. .

NEACRP-A- 83s

REVIEW OF PROTOTYPE FAST REACTOR (PFR) REACTIVITY FEEDBACK

COEFFICIENT MEASUREMENTS

1974 - 1987

BY

D J LORD, D S CROWE, A K DICKSON and A J SUTHERLAND

June 1987

SUMMARY

0 This paper describes the results of a number of experiments carried out to investigate reactivity feedback phenomena on the

0 Prototype Fast Reactor (PFR). The measurements are compared to predictions and it is shown that, in general, good agreement is obtained. Areas of disagreement are highlighted and possible explanations put forward.

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1. INTRODUCTION

A large number of specific experiments have been carried out on PFR to study reactivity feedback effects and these have been supplemented by routine operational reactivity monitoring. Attempts have been made to separate individual components of the feedbacks and this information has been collated to produce this paper. Reactivity feedback is, for the purposes of this paper, subdivided into two parts: namely the effect of inlet temperature changes (inlet temperature coefficient of reactivity) and the effect of power changes (power coefficient of reactivity).

2. CORE INLET TEMPERATURE COEFFICIENT 0~ REACTIVITY

The inlet temperature coefficient of reactivity is defined as the reactivity change associated with a change of core coolant inlet temperature of one degree centigrade. Two categories of

a measurements can be considered, name-ly those carried out under low power (isothermal) conditions and those carried out at power under non isothermal conditions.

The physical components which contribute to the coefficient are shown in Table 1 together with their calculated magnitudes based on a clean core model (1) and an equilibrium core model (2). In both cases the FD5 data set was used and the calculations refer to a temperature of 3OOOC. The inlet temperature coefficient measurements made on PFR are summarised in Table 2 and discussed in sections 2.1 to Z2.3.

2.1 Isothermal Temperature Coefficients

The first measurements of the PFR isothermal temperature coefficient.were made during the period March to May 1974 with

0 the reactor subcritical and the temperature in the range 250°C to 4oopc. The subcritical margin was measured both by special

W fission chambers located at the core centre and the 0 ystart up installed low power fission chambers in the radial shield. The

measurements covered a period in which a number of subassembly loading changes were made which increased the measurement uncertainty. The measurements produced results in the range -1.07 to -1.14 cents/OC and the assessed uncertainty (one sigma) was + 0.06 cents/OC. The more negative values were associated with-the lower part of the temperature range as expected from the non linear behaviour of the Doppler effect, but the measurement uncertainties are such that it is not possible to be definitive.

The next temperature coefficient measurement was made in August 1973 with the reactor critical and the temperature reduced from 420 C to 270°C. On this occasion a mean value of -0.98+0.08 cents/'C was obtained; the large error being associatea with the erratic behaviour of one of the control rod position indicators.

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A further two measurements were made in October 1975 during pool temperature reduction before and after a period of operation at 200 MW(Th). Priory to theopower rug the measurement gave -0.92+0.06 cents/ C (394 C - 315 C) and after the power run the measurement gave -1.09+0.03 cents/OC (376'C - 28OOC). The reason for the difference between the two values was not understood at the time. Although it is possible that the effect of the power run may have been to cause the fuel to swell, contact the clad and then expand axially with the clad (see Table 1 for magnitude of this change) subsequent measurements cast doubt on this suggestion as a reason for the change.

In May 1976 the primary pool temperature was increased from 318'C to 334'C and an isothermal temperature coefficient measurement made. On this, and subsequent measurements, the facility for directly interrogating the DRE (Data Reduction Equipment) to obtain more exact control rod positions was used. The value of the isgthermal temperature coefficient obtained was -1.01+0.05 cents/ C. This value is in good agreement with a meaguresent made between 18 and 21 June 1976 of temperature range 370°C to 3OOOC.

-1.02+0.02 cents/ C over the

In November 1977 an attempt was made to separate one of the components of the coefficient, namely that associated with expansion of the absorber extension rods over and above that associated with the core support structure. The measurements were made at the end of .Run 1 after about 105 full power dags operation and involved temperature changes in the range 300 C to 35oOc. The temperature coefficient was measured in two ways, firstly with the control rods in a curtain (thus maxi:mising the, reactivity effect of any relative movement of absorber rods and core) and secondly with all rods either fully raised or fully lowered except one used to balance the reactor (thus minimising the reactivity effect of absorber rod/core relative movement).

With a control rod configuration such that the differential worth 0 was 0.48 cents/mm the measured isothermal temperature coefficient was -1.00+0.02 cents/OC and this became -1.06+0.02 with a rod a configuration such that the differential worth was 2,6 cents/mm. The effect of the reduction in rod differential worth between the two measurements of 2.12 cents/mm was thus a reduction of 0.06fp.03 cents/OC in the isothermal temperature coefficient. Converting this to a curtain worth of 3 cents/mm (the value appropriate to the curtain of give rods at core mid plane) gives an effect of 0.085+0.04 cents/ C.

At the beginning of Run 2 (June 1978) a reduction in pool temperature from 318'C to 299'C was monitored and a temperature coefficient of -1.0910.05 cents/OC measured, the large uncertainty being associated with the small temperature change. It is noted that this "high" value of the temperature coefficient followed a reload and not a power run.

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No further specific measurements were made until July 1982 when an evaporator tube plate wash took place involving the reactor pool temperature being raised and lowered over the temperature range 300-43OOC. This was carried out at the start of Run 7 and resulted in a measured isothermal temperature coefficient of -0.965+0.015 cents/"C. No evidence of a change in the coefficient with increasing temperature was found. A similar measurement was made in January 1983; 08 this ocgasion the temperature change involved was from 270 C to 430 C and the result obtained was -0.9720.02 cents/OC.

In January/February 1984 a second experiment was carried out to separate the component of the isothermal temperature coefficient associated with absorber rod/core differential ex ansion. 8 The temperature range covered was from 300 'C to 430 C and with the controg rods in a curtain the measured coefficient was -0.97+0.02 cents/ C. With two rods fullyoraised and two rods fully lowered, the value was 8.94+0.02 cents/ C. The reduction in coefficient of 0.03 cents/ C represents the effect of four rods and hence the

0 effect of five is taken to be 0.04 cents/'C.

Two such measurements of this absorber rod/core differential expansion component have thus been made with results of -0.04 and -0.08 cents/°C; ie an average value of -0.06 cents/OC. The uncertainties of the individual assessments are such that both results are consistent with this mean figure.

2.2 Core Inlet Temperature Coefficient at Power .

Measurements discussed so far have been under isothermal conditions: an attractive method of studying reactivity feedback is to change the core inlet temperature at power. This technique has the potential of separating out the Doppler component by

0 invoking its dependence on fuel temperature. One such experiment was carried out in December 1978 when the core inlet temperature

0 was changed by 58OC at a power level of 200 MW(Th).. The measured inlet temperature coefficient was -1.00+0.05 cents/ C. Measurements at low power preceed&ng the high power measurement gave results of -4.06+0.02 cents/ C (November 1977) and -1.09+0.05 cents/ C (June 1978). The ijesult at 200 MW(Th) thus showed a reduction of 0.08+0.05 cents/ C when compared to the low power figures; this is in-good agreement with the value of 0.09 cents/OC predicted on the basis of the calculated Doppler component of the inlet temperature coefficient. The uncertainties, however, remain large for this type of measurement.

2.3 Summary of Inlet Temperature Coefficient Studies

Under isothermal conditions the PFR inlet temperature coegficient has been measuredoasi being in the range -1.14+0.06 cents/ C to -0.93+a.O6 cents/ C. Recent, and more accurate, determinations

have shown values $f -0.97+0.02 cents/'C in the temperature range between 300 to 430 C with no evidence of any variation in the coefficient between 300°C and 43O'C. The reason for this is thought to be associated with difficulties in the absorber rod position measurement at the intermediate temperature levels.

Attempts to separate the different components of the coefficient have met with some success. A component of about -0.06 cents/OC associated with relative expansion of the absorber and core supports have been identified: this value refers to rods in their mid core, start of run positions. fleasurements of the inlet temperature coefficient at power (200 Irw(Th)) have shown the expected reduction in the coefficient associated with the non linear behaviour of the Doppler effect. The uncertainties of this type of measurement, however, remain large. Confirmation that the inlet temperature coefficient is, indeed, the expected function of thermal power is obtained from routine reactivity monitoring in which a much improved fit is obtained when this variation is incorporated in the model than when it is not.

Theocalculated value of the isothermal temperature coefficient at 300 C is in the range -0.896 to -0.933 cents/ C depending on the mode of axial fuel expansion assumed and including a component of -0.06 cents/OC for control rod/core relative expansion effects. The value of C/E using the recent measurements is thus in the range 0.92 to 0.96.

An additional component of the inlet temperature coefficient which has not been included in the calculation is the Doppler' effect is iron. Inclusion of this would result in a value of C/E nearer to unity.

3. POWER COEFFICIENT OF REACTIVITY

The power coefficient of reactivity is defined.as the reactivity change associated with an increase in the reactor thermal power of one megawatt at constant core coolant inlet temperature. This reactivity change is associated with a variety of feedback mechanisms. It is, in principle, a complex function of coolant flow, reactor power, fuel irradiation history etc since these parameters determine the temperatures of the fuel, coolant, core structural materials which then determine core reactivity.

It is useful, and convenient, to regard the power coefficient as being made up of two components; the first being independent of coolant flow and the second being inversely proportional to coolant flow (ie proportional to coolant temperature rise). This second term is then subdivided into those effects associated with the absorber extension rod expansion and those associated with in core effects (eg sodium density change, axial fuel expansion etc). Such a separation enables the power coefficient to be written as:-

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POWER COEFFICIENT = a(P) + 3

1 (1) u

where

a(P) represents fuel temperature effects (ie Eoppler and axial fuel expansion in that they are determined by thermal power).

b represents in core coolant temperature rise effects

c F(z) represents control rod/core support differential expansion effects, lIc" being the maximum effect and F(z) the differential worth of the rods normalised to their maximum value.

U is primary flow normalised to unity at full flow

0 The analysis of the feedback effects can be carried out by studying static reactivity balances and by performing dynamic experiments to exploit the time dependence of the feedbacks. These two types of measurement are considered in turn.

3.1 Static Reactivity Balance Measurements

A key stage in the development of understanding of the PFR power coefficient is to separate the flow dependent term

w tb+cF(z)]t"

0 from the flow independent term "a(P)". Such a separation can, in principle, be achieved by changing the core flow with the control

l rods being moved to maintain the power level constant and noting the required rod movement. Operational restrictions and difficulties make such a manoevre difficult on a power reactor and the first time such a measurement was made on PFR was in February 1978. At that time core flow was varied between 30% and 77% at 58 MW(Th) and between 39% and 83% at 146 MW(Th). The results of this experiment are shown in Figure 1.

The variation in reactivity with flow was found to be as expected and the dominant term was found to be "cF(z)*; the value of c is calculated to be -0.12 and that of b about -0.04 and the measurements confirmed these values. Subsequently other measurements have given similar results. The expression for the power coefficient may thus be written:

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POWER COEFFICIENT = a(P) - 0.04+0.12 F(z) I

1 cents/m u

(2)

A further measurement of this type was carried out in December 1978 when flow was reduced from 89% to 47% at a thermal power of about 195MW. Core inlet temperature changed by only 6'C and the flow dependent component "b+cF(z)" was measured to be -0.137+0.01 cents/MW. F(z) was approximately 0.93 during the measurements and hence "b + c" is estimated to be -0.144+0.01. This is in good agreement with prediction and the earlier measurement.

Most of the difficulty in understanding the power coefficient is associated with the term "a(P)"; the component of the coefficient which is essentially determined by fuel temperature. The problems fall into two parts: firstly how the fuel temperature is related to power. (ie fuel clad gap conductivity, fuel conductivity), and secondly how fuel axial expansion is related to fuel temperature.

The observations on PFR have shown that the value of "a(P)" 0 varies considerably over the operational power range, the value ranging typically from -0.1 at high power to -0.5 at low power. This behaviour has, in general, remained consistent over the life of PFR. The variation in "a(P)" is significantly greater than expected solely from the intrinsic non linearity associated with the Doppler effect.

Table 3 has been constructed as a summary of the many documented measurements of the PFR power coefficient; in this table the measured power coefficient is given and from this the value of "a(P)" is derived using equation 2. In Figure 2 the derived value of "a(P)" is shown as a function of reactor thermal power. In order to explain this behaviour of "a(P)" phenomena such as a changing mode of axial fuel expansion (centre fuel temperature to edge fuel or clad temperature dominated) and/or changing heat transfer from fuel to coolant must be invoked. In Table 4 0 calculated values of "a(P)" are shown for different assumptions. The major uncertainty in the heat transfer from fuel to coolant 0 lies in the fuel/clad gap and hence it is this parameter which has been varied in this particular study.

At low power levels (ie less than 200 MW(Th)) the measurements indicate a value of a(P) in the range -0.3 to -0.5 cents/MW. Such values can be obtained in one of two ways:-

(a) Axial fuel expansion determined by fuel cen$r;_temperature and a gas gap conductivity of about 5 KW/(m L).

(b) Axial fuel expansion determined by clad temperature and a gas gap conductivity of about 1.3 KW/(m2 OC).

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At high power levels the measurements indicate axial fuel expansion at edge fuel or can temyegature and a gas gap conductivity in excess of 5 KW/(m C).

Static reactivity balance measurements cannot allow further development of understanding of "a(P)" and for this reason a number of dynamic experiments have been performed.

3.2 Dynamic Reactivity Feedback Measurements

Two types of dynamic experiment can be readily carried out on PFR; in the first the reactivity change is the result of motoring the absorber rods at their normal operating speed and the second involves a much more rapid reactivity transient caused by dropping a, rod over the last part of its travel.

A number of rod motoring experiments have been analysed (3) for both raising and lowering operation in the power range

0 200-270MW(Th).

Such measurements are not suitable for analysis of in core feedback timescale because of the low rate of imposed reactivity change (0.6 cents/set) but they did confirm the static measurements and showed that there was no significant long term (ie many tens of seconds) feedback mechanism in PFR.

To overcome the deficiencies of the rod motoring transients. a technique has been developed in which a rapid (200 mS) negative reactivity transieht of about -10 cents is inserted and the subsequent power (reactivity) transient analysed. This transient is achieved by dropping an almost fully lowered control rod over the last 120 mm of its travel. Tests at low power (100s of KW) showed the technique produced a reproducible transient and confirmed that under zero feedback conditions no change in

areactivity occurred after the drop.

0 Two series of transient measurements using the rod drop technique have been carried out at power; the first series involved a number of tests in December 1978/January 1979 at a power level of about 200 MW(Th) and the second series involved a single test from 585 MW(Th) in March 1985. A number of deductions have been made from these experiments and these are summarised below:-

(i) Test at 200 MW(Th) in 1978/1979

A typical response is shown in Figure 3. In addition to the measured response two calculated resul$soare shown. In the first a gas gap conductance of 5 IZW/(m C) is assumed and fuel axial expansion is taken as occurring at fuel centre temperature (a combination which gives the correct total power coefficienct). In the second calculation the axial fuel expansion is taken as occurring at clad

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tempesa,$ure and the gas gap conductance reduced to 1.3 kW/(m C) to restore the power coefficient to its measured value. The poor heat transfer in the second case delays the feedback and it is clear that the first calculation gives a much better representation of the measured response.

Support3na evidence for gas gap conductance values of about 4 kW/(m C) for selected subassemblies at the time of these experiments is given by Webster (4) who analysed the response of subassembly outlet thermocouples to power perturbations at the time of the rod drop tests.

It is concluded from these tests,that at power levels of about 200 fiW(Th) the "high" value of "a(P)" is the result of a combination of a low fuel-coolant heat transfer coefficient and a mode of axial expansion in which the axial fuel expansion results from fuel pellet expansion determined by centre (or near centre) fuel temperature.

The fact that the Doppler component is only a part of the 0 component "a(P)" means that tests at these power levels cannot be used to comment on the value of the Doppler coefficients; this deficiency can, however, be removed by tests at high power when the value of "a(P)" is dominated by Doppler.

(ii) Tests at 585 MW(Th) March 1985

This experiment provided a reactor transient in which the dominant fast acting feedback mechanism is thought to be the W238 Doppler effect. The measured and initial calculated response to the transient are shown in Figure 4. In the calculation, fuel axial expansion is assumed to be at clad temperature and reactivity feedback coefficients as calculated in Reference 3. The core Doppler constant was 0 increased, in this and all other predictions, from the calculated value by 5% as recommended2ig Reference 5. A a gas gap conductance value of 10 KW/(m C) was assumed.

Although Figure 4 shows basically good agreement between measurement and prediction the fit can be further improved by a small reduction (~20%) in the fast feedback component (Doppler in core fuel)~and a corresponding increase in the longer term feedback to maintain the total power coefficient in agreement with measured values. The result of this adjusted calculation is shown in Figure 5.

3.3 Summary of Power Coefficient Studies

The combination of static reactivity balance measurements and transient studies has enabled a picture of the reactivity

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.

feedback effects in PFR to be established. The feature which has attracted most attention is the variation of the flow independent component of the power coefficient with power level.

This variation is much greater than the nonlinearity associated with the Doppler effect a.nd is explained by the combination of two effects. These effects are; firstly the increase in fuel to coolant heat transfer coefficient with increasing power level and secondly the changing mode of axial fuel expansion with changing power level.

4. ROUTINE REACTIVITY MONITORING

Using the measured and calculated reactivity feedback data an empirical model of E'FR has been developed (ii) and measured and predicted core reactivity is compared daily during each operating cycle. Although refinements to the model which would improve

e agreement are possiblle the current model has demonstrated that the feedback characteristics of PFR are not changing significantly with time. Over an operating cycle involving reactivity changes of about 1,000 cents agreement between calculated and measured reactivity is within +20 cents. -

5. CONCLUSION

The measured reactivity feedback characteristics of the PFR have ~ generally been found to compare well with predictions. However, larger than expected variations in the power coefficient of reactivity feedback with power level have been observed. These variations are attirbuted to changes in the coefficient of heat transfer between fuel and coolant (for which there is independent evidence) and to chances in the mode of axial fuel expansion.

e d’ ACKNOWLEDGEMENTS -

The work reported in this paper represents the efforts of a large number of people in Fast Reactor Technology Group and PFR over a number of years. The authors wish to acknowledge the contributions made b:y their colleagues past and present.

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7. REFERENCES

1. WEBSTER E B and HIRST I L. Unpublished work. :1973. -

2. WEBSTER E B and MACGREGOR B R. Unpublished work. 1980.

3. LORD D J et al. Unpublished work. 1978.

4. WEBSTER R. A power perturbation technique for measurement of fuel-to-coolant heat transfer coefficients in fast reactors. Nuclear Engineering And Design 62. p 241-252. 1980.

5. ROWLANDS J L. Unpublished work. 1973.

6. LORD D J and WILKES D J. Reactivity monitoring for safety purposes onthe UK Prototype Fast Reactor. Paper to 1986 Guernsey Conference on Science and Technology of Fast Reactor Safety.

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TABLE 1

CALCULATED COMPONENTS OF PFR ISOTBERMAL TEMPERATURE COEFFICIENT

COMPONENT

CLEAN CORE EQUILIBRIUM CORE CALCULATION CALCULATION (cents/'C) (cents/'C)

DOPPbER IN U238 -0.341 (300 C)

-0.354

RADIAL DIAGRID EXPANSION

-0.302 -0.318

FUEL AXIAL EXPANSION

':: FUEL %A, TEMP TEMP

SODIUM DENSITY REDUCTION

-0.093 -0.140 -0.072 -0.109

-0.090 -0.092

REL EXPANSION OF(l) -0.06 CORE/CONTROL ROD SUPPORTS

-0.06

TOTAL -0.886 -0.896

OR OR

-0.933 -0.933

l l NOTE 1 Obtained from measured value

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TABLE 2

SUMMARY OF PFR INLET TEMPERATURE COEFFICIENT MEASUREMENTS

INLET TEMP INLET TEMP RANGE COEFFICIENT

DATE (OC) (cents/OC) COMMENTS

Mar-May '74 250-400 -1.07 -1.14fO.06

Aug '75 270-420 -0.98+0.08

Ott '75 280-380 -0.92+0.06 -1.09~0.03

May '76 318-334 -1.01+0.05

June'76 300-370 -1.02+0.02

Nov '77 300-350 -1.06+0.02

June'78 299-318 -1.09+0,05

Dee '78 355-415 -1.00~0.05

July'82 300-430 -0.9'65iO.015

Jan '83 270-430 -0.97fO.02'

Jan/Feb 300-430 -0.97+0.02 '84

l

Separation of C Rod Effects

Power level 200 IYW(Th)

Separation of C Rod Effects

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. .

PCAERPMGE AVFU’TER rIxrE (mm)) cw

Cct '75 16-50 33 100-200 150

Aq - Nov 25-250 138 '76 10455 232

31me-July O-230 xl5 '77 O-230 115

l ‘%I* O-300 150 '77 O-275 140

O-300 150 O-220 110 o-355 180 O-260 130

Mar '77 20-150 85

FLU? (%I

30 50

77 90

;:

a3

;:

.;z 99

59

PCWERCOEFF (cents/M)

-1.01+0.14 4.76s.04

-0.58+0.02 -0.5@.02

-O-64+0.05 -0.623.05

-O-57+0.03 -0.51s3.03 -0.52%.03 -0.48q.03 -0.46TO.03 -0.523.03

458~0.03

DELRVIED a(P) (CentsFw)

-0.48+0.14 -0.443.04

-0.37M.02 -0.333.02

-0.44+0.02 -0.4570.02

-0.40+0.03 -0.35To.03 -0.37x03 -0.35To.03 -0.33To.03 -0.413.03

-0.463.03

Feb ‘78 O-150 7s ?0.41_+0.02

Dee '78 182 88 -0.47+0.02 -0.36+0.02 -0.54T3.02 -0.30?0.02 , -0.3&X02 -0.2Go.02 -0.443.02 -0.2Cgi3.02

Q.45+0.02 -0.31-bO.02 -0.453.02 -0.353.02

-0.16+o.02(2~-0.16+o.02(2)

a Jan '79

a Sep '84

NW '84

Mar ‘85

Mar '85 585-520(1)

NOIE 1.

480-575

310-560

590620 470-620 310470

185 47 260 90 370 90

208 79 183 82

530 VXUED

430 100 +19+0.02 -O.ll+a.O2

605 100 -0.20+0.05 -O.o7+0.05 545 100 +.23%.03 -0.lOTo.03 390 100 -0.243.03 -0.lqLo3

562 100 -0.225.02 -0.12+0.03

2. Measurement n&e under constant core AT conditions

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.

CALCUIATED FWERCOEFFICIENT FORPFR~VARIOUS FUNERS,MODEs OF FUEL

EXPANSION ANDFUEL-CAN HEATTRANSFER

Gas Gap Fawer Level Frimary Flow Cmduciyye We of Axial Fuel MJ) (kg/s ) wuh . C)) Ekpansion

a(P) (cents/W

0 3400 : 3400 3400

0 3400 300 3400 300 3400 300 3400 300 1700 600 3400 600 3400 600 3400

10 10 5

:0

5 5 :0

5 15

Centre Fuel !Em~rature 0.32 Centre Can Temperature Fuel

Temperature 0.38 0.18

Centre Fuel Temperature 0.50 Centre Eke1 Temperature 0.25 Centre Fuel Temperature 0.31 Can Temperature 0.15 Centre Fbel Temperature 0.30 Can Teqzerature Cl.11 Can Temperature 0.13 Can Wqerature 0.10

NOTES 1. Core inlet temperatures taken as 400°C 2. Full flow (primary pmps at 960 rpn) = 3400 Kg/s

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0

loo- / /

. . . .

go-

/

i*

BO- .f

/ / / / \

70- ./ ./ REACTOR POWER REACTOR POWER / /

/ / lL6 MW lL6 MW

/ / /

so-’

LO- /& (#-

REACTOd POWER REACTOR POWER se HW se HW

30-

20-

lo-

I I I ” f 2 3

960 j. PRIMARY PUMP SPEED

FIG. / Reactivity efjects of varying primary pump speed at confranf power.

.

-0

- 0.’

-0.

T .

I I

T

I

ii

.

I

.

l

l 0

-2

-3

0 -8

a’ -9

-10

TI ME I s.eco”ds I *-

5 10 15 20 - 25

****” CALCULATED RESPONSE I GAS GAP CONOUCTANCE SkW ,-2 *C-l)

. -.- CALCULATED RESPONSE

IGAS G?P CONDUCTANCE

1.3 kWm-2 ‘C -‘I

! FIG.3 Reactivity reJpome aIf PFR to a -10.5 / reactivity step at approx. 30% full power, a896 fun flow.

.

-/a

-12

2,

\

- 2-

o-

2-

4-

;-

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c

I

L

I I

I 5 1 I lo -hMb (5hCOdb5) ‘=

I 20 25