Scientific design of a large-scale sodium thermal–hydraulic test facility for KALIMER—Part I: Scientific facility design

Nuclear Engineering and Design 265 (2013) 497–513

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Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes

Scientific design of a large-scale sodium thermal–hydraulic test facility for KALIMER—Part I: Scientific facility design Soon-Joon Hong a , Doo-Yong Lee a , Jae-Hyuk Eoh b,∗ , Tae-Ho Lee b , Yong-Bum Lee b a b

FNC Tech. Co. Ltd., SNU 135-308, Kwanak-Ro 1, Kwanak-Gu, Seoul 151-742, South Korea Korea Atomic Energy Research Institute, Fast Reactor Technology Development Division, 1045 Daedeok-daero, Yuseong, Daejeon 305-353, South Korea

h i g h l i g h t s • • • • •

A 1/5 scale integral test facility design for a pool type sodium fast reactor. Similarity assessment in heat transfer between the solid and fluid. Reasonable scale-down of the prototype sodium fast reactor. A 1-dimensional verification calculation with the scale-down model. Scale-down approach showed good agreement of overall behaviors.

a r t i c l e

i n f o

Article history: Received 20 November 2012 Received in revised form 2 June 2013 Accepted 7 June 2013

a b s t r a c t A large scale test facility design simulating a pool type sodium fast reactor was carried out on the basis of rigorous scaling approach with a plan of its installation by 2016. In particular, a similarity in heat transfer between solid and fluid were intensively discussed together with the distortion, and viable design parameters were derived. A 1-dimensional verification calculation was also conducted and showed good agreement for the important parameters. This scaling approach in this study is expected to be used in the exact reproduction of heat transfer between fluid and solid in a single phase fluid system. © 2013 Elsevier B.V. All rights reserved.

1. Introduction For an expanded utilization of nuclear energy, uranium supply and waste management issues should be addressed. A sodiumcooled fast reactor (SFR) is one of the most promising options to provide the solutions to these issues since it can make the utilization of uranium resources very efficient, and has the capability of a substantial transuranics (TRU) reduction. According to the long-term nuclear program plan approved by the Korean government, a prototype sodium-cooled fast reactor is scheduled to be constructed by 2028. To support the program plan, a large-scale sodium thermal–hydraulic test program called STELLA (Sodium Test Loop for Safety Simulation and Assessment) is being progressed by KAERI (Korea Atomic Energy Research Institute) with a plan for its installation by 2016. Since reliable decay heat removal (DHR) is one of the most important tasks in a nuclear system design, the program finally aims an integral effect test to evaluate the overall performance of the DHR system.

∗ Corresponding author. Tel.: +82 42 868 8970; fax: +82 42 861 7697. E-mail addresses: [email protected], [email protected] (J.-H. Eoh). 0029-5493/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nucengdes.2013.06.024

The reference design of the program is a prototype SFR called KALIMER (Korea Advanced LIquid MEtal Reactor), and its conceptual design has been carried out (Hahn et al., 2007). The system employs a pool-type primary heat transport system (PHTS), a twoloop intermediate heat transport system (IHTS), a steam generator system (SGS) and a decay heat removal system (DHRS). The configuration of the KALIMER heat transport system and its steady-state heat balance are shown in Figs. 1 and 2, respectively. The main components of the system consist of steam generators (SGs), intermediate heat exchangers (IHXs), mechanical sodium pumps, and several types of heat exchangers for a DHR system, such as a sodium-to-sodium decay heat exchanger (DHX), a helically-coiled sodium-to-air heat exchanger (AHX), and a finned-tube sodiumto-air heat exchanger (FHX) (Hahn et al., 2007). Auxiliary systems including gas supply and a sodium purification system are also equipped to maintain the overall sodium coolant boundary. The DHRS comprises two diverse decay heat removal loops composed of active and passive DHR paths, and both of them remove heat from the primary sodium inventory using DHXs, and reject the heat load to the environment using different types of sodium-to-air heat exchangers located on top of the reactor or auxiliary buildings (Hahn et al., 2007). DHRS provides a highly reliable heat rejection capability from the primary system in case of an unavailability of

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S.-J. Hong et al. / Nuclear Engineering and Design 265 (2013) 497–513

Fig. 1. Heat transport system in the KALIMER prototype.

Fig. 2. Heat balance of the KALIMER prototype.

S.-J. Hong et al. / Nuclear Engineering and Design 265 (2013) 497–513

the main heat transport path from the PHTS to the water/steam system via the IHTS. Each system is able to fulfill the functional requirements for decay heat removal even in case of a complete loss of a single DHR loop. For the demonstration of short- and long-term decay heat removal capability by natural circulation in the safetygrade DHRS and the PHTS, a large-scale sodium thermal–hydraulic test facility called STELLA has been designed on the basis of the prescribed design requirements for the test facility (Eoh et al., 2011). The scaled test facility should be designed in such a way as to preserve the overall system behavior and reproduce major thermal–hydraulic phenomena under conditions corresponding to the test objectives. Hence, the facility should be designed to simulate various thermal–hydraulic phenomena occurring in the reference plant system during all transient modes as closely as possible. Scenario studies with various accident conditions representing design-basis events (DBEs) have been also made for the establishment of the test scopes and conditions at different boundary and initial conditions (Eoh et al., 2011). Based on the experiments using the STELLA facility, a database for the verification of the safety and performance analysis codes will be constructed, and it will be finally used to support the design approval for the KALIMER prototype. In this study, at the first step of the STELLA program, the scientific design parameters for the STELLA facility have been obtained using proper scaling methodologies regarding the reduced-height scale. Some design restrictions imposed on the scaled components design and the scaling distortions of the prototype are discussed as well. A lot of effort was made on the discussion of the heat transfer between the fluid and solid structures. The similarity analysis in this study is based on Ishii et al. (1984, 1998). This scaling law is featured by the independent dimensional scale in flow length and flow cross-sectional area, and the velocity scale of the square root of the length scale. This scaling law has been known to have a wide and easy applicability in the design of test facilities simulating nuclear power plant systems. The hierarchy of the scaling approach in this study is composed of two parts: a topdown approach and a bottom-up approach. This is proposed by Ishii et al. (1984, 1998) and Zuber et al. (1998). Important prerequisite constrains for the design of a scaled facility (Eoh et al., 2011) are -

Length scale (lR ): 1/5. Flow area scale (aR ): 1/25 (a square of length scale). Fluid volume scale (VR ): 1/125. Prototypic decay heat is 7% of full power. Electrical heater design should be practically possible to construct.

• • • • • • •

499

Pump coastdown. Pump characteristics. Pump flow resistance (forward and backward). Heat transfer to heat structures. Break flow. Natural circulation. Heat transfer in heat exchanger.

Therefore, principal phenomena that have to be considered in a bottom-up approach are the mass and energy inventory, heat transfer between solid and fluid, pump behaviors, and multidimensional phenomena. 3. Review of sodium properties Ishii et al.’s scaling law (1984, 1998) was developed for a light water reactor. Thus, in order to apply it to SFR, the sodium properties should be reviewed first. The sodium properties and water properties are compared in Table 2 for the expected operation conditions. The property variation of sodium is far less than that of water. Thus, the assumption of a constant property in Ishii et al.’s scaling law is more valid. 4. Top-down approach 4.1. Dimensionless groups and global similarity requirements Ishii et al.’s scaling law for a single phase flow is based on following governing equations; -

Fluid continuity equation. Fluid integral momentum equation using Boussinesq assumption. Fluid energy equation for ith section. Solid heat conduction equation. Fluid-solid interface boundary condition.

Through the non-dimensionalizing process Ishii et al. (1984, 1998) derived the following dimensionless groups; R≡

Richardson Number

Friction Number

Fi ≡

gˇT0 l0 u20

 fl DH

+K

• Pressure drop and flow distribution. • Multidimensional flow phenomena: asymmetric flow, mixing, temperature distribution, local flow distribution.

i

=

 Sti ≡

Modified S tan ton Number

2. Review of important phenomena considered According to the test requirements (Eoh et al., 2011) the major concerns of the transient in KALIMER (prototype) are a PHTS total loss of flow accident (LOF, loss of low), SG loss of feedwater accident (LOHS, loss of heat sink), and PHTS pump discharge line break accident (pipe break). This report also identified the important thermal–hydraulic phenomena at every component for each transient. For the three transients in KALIMER mentioned above similar phenomena regardless of the transient were reported and can be consolidated as in Table 1. Important phenomena for each system or component can be once more rearranged into the following without regard to the system or component.



=

=

 Ti∗

Time Ratio Number

 Biot Number

Bii ≡

≡

hı ks

l0 /u0 ı2 /˛s

 =

Qsi ≡

(1)

friction inertia force

(2)

4hl0 cp u0 DH



wall convection axial convection

 =

transport time conduction time

wall convection conduction

 Heat Source Number

buoyancy inertia force

q˙  s l0 s cps u0 T0

(3)

(4)

(5)

 i

heat source = axial energy change

(6)

where cp is the specific heat; DH hydraulic diameter; f friction factor; g gravity; h heat transfer coefficient; K minor loss coefficient

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Table 1 Important phenomena identification for selected transient in KALIMER-600. System

Component

Important phenomena

Fuel

Wire wrap

Core

Subassembly

Cold and Hot Pools

Bypass flow Inlet and outlet plenums

Pressure drop due to enhanced turbulence Heat transfer enhancement Pressure drop by inlet orificing and geometry Flow reversal during transient Asymmetric flow Effect on flow mixing Asymmetric flow distribution and mixing in inlet plenum Flow mixing in outlet plenum Local flow distribution Thermal stratification Thermal inertia during transient Local temperatures at IHX, DHX inlet and along CRDL Flow split between IHX and DHX Thermal stratification Thermal inertia during transient Multidimensional flow Flow through UIS Heat transfer to coolant and guard vessel Heat transfer to concrete wall Wall heat transfer to coolant Operating characteristics Flow coastdown characteristics Pump heat Inertia of angular momentum for coastdown Location of pipe break Break flow Heat transfer in forced and natural convection modes Flow resistance Thermal inertia during natural circulation Pressure drop Pressure drop after pump trip Pump coastdown Pressure drop in tube bundle Heat transfer in tube bundle Pressure drop in tube Two-phase heat transfer Dryout of water inventory Pressure control Heat transfer by forced convection inside hot pool Heat transfer by natural convection Multidimensional effect Heat transfer and flow resistance Flow resistance and heat transfer inside tube Sodium freezing Natural circulation Flow resistance and heat transfer inside tube Sodium freezing Flow resistance and heat transfer by air (forced- & natural draft condition) Stack effect EMP failure Blower failure

Cold pool

Hot pool

Reactor Vessel and Internal Structures

Reactor vessel wall Guard vessel wall Internal structures Pump characteristics

Primary Pump

Moving parts Suction and discharge pipes Intermediate Heat Transport System (IHTS)

IHX shell- & tube-sides IHTS loop IHTS pump

Steam Generation System (SGS)

SG shell-side SG tube-side

Safety-grade decay Heat Removal System (SHRS)

SG cover gas DHX shell-side (primary sodium)

DHX tube-side (secondary sodium) Cold- and hot-legs of ADRC & PDRC Tube-side of AHX & FDHX Shell-side of AHX & FDHX Air stack EMP Blower

Table 2 Comparison of properties for sodium and water. Fluid 3

At maximum temperaturea

Sodium Water

Heat conduction (W/m K)

Sodium Water

Specific heat (J/kg K)

Sodium Water

Viscosity (N s/m2 )

Sodium Water

2.3976 × 10−4 0.7912 × 10−4

4.1338 × 10−4 5.4710 × 10−4

72.4 591.5

Prandtl Number (–)

Sodium Water

0.00456 0.9452

0.00815 3.5801

78.7 278.8

a

c

89.85 0.5116 1262 6111

915.5 988.1

Change (%)c

Density (kg/m )

b

831.6 671.2

At minimum temperatureb

83.34 0.6405 1362 4191

Maximum temperature: Sodium: 510 ◦ C (Core outlet temperature); Water: 323 ◦ C (155 bar, Core outlet temperature). Minimum temperature: Sodium: 150 ◦ C (PDRC minimum temperature); Water: 50 ◦ C (1 bar, at refueling). temperature)−(Value at maximum temperature) Change is defined by Change (%) = (Value at mimimum × 100 Reference is El-Wakil (1971). (Value at maximum temperature)

10.1 47.2 −7.24 25.2 7.9 −31.4

S.-J. Hong et al. / Nuclear Engineering and Design 265 (2013) 497–513

k; k thermal conductivity; l length; q˙  volumetric heat generation rate; T temperature; u velocity; ˛ thermal diffusivity; ˇ thermal expansion coefficient;  difference; ı conduction depth; and  density. Subscript 0 means reference section (i.e. heating section); s solid; and i ith section. For the similarity between the prototype and model, all the dimensionless groups have to meet following requirement R ≡

m =1 p

(7)

The subscripts R, m, and p are the ratio between the model and prototype, model, and prototype, respectively. A geometrical similarity requires the following relationships Li,R =

(li /l0 )m =1 (li /l0 )p

(8)

Ai,R =

(ai /a0 )m =1 (ai /a0 )p

(9)

From the similarity in Richardson number in Eq. (1), the following velocity ratio requirement is obtained u0,R =



T0,R l0,R =



l0,R

(10)

In the above equation the same fluid property and same temperature are assumed. Eq. (10) means that the model velocity is scaled to a square root of the length ratio. For the similarity in friction number of Eq. (2), the following relation should be met. Fi,R =

 fl DH

+K

 i,R

=1

(11)

501

This means that the frictional pressure drop can be compensated for by a minor loss coefficient. The time ratio number in Eq. (4) requires the following conduction depth limitation. ıi,R =



1/2 1/4

˛s,R (l0 /u0 )i,R = ˛s,R l0,R

(12)

Under the same solid property condition the conduction depth has to be scaled to a quartic root of the length ratio. However, for the model heating section uranium is not easily used and in general replaced by electrical heaters of stainless steel or nichrome. Table 3 summarizes the solid properties of the substitution material together with uranium. The substitution candidates do not have so much different properties each other, and it is approximately assumed that ks,R ≈ 1/1.9, ˛s,R ≈ 1/3. Thus, if the length ratio is 1/5, the fuel rod diameter ratio should be about 1/2.6, and a relatively thicker rod is required. The similarity requirement for heat source number in Eq. (6) yields the following guideline for the electrical heater capacity. q˙  s,R =

T0,R s,R cps,R



l0,R

=

s,R cps,R



(13)

l0,R

It is evident that the volumetric heat generation rate is affected not only by the length scale but also by solid properties and fluid temperature rise in the heating section. In general meeting the similarity of modified Stanton number and Biot number at the same time is almost impossible as discussed in Ishii et al. (1984). A detailed discussion is presented in the following section.

Table 3 Comparison of thermal properties of uranium and its substitution candidates. Material

SS ANSI 302

Properties

Ratio

Temperature, K

300

Density (kg/m3 ) at 300 K

8055

400 k (W/mK) cp (J/kg K) ˛ (m2 /s)1

SS ANSI 304

Density (kg/m3 ) at 300 K

7900

k (W/mK) cp (J/kg K) ˛ (m2 /s)1

SS ANSI 316

Density (kg/m3 ) at 300 K

8238

K (W/mK) cp (J/kg K) ˛ (m2 /s)1

SS ANSI 347

Density (kg/m3 ) at 300 K

7978

K (W/mK) cp (J/kg K) ˛ (m2 /s)1

Nichrom

Density (kg/m3 ) at 300 K

8400

K (W/mK) cp (J/kg K) ˛ (m2 /s)1

Inconel X-750

Density (kg/m3 ) at 300 K

8510

K (W/mK) cp (J/kg K) ˛ (m2 /s)1

Uranium

Density (kg/m3 ) at 300 K

19070

K (W/mK) cp (J/kg K) ˛ (m2 /s)1

Reference is Incropera et al. (1996). Thermal diffusivity is calculated using the density at 300 K.

*

17.3 512 4.19E−06 16.6 515 4.08E−06 15.2 504 3.66E−06 15.8 513 3.86E−06 14 480 3.47E−06 13.5 473 3.35E−06 29.6 125 1.24E−05

600 20 559 4.44E−06 19.8 557 4.50E−06 18.3 550 4.04E−06 18.9 559 4.24E−06 16 525 3.63E−06 17 510 3.92E−06 34 146 1.22E−05

800 22.8 585 4.84E−06 22.6 582 4.92E−06 21.3 576 4.49E−06 21.9 585 4.69E−06 21 545 4.59E−06 20.5 546 4.41E−06 38.8 176 1.16E−05

1000

400

600

800

1000

1/kR

1.71

1.70

1.70

1.73

1/(·cp )R 1/˛R

0.58 2.96

0.62 2.75

0.71 2.39

0.70 2.46

1/kR

1.78

1.72

1.72

1.73

1/(·cp )R 1/˛R

0.59 3.04

0.63 2.71

0.73 2.35

0.71 2.43

1/kR

1.95

1.86

1.82

1.81

1/(·cp )R 1/˛R

0.57 3.39

0.61 3.02

0.71 2.58

0.69 2.62

1/kR

1.87

1.80

1.77

1.78

1/(·cp )R 1/˛R

0.58 3.22

0.62 2.88

0.72 2.46

0.71 2.50

–

1/kR

2.11

2.13

1.85

–

– –

1/(·cp )R 1/˛R

0.59 3.58

0.63 3.37

0.73 2.52

– –

1/kR

2.19

2.00

1.89

1.83

1/(·cp )R 1/˛R

0.59 3.70

0.64 3.12

0.72 2.62

0.64 2.84

–

–

–

–

–

– –

– –

– –

– –

– –

25.4 606 5.20E−06 25.4 611 5.26E−06 24.2 602 4.88E−06 24.7 606 5.11E−06

24 626 4.51E−06 43.9 180 1.28E−05

502

S.-J. Hong et al. / Nuclear Engineering and Design 265 (2013) 497–513

Table 4 Coefficients of forced convective turbulent flow heat transfer coefficient for sodium or liquid metal. Reseachers

c1

c2

n

Remarks

Lyon-Martinelli (1955) Seban and Shimazaki (1950)

7.0 5.0

0.025 0.025

0.8 0.8

Constant heat flux Uniform wall temperature

Brookhaven National Laboratory (Hoe, R.J. et al., 1957, Rechards, C.L. et al., 1957) (on mercury)

4.03

0.228

0.67

Flow across rod bundles Re is based on maximum flow velocity Pr is based on film temperature

Seban (1969)

5.8

0.02

0.8

Between parallel plates Constant heat flux

Bailey (1950)

5.25

0.0188

0.8

In annulus (D2 /D1 > 1.4)

Werner et al. (1949)

For D2 /D1 < 1.4 use Seban (1969) (D2 /D1 )0.3 is multiplied to PEn

Reference is El-Wakil (1971).

4.2. Discussion on wall heat transfer similarity The modified Stanton number and Biot number similarity constrain the heat transfer coefficient by means of the geometric factors and velocity. However, this constrained heat transfer coefficient is not well matched with the heat transfer coefficient given by the Nusselt number (Nu). For a forced convective laminar flow following Nu is well known. Nu =

hDH = 4.36 k

(14)

For a turbulent flow Nu = c1 + c2 Pen

n/2

(15)

where c1 and c2 are the coefficients, and representative values are given in Table 4, and Pe is Pecklet number defined by Pe = Re · Pr

(16)

where Re is the Reynolds number and Pr is the Prandtl number defined by inertia force u0 l0 Re ≡ =  viscous force Pr ≡

cp  viscous diffusion = thermal diffusion k

(17)

(18)

According to Bejan (2004) the natural convection heat transfer coefficient for the material such as sodium whose Pr is much less than 1 is given by Nu = c1 (Ra)m (Pr)n

(19)

where Ra is Rayleigh number defined by Ra = Gr · Pr Gr =

(20)

gˇ T0 l03 (/)

2

=

buoyancy force viscous force

This is different from those that can be obtained from the similarity requirement of the modified Stanton number of Eq. (3) and Biot number of Eq. (5). This analysis is also applicable to a low velocity case of turbulent flow. For example, if Pe is 3000, Nu is approximately 15, and if Pe is 2000, Nu is about 10. This means that c1 in Eq. (15) plays a more important role than second term. Referring to section 4.3, the prototypic Pe in normal operation is about 37,500 and about 1000 is expected in transient. For the forced turbulent flow of high Pe number the ratio of the heat transfer coefficient is obtained from Eq. (15) by neglecting the constant c1 . n−1 hR = l0,R DH,R

(24)

This is also different from those that can be obtained from the similarity requirement of the modified Stanton number and Biot number. For the natural convective flow, the ratio of heat transfer coefficient is simply obtained from Eq. (19) 3m−1 3m−1 hR = T0,R l0,R = l0,R

(25)

This is also different from those that can be obtained from the similarity requirement of modified Stanton number and Biot number. As discussed above, the ratio of heat transfer coefficient for any flow condition is different from the similarity requirement of the modified Stanton number and Biot number. For a substantial check, the calculated heat transfer coefficient ratio, and St and Bi numbers are suggested in Table 5 for length scale of 1/5. Distortions in the modified Stanton number and Biot number seem inevitable. In summary, because the similarity in the time ratio number is maintained, the generated heat in the solid is all transferred to the fluid. But because of the distortion in the heat transfer coefficient the solid surface temperature may be different in model and prototype.

(21) 4.3. Reference velocity and temperature rise

The coefficients have the following ranges

0 ≤ n ≤ 0.25

The similarity requirement for the Richardson number should satisfy the velocity ratio of Eq. (10) and this should be checked. First, from the steady state energy balance equation between the heat generated in solid and the fluid heat up, the temperature rise can be obtained.

For a forced laminar flow, the ratio of the heat transfer coefficient is simply obtained from Eq. (14)

(u0 a0 ) cp T0 = q˙  s as0 l0

0.32 ≤ c1 ≤ 0.8 0.2 ≤ m ≤ 0.25

hR =

kR 1 = DH,R DH,R

(22)

(23)

or T0 =

q˙  s l0 u0 cp

a  s0

a0

(26)

where a0 is the flow area and as is the heat conductor cross sectional area. Inserting the above result into integral momentum equation

S.-J. Hong et al. / Nuclear Engineering and Design 265 (2013) 497–513

503

Table 5 Calculation of heat transfer coefficient ratio, and St and Bi numbers for various flow conditions. Flow conditions

a St number  ratio

Actual heat transfer coefficient ratioa hR hR =

Laminar (Forced) Turbulent (Forced, n = 0.8) Natural convection (m = 1/4)

hR =

StR =

1 DH,R l

1/2 0,R

DH,R

=

l1.2

0,R

1/1.38

DH,R −1/4

3m−1 hR = l0,R = l0,R

1/0.669

DH,R

l1.7

= =

ks

R

1/4 0,R 1/2 DH,R R (6n+1)/4 l l1.45 0,R 0,R = 1/2 1/2 (ks s cp ) D (ks s cp ) D R R H,R R R H,R 3m−3/4 l 0,R 1 = 1/2 1/2 (ks s cp ) (ks s cp ) R R R R

l

11.18

D2

H,R (3n+1)/2 l 0,R D2 H,R 3m−1/2 l 0,R

 hı 

R

l

1/0.2

(3/2)n 0,R

4hl0 cp u0 DH

Bi number ratioa BR =

0,R

1.621

D2

H,R 1/4 l 0,R

3.344

DH,R

3.344

(ks s cp )

0.485 1

a Hydraulic diameter ratio is assumed to be length ratio, and same properties in fluid and solid are also assume for the simple calculation; Assumption of same hydraulic diameter ratio is valid to circular pipe if area ratio is square of length ratio. Fuel sub-channel has different hydraulic diameter ratio and above calculation is not valid anymore.

reference velocity is easily obtained (See Ishii et al., 1984 for a detailed derivation).

u0 =

⎧ ⎪ ⎪ ⎨

ˇ(q˙  s l0 /cp )lh (as0 /a0 )

⎫1/3 ⎪ ⎪ ⎬

2 ⎪ ⎪ ⎪ ⎩ (1/(2g)) (Fi /Ai ) ⎪ ⎭

=

⎧ ⎪ ⎪ ⎨

ˇTu0 lh

⎫1/3 ⎪ ⎪ ⎬

2 ⎪ ⎪ ⎪ ⎩ (1/(2g)) (Fi /Ai ) ⎪ ⎭

i

following non-dimensionalizing parameters, the above equation can be arranged into a dimensionless form. l0 0 ≡ , u0 ˙ ∗in ≡ m

i

(27)

This is the same as the discussion by Ishii et al. (1984). Using this equation the velocity ratio can be calculated and the results are the same to Eq. (10) under the same fluid condition and friction number similarity In order to get the physical insight on the flow the actual subchannel flow condition in KALIMER can be estimated using the work of Lee et al. (2007). - Hydraulic diameter: 9.25 mm (with fuel rod diameter of 7.4 mm, pitch of 10.57 mm, and triangular arrangement). - Maximum flow expected in fuel channel: 27.34 kg/s. - Minimum flow expected in fuel channel: 12.43 kg/s. The maximum flow is the case in which the core flow flows only in the middle core and inner core, and the minimum flow is the case in which the core flow flows through the entire core including reflector. Thus, the actual flow lies between the two values (Eoh et al., 2011, Fig. 2-2)). The corresponding Re and Pe numbers are 27.34 kg/s ˙ m ≈ 1.20 × 107 = (/4)DH (3.1458 × 10−4 N · s/m2 )(/4)(9.25 mm) 12.43 kg/s ˙ m ≈ 5.44 × 106 Remin = = (/4)DH (3.1458 × 10−4 N · s/m2 )(/4)(9.25 mm) 4 Pemax = Re · Pr ≈ 1.66 × 10 Pemin = Re · Pr ≈ 7.51 × 103 Peavg = 1.21 × 104

˙ in m = ˙0 m



 

≡



0

u0



out

u

a0

out

0

,

0

 u a  in in in

˙ out m = ˙0 m

˙ ∗out ≡ m

 ∗

t t ≡ , 0 ∗

(29)

,

a

out

u0



a0

The dimensionless equation is

  V  d  ∗  0 dt ∗

˙ 0 0 m

=

˙ ∗in − m

˙ ∗out m

(30)

where V is a system volume.  means volume average. For the   above equation to have the same solution, ∗ (t ∗ ) at homologous dimensionless time t* , all the coefficients should be same each other between the prototype and model.

 V  0 ˙ 0 0 m

=1

(31)

R

˙ ∗in )R = 1 (m

(32)

˙ ∗out )R = 1 (m

(33)

Eq. (31) is self-evident. Eqs. (32) and (33) indicates that all the inflow and outflow should be scaled to the reference flow scale. Under the no-choked flow condition the velocity ratio follows the reference velocity ratio and the flow area also has to follow the reference area scale. It is a very easy constrain.

Remax =

5.2. Energy inventory Energy conservation in the entire system can be expressed as;

dE ˙ in hin − ˙ out hout , = q˙ − w˙ + m m dt

As a consequence Table 6 presents a summary of the important global scaling factors.

where E is the total energy of the system, q˙ heat generation rate, w˙ shaft work, and h specific enthalpy. Let us introduce the following non-dimensionalizing parameters



5. Bottom-up approach

h∗ 

 ∗

  h t  , t ∗ ≡ , q˙ ∗ ≡ ≡ 

˙ ∗in h∗in m

dM ˙ in − ˙ out = m m dt

0

h0 0

5.1. Mass inventory and boundary flow Mass conservation in entire system can be expressed as;

(34)

q˙ w˙ , w˙ ∗ ≡ ˙ 0 h0 ˙ 0 h0 m m

(35)

˙ h ˙ out hout m m ˙ ∗out h∗out ≡ ≡ in in , m ˙ 0 h0 ˙ 0 h0 m m

The final dimensionless form is

(28)

˙ mass flowrate. where M is total mass of the system, t time, and m The subscript ‘in’ indicates inflow and ‘out’ outflow. Using the

 

V h0 0

 

˙ 0 h0 0 m

d h∗ ∗ dt ∗



= q˙ ∗ − w˙ ∗ +

˙ ∗in h∗in − m

˙ ∗out h∗out m (36)

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S.-J. Hong et al. / Nuclear Engineering and Design 265 (2013) 497–513

Table 6 Important global scaling factors. 1/2

Parameter

Scaling law

Values (T0,R = 1)

Basis

Length ratio Area ratio Volume ratio

l0,R 2 l0,R 3 l0,R

1/5 1/25 1/125

Test requirement Test requirement Test requirement

1/25

Length ratio and shape

1/2.2

Richardson number

1/2.2

Length ratio and time ratio

1/1.5

Time ratio number (Same solid material)

1/0.45

Heat source number

1/55.9

Heat source number and volume ratio

Hydraulic diameter ratio Velocity ratio

0,R

R

= l0,R 1/2 1/2

T0,R l0,R 1/2 0,R 1/2 T 0,R

l

Time ratio Wall thickness ratio Power density ratio Power ratio (heat transfer between fluid and solid)

1/2 1/4 ˛s,R l0,R −1/2 l0,R 5/2 l0,R



St numbera

4hl0 cp u0 DH

 hı 

Bi number ratioa

a

l2

ks

R

=

 R

=

1/2 0,R

hR l

DH,R

1/4 0,R 1/2 (ks s cps ) R

hR l

11.2

Forced laminar

1.62 3.34

Forced turbulent Natural convection

Actual Nu number

3.34

Forced laminar

0.49 1

Forced turbulent Natural convection

Actual Nu number

In this calculation hydraulic diameter ratio is assumed to be length ratio. See Table 5.

5.3. Heat transfer between fluid and solid In order to have the same solution in both prototype and model all the coefficients should be the same.

 

V h0 0

 =1

˙ 0 h0 0 m

(37)

R

A simple lumped model can be setup for the heat transfer simulation between a solid and fluid (Incropera et al., 1996).



q˙ s = Vs s cps

  d T dt

+ as h(Ts − Tf )

(43)

(q˙ )R = 1

(38)

where q˙ s is the heat generation rate in the solid, as is the heat transfer area, Ts is the solid temperature, and Tf is the fluid temperature. Subscript s indicates a solid. In order to make the above equation dimensionless form, the following parameters are introduced.

(w˙ ∗ )R = 1

(39)

 

∗

˙ ∗in h∗in )R = 1 (m ˙ ∗out h∗out )R (m

(41)

Eq. (37) is automatically met under the same fluid property conditions. Eqs. (38) and (39) show that the heat addition and shaft work should be scaled to the energy flow scale, or to the mass flow scale under the same fluid property conditions. Eqs. (40) and (41) show that the boundary energy flow is to be scaled according to the reference energy flow scale. If the same fluid property conditions are kept in the prototype and model, such requirements are easily met if only the mass inventory similarity is conserved. Reconsidering Eq. (39), the following equation can be derived. 1/2

˙ R = a0,R l0,R q˙ R = w˙ R = m

(42)

When calculating the heat addition rate using Eq. (13) of the volumetric heat generation ratio, it should be carefully noted that the electrical heater should be designed to have the heat addition to the fluid follow Eq. (42) rather than the heat generation rate in solid. Some of the heat generated in solid is used to increase the solid temperature and the other is transferred to the fluid in unsteady condition. In order to match the transient time in a solid and fluid the time ratio number should be conserved. The energy inventory scaling analysis shows that the heat which is transferred to the fluid has to follow Eq. (42).

Tout − T

Tout − Tin

 

=

Tout − T

,

T0

t∗ ≡

t , 0

q˙ ∗s ≡

q˙ s ˙ 0 h0 m

(44)

Eq. (43) then becomes

(40)

=1

 

≡



q˙ ∗s



 

Vs s cps T0 d

+ 0 dt ∗ ˙ 0 h0 m

=

as h(Ts − Tf ) ˙ 0 h0 m

(45)

The right-hand side of above equation is the ratio of the heat transfer between the solid and fluid to the reference energy flow scale. This term is most important, and the ratio should have the same solution both in the prototype and model in order to meet the requirement discussed in the energy inventory. Thus, each term of left-hand side has to meet the following relation. q˙ ∗s,R = 1





(46)



 

Vs s cps T0 d

0 dt ∗ ˙ 0 h0 m

=1

(47)

R

These criteria will be applied to the electrical heater of a circular rod and to a general plate of a slab shape. 5.3.1. Fuel rod (electrical heater) Electrical heat is composed of several materials such as stainless steel sheath, nichrome heating element, insulator, and manganese dioxide core, and so on. According to Hong et al. (2012) the equivalent properties of electrical heat are given by • Heating section

S.-J. Hong et al. / Nuclear Engineering and Design 265 (2013) 497–513

505

5107 kg/m3 0.966 kJ/kg K 12.95 W/m K

Density: Specific heat: Heat conductivity:

• Non-heating section 4829 kg/m3 0.928 kJ/kg K 11.03 W/m K

Density: Specific heat: Heat conductivity:

These properties will be used for further analysis. From Eq. (46) the heater capacity scale can be obtained. q˙ ∗s,R = 1 (48)

or ˙ 0,R h0,R = q˙ s,R = m

1/2 (a0,R l0,R )

≈ 1/55.9

This means the heater capacity scale has to follow the mass flowrate scale under the same fluid property conditions. Arranging Eq. (47), the following solid volume constrain is obtained.



Vs,R =

˙ 0,R h0,R / s cps m

 

(d





R 0,R /dt ∗ ) R

/T0,R

=



 

s cps

V0,R



 

R

(d /dt)

(49) R

In the above equation, (d /dt ∗ ) = 1 is easily obtained if the R dimensionless heat conduction equation has the same solution, which is already realized because the time ratio number and heat source numbers are conserved. That is,



ıi,R =

q˙  s,R =

˛s,R

l 

1/2 1/4

0

u0

i,R

T0,R s,R cps,R



l0,R

= ˛s,R l0,R ≈

=

1 3.225

(50)

s,R cps,R



(51)

l0,R

Eq. (50) constrains the diameter of the heater rod. The prototypic rod diameter is 7.4 mm(Song, 2011), and thus model rod diameter is around 2.3 mm. Eq. (51) can also be further developed.



q˙ s,R =

q˙  s,R Vs0,R

=

s cps





R

l0,R



s cps

V0,R



 

R

1/2

(d /dt ∗ )

= a0,R l0,R R

1 = 55.9

(52)

This is identical to Eq. (42) and does not conflict with any other constrains that are already imposed. Because the prototypic power is 108.4 MW which is 7% of full power, the required model power is 1932 kW. Here, reviewing Eq. (49) again, the following solid volume constrain is obtained. Vs,R =



V0,R s cps

 ≈ R

1 223.2

(53)

This means that the total rod number in the model should be reduced to 1/4.25 of that in the prototype. If the number of assemblies is conserved (actually no condition is found to constrain the number of assemblies) the number of rods per assembly should be reduced to 1/4.25. Referring to Fig. 3, the rod number in an assembly is

(54)

nrod/ass = (m + 2m − 2)(2m − 2 − m + 1) + (2m − 1)

The total prototypic fuel volume is calculated as follow Vs,core =

 2 lrod nass nrod/ass drod 4

where nass is the number of assemblies in the core, and nrod/ass is the number of rods per assembly. From Eqs. (50), (53), and (54) the ratio of rod number in the core is calculated. 2 Vs,core,R = (nass nrod/ass )R drod,R lrod,R =



V0,R s cps

 R

or (nass nrod/ass )R =

(55)



s cps

3/2

V0,R



1/2 1/4 2

R

lrod,R (˛s,R l0,R )

=

l0,R

ks,R

1 ≈ 4.25

Fig. 3. Fuel arrangement.

= 3m2 − 3m + 1,

(56)

where m is the rod number in each side line in the assembly (Fig. 3 (a)). The prototypic rod number in a side line is 10 and the total rod number is 271 (Song, 2011). Under the same assembly number in the model, the model rod number in a side line should be 2.352. This means that the rode number in a side line should be 2 or 3, and 2 is more appropriate considering pitch ratio which will be discussed at the end of this sub-section. This result has a defect that there is very large error in total rod number. The another way is that the total rod number is reduced to 1/4.25 with a rearranging

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S.-J. Hong et al. / Nuclear Engineering and Design 265 (2013) 497–513

of the assembly wrappers. According to Song, H. (2011) inner core has 151 assemblies, and the outer core has 174 (Fig. 3 (b)). Thus the model rod numbers in each section should be Inner Core : 151 × 271 × 1/4.25 9626.025 ≈ 9626 Outer Core : 174 × 271 × 1/4.25 11092.241 ≈ 11092

(57)

1/4

1.7/2

Turbulent : DH,R = l0,R

1 1.495 ≈

1 3.928

(58)

If the turbulent flow is too slow the resultant hydraulic diameter ratio then becomes the same as that of a laminar flow because the effect of the Pe number becomes smaller. Forced convection is assumed because the local heat transfer is governed by forced convection rather than global natural circulation as mentioned in Ishii et al. (1984). Under such hydraulic diameter ratios the Biot number ratios are calculated as follows. Laminar : BiR =

hR ıR ıR = ≈ 1.22 ks,R ks,R DH,R

Turbulent : BiR =

1.2 ıR l0,R hR ıR = ≈ 0.464 ks,R ks,R DH,R

(59)

Thus, if the flow is so slow that the flow is laminar or the effect of Pe is small in a turbulent flow, the Biot number is approximately conserved. As a final step, using the laminar flow condition the rod pitch (p) ratio of triangular arrangement in Fig. 3 can be calculated (Prototypic pitch is 8.9 mm (Song, 2011)). DH =

(61)

or 3/2 l0,R

Thus, since the prototypic material is SS ANSI 316, a candidate alternative material can be listed as follows (Incropera et al., 1996, Table A.3). Cement mortar : ˛s = 4.963 × 10−7 m2 /s, Brick : ˛s = 4.491 × 10−7 m2 /s,

ks = 0.72 W/m · K

ks = 0.72 W/m · K

It is very difficult to select such a material because of its strength as a structure. Another alternative is a compound of the above material and metal. However, it is still a very expensive way. Moreover, the above material induces a severe distortion in the Biot number because ks,R ≈ 125.4 and resultantly BiR ≈ 75. It is not so desirable modeling. Let us turn our interest to the role of a solid that does not have heat source. Actually heat structures that do not have a heat source are expected to play just a role of flow guides rather than the heat source or sink. In the following sub-section, the effect of such heat structures as a heat source is evaluated. 5.3.3. Distortion evaluation of non-heat source structure In this section the effect of a non-heat source structure is evaluated except the outer most wall because this wall is easy to thicken. According to chapter 3 of Lee et al. (2007) and Eoh et al. (2011) the core outlet sodium temperature in transient changes from 783 K to 650 K at 300 s and the core inlet temperature remains nearly constant at 628 K or rises to 650 K. Thus, an overall 60 K change was assumed. During the temperature drop of 60 K, the heat is transferred from solid to fluid. This heat should be calculated. The total mass of prototypic reactor system except the containment vessel and reactor vessel is 878 ton of SS ANSI 316. Thus, the total transferred heat is Q1 = Mcp T = (878 × 103 kg)(550 J/kg K)(60 K) = 2.897 × 107 kJ (62)

√ 2 ] 4[( 3/4)p2 − (/8)drod drod

Thus, √ 2 ) =D (2 3p2 − drod H,R drod,R R or

1/2 1/4

ıi,R = ˛s,R l0,R = l0R ˛s,R =

Through the above analysis, the flow ratio and heat addition ratio are conserved, and the temperature difference from a reference point in the heat structure is conserved (the target heat conduction equation for solution is not the dimensional form but dimensionless one!). In order to conserve the absolute solid temperature, the modified Stanton number and the Biot number should be conserved. First, the modified St is considered to obtain the hydraulic diameter ratio. Let StR = 1, the following hydraulic diameter ratio is then obtained depending on the flow regime (See Table 5 for actual heat transfer coefficient ratio). Laminar : DH,R = l0,R ≈

materials should be sought. From Eq. (12), the following thermal diffusivity requirement can be derived.



√ 1 2 2 )p + (drod )m } ≈ 3.302 mm √ {DH,R drod,R (2 3p2 − drod 2 3 1 pR ≈ 2.695 (60)

pm =

A slow flow can be justified in the late phase of the transient as discussed in section 4.3. 5.3.2. Slab (no heat source) As shown in Table 6 if the same solid material is used in the model the wall thickness increases compared with a fluid passage, and this can distort the shape of the flow passages and the overall shape of model reactor except the most outer wall. To conserve a similar shape it is desirable to design the wall thickness ratio to be the length ratio (a square root of flow area ratio). And alternative

If setting the wall thickness ratio at 1/5 instead of 1/1.5 only about 30% of the structure that are required for strict similarity is constructed. 70% of the heat addition is omitted. Thus, the heat not simulated in model is Q1 × 70% = 2.028 × 107 kJ

(63)

Decay heat until 300 s also can be calculated using Lee et al. (2007) as 3.35×107 kJ. Comparing this value to the result of Eq. (63), the heat that does not simulated in the model is considerable. However, according to the test requirement (Eoh, J.H., 2011) the initial power in the model is 7% of full power, which is expected after 50 s in the prototypic transient. Thus, the temperature drop after this time is very small. Thus, the effect of heat transfer from the heat structure is thought to be negligible, and it is reasonable to regards the structure as just a flow guide. 5.4. Pressure drop, flow distribution, and flow resistance A pressure drop similarity is obtained if only the friction number is conserved, which was already discussed in section 3. Also, the flow distribution by a multi-dimensional effect is discussed in subsection 5.6.

S.-J. Hong et al. / Nuclear Engineering and Design 265 (2013) 497–513 Table 7 Requirement of pump scaling and scaling ratio.

5.5. Pump behaviors According to White (1994), the geometrical similarity with a homologous curve as well as three non-dimensional parameters such as the specific velocity, specific flow, and specific head that determine the characteristics of the pump should be conserved between the prototype and scaled model to preserve the similarity of pump performance. The specific velocity is expressed as Ns =

NQ 1/2 H 3/4

Q Nd3

(65)

where Qs and d are the specific flow and impeller diameter, respectively. Also, the following equation represents the specific head as

Hs =

g H N 2 d2

(66)

where Hs is the specific head. Since the head ratio (HR ) and impeller diameter ratio (dR ) are same as the length ratio (l0R ) and 1/2 square root of the area ratio (a0R ), respectively, the rotational speed ratio (NR ) is obtained from Eq. (66) as −1/2 1/2

NR = a0,R l0,R

(67)

Combining Eq. (65) with Eq. (67), the flowrate ratio is expressed as 1/2

QR = a0,R l0,R

(68)

On the other hand, the torque, inertia and power between the prototype and model should also be preserved to preserve the characteristics of a pump coastdown. Eq. (69) represents the power as P = Q · H ⇔ ω · T

(69)

where ω is the angular speed, and T is the torque. The relation between the inertia and torque is obtained from Eq. (70) as I

 dω  dt

=T

(70)

The power ratio (PR ) is obtained from Eq. (69) as 3/2

PR = a0,R l0,R

(71)

Since the angular speed ratio (ωR ) is the same as the rational speed ratio (NR ), the torque ratio is obtained from Eq. (69) as 3/2

TR = a0,R l0,R

(72)

Combining Eq. (70) and Eq. (72), the inertia ratio is represented as IR = a20,R l0,R

Parameter

Requirement of pump scaling

Scaling ratio

Head (HR )

l0,R

1/5

Flowrate (QR )

a0,R l0,R

1/55.9

Rotational speed (NR )

a0,R l0,R

1/0.45

Power (PR )

a0,R l0,R

1/279.5

Torque (TR ) Inertia (IR )

a0,R l0,R a20,R l0,R

1/625 1/3125

1/2

−1/2 1/2 3/2

3/2

(64)

where Ns , N, Q, and H are the specific velocity, rotational speed, flow, and head, respectively. Also, the following equation represents the specific flow as; Qs =

507

(73)

Table 7 shows the requirement of pump scaling for a single phase flow and the scaling ratio for the model. It is seen in Table 7 that the model pump needs a 2.2-times faster rotational speed than the prototypic pump to conserve the specific velocity even though the size of the pump in the model is smaller with the geometrical scaling ratio than that in the prototype.

5.6. Multi-dimensional flow Scaling for a multi-dimensional flow has not been broadly studied yet. Hong et al.’s (2009) approach seems useful in this study because they deal with a single phase water flow. Their approach is based on the following governing equations. ∂ + ∇ · (u) = 0 ∂t

 a

∂u + u∇ · u ∂t

(74)

 = −∇ p − gk + ∇ 2 u

∂(cp T ) + (u · ∇ )(cp T ) = ∇ · (k∇ T ) + ˚ ∂t

(75)

(76)

According to Hong et al. (2009) the velocity scale is reduced to a square root of the length scale from the similarity of Richardson number, which is identical to Ishii et al.’s approach and this study. Therefore if the geometrical similarity is kept, the multidimensional flow phenomena are expected to be conserved. The validation of this multi-dimensional behavior will be discussed in Part II of these paper series (Park et al., 2012). 5.7. Heat exchanger A total of five sodium-to-sodium and sodium-to-air heat exchangers are considered for the scaling design of the STELLA facility, which are IHX, DHX, AHX, FHX, and UHX. The UHX is an ultimate heat exchanger used to simulate a steam generator in the KALIMER prototype, which is composed of a finned-tube sodiumto-air heat exchanger to provide enough heat sink capability to make the system heat balance and adequate boundary conditions. The capacity of the single UHX unit is basically scaled from the prototype SG by considering a forced-draft air cooling mechanism instead of a water/steam cooling process in the prototype. The key design parameters and a schematic of the UHX unit are provided in Table 8 and Fig. 4. Based on the global scaling criteria shown in Table 6, heat exchangers of the STELLA facility have been designed to preserve similarities of heat transfer rate to the prototype according to the integral scaling criteria of 1/55.9. Thus heat capacities of each heat exchanger and corresponding pressure drops are properly scaled down complying with the specified scaling criteria. The scaling ratio of the pressure drops, flow rates and heat capacities are also maintained as the integral scaling criteria. All scaled heat exchangers of the test facility have the same configurations and tube materials as the prototype, and identical heat transfer tube diameters (ID/OD) to the prototype were also employed to verify the overall performance of each heat exchanger unit. The design parameters of the scaled heat exchangers are listed in Table 9. As shown in Table 9, similarities of the parameters such as {UA}, heat transfer tube lengths, and heat transfer surface areas for each model heat exchanger are reasonably preserved reflecting the ideal scale ratio. The major dimensionless numbers such as Richardson,

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S.-J. Hong et al. / Nuclear Engineering and Design 265 (2013) 497–513

Fig. 4. Schematic of STELLA UHX unit.

Table 8 STELLA UHX design parameters. Design parameters

Design value

UHX

No. of unit Therma duty (MWt) No. of tubes Tube arrangement Pitch-to-diameter ratio Tube material Bare tube OD/ID (mm) Thickness (mm) Finned tube length (Total, m) Overall unit size *(W × D × H, m)

2 13.9 138 4-pass serpentine tubes PL = 2.05 & PT = 2.5 STS316 34.0/30.7 1.65 14.044 4.413 × 3.849 × 4.825

Shell-side

Flow rate (kg/s) Inlet temp (◦ C) Outlet temp (◦ C) Pressure drop (kPa)

42.9 20 347 2.473

Tube-side (Sodium) Flow rate (kg/s) Inlet temp (◦ C) Outlet temp (◦ C) Pressure drop (kPa)

54.97 502 305 3.734

exchanger design considerations regarding the reduced-height scale of the heat exchanger unit should be provided to avoid such kind of large scaling distortions in the natural circulation flow regime. For the air-side of the AHX and FHX, the scaling distortions of the Richardson number, representing the balance between buoyancy and inertia, also reaches around 80–98% from unity. This may come from geometrical similarities employing real dimensions and/or configurations of heat transfer tubes as mentioned above. To this end, it was found that more reasonable scaling approaches based on the mathematical identity of analogous physical systems for naturally circulated sodium and air flow is necessary to reduce the scaling distortions. 6. Design parameters

friction, modified Stanton, Biot and time ratio numbers have been considered in the local scaling processes, which were quantitatively evaluated to understand the scaling distortions for the scaled heat exchanger design parameters obtained in this work. For the sodium-to-sodium heat exchanger designs for IHX and DHX, the dimensionless numbers representing the characteristics of natural circulation of sodium flow show large scaling distortions of around 20–35% for the Richardson numbers, and around 60% for the modified Stanton numbers. Hence, more appropriate heat

Based on the intensive discussion in sections 4 and 5 the important constrains were fixed. To conserve multi-dimensional phenomena the geometrical similarity should be conserved to the extent possible and resultantly, the wall thickness should be scaled to length ratio rather than original ratio except for the fuel rods. Under this constrain some important design parameters are presented in Table 10 and Table 11. The design of the core was discussed in section 5.3. 7. Sample calculation for validation assessment The scaling approach used in this study was assessed using the MARS-LMR code which is a modified version of the MARS code (KAERI, 2004) for an SFR system analysis and was developed by

Table 9 Design parameters for scaled heat exchangers. ∗ : Ratio =

Model Prototype

Heat transfer rate, Q (kWt) U (W/m2 /K) Heat transfer Area (m2 ) {UA} (W/K) TLMTD (◦ C) Tube Length (m) Tube bundle height (m) Number of tubes (EA) Flowrate (tube-side) (kg/s) Flowrate (shell-side) (kg/s) Velocity (tube-side) (m/s) Velocity (shell-side) (m/s)

Ideal scale IHX

1/55.9 √ 1/ 5 1/25 1/55.9 1/1 1/5√ 1/ 5 – 1/55.9 1/55.9 √ 1/√5 1/ 5

DHX

AHX

FHX

[P]

[M]

Ratio* [P]

[M]

Ratio* [P]

[M]

Ratio* [P]

[M]

Ratio*

387470 9700 1571 15242 25.6 4.80 N/A 6558 1536.5 2091.5 1.889 1.284

6932 7665 35.61 273 25.6 0.96 N/A 742 27.5 37.4 0.299 0.203

0.018 0.790 0.023 0.018 1.000 0.200 N/A 0.113 0.018 0.018 0.158 0.158

161 5578 0.57 3.18 50.8 0.35 N/A 24 0.57 0.68 0.10 0.06

0.018 0.926 0.019 0.018 1.002 0.202 N/A 0.096 0.018 0.018 0.188 0.185

161 27.4 34.65 0.95 170.0 13.52 2.38 24 0.57 0.55 0.036 2.2

0.018 0.405 0.044 0.018 0.998 0.564 0.568 0.079 0.018 0.018 0.229 0.218

161 12.64 75.41 0.95 170.0 2.78 1.819 24 0.57 0.55 0.036 4.311

0.018 0.520 0.035 0.019 0.998 0.198 0.425 0.174 0.018 0.018 0.104 0.488

9000 6025 29.5 178 50.7 1.732 N/A 250 31.6 37.8 0.533 0.324

9000 67.6 781.2 52.94 170.3 23.98 4.19 305 31.6 30.7 0.157 10.1

9000 24.3 2185.5 50.14 170.3 14.013 4.283 138 31.6 30.7 0.347 8.841

S.-J. Hong et al. / Nuclear Engineering and Design 265 (2013) 497–513

509

Table 10 Design parameters for reactor vessel. Structures

Reactor head Reactor vessel Containment vessel Core Core support Inlet plenum Core shield Flow guide Support barrel Separation plate Reactor baffle Former ring Insulation plates

Prototype

Model

Scale

Remarks

Outer dia. (cm)

Thickness (cm)

Outer dia. (cm)

Thickness (cm)

Outer dia.

Thickness

1250 1200 1245 497.4

50 5 2.5 –

250.0 240.0 249.0 99.5

33.3 3.3 – –

(1/5) (1/5) (1/5) (1/5)

(1/1.5) (1/1.5) – –

Time ratio number Time ratio number – –

15

112.0 132.0

3.0

(1/5) (1/5)

(1/5)

Multi-dimensional flow

10 5 5 5 5 2.5 10 3

112.0 106.8 110.0 112.0 236.0 236.0 106.8 238.0

2.0 1.0 1.0 1.0 1.0 0.5 2.0 0.6

(1/5) (1/5) (1/5) (1/5) (1/5) (1/5) (1/5) (1/5)

(1/5) (1/5) (1/5) (1/5) (1/5) (1/5) (1/5) (1/5)

Multi-dimensional flow Multi-dimensional flow – Multi-dimensional flow Multi-dimensional flow Multi-dimensional flow Multi-dimensional flow Multi-dimensional flow

50

114.0 87.0

10.0

(1/5) (1/5)

(1/5)

Multi-dimensional flow

560(t) 660(b) 560 534 550 560 1180 1180 534 1190

Rotating plugs

570 435

UIS

328

2.5 5

65.6

0.5 1.0

(1/5)

(1/5) (1/5)

Multi-dimensional flow

Inlet pipes Core catcher

72.6 360

1.3 –

14.5 72.0

0.26 –

(1/5) (1/5)

(1/5) –

Multi-dimensional flow –

Pump barrels

260(t) 280(b)

2.5

52.0 56.0

0.5

(1/5) (1/5)

(1/5)

Multi-dimensional flow

t: top, b: bottom.

Table 11 Design parameters of elevation for reactor vessel. Location

Prototype Elevation (m)

Model Elevation (m)

Scale Elevation

Remarks

Top head Lower shield Free surface at hot pool Free surface at cold pool IHX inlet top Core top Pump impeller Fuel slug top Pump outer cylinder Upper plate Lower plate RV out wall

0.0 1.2 2.5 6.0 6.5 9.9 10.0 12.2 13.5 14.1 15.2 17.0

0.00 0.24 0.50 1.20 1.30 1.98 2.00 2.44 2.70 2.82 3.04 3.40

(1/5) (1/5) (1/5) (1/5) (1/5) (1/5) (1/5) (1/5) (1/5) (1/5) (1/5) (1/5)

Length ratio Length ratio Length ratio Length ratio Length ratio Length ratio Length ratio Length ratio Length ratio Length ratio Length ratio Length ratio

IHX: Intermediate Heat Exchanger; RV: reactor vessel.

KAERI. The MARS-LMR nodalization model shown in Fig. 5 (Ha et al., 2010) was scaled down with the global and local scaling ratio shown in sections 4 and 5. Table 12 shows the major parameters of the model at a steady state condition. To preserve the same

temperature difference between the core inlet and outlet in the model as the prototype at 100% scaled power (full power), the scaled core inlet flowrate at 100% scaled power was used. It can be seen in Table 12 that the target values scaled from the prototype

Table 12 Comparison of major parameters at a steady state condition. Parameters

Prototype

Target value of model

Scaling ratio

Calculation of model

Error (%)

Core thermal power (MWt) Core inlet temperature (◦ C) Core outlet temperature (◦ C) Core  T (◦ C) PHTS circulation flowrate (kg/s) IHX shell-side inlet temperature (◦ C) IHX shell-side outlet temperature (◦ C) IHX tube-side inlet temperature (◦ C) IHX tube-side outlet temperature (◦ C) IHTS total flowrate (kg/s) SG inlet temperature (◦ C) SG outlet temperature (◦ C) 1 IHX heat removal rate (MW) 1 SG heat removal rate (MW)

1548.2 365.0 510.0 145.0 8366.1 509.8 365.0 305.4 503.1 6146.0 502.0 305.0 387.475 776.7

27.7 365.0 510.0 145.0 149.7 509.8 365.0 305.4 503.1 109.9 502.0 305.0 6.932 13.89

1/55.9 1/1 1/1 1/1 1/55.9 1/1 1/1 1/1 1/1 1/55.9 1/1 1/1 1/55.9 1/55.9

27.7* 361.24 508.63 147.39 147.78 505.71 361.28 309.59 501.81 112.77 500.74 309.45 6.904 13.79

0.0 1.03 0.27 −1.65 1.28 0.80 1.02 −1.37 0.26 −2.61 0.25 −1.46 0.40 0.72

*

This power on scale model is based on full power.

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Fig. 5. Nodalization of MARS-LMR for Model and Prototype.

Table 13 Sequence of events for LOF in initiation phase. Events

Prototype (s)

Model (s)

All PHTS pump failure Reactor scram Loss of offsite power Turbine trip Feedwater trip IHTS pump trip Air damper fully open

0 – Reactor scram + 5 s Loss of offsite power + 0 s Loss of offsite power + 0 s Loss of offsite power + 0 s Loss of offsite power + 0 s

0 – Reactor scram + 2.2 s Loss of offsite power + 0 s Loss of offsite power + 0 s Loss of offsite power + 0 s Loss of offsite power + 0 s

were reasonably simulated within a ±1% error range. A full power simulation may be a severer condition than a 7% power level in terms of distortions in heat transfer between a solid and fluid as discussed in previous sections, but the calculation results in the following show good agreement between prototype and model. This means the period during which the power level is between 100% and 7% is relatively short and this period does not play a fatal

Remarks PN /QN > 1.214 Time scale ratio = 1/2.2

role in the distortion of a heat transfer between a fluid and solid against entire transient. On the other hand, it is noted that since the stored energy in the fuel is released into the coolant during the transient from the 100% power to 7% power after the reactor scram until the fuel temperature reaches the coolant temperature, this stored energy released from the fuel rods should be properly scaled and added in the scaled model power when the simulation

Table 14 Fuel rod model used in sample verification calculation. Prototype

Model

Scaling ratio





Material

Uranium

Electric heater

–

Pin outer diameter

7.4 mm

2.3 mm

Pin pitch

8.9 mm

3.5 mm

1 drod,R = ˛s,R l0,R ≈ 3.2  √ 2 (2 3p2 − drod )R = DH,R drod,R ≈

Heated section length

940.7 mm

188.1 mm

l0,R =

Rod heat transfer area

0.0219 m2

0.00136 m2

Ah,R = drod,R l0,R =

1/2 1/4



 1 5



1 16



1 2.54



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Fig. 6. Power curve for LOF generated from prototype.

of scaled model starts from 7% power. The following are the calculation results and discussions. A transient capability of the scaling approach was assessed for the PHTS total Loss of Flow (LOF) by an all PHTS pump failure. As shown in Table 13, which describes the sequence of events for the LOF in transient initiation phase, the accident is initiated with all PHTS pump failure at 10 s. The reactor scram occurs at a PHTS low flow signal in which the ratio of normalized reactor power (PN ) to normalized core inlet flow (QN ) is larger than 1.214. After 5 s from the reactor scram in prototype, the turbine, feedwater and IHTS pumps are tripped with a loss of offsite power. At the same time, the air dampers in AHXs are fully opened. It should be noted that the model used the electric heater for the fuel rod (core) simulation with the derived scientific scaling ratios shown in Table 14. Fig. 6 shows a power curve for the LOF generated from the prototype based on the point kinetics model. The power curve for the model was scaled down for the scaled time from Fig. 6. It was noted that the assessment results of the model were scaled up for the time by 2.2, power by 55.9 and mass flowrate by

Fig. 7. Reactor power.

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Fig. 8. Normalized reactor power and normalized core inlet flow.

55.9 to compare with those of the prototype. It can be seen in Fig. 7 that the reactor power of the model is identical to that of the prototype, since the model used the power curve scaled down from the prototype. Fig. 8 represents the normalized reactor power and normalized core inlet flow. The core inlet mass flow decreased with the pump coastdown after the PHTS pump failure. The reactor scram of the model occurred at 3.29 s after the PHTS pump failure due to the PHTS low flow signal. Since the reactor scram of the prototype occurred at 6.91 s after the PHTS pump failure, one can know that the time of reactor scram would be properly accelerated by the time scale ratio. The core inlet flow shown in Fig. 8 indicates a reasonable similarity between the prototype and model for the pump coastdown as well as natural circulation flow after the pump coastdown. As shown in Fig. 9 which represents a ratio between the normalized core inlet flow and normalized reactor power, the behavior of the

Fig. 9. Ratio between normalized core inlet flow and normalized reactor power.

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Fig. 10. Core inlet/outlet temperature.

model gives a reasonable similarity against the prototype as well, although a slight difference is locally observed. Fig. 10 shows the behavior of the core inlet and outlet coolant temperature. The core outlet coolant temperature increases since the core inlet flow is not enough to remove the core power owing to the pump coastdown before the reactor scram and then rapidly decreases after the reactor scram. The core decay heat raises the core outlet coolant temperature again after the reactor scram. The core outlet coolant temperature continuously decreases by the continuous decrease of the decay power as well as heat removal from the residual heat removal systems such as AHX and DHX. As shown in Fig. 10, the model reasonably simulates the behavior of the prototype. The discrepancy of core coolant temperature between the model and prototype after 150 s is caused by the difference in the ratio between the core inlet flow and core power as shown in Fig. 9. The fuel surface temperature for the hot channel shown in Fig. 11 has a similar behavior as the behavior of the core coolant

Fig. 11. Fuel surface temperature (hot channel).

Fig. 12. Heat removal from residual heat removal systems.

temperature shown in Fig. 10. The fuel surface temperature of the model properly simulates that of the prototype as well. On the other hand, as shown in Fig. 12 which represents the power removal against the decay power from the residual heat removal systems, although there is an actuation time difference of power removal through the residual heat removal systems between the prototype and model, the amount of power removed through the residual heat removal systems, and the time when the power removal overcomes the decay power, are properly simulated in the model. As described in Figs. 7–12, the model ideally scaled down from the prototype has sufficient capability to reproduce the integral thermal–hydraulic phenomena and behaviors shown in the prototype with a reasonable quantitative and qualitative similarity based on the scaling methodology adopted in this study. 8. Conclusion A large-scale sodium thermal–hydraulic test facility to demonstrate a safety-grade decay heat removal performance has been designed complying with a proper scaling method for geometric, hydrodynamic and thermal similarities to the reference system of the KALIMER prototype. The facility has been designed from the viewpoint of both global and local scaling, based on Ishii’s methodology, which is suitable for preserving the natural circulation phenomena in a reduced-height scale facility. The preliminary design has the following characteristics: (a) 1/5-height, 1/125-volume, prototypic pressure and temperature simulation of the reference reactor; (b) geometrical similarity with the reference reactor, including all major components reflecting the real configuration for the main test section; (c) sodium as a main working fluid; (d) 7% of the scaled nominal core power to account for decay heat generation; (e) and a simulation of various design basis events. In particular much attention was paid to the reproduction of heat transfer between fluid and solid and the distortion in this scaling was also discussed. The scaling distortions with respect to the heat exchanger characteristics were also quantitatively discussed. A sample 1-dimensional calculation for verification for the PHTS total loss of flow with full power condition rather than 7% power level showed wonderful agreement of behaviors for important parameters including fuel cladding temperature and coolant temperatures. This scaling approach in this

S.-J. Hong et al. / Nuclear Engineering and Design 265 (2013) 497–513

study is expected to be used in the exact reproduction of heat transfer between a fluid and solid in a single phase fluid system. In part-II of the series of this paper, we will discuss the validity of the conservation of multi-dimensional fluid behaviors. Acknowledgements This work has been supported by the Ministry of Education, Science and Technology of Korea. References Bejan, A., 2004. Convection Heat Transfer, 3rd ed. John Wiley & Sons. El-Wakil, M.M., 1971. Nuclear Heat Transport. International Textbook Company, New York. Eoh, J.H., et al., 2011. Test Requirements for the Integral Effect Test to Simulate a Sodium-cooled Fast Reactor. Korea Atomic Energy Research Institute, KAERI/TR4424/2011(Korean version). Ha, K.S., et al., 2010. Generation of the MARS-LMR Base Input Data for DFR-600. Korea Atomic Energy Research Institute. Hahn, D., et al., 2007. KALIMER-600 Conceptual Design Report. Korea Atomic Energy Research Institute, KAERI/TR-3381/2007.

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