtained from two considerations; first, the balance of the forces exerted on the vapor bubble while it is in contact with the wall (buoyancy, surface tension, and friction), and, second, the temperature distribution in the single phase liquid away from the walla.

Determination of the buoyancy forces resulting from the formati,pn and subsequent detachment of vapor bubbles is complicated by the difficulty in predicting the point at which the vapor detaches, and the fraction of that vapor which subsequently condenses. The problem was simplified by making use of an analysis performed by Levy (Ref. 31) to determine the position at which the vapor detaches from the wall, assuming that at that point all of the vapor detaches and, finally, that there is no recombination of the vapor with subcooled fluid.

According to Levy the position at which the vapor leaves the surface is obtained from considering the balance of forces exerted on the vapor bubble while it is in contact with the wall, and the temperature distribution in the single phase liquid away from the wall.

The forcea acting on the bubble in the vertical direction consist of a buoyant force, 3F : a frictional force, F p, exerted by the liquid on the bubble; and a vertical component of the surface tension force, F '

S The buoyant force, F ' '" 8 """ Y B

3 C3rg (pL -p y

)g F = ,

(34)

. B g 3-48 i

where Br is the bubble radius, C3 is a proportionality constant, pgand py are the liquid and vapor density, g is the acceleration due to gravity and g is a conversion ratio from Ib-force to Ib-mass. The frictional force, Pp , is related to the liquid trictional pressure drop per unit length,

(-dp/dz)F. The pressuto differential across the bubble is proportional to the pressure differential times the bubble radius and it acts across an area proportional to the square of the bubble radius. Relating the pressure differential to the wall shear stress T, by

-(dp/dz)F =4T /Dg ,

there results for F :

7 F, = Cp r B

(35)

H where pC is a constant of proportionality and Dgis the hydraulic M ameter (four times the cross-sectional area divided by the wetted perimeter). The surface tension force, Fg , is given by F =C r a 3 3 B ,

( 6) where C 3 is a proportionality constant and o is the surface tension. Assuming upward flow the balance of these forces results in the following solution for the bubble radius:

" ~

Cg a 1/2 r

• B T (P +

B L -E v F e

l l

l 3-49

Assuming thaf the distance from the wall to the tip of the bubble is proportional to the bubble radiun, a non-dimensional distance corresponding to this real distance can be given by

-1/2 (o g# Dg p 7') 1/ 2-1 + C' E (p *

-p

") D" Y =C , (38)

U E w L _ c _

where C and C' are appropriate constants. For those cases where the fluid forces are considerably greater than the buoyant forces this expression reduces to Y = C (o 3; Dg p 3

)1/2 1- .

L

'For the bubble to detach, the fluid temperature at the tip of the bubble must exceed the saturation temperature by an amount such that the pressure differential acting across the interface at the tip of the bubble balances the surface tension forces at the same position. By using the Clausius-

~

Clapeyrnu solution for this pressure differential one finds that the fl'uid temperature-saturation temperature dif ference can be assumed to be zero.

The temperature at the tip of the bubble can also be specified from existing solutions for the fluid temperature distribution. Thus, if the flow is assumed to be turbulent, and using the solution proposed by Martinelli, we have T -T = 0P Y ;OsY s5 w B r B B y g-B T

= 50 Pr + in 1 + Pr p-1 1 ;5sY B

30 (39)

. l-

= 50 Pr + In 1 + SPr + 0.5 In ;Y

• B 3-50

The parameter 0 is a non-dinensional term defined through the heat flux and Liquid specific heat, that is, O= 9^

• I40}

p C L pl (t wg c/pL)1/2 Levy obtained values for the constants C and C' by correlation with available experimental data. Using the accepted heat-transfer relation from Dittus-Boelter, one obtains hDg /k = 0.023 (WDg /p ) *

(Pr)

(41)

Calculating the friction factor from

, f = 0.0055 1 + [20,000 (c/Dg ) + 106 /(WDg /p )]13 ,

, we are able to find the wall shear stress from r - (f/8)(W /p g) .

(42)

The correlation with experiment yielded values for the constants of C = 0.015 C' = 0 .

Finally, from the definition of the heat transfer coefficient, one obtains T - T = q"/h , (43) and setting the bubble tip temperature, T , equ 1t e saturation tempera-B ture, Tsa, w can express the relationship between the saturation temperature, 3-51

the wall temperature, and the fluid temperature at which the bubble would detach from the wall by

~ *

(f/8) 0.5 g , (44)

(Tw -Tsat)/(T -w T) = 0.023 (WD /pL)-

• 11 (F r) where O = Pr Y 0<Y B B

=5 Pr + In [1 + Pr (0.2 Y 3 -1 ;55Y <g 30 M

= 5 fPr + in (1 + SPr) + 0.5 In (Y g/30)f ; Y B 2 0 The solution of the force balance equation with void detachment was accomplished by iterating on the void detachment point to find where the right and left sides of Eq. 44 were equal. The point at which the void was assumed to separate from the surface was taken as the point at which equality obtained.

, The peak heat flux, that is, the heat flux at which there is a departure from nucleate boiling and the transition to film boiling begins, was deter-mined by two correlations. The first, given by McAdams (Ref. 32), indicates tha t the peak heat flux is a function of the fluid velocity and the fluid only. The second correlation is due to Bernath (Ref. 33). It encompasses a wider range of variables over which the correlation wcs made and it takes into account the effect of different flow geometries. It generally gives a lower value for the peak heat flux and is the value used here for determin-ing the minimum DNB ratio, that is, the minimum ratio of the local allowable heat flux to the actual heat flux. In general, the McAdams correlation gives a DNB ratio 50% to 80% higher than the Bernath correlation.

Figure 3-22 shows the results of this analysis. Here we have plotted the maximum channel heat flux for which the DNB ratio is 1, with bulk pool water temperature as a parameter. It is assumed that all the vapor above the detachment point separates from the heated surface. From the figure it can be seen that with the design cooling water temperature at the core iniet (90*F) the maximum heat flux is 395,000 BTU /hr-ft . For a 63-element core 3-52

4. 5 9

4. 0 n~

4

$ 3. 5 S

U".0 3

2. 5 80 90 100 llo 120 130 140 Coolant inlet temperature ('F)

Fig. 3-22. Maximum heat flux for which DNB ratio

. is 1.0 versus coolant temperature with an overall peak-to-average power-density ratio of 2.0, this heat flux corresponds to a maximum reactor power of 1700 kW.

~'

NOMENCLATURE A cross-sectional area, ft A channel free flow area, ft f

C coolant specific heat, Btu /lb *F d diamotar. in.

D channel equivalent diameter, f t Dg hydraulic diameter, ft

- f f riction factor with subcooled boiling, dimensionless b

f friction factor without boiling, dimensionless F forces acting on vapor bubble g constant, 4.18 x 10 ft/hr 3-53

cJ.

2 b heat transfer coefficient with subcooled boiling, Btu /hr-ft *F b

11 distance from midplane of heated channel to free surface of pool, ft K pressure loss factor at. channel inlet or exit, dircnsionless n number of equal axial increments into which heated length of core is subdivided N number of channels which receive their flow from a single opening in the lower grid plate

! p absoluto pressure, Ib/ft p heated perimeter of channel, ft Pr Prandtl number a pressure loss, Ib/ft P

q heat load, Btu /hr q total heat load to channel, Btu /hr q" heat flux, Btu /hr-ft q" 2 I

, peak or " burnout" heat flux, Btu /hr-ft P

r bubble radius 3

R Reynolds number, dimensionless S Stanton number, dimensionless channel surface to volume ratio, in.

T coolant temperature. *F 2

1 T coolant saturation temperature. *F 3

v specific volume, fr /lb i

V flow velocity, ft/hr 4

W mass flow rate, Ib/hr l

Y non-dimensional radius

, z axial coordinate in channel, ft z total length of channel, ft 3-54 l

Az length of a calculation increment in the channel, ft p dynamic viscosity, ft-lb/hr

, a void fraction or fraction of a channel cross section which is occupied by vapor, dimensionless o surface tension, Ib/ft r, vapor volume or volume of vapor produced per unit area of heated surface,in.5/in.2 v kinematic viscosity, ft /hr i shear stress, Ib/ft p density, Ib/ft c/D relative roughness Subscripts e conditions at channel exit

, i conditians at channel entrance or inlet t conditions in portion of channel adjacent to lower reflector m conditions averaged over the liquid and vapor phases o bulk pool conditions J

u conditions in portions of channel adjacent to upper reflector j axial increment index k axial station index w conditions at cladding outer surface v vapor I. liquid i

3-55

3.2. NUCLEAR DESIGN AND EVALUATION The characteristics and operating parameters of this reactor have been calculated and extrapolated using experience and data obtained from existing TRIGA reactors as bench marks in evaluating the calculated data. There are several TRIGA systems with essentially the same core and reflector relation-ship as this TRIGA so the values presented here are felt to be accurate to within 5%.

Table 3-3 summarizes the typical Mark I TRIGA reactor parameters for a core containing high-hydride, stainless steel clad fuel elements.

3.2.1. Reactivity Effects The reactivity effects associated with the insertion and removal of experiments in or around the core are difficult to predict; however, Tabic 3-4 is supplied to provide'a guide to the magnitude of the reactivity effects associated with the introduction of experiments in the reactor core.

The reactivity associated with the control rods is of interest both in r

the shutdown margin and in calculations of possible abnormal conditions related to reactivity accidents. Table 3-5 gives approximate reactivity values associated with a total control rod travel of 15 in., the full travel in the core.

The maximum reactivity insertion rate is that associated with the safety--

transient rod which can be-fully removed from the core in 0.1 sec producing an average reactivity insertion rate of 15% 6k/k-sec.

The total reactivity worth of the control system is about 5.1%. With a core excess reactivity of 2.1%, the shutdown matgin with all rods down is about 3.0% and with the most reactive rod stuck out is about 0.3%.

The reactivity worth of the fuel elements is dependent on their position ,

1 within the core. Table 3-6 indicates the values that are expected in this j installation.

3-56

__ - ._ - - .l

TABLE 3-3 TYPICAL TRIGA CORE NUCLEAR PARAMETERS Cladding material SS-clad U-ZrH

~' 1.6 Cold clean critical loading %54 elements

%2.1 kg U-235 Operational loading %63 elements

%2.4 kg U-235 i Prompt neutron lifetime 43 usec 8 Effective delayed neutron fraction 0.0070 a Prompt negative temperature coefficient 41.0 x 10 6k/k'C Tg Average fuel temperature 23*C 400*C Ty Average water temperature 23*C 23*C nf 1.5011 1.4685 p 0.8729 0.8655 c 1.0544 1.0564

k. 1.3816 1.3427 Non-leakage probability 0.7569 0.7511 k,gg 1.0460 1.0085

! TABLE 3-4 EXPECTED REACTIVITY EFFECTS ASSOCIATED WITil EXPERIMENTAL FACILITIES l

Worth (% 6k/k)

Central thimble, void vs 110 -0.6 2

Pneumatic transfer tube, (F ring) void vs 110 -0.15 2

Rotary. specimen rack, void vs 110 -0.15 2

TABLE 3-5 ESTIMATED CONTROL ROD NET WORTH

~

Worth (% 6k/k)

C ring - shim, 1.25-in.-diam 2.7 D ring - safety-transient, 1.0-in.-diam 1.6 E ring - regulat ing. 0.875-in.-diam 0.3 3-57

TAllLE 3-6 ESTIMATED FUEL ELFMENT REACTIVITY WORTli COMPARED WITil WATER AS A FUNCTION OF POSITION IN CORE Worth (% ok/k)

Core Position SS Clad U-ZrlII .6 B ring 0.81 C ring 0.67 D ring 0.50 E ring 0.33 F ring 0.21 Because of the prompt negative temperature coefficient a signifAcant amount of reactivity is needed to overcome temperature and allow the reactor to operate at the higher power levels in steady-state operation. Figure 3-23 shows the relationship of reactor power level and associated reactivity loss to achieve a given power level. Figure 3-24 relates fuel temperature to a given steady-state reactor power invel.

I i

3.2.2. Evaluation of Nuclear Design The TRICA reactor system is well-known for its conservative design. The stability of this reactor type has been proven both through calculation as well as through tests performed with the many TRICA reactors in opetation

) throughout the world. The stability of the TRICA type reactor stems from the prompt negative temperature coefficient associated with the U-ZrH fuel in conjunction with a suitable neutron thermalizing material. This TRIGA will have the stability that has been demonstrated on other TRIGA systems over the years.

A review of the reactivity worths associated with the reactor core

. Indicates that no single item listed can produce a step reactivity insertion 3-58

0 a

I 0

0 1

0

' 0 r 8

e w

o p

s u

s r

e v

s 0 s i

0 o 6 l

) y w t

. K i

(

i v

R t E c W a O e P r d

j 0 e I

0 t 4 a m

i t

s E

3 2

3 0 .

i I

0 g 2 i F

O

. 0 0 0 0 0 4 3 2 1 O v o.?$Oa U555cc ub

400-O T L

w g 300-

=

w

$ T Y $

$ w g 200-s N

w Q.

I b r

100-I l 0 , , , , ,

0 200 400 600 800 1000 POWER (KW)

Fig. 3-24. Estimated maximum B ring and average core temperature versus power l

l

e greater than the design maximum excess reactivity in the core of $3.00.

• This excess reactivity value is equivalent to a routine step reactivity inser-tion for similar reactors. In the pulsed mode of operation the results of a step insertion of $2.00 are far below those attributed to test pulses on the advanced TRIGA prototype reactor in which 3.5% 6k/k was inserted in a step as is shown in Table 3-7.

TABLE 3-7 COMPARISON OF REACTIVITY INSERTION EFFECTS Pulse Resulting from Max Pulse Tested Insertion of Maximum on SS-Clad, High Excess Reactivity in Hydride Fueled This TRICA TRIGA Types Reactivity insertion, $ 2.00 5.00 Steady-state power before pulse, kW <1 <1 Peak power, Fni N250 48400 Total energy release, MW-sec N16 N54 Period, msec NIO N1.4

. Max fuel temperature, *C N360 %890 Pulse width, msec m 35 45.5 The possibility of a reactivity accident which could produce reactor powers and fuel temperatures attributed to a $3.00 step insertion has been considered and evaluated in the accident analysis section of this report.

It is concluded from this analysis that the peak and average fuel tempera-tures resulting from this accident are well below the temperatures indicated as safety limits described in the reactor design bases of this document.

It is further concluded 't hat the integrity of the fuel containment will not be jeopardized and no adverse ef fects to the reactor system or personnel will arise from the advent of such an accident.

• Therefore before these experimental facilities are used, the worth of the experiment should be carefully evaluated. If the experiment is worth more than $3.00, a special safety analysis should be prepared.

3-61

( l l -

l -

3.3. TilERMAL AND IfYDRAULIC DESIGN This TRIGA reactor will be operated with natural convective cooling by

+

reactor pool water. This method of heat dissipation in more than adequate for the power level of the reactor; i.e., 250 kW(t). That is, thermal and hydraulic design of the reactor is well within the safety limits required to assure fuci integrity.

3.3.1. Design Bases The thermal and hydraulic design for this TRICA is based on assuring that fuel integrity is maintained during steady-state and alsed mode c.opera-tion as well as during those abnormal conditions which might be postulated for reactor operation. During steady-state operation fuel integrity is maintained by limiting reactor powers to values which assure that the fuel cladding can transfer heat from the fuel to the reactor coolant without reaching fuel-clad temperatures that could result in clad rupture. If these temperature conditions were exceeded, the maximum local heat flux in the core would be greater than the heat flux at which there is a dcparture from the nucleate boiling regime and consequently flim blanketing of the fuel.

This heat flux safety limit is a function of the inlet coolant temperature.

Figure 3-22 summarizes the results of the thermal and hydraulic analysis for steady-state operation of the TRIGA. In the figure critical heat flux for departure from nucleate boiling is plotted as a function of the coolant inlet temperature. The maximum power density in a TRIGA core is found by multiplying the average power density by a radial peak-to-average power generation ratio of 1.6 and an axial value of 1.25.

The correlation used to determine the heat flux at which there is a departure from nucleate boiling is from Bernath (Ref. 33). This correlation encompasses a wider range of experimental data than the usual correlations, e.g., the correlation due to McAdams, and, generally gives a lcwor value for the DNB ratio than the other correlations.

3-62

, During pulsing operation the limiting thermal-hydraulic condition is the fuel temperature and the corresponding H verpressure beyond which clad 2

rupture may occur. As indicated in Section 3.1, coolant temperature is not a limiting condition in pulsing since heating conditions are essentially adiabatic and significant transfer of heat energy to the coolant does not occur until af ter peak fuel-clad temperatures occur.

The safety limit on fuel temperature occurring in the pulse mode of operation is 1150*C. This temperature will give an internal equilibrium hydrogen pressure (U-ZrH 1.6 fu 1) 1 ss than that which would produce a stress equivalent to the ultimate strength of the clad at a temperature of 680*C.

This clad temperature is higher than would actually occur and therefere con-servative even in the case of a pulse producing a peak adiabatic fuel temper-ature of 1150*C.

Table 3-8 lists the pertinent heat transfer and hydraulic parameters for the TRIGA operating at 250 kW. These data were taken from the results

, of calculations described in Section 3.1.

3.3.2. Thermal and Hydraulic Design Evaluation The validity and safety of the TRIGA thermal-hydraulic design is established in Section 3.1. In that section it is shown that design-basis conditions evaluated for TRIGA reactors using stainless steel clad U-ZrH 1.6 fuel elements provide a generous safety margin for this TRIGA. These general evaluations are supported by extensive experience in operation of TRIGA cores at substantially higher fuel temperatures and reactor power levels than in this TRIGA without adverse results.

3-63

TABLE 3-8 250 kW(t) TRICA IIEAT TRANSFER AND HYDRAULIC PARAMETERS Number of fuel elements 63 Diameter 1.475 in.

Length (heated) 15.0 in.

Flow area 0.372 ft Wetted perimeter 24.33 ft flydraulic diameter 0.0612 ft lleat transfer surface 30.41 ft Inlet coolant temperature 90*F (32.2*C)

Exit coolant temperature (average) 120*F (48.9'C)

Coolant mass flow 28,000 lb/hr Average flow velocity 0.30 ft/sec Average fuel temperature 355*F Maximum wall temperature 252*F Maximum fuel temperature 510*F Average heat flux 2 28,100 BTU /hr-ft Maximum heat flux 56,300 BTU /hr-ft Minimum DNB ratio 7.0 3.4. MECilANICAL DESIGN AND EVALUATION 3.4.1. General Description The TRIGA Mark I reactor core assembly is located near the bottom of a elongated cylindrical aluminum tank surrounded by a reinforced concrete struc-ture. A typical :Srk I installation is shown in Fig. 3-25. The standard reactor tank is a welded aluminum vessel with 1/4-in.-thick walls, a diameter of approximately 6-1/2 ft, and a depth of approximately 21 ft.

The tank is all-welded for water tightness. The integrity of the weld joints is verified by radiographic testing, dye penetrant checking, and leak testing. The outside of the tank is coated for corrosion protection.

3-64

l

[ - CONTROL RCD DRIV [

SPECIMEN ttfitNC ASSE MBLY A

f 7 8 tiff ARO INDICATOR

~a

( 'f -4, CINi[R

=,

,/$ p k

(

r  ?

IJ p'

's

p e 15DTOP! f i

, J II IRI ENTAL 3* NTROL l d .. (

ll PhEUM AllC M

, , [ I IRANSFER

':t

g g ' .d g se- .'. F SYSTEM 7

i

' 1

)

)

/f."[ $

g,y T2 [ ,

SC ,

RACK . g. q.  % .

7 -REilICTOR

\ ..

.y

0;,,,,- g_ -* .

i

' ' E  ? - ALUMINUM IANK Fig. 3-25 Typical Mark I TRIGA Reactor 3-65

An aluminum angle used for mounting the ion chambers, fuel storage racks, undervater lights, and other equipment, is located around the top of the tank. Demineralized water in the tank provides approximately 16 f t of shiciding water above the core. The core is shielded radially by a minimum of 3 f t 6 in, of ordinary concrete with a density of 2.7 g/cm3 ,1.75 f t of unter, and 12 in of graphite reflector (see Fig. 3-26).

3.4.2. Experimental and Irradiation Facilities The experimental and irradiation facilities of the TRIGA Mark I reactor are extensive and versatile. Physical access and observation of the core are possibic at all times through the vertical water shield.

A rotary, multiple-position specimen rack located in a well in the top of the graphite reflector provides for the large-scale production of radio-isotopes and for the activation and irradiation of small specimens. All positions in this rack are exposed to neutron fluxes of comparable intensity.

Samples are loaded from the top of the reactor through a water-tight tube f r o the rotary rack using a specimen lif ting device (essentially a fis'hing pole with a grapple mechanism on the end of a power cord). The rotary rack can be turned manually or by using a motor drive at the top of the reactor.

The reactor is equipped with a central thimble for conducting experi-ments or irradiating small samples in the core at the point of maximum flux.

The central thimble consists of a 1-1/2-in.-o.d. aluminum tube that fits through the center hole of the top and bottom grid plates. Holes in the tube assure that it is normally filled with water; however, a special cap may be attached to the top end, compressed air applied, and the water column removed to obtain a well-collimated beam of neutrons. Experimental tubes can ea'ily s be installed in the core region to provide additional facilities for high-level irradiation or in-core experiments.

, A pneumatic transfer system permits the use of short-lived radioisotopes.

The in-core terminus of this system is normally located in the outer ring of fuel element positions, a region of high neutron flux. The sample container 3-66

1 ' ' 1 l 4 , 4 '  ;

r.

.u-e ,

+

1 2

0' r * - 7 _

s '

v v.-

- 3

. 3 R C e

o. o f

.. r l e e s c

- c t a

l o

r e

l J

_- /I e 4 N

, = 3 l 3' e

d '

F i

g 3

y 2

6 j' ,

9

- g 6 2

R r

e 6'"

a I c

t i1

- l 1 lI1 l l l l N ]

o l

l r 0'"

T a

n k

a - R n e

- d a c

S t o

h i r e

l d

S t

r u

c

- 0'"

t -

u -

r e

2 0

i w ' '

1 0

g [

l~

jG

,  ! t , r  !, l

(rabbit) is conveyed to a receiver-sender station via 1-1/4-in.-o.d. aluminum tubing. An optional transfer box may be employed to permit the sample to be sent and received from up to three dif ferent receiver-sender stations. .

3.4.3. Reflector Assembly and Grid Plates The reflector asstably and grid plates (see Fig. 3-25) form a cylinder approximately 43 in, in diameter and 23 in, high. The reactor core compo-nents are contained between top and bottom aluminum grid plates surrounded by the graphite reficctor, and, as shown in Fig. 3-27, consist of a ..attice of fuel-moderator elements, graphite dummy elements, control rods, sou.rce element, pneumatic system terminus and in-core experimental devices such as the central thimble.

The reflector is a ring-shaped block of graphite that surrounds the core.

it is 12 in, thick radially, with an inside diameter of 18 in, and a height of 22 in. The reflector is encased in a leak-tight, welded aluminum can to pre-vent water penetration of the graphite. A "well" in the top of the graphite reflector is provided for the rotary specimen rack. The reflector assembly, which is supported by an aluminum platform, provides support for the two grid plates.

Vertical tubes attached to the reflector assembly permit accurate and reproducible positioning of the ion chambers used for monitoring reactor operation.

The top grid plate (Fig. 3-27) provides lateral positioning of the core components. The grid plate rests on pads welded to the top of the reflector container. Stainless steel dowel pins orient the grid. The grid plate is made of 3/4-in.-thick anodized aluminum and contains 91 holes approximately 1-1/2 in. in diameter; these holes are distributed in five rings about the 9

central thimble. Cooling water passage through the top plate is provided by

. the differential area between a triangular spacer block on top of the fuel element and the round hole in the grid.

3-68

e 1

00O O

~

i .

W O $Nin O '?$ 0 800-i O O O ruc' c'cacar h GRAPHITE ELEMENT

]' h CONTROL R0D j

h SOURCE ELEMENT h TRANSIENT R0D

~

1 i Fig. 3-27. Typical core diagram 3-69 i

The anodized aluminum lower grid plate supports the weight in the core in addition to providing accurate spacing between the fuel-moderator elements.

Countersunk holes are machined in alignment with fuel element holes in the

~

top grid plate. The grid plate is supported by L-shaped lugs welded to the underside of the reflector contniner .

3.4.4. Fuel-Moderator Elements The active part of each fuel-moderator element, shown in Fig. 3-28, is approximately 1.43 in. in diameter and 15 in. long. The fuel is a solid, homogeneous mixture of uranium-zirconium hydride alloy containing about 8-1/2%

by weight or uranium enriched to 20% U-235. The hydrogen-to-zirconium atom ratio is approximately 1.6. To facilitate hydriding, a small hole is drilled through the center of the active fuel section and a zirconiun rod is inserted in this hole after hydriding is complete.

Each element is clad with a 0.020-in.-thick stainless steel can, and all closures are made by heliarc welding. Two sections of graphite are inserted in the c'an, one above and one below the fuel, to serve as top and botto'm reflectors for the core. Stainless steel end fixtures are attached to both ends of the can,' making the overall length of the fuel-moderator element 28.8 in.

The lower end fixture supports the fuel-noderator element on the bottom grid plate. The upper end fixture consists of a knob for attachment of the fuel-handling tool and a triangular spacer, which permits cooling water to flow three h the upper grid plate. The total weight of a fully-loaded fuel element is about 7 lb.

An instrumented fuel-moderator element will have three thermocouples embedded in the fuel. As shown in Fig. 3-29, the sensing tips of the fuel element thermocouples are located about 0.3 in. from the vertical centerline.

3-70 i

STAINLESS STEEL TOP END FITTING m

s 1 w)

GRAPHITE 3.45 IN.

< m STAINLESS STEEL TUBE CLADDING THICKNESS 0.02 IN.

URANIUM ZlRCONIUM HYDRIDE-WITH AXIAL -

ZlRCONIUM ROD 28*8 IN* 15 IN.

TOTAL 1.43 IN. -

~

=

- 1.47 IN.

v W

• n Y I GRAPHITE 3.45 IN.

STAINLESS STEEL v

BOTTOM END FITTING [

\

[ Fig. 3-28. TRIGA stainless steel clad fuel element with trifiute end fittings 3-71

" h u k- - e . - m-a JC j.,r STAINLESS STEEL 4

6' d LEAD-0UT TUBE i r

( 3 /f+ IN. DIAM) 0 E

, .^

f

,e

.y y TRIANGULAR SPACER

$ I END PLUG d $8 r

, GRAPHITE END REFLECTOR 28.8 IN. #

W", <

l L'

} ZlRCONfUM ROD l f.YD FUEL-MODERATOR 1/2 1 IN- l ',:'-

T 2-  ;

MATERIAL a i

! .s..

M ..

s hfbYil)

'3--

7- 1/2 y  ; o ' SECT 10N A-A uN. ,

c %-.

l IN.

{

THERMOCOUPLES (3)

]llf3.'

M ]* ~3 GRAPHITE END REFLECTOR i N STAINLESS STEEL

_j CLADDING l

"== I c

1 o

f.l*7 IN. =

1 Fig. 3-29. Instrunented fuel element 3-72 l

The thermocouple leadout wires pass through a seal in the upper end fixture.

A leadout tube provides a watertight conduit carrying the leadout wires above the water surface in the reactor pool. Thermocouple specifications are listed la Table 3-9. In other respects the instrumented fuel-moderator element is identical to the standard element.

An initial core loading of about 63 fuel elements, including instrumented elements, will produce a cold, clean excess reactivity of N2.1% 6k/k. Table 3-10 gives a summary of the fuel element specifications.

3.4.4.1. Evaluation of Fuel Element Design. General Atomic has acqui, red extensive experience in the fabrication and operation of high hydride,'

stainless steel clad fuel elements. As shown in other sections of this report, the stresses associated with the fuel and cladding temperatures in all modes of operation, normal and abnormal, are within the safety limits described in the Reactor Design Bases.

It is concluded that the chemical stability of U-ZrH

' 1.6 fuel-m derator material does not impose a safety limit on reactor operation (see S'oction 3.1.1).

Dimensional stability of the overall fuel element has been excellent in the TRIGA reactors in operation. Analysis of the heat removal from ele-ments that touch owing to transverse bending shows that the contact will not result in hot spots that damage the fuel.

Tests have been conducted on TRICA fuel elements to determine the strength of the fuel element clad when subjected to internal pressure. At room temperature the clads ruptured at about 2050 psig. This corresponds to a hoop stress at rupture of about 72,000 psi which compares favorably with

. the minimum expected value for 304 stainless steel.

3-73

_~. -

TABLE 3-9 THERMOCOUPLE SPECIFICATIONS Type Chromel-alumel Wire diameter 0.005 in.

Resistance 24.08 ohms / double foot at 68'F Junction Grounded Sheath material Stainless steel Sheath diameter 0.040 in.

Insulation Mg0 Lead-out wire Material Chromel-alumel Size 20 AWG Color code Chromel - yellow (positive)

Alumel - red (negative)

Resistance 0.59 ohms / double foot at 75'F TABLE 3-10

SUMMARY

OF FUEL ELEMENT SPECIFICATIONS Nominal Value Fuel-Moderator Material H/Zr ratio 1.6 Uranium content 8.5 wt %

Enrichment (U-235) 20%

Diameter 1.43 in.

Length 15 in.

Graphite End Reflectors Upper Lower Porosity 20% 20%

Diameter 1,43 in. 1.43 in.

Length 3.44 in. 3.47 in.

Cladding Material Type 304 SS Wall thickness 0.020 in.

, Length 22.10 in.

End Fixtures and Spacer Type 304 SS Overall Element Outside diameter 1.47 in.

Length 28.37 in.

Weight 7 lb 3-74

3.4.5. Graphite Dummy Elements Craphite dummy elements may be used to fill grid positions not filled by the fuel-moderator elements or other core components. They are of the same general dimensions and construction as the fuel-moderator elements, but are filled entirely with graphite and are clad with aluminum.

3.4.6. Neutron Source and Holder The neutron source consists of a mixture of americium and beryllium, double encapsulated to ensure leak-tightness. Its initial strength at manu-facture is 2 Ci. The upper and lower portions of the holder are, screwed together to enclose a cavity that contains the source. A shoulder at the upper end of the neutron source holder supports the assembly in the upper grid plate. The source can be located in any fuel element position.

3.4.7. Control System Design The reactor uses three control rods:

i

. 1. A safety-transient rod

2. A regulating rod

3. A shim rod The regulating, shim, and safety-transient rods are described in , _corial and tabular form in Fig. 3-30 and Table 3-11. They are aligned and operate within perforated aluminum guide tubes.

Each control rod is connected to a drive unit. Vertical travel of each rod is approximately 15 in. Reactivity worths and core positions for each

- rod were summarized in the section on nuclear design (Section 3.2). i l

3.4.7.1. Control Rod Drive Assemblies. The control rod drive assemblies for the shim and regulating rods are mounted on a bridge assembly over the pool and consist of a motor and reduction gear driving a rack-and-pinion 3-75

4 i

i I

I j

i I $.' , , ._

C ,

. i j y ..

i I

i 3 <

1 .,

4 I'

p i ..

- r 4

i 4.5.

4;.c M-4p. . . .

1

~ ', .. ,

s A h.

.) , f l : .. ".

"% g .

?, ^ t g.. , .

j i ..; , ,

F . ; :- i g.c/.%:p . -

s 1

l i

l Fig. 3-30. Control rod poison container l 3-76

TABLE 3-11

SUMMARY

OF CONTROL ROD DESIGN PARAMETERS Cladding Material Aluminum alloy 6061-T6 Outside diameter 1.25 in. (shim), .875 in (reg) 1.0 in. (transient)

Wall thickness 0,028 in.

Length 16.25 in.

Absorber Mat-rial Boron carbide compacts (B4 C)(shim, reg)

Borated Graphite (transient)

Length 15.0 in.

G h

as indicated in Fig. 3-31. A helipot connected to the pinion generates the position indication. Each control rod drive has a tube that extends to a dashpot below the surf ace of the water. The control rod assembly is connected to the rack through an electromagnet and armature. In the event of a power failure or scram signals, the control rod magnets are de-energized'and the rods fall into the core. The time required for a rod to drop into the core from the full-out position is about 1 second. The rod drive motor is non-synchronous, single-phase, and instantly reversible, and will insert or withdraw the control rod at a rate of approximately 11.5 in. per min for the regulating "od drive or shim rod. A key-locked switch on the control console power supply prevents unauthorized operation of all control rod drives.

Electrical dynamic and static braking on the motor are used for fast stops.

Limit switches mounted on the drive assembly actuate circuits which indicate the following:

1. The "up" and "down" positions of the magnet

2. The "down" position of the rod

3. The magnet in contact with the rod 3-77

-l l

- y ..m . - :. - - ;.. .ky ,.,o .,.r .

' . w' ##., . np A, . ,n ,'1 ~RMATURE

~

~

. S P.R I NG ' LO AD. .ED ~ '.'.J.. : . .

'<,').{ 6t,,]'PULLQROD.. , 7 fl; .y}t9

..y ut f f- v7 gy

. y .,.~. . m ,

e pf)

W. > , '.,e 9 M. ;;-: ;,.;.;y . ym. y g . . ,

gg.g L-i%. ":q~.4

. , ,, 4 ... & .9. n,y -

., :q.(.'

m h.g. . - t :- ^% zM;Lt.

~ 2% %y w:jn v;+.: tyy; .po k*$.V^  %.. l;y%(,. M +.,gss.)%.;3*mef,.5 s-t ,'W43j y

F.>;;*..+.~QDlC*k:%;r*:t u w,. .c,,

-y s. -

s

. * %u.s+;

.s, .., .

j. Y' . " *

• 4Q; ,". ".

.r , ,r.

e .~ gy. . < y4. s, v- c.,. ,,

ap..1

t

. u r a .o.p.d.. , r.bg e.'.M.n 'a.g),b s .y . - @

gL %,

0,g 'J >a(;.y. w.ig-l.,m?# p c

, c 4tp , . o4h.f. , R.p j Ply,V  ;  %'94>.,n.e

.). .x .

.o i 'ig nA

,7 ~;- w; .,;' <:<!.o 1

1$

.i. Y.X:1 ** .' A

' ' Q'i 'l ' y.' %. f-Nj', ,g,g 53 i. ' .,, ': j CABLE GUIDE 2 .7 v?:%.4On>v vh ., .c . -

.., ~~~ .

4;~- 1 n-L.,.m. , .

' [. ' jJ [ Mk; r. .,N.* -M'1 ' W ' J.y

. * .g ; t., . t .,, t. ,..

g[< ?

. . > w. $.,[j#I $*,,t;3 3. , M,. .; ,  ; U. f. Mi MlCR0$ WITCHES [^".t&f,i, jg'gj n = , v. ,y

?&','g:

L..-

y M.elSTON

.. . y . L. ,

. $ kri.-h 'h) ~ ' Y *'W' ? ' '

,a M.$.-rT 5': .p. - -

9 '.

-A %ups.g I.3,*$ . .1 *r,.4gp FO,s :

u,Mm,OT.a'> ,  %. , .

. M 34,,' . g g T

')

- POTENT 10 METE 8,

. 34(epi ';1'  ;

. p%n}f CM, A. ~ggerf

..x

',:*r'n WWk

.: og .

/,.ye 'N9.,y.de Nm L'V. ',f, ?

, ,5% .i ,d.,a.j e 4 ^:

• ta ] W3 'p .'"j -T j ,p' *f a

(,,gp - .f.c 'c  %. " !

D R AW T,U B E.4M, .%.

n .. g.

p . ;i'ppgr.

j.,

Asl..:g.r.

. ,i

. ;{.sj$

W:d$.p>.*.?.ho ~% 5,g+y-n.

3 p % k@M N.f;' e +W s N. u*J ug %

t/y.y[j.  ; j;j,. 4;,M,o

. , J. 4

?a. e. **

ww '",'t '4s !,' a'  ; (A 'j. *1; y$p{ '

,., 'A y

qf' . , ' ' ' '

• g? 8  % %

E L E CTR0 MAGN. 'ET  %. -- ',h

.4 I'7.

3 ]/ - @9 .

4... 41.:

984..t.il,,

g d .MGJ5 .'{. (J ,M f lp yg?. 'M.

<.ds',',.N iv

@ O.RIV 6 '6.

M' R.4 m 1 .v, N4

?4.ep'- ' W^m. .. y s ,

t.

iL p+ W D ~r:g . 1 i % : ;;,a y Q n , &M

.. 1. , ..w.. rib.k.a

~ a .' (

:,

q.,3 t, . r~ u.. ., y.. . y . 1w%M -

• 'm -

' ('Y4 '*',MC A;:n.;fMML;M*y,y.gw.BARR Q f.i.W'  ;' ,L%y..; '#; ~%

~g~'3"2 CONNECTING ROD

.- t c%

M H.s p

PL .n.k..,Q.*o,,r*w.4; ft~,< ; M.

a h,

~

..g~ (%..y. ..g.g.

m a r.m y...+ . ov'", N.q D N,$skid,,L.h . j$.Y.$.#.)h. 4 u$ gg,z

'r' k.[-

e I.E.%#. $

&m*N: w&p. . a' q ?i U y % g?d -W. yg $,4

.ra. b

< 'i:fi&?

u%W+y hk f; hn'ded,.

- n hs .r ; .4. & ,

t$hf

%"yt t.($pg . s .-

sn* ....t m.Mw~ g I.1p;.as...

ye N@p.

khf

'M.

&v.sey

.%99:.

%et.c:49:$ k w mn $. 'Cr*z.'y'n S. p+;,' Jn.,c' v&2;&d,, t.

e;y y >

g.~ o- ~

in dT . .bb[/.h$7.h '!

. .h )

Fig. 3-31. Rack-and-pinion control rod drive 3-78 D"*D "D '

sa e m

~T]h@L

_ _ . .. _- . ~ _ -_. - . - -- .

4 4

i 3.4.7.2. Transient Rod Drive Assembly. The safety transient control rod on pulsing TRIGA Mark I reactors is operated with a pneumatic rod drive (see Figs. 3-32a and 3-32b). Operation of the transient rod drive is con-

. trolled from'the reactor console.

The transient rod drive is mounted on a steel frame that bolts to the bridge. Any value from zero to a maximum of 38.1 cm (15 in.) of rod may be withdrawn from the core; administrative control is exercised to restrict its travel so as not to exceed the maximum licensed step insertion of reactivity ($2.15 or 1.5% 6k/k) .

i.

The transient rod drive is a single-acting pneumatic, cylinder with its

. piston attached to the transient rod through a connecting rod assembly.

l The piston rod passes through an air seal at the lower end of the cylinder.

4 Compressed air is supplied to the lower end of the . cylinder from an accumulator tank when a three-way solenoid volve located in the piping ,

between the accumulator and cylinder is energized. The compressed air i

drives the piston upward in the cylinder and causes the rap *'. withdrawal of the transient rod from the core. As the piston rises, the air trapped above it is pushed out through vents at the upper end of the cylinder. At the end of its travel, the piston strikes-the anvil of an oil-filled hy-draulic shock absorber, which has a spring return, and which decelerates j the piston at a controlled rate over its last 5 cm (2 in.) of travel. When the solenoid is de-energized, the valve cuts off the compressed air supply and exhausts the pressure .n the cylinder, thus allowing the piston to drop 1

by gravity to its original position and restore the transient rod to its fully inserted position in the reactor core.

The extent of transient rod withdrawal from the core during a pulse,is determined by raising or lowering the cylinder, thereby controlling the distance the piston travels.

The cylinder has external threads running most of its length, which engage a series of ball bearings contained in a ball-nut mounted in the i

3-79 l

m" SHOCK ABSORBER VENT HOLES  %  !

/ SHOCK ABSORBER ANVIL

'f n

~

EXTERNALLY THREADED CYLINDER PISTON anvil SUPPORT

_. rm rmi / ---

o

! 1 l

- 1: !I l; !l 1 I __ , , l :D DEARINGS

[ p = WORM

/

' ' BALL NUT WORM GEAR- -

~

7

- 6 4 I -

= HOUSINU PISTON SEAL

-.3 cl.r-PISTON ROD =

VENT

• SUPPLY AIR SUPPLY HOSE SOLENOID VALVE

-b BOTTOM LIMIT =

PISTON ROD CONTROL ROD Fig. 3-32a. Adjustable transient rod drive operational schematic 3-80 4

y SHOCK ABSORBER RETAINING NUT t

.l SHOCK ABSORBER SUPPORT

!'{I SHOCK ABSORBER k

.r i .g AIR VENT

'3 d

1. I[ SHOCK ABSORBER

~

I' '

AIR CYLINDERd..(

,i pisioN ANVIL tro'x i THRUST

./..

REMOVABLE b., '

BEARING

' HAND

r. Y, CRANK p BALL NUT

[, . ',

y ,#

yCYLINDER SCREW or BA!L NUT

'Y~h '

[.2Ih

,n

.. ? DRIVE GEAR POTENTIOMETE R DRIVE WORM BALL NUT ', -

POTENTIOME TER DRIVE WORM DRIVE GEAR CYLINDER SCREW END CAP "O" RING SEAL AIR SUPPLY i

ROD GUIDE

e. SUPPORT PISTON ROD ROD CONNECTOR I

v DAMPER f CONNECTING ROD Fig. 3-32b Adjustable Transient Rod Drive 3-81

1

• drive housing. As the ball-nut is rotated by a worm gear, the cylinder moves up or down depending on the direction of worm gear rotation. A mechanieni indicator driven by the worm shaft provides a monitor of the position of the cylinder and the distance the transient rod will be ejected from the reactor core. Motor operation for pneumatic cylinder

_ positioning is controlled by a switch on the reactor control console. A key-locked switch on the control console power supply prevents unauthorized *'

operation of the transient rod drive.

Attached to and extending downward from the transient rod drive hous-

, ing is the rod guide support, which serves several purposes. The air inlet connection near the bottom of the cylinder projects through a slot in the rod guide and prevents the cylinder from rotating. Attached to the lower end of the piston rod is a flanged connector that is attached to the con-necting rod assembly that moves the transient rod. The flanged connector stops the downward movement of the transient rod when the connector strikes the damp pad at the bottom of the rod guide support. A microswitch is mounted on the outside of the guide tube with its actuating lever extending Inward through a slot. When the transient rod is fully inserted in the reactor core, the flange connector engages the actuating lever of the j

nicroswitch and indicates on the instrument console that the rod is in the core.

In the case of the safety-transient rod a scram signal de-energizes the solenoid valve which supplies the air required to hold the rod in a 7

withdrawn position and the rod drops into the core from the full out posi-1 tion in about 1 second.

3.4.7.3. Evaluation of Control Rod System. The reactivity worth and speed of travel for the control rods are adequate to allow complete control of the

- reactor system during operation from a shutdown condition to full power.

The scram times for'the rods are quite adequate since the TRIGA system does not rely on speed of control as being paramount to the safety of the reactor.

The inherent shutdown mechanism of the TRIGA prevents unsafe excursions and the control system is used only for the planned shutdown of the reactor and

}

to control the power level in steady-state operation.

3-82

. . ~ . - - _ _ - . - . _-- _ . . -

j i

i 3.5. SAFETY SETTINGS IN RELATION TO SAFETY LIMITS ,

As has been indicated, fuel temperatures are the main safety

)

• 4 considerations in the operation of the TRICA system. The temperature of the i fuel may be controlled by setting limits on other operating parameters. The operating parameters of interest for TRIGA are:

1. Maximum excess reactivity in the core

2. Maximum licensed steady-state power level i

+

The safety settings as listed in Table 3-12 are such that in all, opera-3 tion, normal and abnormal, the safety limits indicated in the reactor ' design bases will not be exceeded.

, TABLE 3-12  ;

TRIGA SAFETY SETTINGS

. Parameter Limited Safety Setting Function Max steady-state power level 275 kW(t) Reactor scram ,

Max excess reactivity in core 2.25% 6k/k Limit reactivity insertion These safety settings are conservative in the sense that if they are adhered to, the consequence of normal or abnormal operation would be fuel j

and clad temperatures well below the safety limits indicated in the re - tor ^

design bases. Because of the conservatism in these safety settings is reasonable that at some later date less restrictive safety system set. as Ecould be assigned in conjunction with the uptrading of the reactor to operate  :

5 j at higher steady-state power levels or in the pulsing mode, while still using

the same fuel and core configuration.  !

0 1

3-83 l 1

1

Chapter 3 References

1. Merten, U., et al., " Thermal Migration of Hydrogen in Uranium-Zirconium Alloys," General Dynamics, General Atomic Division Report GA-3618, 1962.

2. Cof fer, C. O. , _et al. , "Research in Improved TRIGA Reactor Performance, Final Report," Ceneral Dynamics, General Atomic Division Report GA-5786, 1964.

3. Johnson, H. A., et al., " Temperature Variation, Heat Transfer, and Void Volume Developpent in the Transient Atmosphere Boilingcof Water,"

SAN-1001, University of California, Berkeley, 1961.

.4. McAdams, W. H., Heat Transmission, 3rd ed, McGraw-Hill Book Co., New York, 1954.

5. Sparrow,'E. M. and R. D. Cess, "The Effect of Subcooled Liquid on Film Boiling," Heat Transfer, 84, 149-156 (1962).

6. Speigler, P., et al., " Onset of Stable Film Boiling and the Foam Limit,"

Int. J. Heat and Mass Transfer, 6, 987-989 (1963). '

7. Zuber, W., " Hydrodynamic Aspects of Boiling Heat Transfer," AEC Report AECV-4439 TIS, ORNL, 1959.

8. Rohsenow, W., and H. Choi, Heat, Mass and M mentum Transfer, Prentice-Hall, 1961, pp. 231-232.

9. Ellion, M. E., "A Study of the Mechanism of Boiling Heat Transfer,"

Jet Propulsion Laboratory Memo. No. 20-88, 1954.

10. Coffer, C. O., et al., " Characteristics of Large Reactivity Insertions in a High Performance TRIGA U-ZrH Core," General Dynamics, General Atomic Division Report GA-6216, 1965.

11. Fenech, H., and W. Rohsenow, " Thermal Conductance of Metallic Surfaces in Contact." USAEC NY0-2130, 1959.

12. Graf f, W. J. , "Thernal Conductance Across Metal Joints," Machine Design, Sept. 15, 1960, pp. 166-172.

13. Fenech, H., and J. J. Henry, 'An Analysis of a Thermal Contact Resistance,"

. Trans. Am. Nucl. Soc. 5, 476 (1962).

3-84

i b

t l 14. Bernath, L., "A Theory of Local Boiling Burnout and Its Application to l -

Existing Data," lleat Transfer - Chemical Engineering Progress Symposium Series Storrs, Connecticut, v. 56, No. 20, 1960.

15. Spano, A. H. , " Quarterly Technical Report SPERT Project, April, May, June, 1964," ISO-17030.

16. Dee, J. B. , et al. , " Annular Core Pulse Reactor," General Dynamics, i General Atomic Division Report GACD 6977 (Supplement 2),1966,

17. Adler, J. , et al. , " Users and Programmers Manual for the GCC-3 Multigroup

{ Cross Section Code," General Dynamics, General Atomic Division Report l GA-7157,'1967.

19. Lenihan, S. R., " GAZE-2: A One-Dimensional, Multigroup, Neutron Diffu-sion Theory Code for the IBM-7090," General Dynamics, General Atomic Division Report GA-3152, 1962.

19. Dorsey, J. P. , and R. Frochlich, "CAMBLE A Program for the Solution l of the Multigroup Neutron-Diffusion Equations in Two Dimensions, with Arbitrary Group Scattering, for the UNIVAC-1108 Computer," Gulf General Atomic Report GA-8188, 1967. ,

20. Lathrop, D. K., "DTF-IV, A FORTRAN-IV Program for Solving the Multi-group Transport Equation with Anisotropic Scatterings," USAEC Report LA-3'373, Los Alamos Scientific Laboratory, New Mexico, 1965.  !.

21. Adler, F. T., G. W. Hinman, and L. W. Nordheim, "The Quantitative

Evaluation of Resonance Integrals," in Proc. 2nd Intern. Conf. Peaceful Uses At. Energy (A/ CONF. 15/P/1983), Geneva, International Atomic Energy Agency, 1958.

22. Brown, H. D., Jr., Culf General Atomic Inc., "THERMIDOR - A FORTRA II 4 .

Code for Calculating the Nelkin Scattering Kernel for Bound Hydrogen (A Modification of Robespierre)," unpublished data.

23. Nelkin, M. S., " Scattering of Slow Neutrons by Water," Phys. Rev. 119, _

741-746 (1960).

24. McReynolds, A. W., et al., " Neutron Thermalization by Chemically-Bound

,e 4

Hydrogen and Carbon," in Proc. 2n'd Intern. Conf. Peaceful Uses At. .

Energy (A/ CONF. 15/P/1540), Geneva, International Atomic Energy Agency, h 1958. b I.

i 3-85 a

- - .-..---c - . . - . - - - . , ,- ,- m - i , ,er .- -,--y,,-----y , - - , --

y ,, , .. . . - - - -

25. Whittemore, W. L., " Neutron Interactions in Zirconium Hydride,"

USAEC Report GA-4490 (Rev.), General Dynamics, General Atomic Division, 1964

26. Bell, J., " SUMMIT: An IBM-7090 Program for the Computation of Crystal-line Scattering Kernels," USAEC Report, General Dynamics, General Atomic Division Report GA-2492,1962.

27. Beyster, J. R., et al., " Neutron Thermalization in Zirconium Hydride,"

USAEC Report, General Dynamics, General Atomic Division Report GA-4581, 1963.

28. Woods, A. D. B. , et al. , " Energy Distribution of Neutrons Scattered from Graphite, Light and Heavy Water, Ice, Zirconium Hydride, Lithium Hydride, Sodium Hydride, and Ammonium Chloride, by the Beryllium Detector Method," in Proc. Symp. Inelastic Scattering of Neutrons in Solids and Liquids, Vienna, Austria, Oct. 11-14, International Atomic Energy Agency, 1960.

29. Jordan, D. P. and G. Leppert, " Pressure Drop and Vapor Volume with Subcooled Nucleate Boiling," Int. J. Heat Mass Trans. 5, 751-761 (1962).

30. McAdams, op. cit., pp. 390-392.

31. Levy, S., " Forced Convection Subcooled Boiling-Prediction of Vapor Volumetric Fraction," Int. J. Heat Mass Trans. 1_0, 961-965 (1967).

32. McAdams, op. cit., p. 392.

33. Bernath, op. cit., pp.95-116.

1 l

h 3-86 -