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PHYSOR 2018: Reactor Physics paving the way towards more efficient systems

Cancun, Mexico, April 22-26, 2018

Proceedings of the PHYSOR 2018, Cancun, Mexico

DEVELOPMENT OF CRITICAL EXPERIMENTS TO PROVIDE

VALIDATION DATA FOR MULTIPHYSICS COUPLING CODES

Mathieu Dupont, Matthew D. Eklund, Wei Ji, and Peter F. Caracappa

Department of Mechanical, Aerospace, and Nuclear Engineering

Rensselaer Polytechnic Institute

Troy, NY 12180, USA

[email protected], [email protected], [email protected], [email protected]

ABSTRACT

Modern reactor simulation tools provide advanced prediction capabilities by coupling multi-

physics models to simulate reactor behaviors, involving thermal, neutronic, and mechanical

interactions. To assure high-fidelity predictions by these tools, experimental data are needed

to validate coupled-physics models deployed by these tools. In order to provide data to

benchmark the feedback between temperature and neutronic simulations, coupled-physics

critical experiments have been designed and performed at a Reactor Critical Facility (RCF).

The facility’s low power and open-pool atmospheric pressure configuration allows for many

unique critical experiments. Recently, a water loop system has been designed and installed in

the facility with the heated water circulating through the center of the core, which broadens

the range of validation experiments available. Direct effects of the temperature on reactor state

and excess reactivity are demonstrated, through a series of different measurements, including

reactor change of state through moderator temperature change, influence of heated water in

the center of the core on the reactivity, and transient temperature influence on reactor power

evolution. Changes as low as of 1% in the reactor power caused by small water temperature

perturbations are observable experimentally.

1. INTRODUCTION

Computational simulation of nuclear reactors for design and analysis requires accurately modeling several

different interrelated physical processes including neutronics, heat production, fluid/thermal physics,

structural mechanics, fuel behavior, chemistry, and balance-of-plant. Modern codes have been developed

which couple together the behavior of these different physical models to accurately consider the feedback

effects between different physical effects. The SHARP toolset, part of the Nuclear Energy Advanced

Modeling and Simulation (NEAMS) project, is an example of an effort to combine models of neutronics,

thermal-hydraulics, and structural mechanics in a coupled simulation to model any type of nuclear reactor

[1]. The multi-physics coupling in these codes required experimental validation that is in addition to the

validation data that exists for the individual physics routines, with benchmark experiments specifically

designed for that purpose [2]. To focus on the feedback between thermal-hydraulics and neutronics, a set

of experiments are developed in which the temperature conditions can be adjusted in a controlled manner

to affect the reaction rate. The RCF is uniquely suited to these types of experiments, due to its flexible

configuration, low power, and detailed instrumentation [3]. After a description of the facility and the

presentation of non-coupled experiments results, the design, execution and results of the new coupled-

physics experiments are presented, and an overview of the upcoming tasks remaining in this project is

shown.

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mailto:[email protected]

Mathieu Dupont et al., Development of Critical Experiments to Provide Validation Data for

Multiphysics Coupling Methods


2. FACILITY DESCRIPTION

The facility adopted for these experiments is Walthousen Reactor Critical Facility (RCF) at Rensselaer

Polytechnic Institute (RPI). The RCF is a critical assembly fueled in a standard core configuration of 332

or 333 UO2 fuel pins, each containing a total of 35.2 grams of U-235 (4.81 % enriched) within stainless

steel cladding, originally manufactured for the SPERT reactor experiments. Each fuel pin is 106.45 cm in

length, and 1.18 cm in diameter, with an active fuel length of 91.44 cm. These fuel pins are arranged in a

regular lattice with a pitch of 1.6256 cm, as seen in Fig. 1. The reactor thermal power is typically limited

to no more than 15 W, which permits manipulation and modification of the core configuration (within safety

constraints). The reactor tank volume is of about 7500 L, and regular light water is used as

moderator/reflector. In the standard configurations, the reactor is significantly under-moderated. As the low

thermal output of the reactor does not induce any measurable temperature changes, the temperature effect

is observed by applying two 18-kW electric heaters to the water moderator, with mechanical agitators to

maintain uniformity in moderator temperature. A 5-Ci PuBe neutron source is used to start the reactor, and

4 boron-impregnated steel control rods are used for reactor control. The control rods have a stroke length

of 91.44 cm, and the pulling out duration is 12 minutes from fully in to fully wthdrawn. Prior to reactor

measurements, each fuel pin used was surveyed for mechanical defects (bending or warping) that may

contribute to uncertainty in core behavior. A complete description of the reactor parameters is given in the

Safety Analysis Report [4].

Figure 1. Top view of the core in the standard configuration.

3. DESIGN OF COUPLED-PHYSICS EXPERIMENTS

3.1. Temperature Effects in the RCF

In the standard lattice configuration of the RCF, the reactor is a classically under-moderated assembly.

Increasing the temperature of the reactor results in thermal expansion of the materials, including decreasing

the density of the water moderator and doppler-broadening of the neutron reaction cross-sections. In a

typical power reactor, this temperature increase would come from the fission power of the reactor, but in

the RCF, the temperature increase is achieved artificially with electric heaters. Since the reactor is under-

moderated to begin with, decreasing the density of the moderator further reduces moderating power, and

reduces the total excess reactivity of the reactor. The water level height in the reactor tank is approximately

25 cm above the active fuel length, so the small change in total volume of the moderator has no influence

on the reactor reactivity.

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Reactors Physics paving the way towards more efficient systems


The reactor being an open-pool, all experiments are performed at atmospheric pressure, with the

temperature range limited to roughly 20-80 °C. The available temperature range for the standard lattice at

the RCF is smaller than that, as the total excess reactivity becomes negative at roughly 43°C.

3.2. Test Section Design and Capabilities

To expand the range of parameters that can be addressed in the neutronics and thermal hydraulics coupling

effects in the reactor, a circulating heated fluid loop test section has been designed and installed in the center

of the reactor, as seen in Fig. 2. The addition of this loop to the core increases the moderator temperature

range that can be achieved in a small volume of the core and increases the speed at which the temperature

change can evolve.

Figure 2. Top view of the core, with the test section on its center.

The test section is constructed of stainless steel, with a central flow pipe, surrounded by 4 smaller pipes

connected through a welded manifold to it at the bottom. These pipes are placed in the center of the core,

where a 5 by 5 array of fuel pins has been removed. To maintain sufficient excess reactivity, additional

fuel has been added to the core periphery. The assembly is connected via flexible hoses to a 310 L water

tank and pump, equipped with 16 kW immersion heaters. With this system, a circulating flow of water is

obtained at the center of the core. Within the central pipe section, a 2x2 array of fuel pins has also been

added. These fuel pins are fixed in place with an aluminum pin holder, as seen in Fig. 3. The system permits

multiple neutronics and thermal hydraulics coupled experiments through varying parameters. In this test

section the water can reach temperatures in excess of 75 °C, and the flowrate can be controlled between 3

and 12 gallons per minute, equivalent to a linear speed of water between 0.02 and 0.30 m/s.

The test section is monitored with 4 type T thermocouples and one pressure transducer. There are 3

thermocouples at varying radial depths and 1 pressure transducer on the inlet leg of the loop at the top of

the central pipe, and one thermocouple on the outlet part of the loop. In addition, there are 2 thermocouples

inserted inside the loop water tank to monitor the reservoir temperature.

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Figure 3. Schematic top view cross section of the core, with the test section on its center.

As heated water circulates through the loop, heat transfer through the loop wall to the surrounding reactor

water results in a drop in temperature along the test section. A heat loss model of the test section has been

developed to predict the temperature profile. For a loop inlet temperature of 70 °C and reactor tank water

temperature of 25 °C, the temperature drop along the test section length is shown in Fig. 4 for different

flowrates.

Figure 4. Calculated water temperature drop across the test section height for different flowrates,

for 60°C initial and moderator temperature at 25°C.

In this experimental configuration, the central region of the reactor is over-moderated, while the periphery

of the reactor remains under-moderated. Under these conditions, a higher loop water temperature increases

the excess reactivity of the reactor. The effect is integrated over the axial temperature, so for the same inlet

temperature, a higher flowrate leads to a smaller temperature profile gradient in the test section, and

therefore a greater excess reactivity. Fig. 5 shows an overall side view of the reactor with the test section

installed.

35

40

45

50

55

60

0 50 100 150

Wat

er t

emp

erat

ure

(°C

)

Test section position (cm)

13 GPM 7 GPM 3 GPM

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T

t

ePtP 0)(

6

1

*

1i i

i

TT

l

Figure 5. Schematic side view of the reactor tank, core with test section inserted.

4. TEMPERATURE REACTIVITY EXPERIMENT METHODS

4.1. Reactor Period – Reactivity Measurements/Calculation

The neutronic behavior of the reactor is characterized by the degree to which the reaction may be super-

critical (or sub-critical, in the case of negative excess reactivity) in relation to a reference condition. A

measurement of the reactor without any included control mechanism (in the case of the RCF, when the

control rods are fully withdrawn), provides what is referred to as the total excess reactivity. The reactivity

value is derived from a measure of the period of the reactor. To obtain power measurement, a calibrated

fission chamber records the neutrons flux as a function of time, and converts the measurement to total

reactor power. The evolution of the power of a super-critical reactor with time follows a known law, giving

the reactor period T (after a fit of the data points).

, (1)

The excess reactivity value is then obtained from the inhour equation, and the established kinetics

parameters for low-enriched-fuel, as shown in Table I for the RCF.

, (2)

Table I: Kinetics Parameters for the RPI RCF with LEU fuel. [5]

l* eff Group # i / eff i, s-1

1.22E-4 sec 0.00765 1 0.041 3.0100

2 0.115 1.1400

3 0.396 0.3010

4 0.196 0.1110

5 0.219 0.0305

6 0.033 0.0124

A set of benchmark experiments performed with the standard and test section configurations are described

in the following sections.

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4.2. Standard Lattice Configuration, Moderator Temperature Feedback

The first set of experiments demonstrates temperature feedback effects from uniform heating of the reactor

moderator. The control rods are set such that the reactor is slightly super-critical, or has a small excess

reactivity. Typical starting conditions for the measurements are about 1 cent of excess reactivity. The

moderator is heated with the electric heaters, resulting in a temperature increase of about 7 degrees per

hour. A submerged agitator is also operated to maintain a uniform temperature throughout the moderator.

As moderator temperature increase in this configuration has a negative reactivity effect, the reactor period

is observed to slow until the reactor becomes critical, and then becomes negative resulting in power

decrease. This experiment is repeated for various initial temperature values.

4.3. Test Section Temperature Profile Effects

In this set of experiments, the test section is operated with varying inlet temperatures and flow speeds,

resulting in different temperature profiles along the axial length. Here the purpose is not to observe

temperature feedback effects, but to characterize the temperature profile effects under effectively steady-

state conditions. The loop reservoir water is heated until the desired temperature is reached, and the reactor

control rods are set at the critical height for the bulk moderator temperature (i.e. power is constant with zero

excess reactivity). The pump is then activated at the desired flowrate. Due to the over-moderated conditions

near the test section, the increased temperature in the loop results in an insertion of positive excess

reactivity. Outside the test section, the submerged agitators are operated as noted above to maintain

uniformity in the moderator temperature. The heat transfer through the test section results in a gradual

increase in the moderator temperature, but the magnitude is small over the course of a single measurements

(less than 0.5 degree C per minute). Also, the feed length between the reservoir and the test section results

in several seconds of temperature variation at the onset of pump operation, and the finite volume and heating

capacity of the reservoir means that the test section inlet temperature will also begin to decrease over the

course of a measurement. Data in which moderator and inlet temperatures are effectively constant is

isolated for analysis.

4.4. Test Section, Dynamic Flow Rate

The configuration of these experiments is similar to those described in section 4.3, except that the pump

speed is varied to observe the feedback effects of changing temperature conditions. Three different pump

speed patterns are performed. In the first two, the reactor begins in a critical condition, and the pump either

begins at a minimal flow rate that is linearly increased to the maximum flow rate (ramp-up), or begins at

the maximum flow rate and is linearly decreased to the minimum (ramp-down). Measurements are

completed at various ramp-up and ramp-down periods. In the third pattern, the pump speed is varied

sinusoidally. For this last case, the initial condition of the reactor is set near the critical state for the average

flow rate, such that the oscillating flow rate may result in alternating positive and negative reactivity

insertions.

4.5. Data Collection and Analysis

In each set of experiments, instrument measurement are recorded with a 1 Hz sampling rate using digital

data recorders installed in the RCF control room. In parallel, the Ethernet controlled pump data (flowrate,

power) is also recorded at one second intervals and combined with the reactor instrumentation data. A

Matlab script has been created to extract and analyze the relevant data sections from the data files (utilizing

Matlab shaping and fitting functions) in order to calculate the reactor period and excess reactivity values.

Reactor power measurements are fitted to a function corresponding with changes in the circulating water

temperature profile for comparison with the coupled simulations developed separately.

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5. RESULTS AND DISCUSSION

5.1. Standard Lattice Configuration, Moderator Temperature Feedback

Fig. 6 shows the evolution of reactor power with increasing moderator temperature over time. Between

t=0s and t=800s, the reactor is slightly super-critical. After that, it becomes critical and sub-critical.

Figure 6. Reactor power and moderator temperature evolutions with time.

Fig. 7 shows the evolution of reactor excess reactivity with increasing moderator temperature. Starting

around 1 cent, the reactivity decreases, reaching exactly critical around t =900s, and a negative value of

around -0.4 cents at t=1200s.

Figure 7. Reactor excess reactivity and moderator temperature evolutions with time.

The reactor is changing state purely because of the moderator temperature effects: the core being in an

under-moderated configuration, increasing the moderator temperature decreases the density and the

moderation, decreasing the reactor excess reactivity.

36

36.4

36.8

37.2

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0

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0.4

0.6

0.8

1

1.2

-100 400 900 1400

Tem

per

atu

re (

°C)

Po

wer

(W

)

Time (sec)

Power (W)

Temperature (°C)

36

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36.8

37.2

37.6

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-0.6

-0.3

0

0.3

0.6

0.9

1.2

-100 400 900 1400 Tem

per

atu

re (

°C)

Rea

ctiv

ity

(cen

ts)

Time (sec)

Reactivity (cents)

Temperature (°C)

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5.2. Test Section Temperature Profile Effects

Fig. 8 illustrates the reactor excess reactivity versus loop inlet temperature and loop flowrate. As loop

temperature increases, reactor excess reactivity increases due to the over-moderation in the test section

region. At higher pump flowrates, the delta T between inlet and outlet decreases and the reactor excess

reactivity likewise increases.

Figure 8. Reactor excess reactivity evolution with loop inlet temperature and pump flowrate.

The reactor being over-moderated in this configuration, any water temperature increase inside the loop is

increasing the excess reactivity, by reducing the neutron absorption in water. Heating the loop water and

increasing the pump flowrate both have a positive effect on the excess reactivity. At low loop temperature,

the difference between inlet and outlet temperatures of the loop is small, and the influence of the flowrate

on reactivity is negligible.

5.3. Test Section, Dynamic Flow Rate

Fig. 9 shows the evolution of the loop water flowrate and reactor power (logarithmic scale) with time. The

pump is set up to increase from minimal to maximal flowrate in 200s. The reactor is super-critical, and the

power rate of increase accelerates as the pump speed increases.

0.00

2.00

4.00

6.00

8.00

10.00

20 30 40 50 60 70 80

Exc

ess

reac

tivi

ty (

cen

ts)

Loop inlet temperature (°C)

3.0 gpm 7.2 gpm 13.0 gpm

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Figure 9. Reactor power (logarithmic scale) and loop water flowrate evolutions with time during a

200 s ramp-up.

Fig. 10 shows the evolution of the inlet-outlet temperature difference and reactor excess reactivity with

time. As the pump speed increases, the difference in temperature between inlet and outlet becomes lower.

Excess reactivity starts around 0 as the reactor is critical, and increases until it becomes nearly constant

when the ramp concludes.

Figure 10. Temperature difference Inlet-Outlet (°C) and reactor excess reactivity evolutions with

time during a 200 s ramp-up.

A dynamic increase of loop water flowrate decreases the inlet-outlet temperature gradient, increasing the

reactor period with time which is equivalent to the reactor excess reactivity. Fig. 11 shows the evolution of

the loop water flowrate and reactor power (logarithmic scale) with time. The pump is set up to decrease

from maximal to minimal flowrate in 200s. The reactor is super-critical, and the period keeps decreasing

0

2

4

6

8

10

12

14

1.00E-02

1.00E-01

1.00E+00

14:03:33 14:05:00 14:06:26 14:07:52

Pu

mp

Flo

wra

te (

gpm

)

Po

wer

(W

)

Time

Reactor Power Loop Water Flowrate

-2

0

2

4

6

8

10

12

14

-10.00

0.00

10.00

20.00

30.00

40.00

14:03:33 14:05:00 14:06:26 14:07:52 Exc

ess

reac

tivi

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cen

ts)

Tem

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re d

iffe

ren

ce I

nle

t-O

utl

et (

°C)

Time

Temperature Difference Inlet-Outlet Excess Reactivity

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as the pump speed decreases. A few seconds after the pump is stopped, the power evolution becomes

constant and the reactor becomes critical again.

Figure 11. Reactor power (logarithmic scale) and loop water flowrate evolutions with time during a

200 s ramp-down.

Fig. 12 compares the inlet-outlet temperature difference and reactor excess reactivity with time for the same

experiment as Fig. 11. As the pump speed decreases, the difference in temperature between inlet and outlet

becomes larger. Excess reactivity starts around 10 cents as the loop water flowrate is maximal, keeps

increasing slightly and starts decreasing to reach 0 a few seconds after the ramp is over.

Figure 12. Temperature difference Inlet-Outlet (°C) and reactor excess reactivity evolutions with

time during a 200 s ramp-down.

0

2

4

6

8

10

12

1.00E-01

1.00E+00

1.00E+01

17:16:48 17:18:58 17:21:07 17:23:17

Pu

mp

flo

wra

te (

gpm

)

Po

wer

(W

)

TimeReactor Power Loop water flowrate

0

2

4

6

8

10

12

14

-10.00

0.00

10.00

20.00

30.00

17:16:48 17:18:58 17:21:07 17:23:17 Exc

ess

Rea

ctiv

ity

(cen

ts)

Tem

per

atu

re d

iffe

ren

ce I

nle

t-O

utl

et (

°C)

Time

Temperature Difference Inlet-Outlet Excess Reactivity

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A dynamic decrease of loop water flowrate increases the inlet-outlet temperature gradient, decreasing the

period of the reactor with time which is equivalent to the reactor excess reactivity. Fig. 13 shows the

evolution of the Inlet-Outlet temperature difference and loop water flow rate with time. The oscillation has

a 60s period. The power change is very small, but observable. The period of oscillation of the reactor power

is the same as the pump, in opposition of phase.

Figure 13. Temperature difference Inlet-Outlet (°C) and loop water flowrate evolutions with time

during a 60s oscillation period.

In all 3 cases of dynamic flowrate experiments, delays are observable between the flowrate given by the

pump and the effects in the test section. This is explained by the flowrate measurement being located at the

pump spot, and loop water takes about 30 seconds to reach the test section.

6. FUTURE WORK

To provide effective uncertainty quantification of the thermal-hydraulic behavior of the test section, direct

measurements of water temperature under various flow conditions are desired. However, the space

limitations of the fuel lattice do not permit such instrumentation to be installed within the active core

volume. In a separate set of experiments, fuel immediately surrounding the test section will be removed

and instrumentation will be added to collect temperature data along the direction of flow. In addition, the

composition and dimensions of core support structures will be characterized. The fuel pins and control

rods have previously undergone high precision material analysis.

7. CONCLUSIONS

Coupled-physics experiments have been designed and performed at the RCF in order to benchmark the

feedback mechanism in multi-physics reactor simulations. Reactivity insertion with change in temperature

is demonstrated through different measurements. The addition of the circulating heated water loop in the

center of the core broadens the range of validation experiments available. Insertion of around 10 cents of

reactivity over a 60 °C temperature change is observable experimentally.

28.5

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4.00

5.00

6.00

7.00

8.00

14:12:29 14:15:22 14:18:14 14:21:07 14:24:00

Rea

cto

r P

ow

er (

% o

f fu

ll s

cale

)

Tem

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atu

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iffe

ren

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nle

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utl

et (

°C)

Time

Temperature difference Inlet-Outlet Reactor Power

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ACKNOWLEDGMENTS

This material is based upon work supported by the Department of Energy Office of Nuclear Energy under

Award Number, DE-NE0008439.

Special thanks to the RCF staff members and operators, Glenn Winters, Jason Thompson, Emily Frantz,

and Nicholas Thompson.

REFERENCES

1. VS. MAHADEVAN, E. MERZARI, T. TAUTGES, R. JAIN, A. OBABKO, M. SMITH, P. FISCHER,

“High-resolution coupled physics solvers for analyzing fine-scale nuclear reactor design problems”

Phil. Trans. R. Soc. A 372: 20130381 (2014).

2. K. IVANOV, M. AVRAMOVA, “Challenges in coupled thermal-hydraulics and neutronics

simulations for LWR safety analysis,” Annals of Nuclear Energy 34(6), 501-513 (2007).

3. J. SENECAL, N. THOMPSON, “The Walthousen Reactor Critical Facility: A Unique Tool for

Education” ANS Winter Meeting and Nuclear Technology Expo, Washington D.C (2015).

4. J. STEPHENS, “Rensselaer Polytechnic Institute Reactor Critical Facility Safety Analysis Report” RPI,

(2011).

5. T.H. TRUMBULL, “Reactor Critical Facility: A Manual of Experiments” RPI, (2017).

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