Thermal Hydraulics of the Very High Temperature Gas Cooled ...

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INL/CON-09-16110PREPRINT

Thermal Hydraulics of the Very High Temperature Gas Cooled Reactor

NURETH-13

Chang Oh Eung Kim Richard Schultz Mike Patterson David Petti

October 2009

The 13th International Topical Meeting on Nuclear Reactor Thermal Hydraulics (NURETH-13) Log Number: N13P1197 Kanazawa, Japan. September 27-October 2, 2009.

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Thermal Hydraulics of the Very High Temperature Gas Cooled Reactor

Chang Oh, Eung Kim, Richard Schultz, Mike Patterson, and David Petti

Idaho National Laboratory P.O. Box 1625

Idaho falls, ID 83415 [email protected]

ABSTRACT The Idaho National Laboratory (INL), under the auspices of the U.S. Department of Energy, is conducting research on the Very High Temperature Reactor (VHTR) design concept for the Next Generation Nuclear Plant (NGNP) Project. The reactor design will be a graphite moderated, thermal neutron spectrum reactor that will produce electricity and hydrogen in a highly efficient manner. The NGNP reactor core will be either a prismatic graphite block type core or a pebble bed core. The NGNP will use very high-burnup, low-enriched uranium, TRISO-coated fuel, and have a projected plant design service life of 60 years. The VHTR concept is considered to be the nearest-term reactor design that has the capability to efficiently produce hydrogen. The plant size, reactor thermal power, and core configuration will ensure passive decay heat removal without fuel damage or radioactive material releases during reactor core-accidents. The objectives of the NGNP Project are to: Demonstrate a full-scale prototype VHTR that is commercially licensed by the U.S. Nuclear Regulatory Commission, and Demonstrate safe and economical nuclear-assisted production of hydrogen and electricity. The DOE laboratories, led by the INL, perform research and development (R&D) that will be critical to the success of the NGNP, primarily in the areas of: • High temperature gas reactor fuels behavior • High temperature materials qualification • Design methods development and validation • Hydrogen production technologies • Energy conversion. This paper presents current R&D work that addresses fundamental thermal hydraulics issues that are relevant to a variety of possible NGNP designs.

KEYWORDSNext Generation Nuclear Plant, Very High Temperature Gas-Cooled Reactor, Method Development

Oh et al NURETH-13 Thermal Hydraulics of the Very High Temperature Gas Cooled Reactor N13P1197

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INTRODUCTION The NGNP reference concepts are helium-cooled, graphite-moderated, thermal neutron spectrum reactors with an outlet temperature only limited by the hardware material limits. Consequently, the average outlet temperatures experienced in the reactor outlet plenum may be as high as 900 °C although the peak gas temperatures will be higher still. The NGNP reactor core will likely be either a prismatic graphite block-type core or a pebble bed core. Because the NGNP may be used to generate process heat an intermediate heat exchanger will likely be a part of the primary system. Also, because the NGNP will likely be used to generate electricity, the plant may be either a direct-cycle or an indirect cycle system. The Rankin cycle is proposed by General Atomics as a means to produce the process heat and generate electricity. The reactor will be designed to ensure passive decay heat removal without fuel damage throughout the accident envelope. In summary, the NGNP program is focused on building a plant to publicly demonstrate the safety and economics of the VHTR, rather than simply confirming the basic feasibility of the concept.

. The basic technology for the NGNP has been established in former high-temperature gas-cooled reactor plants (e.g., DRAGON, Peach Bottom, Albeitsgemeinschaft Versuchsreaktor [AVR], Thorium Hochtemperatur Reaktor [THTR], and Fort St. Vrain). These reactor designs are representative of the pebble bed reactor and the prismatic modular reactor concepts. Current commercial examples of potential NGNP candidates are the Gas Turbine-Modular Helium Reactor (GT-MHR) from General Atomics (General Atomics [1996]), the High Temperature Reactor concept from AREVA (Hittner et al. [2006]), and the Pebble Bed Modular Reactor (PBMR) from the PBMR consortium (Koster et al. [2003]). Presently the High-Temperature Engineering Test Reactor (HTTR) in Japan (Shiozawa et al. [2004]) and the High-Temperature Reactor (HTR) in China (Wu et al. [2002]), both test reactors, are being used to demonstrate the feasibility of the reactor components and materials needed for the NGNP. (The HTTR reached a maximum coolant outlet temperature of 950°C in April, 2004.)

BACKGROUND

The ultimate goals of the NGNP thermal-fluids Research and Development (R&D) are to identify the important phenomena that must be analyzed, to define the capability of the tools that must be developed and validated, to prescribe the experiments and validation studies that must be performed, and to formulate the analyses which must be performed for the NGNP reference designs. Because the NGNP reference designs include both the prismatic-block-type VHTR as well as the pebble-bed VHTR designs, ongoing R&D is applicable to both types of reactors. However, for illustrative purposes, the prismatic-block type reactor will be used as an example herein, although from time-to-time examples of R& D applicable to the pebble-bed design will also be discussed. A typical prismatic-block type reactor is shown in Figure 1.


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Figure 1. General Atomic Gas Turbine Modular Helium Reactor (General Atomics [1996]). Typical system analysis codes such as RELAP (Fletcher and Schultz [1995]) or TRACE (Chain et al. [1997]) use a one-dimensional transient approach and employ correlations such as the Dittus-Boelter correlation to calculate the heat transfer in turbulent flow. Consequently, system analysis predictions can be optimistic for low-Reynolds-number flow with significant buoyancy contributions. Figure 2a demonstrates that Nusselt numbers (convective heat transfer coefficients) can be factors of two or three lower - and thermal resistances higher - than the correlation suggests for heated gas flow through a circular tube. Conventional wisdom is that buoyancy forces aid in air upflow. Wang, Li and Jackson [2002] show that, in turbulent upflow, the effect of significant buoyancy forces can be to lower the Nusselt number compared to forced flow by 50 % in a pipe and 35 % in a channel (Figure 2b). The magnitude of the effect varies with geometry and position. These examples demonstrate the need to validate systems analysis codes using relevant experimental measurements. A similar argument is applicable to computational fluid dynamics (CFD) codes.

23.7 m

5.4 m

11.0 m

2.4 m

4.5 m

0.4 m

GT-MHR 600 MWt

6.8m

0.5 m

01.5 m

12.1 m

25.2 m

0.4 m


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Figure 2 (a) Figure 2 (b)

Figure 2. Typical correlations in typical systems analysis codes overpredict convective heat transfer parameters for gases in some scenarios: (a) at low Reynolds numbers in a circular tube and (b) with buoyant effect in turbulent upflow through circular tubes and rectangular channels (Wang, Li and Jackson [2002]) REACTOR THERMAL HYDRAULICS GAMMA CODE DEVELOPMENT

GAMMA code was developed specifically for air ingress (Oh et al. [2006]). The governing

equations and numerical methods adopted for this project are described below.

The multi-dimensional governing equations for a chemically reacting flow (Oh et al. [2006], Lim and No [2006]) consist of the basic equations for continuity, momentum conservation, energy conservation of the gas mixture, and the mass conservation of each species. Six gas species (He, N2, O2, CO, CO2, and H2O, (NO et al. [2004]) are considered in the present analytical model, and it is assumed that each gas species and the gas mixture follow the equation of state for an ideal gas. The GAMMA code has the capability to handle the thermo-fluid and chemical reaction behaviors in a multi-component mixture system as well as heat transfer within the solid components, free and forced convection between a solid and a fluid, and radiative heat transfer between the solid surfaces. Also, the basic equations are formulated with a porous media model (Neild and Bejan [1999]) to consider heat transport in a pebble-bed core) as well as solid-fluid mixed components. The equation of continuity for the gas mixture:

� � ss

Rt��

��

� �u (1)

The equation of momentum conservation:

� �2

1 1 1 FCt K K

P ��

� � � � �� u u u u u uu g (2)

The equation of sensible energy conservation:


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� � � � � �

� �1

m

f disp f s ss

of s sf sf p fs

s

H H T Ht

h R h a T T

� � � ��

�

� ��

� � � �

� �

�

u J (3)

The conservation equation of each species, s:

� � � � � �+s s s sY Y Rt

� � � � ��

�� u J (4) 1

1and for He, 1

m

m ss

Y Y�

��

The equation of state for an ideal gas:

1m

s ss 1

P Y / WRT

��

� � �

� �� (5)

For a solid and a pebble bed, the same heat conduction equation is used. A thermal non-

equilibrium model for porous media is used to consider the heat exchange between the fluid and the pebbles as follows:

� �� '''1 peff p sf sf p fp

TC T q h a T T

t� � �

�� (6)

Radiative heat transfer in the enclosure is well-modeled by using an irradiation/radiosity method

(Holaman [1986]) which assumes that the fluid is non-participating and the radiation exchange between surfaces is gray and diffuse. The net radiative flux from agglomerated surface k, which consists of Nk faces of the original mesh, is given by

� �

� �

1'' 4

4

1

1

M M M

r kj k k k kj j k k kjkj k j k j k

M

j j j j j j ji ii j

q F T F J F

J C T C F J

� � � �

� � �

�

� � �

�

� � � � � � � ��

� �

� � �

� (7)

The ordinary diffusion flux (Js) is given in two forms, the full multi-component diffusion

(Hirschfelder et al. [1964]) and the effective diffusion (Walker et al. [1960]) by the assumption that a dilute species, s, diffuses through a homogeneous mixture:

� �21,

sk k

ms

sk k s

D Y WWW

� �

� �� J (8) -1

1, / (m 3)

m

s mix s s mix k skk k s

s D Y where D X� � � �

� ��

� � � �J D (9)

Although Eq. (8) predicts the accurate diffusion behaviors of species in a multi-component

mixture, Eq. (9) is generally used in numerical calculation because of its computational efficiency and its accuracy close to that of Eq. (8). Physical properties, such as molar weight, viscosity, thermal conductivity, and sensible enthalpy, for each gas component and gas mixtures, are obtained from the handbooks of gas properties (Poling et al. [2001], Raznjevic [1976]) Nomenclature of equations above can be found in Oh et. al (2006).


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AIR INGRESS ANALYSIS BY MULTISTEP APPROACH

(a) Initial Condition Calculations by GAMMA Following the depressurization that occurs after a break, the high pressure helium will be released

to the confinement. The GAMMA code is used to calculate the temperature, pressure, and gas concentration in the confinement after the depressurization. Then the calculated values at the pressure equalization between the reactor vessel and the confinement are used as initial conditions to the FLUENT code (ANSYS [2006]).

Figure 3 shows the code input nodalization where 2-D geometry models are used for the reactor cavity to consider the heat removal by natural convection flow, and for the solid structures including the core and reflector blocks to consider multidimensional heat conduction. The heat transport in the prismatic core is greatly complicated by the combined effect of solid conduction in the fuel, the graphite matrix, and gas and contact conduction and radiation in the fuel and fuel block gaps. In this simulation, the coolant channel and the fuel compact were separately treated by 1-D fluid equations and a 2-D heat conduction equation from the graphite matrix, respectively. A porous media approach was applied to the reactor core, reflector, and plenum regions. The radiation heat exchanges were considered in every cavity and plenum. The air-cooling reactor cavity cooling system (RCCS) was modeled using the 1-D pipe network for the air flow loop and the 3-D tube model for the cooling tubes. Following the accident, since a reactor trips immediately, the core power is determined directly from the decay heat curves.

520

515(9x2)

513(9x3)

604

603

512(9x1)

Block Core514

(9x10)

511

605

701

602 160 110

105

115

130

200205

220

165

210

225231~235

251~255

260 265

125

120(

7)

215~216

702

Figure 3. GT-MHR 600 MWt code nodalization

(b) CFD Calculation

Air ingress analysis of a small pipe break (82 cm2) on the top of the steam generator is in progress. The rationale for this simulation is that General Atomics, one of the NGNP vendors, believes that this event has a higher probability of occurrence than other accident scenarios related to the depressurization loss-of-coolant accident. A two-dimensional (2-D) FLUENT model was developed


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based on the General Atomics gas turbine modular helium reactor, GT-MHR design. The simulation continues, and some preliminary results are presented in this paper.

Air ingress from a double-ended guillotine break (DEGB) of the concentric pipe on the GT-MHR is also being developed. A three-dimensional (3-D) CFX model (Version 12) includes the reactor, the concentric pipe, and the confinement so that the density-gradients of gases between the reactor and the confinement are taken into account as the driving force for the air ingress phenomena. The three-dimensional model developed to represent the exact lower plenum geometry will be used to calculate the detailed flows in the complicated lower plenum geometry. The reactor core structure was modeled using a FLUENT porous media model because of the complexity of the geometry and to avoid a large CPU time requirement. A steady-state run was made to ensure the pressure drop of the core during normal operation. A transient 3-D simulation is in progress.

Small Pipe Break

The air-ingress caused by a small pipe break is an important issue because it has a higher probability of occurrence than the double-ended guillotine break (DEGB). The purpose of this simulation is to (1) determine what mechanism dominates the initiation of air ingress either by molecular diffusion or density-gradient induced flow and (2) find the timing of the natural convection that fills the reactor with air. We strongly believe that the air ingress mechanism is dependent on the geometry and conditions of the break. In this calculation, we are interested in the air ingress mechanism, the flow path, and the timing of natural convection. We used FLUENT (Version 6.3) CFD code and simplified the GT-MHR (Gas turbine modular high temperature reactor) into a 2-D geometry, which includes GT-MHR confinement, a reactor pressure vessel, and a steam generator. The break was assumed to occur at the top of the steam generator, which mimics a small break of the relief valve failure. Figure 4 shows snapshots of the time dependant progression of air mass fraction.

Figure 4. Two-Dimensional FLUENT results on air mass fractions up to 1000 seconds.

10 sec 20 sec 30 sec 40 sec 50 sec

60 sec 80 sec 100 sec 200 sec 1000 sec


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Figure 5 shows a x-y plot of the air mass fraction. As shown in Figure 5, at approximately 500 seconds (over 8 minutes) air mass fraction reaches a quasi-steady state value of 0.43. This result indicates that the air ingress into the reactor core occurs very rapidly. For these calculations, the initial air mass fraction in the confinement was assumed to be 1 as part of a parametric study. In reality, the air concentration depends on the size of the confinement and the leakage rate from the confinement. Typical confinement leakage rate in Japanese design of GTHTR-300 is 5% to 10%, which is high and air concentration in the confinement will be higher than that of GAMMA calculations for the depressurization.

Figure 5. Average air mass fraction in the core and the lower plenum.

Double-Ended Guillotine Break using 3-D Model

A 3-D model was developed using the GT-MHR design. This model includes the GT-MHR

confinement and the reactor pressure vessel with real geometry of the lower plenum. Figure 6 shows initial conditions (calculated from GAMMA code) used in CFX simulations.


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Figure 6. Initial conditions used in CFX simulation.

For the CFX calculations, an initial air mass fraction of 0.5 was used as 0.5, which was calculated with the GAMMA code.

Figure 7 shows results of air mass fraction up to 27.56 seconds. As shown in Figure 4, air filled the lower plenum at approximately 9.86 seconds and this agrees very well with 2-D FLUENT results at 10 seconds (inserted between 9.86 seconds and 15.86 seconds).

Figure 7. Snap shots of air mass fractions from 3-D CFX calculations and comparison with 2-D FLUENT

calculation at 10 seconds.

Figure 8 shows the air mass fraction at 3.4 m above the core bottom at 17.86 seconds. At this location, the air mass fraction is 0.27 and the overall volume averaged mass fraction is 0.174. This


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indicates that the convection takes places so rapidly in the core driven by the buoyancy force created by hot air from the lower plenum.

Figure 8. Local air mass fraction at 17.86 seconds and 3.4 m from the core bottom.

GRAPHITE OXIDATION

Experiments have been carried out at the graphite oxidation test station at INL, which is built for evaluation of the American Society for Testing and Materials (ASTM) standard test method (Contescu et al. 2008) for graphite. The ASTM test standard was developed for determining and rating the oxidation resistance of nuclear grade graphite. A protocol containing instructions for setting up a test station was developed by the Oak Ridge National laboratory (ORNL) and distributed to several laboratories for independent evaluation of the protocol’s robustness in terms of repeatability. In this work, basically the same experimental setup as ASTM protocol has been maintained, but it was slightly adjusted for this purpose.

The schematic of the oxidation test station (see Figure 9) shows the graphite sample suspended below a balance inside the Inconel tube, which is surrounded by the furnace. The Inconel tube is connected to nitrogen and air supplied from the bottom and desiccated to eliminate oxidation from moisture. The nitrogen is used during this process to avoid oxidation when the furnace is heating up. When the gas temperature is stabilized at target value, it is switched to air to start oxidation. The test can take from a couple of hours to a few days, so the data is gathered automatically using LabVIEW (National Instruments) until the desired burn-off is achieved.


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Figure 9. Schematic of the graphite oxidation test station setup.

Figure 10 shows the schematic of the sample holder that was set up for the experiment. It was installed at the center of the electrical furnace. The sample holder is made of Titanium and has a rectangular cage shape with a loading material and graphite sample inside. The loading material is made of titanium and initially placed on the top of the graphite sample.

The graphite sample is a cylinder with a hole at the center. Its dimensions are 1.0 inch outer diameter, 1.0 inch height, and 0.5 inch in inner-hole diameter. The loading material has the cylindrical shape with a small tip at the bottom center to fit the loader to the sample. The size of the tip is made to be a little bit smaller than the hole to avoid thermal expansion problems. The experiment is performed at relatively low temperature (650°C) during which the reaction kinetics dominate the graphite corrosion process. In this regime, the graphite corrosion mainly decreases the graphite density with degradation of mechanical strength, maintaining its original shape and size. If the graphite is fully corroded, the sample will be collapsed by the loading materials. The broken ashes will then fall down through the metal mesh at the bottom of the cage, sending a signal of suddenly decreased graphite mass as detected by the balance connected to the cage and the sample.

Figure 10. Schematic of the sample holder and loader setup.


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The effect of burn-off is very important for predicting the oxidation rate of graphite because the reaction rate is highly dependent on the degree of burn-off. Usually, the reaction rate increases with the increasing burn-off in the beginning (Velasquez et al., 1978). This is because of the increase of the reaction surface as the pores grow larger and the closed porosity opens. Then, the reaction rate decreases at high burn-off because the pores join together, thus decreasing the reaction surface area. The effect of burn-off is usually considered by an empirical factor, Fb, as

bn

OA

g FPTR

Ekr ��

�2

)exp(0 (10)

where

gr = reaction rate

0k = pre-exponential factor

AE = activation energy

R = gas constant

T = temperature n

OP2 = oxygen partial pressure

n = order of reaction

bF = empirical factor.

The physical meaning of Fb is the ratio of reacting surface area of oxidized graphite to that of original graphite. Therefore, Fb is 1.0 for the original graphite and 0.0 for the completely burned graphite. Fb is given as:

originaloxidizedb AAF / (11)

where

Aoxidized = reacting surface area for the oxidized graphite

Aoriginal = reacting surface area for the original (unoxidized) graphite (burn-off = 0%).

As described above, the reacting surface area initially increases with the reaction because of the increased pore size. However, as the reaction proceeds, the reacting surface area decreases again because of the collapses of the enlarged pores. Therefore, the Fb value starts at 1.0, and then initially increases with oxidation. After a certain level of burn-off, it starts to decrease again and finally drops to 0.0 at 100% burn-off.

In Oh et al. (2008), the Fb factor has been experimentally obtained as a function of burn-off for various forms of graphite: IG-110, H451, NBG-10, NBG-18, and V483T. The Fb factors of IG-110 and H451 were measured by the experimental setup and for NBG-10, NBG-18, and V483T, the data published in Fuller and Okoh (1997).

Figure 11 plots the surface area densities for IG-110 and H451 graphite as a function of burn-off. The surface area densities were obtained by multiplying the initial surface area density of the graphite by the Fb value (See Equations 10 and 11). Generally, the reaction rates are proportional to the reacting surface


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area. Therefore, the initial oxidation rate is smaller in IG-110 graphite (890 m2/m3) than that in H451 graphite (1,320 m2/m3). However, as the oxidation progresses, the surface area density of IG-110 increases more rapidly than that of H451. And finally, the oxidation rate of IG-110 becomes larger than that of H451 for more than 10% burn-off. This means that comparisons based only on the surface area densities or reaction rates of the original graphite can lead to the misunderstanding on the graphite oxidation characteristics. For example, comparisons show that H451 graphite has better oxidation resistance than IG-110 in the long process, which is more important in the air-ingress accident. Therefore, the comparisons on the other graphite based on this method are highly recommended, and more tests will be carried out in the years 2009 and 2010. It is strongly suggested that this new method be used to select the nuclear graphite for the NGNP.

Figure 11. Comparisons of surface area density and oxidation rate between IG-110 and H451.

HEAT EXCHANGER DESIGN AND OPTIMIZATION In the compact heat exchanger, two costs are negatively correlated; (1) Capital cost, and (2) Operating cost. For example, the increase of flow area enhances the heat transfer capacity increasing flow velocity, but it requires more pumping power increasing the pressure drop. Therefore, the size of heat exchanger should be determined under consideration of various economic factors (Kim and Oh [2008]). In this section, we qualitatively investigate the relationship between the size and the total cost by scaling analysis. This qualitative study helps us understand how each thermal hydraulic and economic parameter is related.

Optimum Sizing Model for Minimum Cost of Compact heat Exchanger In this section, we developed the analytic model to determine the total cost and optimum heat exchanger size approximately. In this study, it is assumed that the hot and cold channel have the same geometry and portion in the heat exchanger. So, the hot and cold channel properties can be expressed as follows.

0 10 20 30 40 50 60 70 80

1000

2000

3000

4000

5000

6000 650oC

Surfa

ce A

rea

Den

sity

(m2 /m3 )

Burn-off (%)

IG-110H-451

0 10 20 30 40 50 60 70 80

1000

2000

3000

4000

5000

6000 650oC

Surfa

ce A

rea

Den

sity

(m2 /m3 )

Burn-off (%)

IG-110H-451

Sur

face

are

a D

ensi

ty (m

2 /m

3 )


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(i) frontal area fhf AA 5.0, (hot channel)

fcf AA 5.0, (cold channel)

(ii) flow area AAh 5.0 (hot channel) AAc 5.0 (cold channel)

(iii) heat transfer surface

Hh AS 5.0 (hot channel)

Hc AS 5.0 (cold channel)

(iv) equivalent diameter ehe dd , (hot channel)

ece dd , (cold channel) In the heat exchanger, the heat transfer relation is written as

mSUQ �� (12) where: Q : total power, [J/s or W] U : overall heat transfer coefficient [W/(m2 K)] S : heat transfer surface area [m2] m : log mean temperature [K] From Eq (12), heat transfer surface in the hot channel is expressed by

mhh U

QS �

. (13)

The overall heat transfer coefficient in Eq.(13) can be expressed as follows,

cc

hwh

h

h

ShS

RSh

U��

1

1 (14)

If we assume that the heat resistance of the CHE wall is relatively small in comparison to the convective heat resistance (Song [2005]), then the overall heat transfer coefficient expression becomes,

cc

h

h

h

ShS

h

U�

!1

1 (15)


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Then, Hch ASS 5.0 (16) Therefore, Eq (15) becomes

ch

h

hh

U11

1

�! . (17)

The heat transfer coefficients is usually expressed as follows,

cbe akdh

Nu PrRe�

(18)

Therefore,

bbch

bhe

e

hbh

ch

bhe

e

hh AFACTA

mddak

Amd

dak

h ��

�

��

��

��

��

��

�

��

�

��

��

��

��

��

1Pr

5.0Pr

��

(19)

bbcc

bce

e

cbc

cc

bce

e

cc AFACTA

mddak

Amd

dak

h ��

�

��

��

��

��

��

�

��

�

��

��

��

��

��

2Pr

5.0Pr

��

(20) If we insert Eq (19) and Eq (20) into Eq (17), the overall heat transfer coefficient can be expressed by

bbbbh AFACTA

FACTFACTFACTA

FACTA

U ��

�

�

��

�

�

� 3

21

11

1

21

1. (21)

From Eq (13), the heat transfer surface area of the compact heat exchanger is

mh

H UQVA

"��

�2

, (22)

Therefore, the volume of the CHE becomes

bb

mmb AFACTA

FACTQ

AFACTQV ��

�

��

��

�

�� 4

32

321

" ". (23)


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If we only consider the metal volume, the volume of metal can be expressed by

bMaterial AFACTVV �� 4)1()1( �� . (24)

where � represents ratio of free flow area to frontal area in the compact heat exchanger. Since the volume of the heat exchanger is

LALAV f ��

, (25)

the length becomes

� � 144 �� bb AFACTAFACTA

VA

L ��. (26)

The friction loss of the heat exchanger is expressed as:

edLGf

ASGfP 4

22

22

�� (27)

where ieff Re(Re)2 .

The hot channel pressure drop can be obtained as,

2

2

2

2 45.0

42 ��

��

�

��

��

��

��

��

��

��

�

��

�

��

��

��

��

��

��

��

� i

eh

hi

h

hei

heh

hi

h

heh A

Ld

mmde

AL

dmmd

eP��

(28)

Replacing L in Eq. (28) with Eq. (26), it becomes

� �

2

12 445.0 �

��

��

�

��

��

��

��

��

��

��

� i

b

eh

hi

h

heh A

AFACTd

mmdeP �

��

� � 332

5445.0

��

�

��

��

��

��

��

��

��

ibib

eh

hi

h

he AFACTAFACTd

mmde �

��

. (29)

The pressure drop of the cold channel can be obtained by the same method.

� cP � � 332

6445.0

��

�

��

��

��

��

��

��

��

ibib

ec

ci

c

ce AFACTAFACTd

mmde �

��

(30)

From the pressure drops, the pumping power can be approximately calculated as follows,


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3,

5 ��

��

ib

h

h

h

hhhpower A

FACTmPmP

��

(31)

3,

6 ��

��

ib

c

c

c

cccpower A

FACTmPmP

��

(32)

The cost of the heat exchanger is the summation of the capital cost and operating cost. The capital cost of the compact heat exchanger is determined based on the weight or mass. From Eq (25), the mass of the heat exchanger is

bMateralMaterialMaterialCHE AFACTVM �� 4)1( �� . (33)

Therefore, the capital cost can be expressed by b

MateralCHEmassCHECHEmass AFACTCMCCP �� 4)1( �� (34) where: CP = capital cost of CHE

CHEmassC = price($) per CHE unit mass (kg) The operating cost can be assumed to be proportional to the pumping power. Therefore, YPPCOP cpowerhpowerop �� )( ,, (35) where: OP = operating cost of CHE opC = cost($) per wh Y = total duration of operation Therefore,

3)65

( ��

��

�� ib

c

c

h

hop A

FACTmFACTmYCOP

��

(36)

The total cost becomes � � b

MateralCHEmasstotal AFACTCOPCPC �� 4)1( ��

3)65

( ��

��

��

�� ib

c

c

h

hop A

FACTmFACTmYC

��

(37)

It can be simplified as follows 3

21�� ibb

total AKAKC . (38)

1K and 2K is determined as follows.

4)1(1 FACTCK MateralCHEmass �� (39)


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)65

(2c

c

h

hop

FACTmFACTmYCK

��

��

��

(40)

Where,

ch

bhe

e

h mddak

FACT Pr5.0

1 ��

��

��

��

��

(41)

cc

bce

e

c mddak

FACT Pr5.0

2 ��

��

��

��

��

. (42)

21

11

13

FACTFACT

FACT�

(43)

mFACTQFACT

" ��

3

24 (44)

� �445.0

52

FACTd

mmdeFACT

eh

hi

h

he ��

�

��

��

��

��

��

��

��

�

��

(45)

� �445.0

62

FACTd

mmdeFACT

ec

ci

c

ce ��

�

��

��

��

��

��

��

��

�

��

(46)

To find out the optimum flow area, differentiation of Eq. (38) was obtained.

42

11 )3( �� ibbtotal AibKAbK

dAdC

(47)

At the optimum point, since the differentiation is zero, it satisfies

0)3( 42

11 �� ib

optb

opt AibKAbK . (48)

Therefore, the optimum surface area can be written as

i

opt KK

bibA

�

��

��

��

��

��

��

��

31

1

23. (49)

The optimum aspect ratio is

� �

44

/5.1

5.1

1

5.0

FACTA

AFACTA

LH

bopt

bopt

opt

opt �

��

�

� ��

�. (50)

DEVELOPMENT OF TRITIUM TRANSPORT ANALYSIS CODE


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Tritium is produced in the VHTR by various sources; ternary fissions and activation reactions

with impurities and borons in the materials. In addition, the helium coolant itself is also a tritium source in the form of neutron absorbing nuclide 3He with its extremely low isotope abundance. Tritium emissions from nuclear facilities are regulated by the U.S. Nuclear Regulatory Commission (NRC) and the Environmental Protection Agency (EPA). Because the limits for tritium emissions are quite stringent, the Next Generation Nuclear Plant (NGNP) Project needs to understand how, and to what extent, tritium may be generated and transported from the NGNP to an associated industrial process and its effect on NGNP design and NRC licensing. Appropriate systems can then be designed to mitigate potential tritium impacts.

In order to predict tritium behavior for quantified differences in materials, sizes, conditions, and configurations in the NGNP, INL is developing a tritium permeation analysis code version 1(TPAC-1). The tritium generation core models were implemented into the TPAC-1. The core models are provided in the following equations. 1. Ternary fission

� �)(

)(TerT

TerT NYPKdt

Nd�� (51)

where )(TerTN = number of tritium atoms due to ternary fission

K = fission rate per thermal megawatt [fission/MW/s] P = reactor power [MW] Y = average yield per fission [1/fission] � = tritium decay constant [1/s].

2. Birth from 6Li

� �66

6LiTLith

Li NdtNd

�� # (52)

� �)6(66

)6(LiTLiTLith

LiT NNdt

Nd�� # (53)

where 6LiN = number of 6Li atoms

)6(LiTN = number of tritium atoms from 6Li

th# = thermal neutron flux [neutrons/cm2/s]

TLi6� = effective cross section for 6Li (n, �) 3H [cm2].

3. Birth from 7Li � �

7377

LiHLifLi N

dtNd

�� # (54)

� �)7(77

)7(LiTLiTLif

LiT NNdt

Nd�� # (55)

where


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7LiN = number of 7Li atoms, excluding 10B source

)7(LiTN = number of tritium atoms from 7Li, excluding birth from 10B

f# = fast neutron flux [neutrons/cm2/s]

TLi7� = effective cross section for 7Li (n, n�) 3H [cm2].

4. Birth from 3He � �

33333

HeTHeHeHeHeHe NNfNf

dtNd

�� #� (55)

� �)3(33

)3(HeTHeTHeHe

HeT NNdt

Nd�� # (56)

thtotal

coreHe W

W ## � (57)

where 3HeN = number of 3He atoms

)3(HeTN = number of tritium atoms from 3He

f = fractional supply rate of helium coolant [1/s] �

3HeN = number of 3He atoms in the supply helium

THe3� = effective cross section for 3He (n, p) T [cm2]

He# = average thermal neutron flux experienced by the total primary helium inventory [n/cm2/s]

coreW = helium inventory in core [kg]

totalW = total primary helium inventory [kg].

5. Birth from 10B � � � � 1010710

10BTBfLiBth

B NdtNd

�� #�# (58)

� �)10(7710710

)10(7BLiTLifBLiBth

BLi NNdt

Nd�� #�# (59)

� �)10(1010)10(77

)10(BTBTBfBLiTLif

BT NNNdt

Nd�� #�# (60)

where 10BN = number of 10B atoms

)10(7 BLiN = number of 7Li atoms from 10B

)10(BTN = number of tritium from 10B

710LiB� = effective cross section for 10B (n, �) 7Li [cm2] TB10� = effective cross section for 10B (n, 2�) 3H [cm2].

TPAC-1 is being validated with Peach Bottom data and will be validated using tritium data to be

collected by HTTR in Japan.


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Figure 12 shows the TPAC-1 model for the Peach Bottom reactor. The system is composed of reactor, steam generator, concentric pipe, containment, and purification system. For simplicity, two steam generator loops have been simplified to a single steam generator loop in the model. In this system, the tritium flow path is as follows. First, the tritium is generated in the reactor core and released. The majority of the released tritium enters into the main flow distributed in the whole system. The rest of the tritium from the core is purged to the purification system for removing tritium from the primary loop. Some of the tritium in the main flow is permeated to the secondary side through the steam generator walls or leaked to the containment through the pipe lines. A small portion of main flow is purged to another purification system. The temperature and pressure of all the components were set as 809 K and 23 atm, which are the average temperature and pressure in the system.

Figure 12. INL tritium code modeling for Peach Bottom reactor.

CONCLUSIONS

R&D projects have been initiated, and a NGNP thermo-fluids R&D has been formulated and is underway to support the effort required to ensure the necessary software tools are ready to support the VHTR design effort.

This paper presents overall thermal hydraulics aspects of the VHTR. The GAMMA code was used to calculate input parameters at the depressurization from the depressurized conduction cooldown and those parameters were used as initial conditions to the CFD code calculations. The phenomenon of the density-gradient stratified flow air ingress was found and preliminary calculations indicate that the onset of natural convection was significantly accelerated by the stratified flow consideration leading to much faster corrosion in the graphite structure. This means that the previous assumptions on the air-ingress accident will lead to the underestimation on their consequences. Therefore, it is highly recommended that the original air-ingress scenario based on molecular diffusion is replaced with the new assumption considering stratified flow. The higher burnoff test that was used in this paper is recommended for selecting nuclear graphite for the VHTR. The validation of the numerical models will be performed using air ingress experiments.


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On the intermediate heat exchanger (IHX), the optimum size of the compact heat exchanger of the printed circuit heat exchanger for the VHTR has been investigated from the economic point of view. To avoid complications, we developed an optimum sizing model by analytical method considering only size and friction loss effects, which are considered to be two dominant factors determining heat exchanger cost. In this work, we focused on investigating the effects of various design parameters on the optimum design rather than providing the accurate optimum point because the real design and selection process is much more complicated and plant-specific than we could achieve here with generalized calculations. In the larger view, the IHX cost and design are not independent of the full plant economics. Therefore, the optimum size estimated here might be a little bit different from the real optimum point, which considers the full plant economics. Despite that, our model is still considered to be useful for developing preliminary estimations of optimum heat exchanger sizes before detailed plant design can begin. In addition, this model gives good insight on the optimum sizing of compact heat exchangers. We also develop an analytical model to estimate the total cost for the PCHE IHX based on the reference design of the GA-600 MWt VHTR system. Also the tritium analysis code is being developed to be used for analyzing the tritium permeation from the primary loop to the secondary loop of the VHTR system, and this code will be also validated using the HTTR tritium data to be collected from HTTR in Japan. ACKNOWLEDGMENT This work was supported through the Department of Energy’s Republic of Korea/United States International Energy Research Initiative (research grant started in FY-08) under DOE Idaho Operations Office Contract DE-AC07-99ID13727. REFERENCES ANSYS Inc, FLUENT 6.3 User’s Guide (2006). Bejan A., Klaus A.D., Heat Transfer Handbook, John Wiley & Sons (2003). Chanin, D., Young, M.L., Randall, J. & Jamali, K., Code Manual for MACCS2: Volume 1, User’s Guide (1997). Contescu, C.I., Azad, S., Miller, D., Lance, M. J., Baker, F. S., and Burchell, T. D., Practical aspects for characterizing air oxidation of graphite, Journal of Nuclear Materials, in press (available online) (2008). Fletcher, C.D. & Schultz, R.R. RELAP/MOD3 code manual: User`s guidelines. Volume 5, Revision 1. (1995). Fuller, E. L., Okoh, J. M., Kinetics and mechanisms of the reaction of air with nuclear grade graphite: IG-110, J. Nuclear Materials, Vol. 240, pp. 241-250 (1997). General Atomics, Gas Turbine-Modular Helium Reactor (GT-MHR) Conceptual Design Description Report, GA-A910720, Project (1996). Hirschfelder, J.O., Curties, C.F., and Bird, R.B., Molecular Theory of Gases and Liquids, John Wiley & Sons, Newyork (1964).


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Hittner, D. et al., RAPHAEL: A European Project for the Development of HTR/VHTR Technology for Industrial Process Heat Supply and Cogeneration, Proceedings of HTR 2006, 3rd International Topical Meeting on High Temperature Reactor Technology, October 1-4, Johannesburg, South Africa (2006). Holaman, J.P., Heat Transfer, McGraw-Hill (1986). Kim, E.S, and NO, H.C., Experimental study on the oxidation of nuclear graphite and development of an oxidation model, Journal of Nuclear Materials, 349, pp. 182-194 (2006). Kim, E.S. and Oh, C., Simplified Optimum Sizing and Cost Analysis for Compact Heat Exchanger in VHTR, Nuclear Engineering and Design 238, pp.2635-2647, (2008). Koster, A., Matzner, H.D. & Nicholsi, D.R. PBMR design for the future. Nuclear Engineering and Design 222, 231-245(2003). Lim, H.S. and NO, H.C., GAMMA multidimensional multicomponent mixture analysis to predict air ingress phenomena in an HTGR, Nuclear science and engineering 152, 1, pp. 87-97 (2006). NO, H.C., Kim, E.S., and Lim, H.S., Multi-Dimensional Multi-component Mixture Air-ingress Analysis and Air-ingress Experiment in an HTGR, The Sixth International Conference on Nuclear Thermal Hydraulics, Operation and Safety (NUTHOS-6), Nara, Japan, October 4-8 (2004). Nield, D.A. and Bejan, A., Convective in Porous Media, Springer-Verlag, Newyork (1999). Oh, C. H., Davis, C., Siefken, L., Moore, R., NO, H. C., Kim, J., Park, G. C., Lee, J. C., and Martin, W. R., Development of Safety Analysis Codes and Experimental Validation for a Very High Temperature Gas-Cooled Reactor, Final Report, Idaho National Laboratory, INL/EXT-06-01362 (2006). Oh, C.H., Kim, E.S., NO, H.C., Cho, N.Z., Experimental Validation of Stratified Flow Phenomena, Graphite Oxidation, and Mitigation Strategies of Air Ingress Accidents, INL/EXT-08-14840 (2008). Poling, B.E., Prausnitz, J.M., and O’Connel, J.P., The Properties of Gases and Liquids, fifth ed, McGraw-Hill, New York (2001). Raznjevic, K., Handbook of Thermodynamic Tables and Charts, Hemisphere, Washington (1976). Shiozawa, S. et al. Overview of HTTR design features. Nuclear Engineering and Design 233, 11-21 (2004). Song, S.C., Thermal-hydraulic performance of a printed circuit heat exchanger in an air test loop, M.S. Thesis of Korea Advanced Institute of Science and Technology (KAIST) (2005). Velasquez. C, Hightower, G., and Burnette, R., The oxidation of H-451 graphite by steam, Part 1: reaction kinetics, General Atomics Report GA-A14951. Walker, R.E., Dehaas, N., and Westenberg, A.A., Measurements of Multi-component Diffusion Coefficients for the CO2-He-N2 System Using the Point Source Technique, J. Chem. Phys., 32, 5, pp. 1314 (1960). Wang, J., Li, J. & Jackson, J. A study of the influence of buoyancy on turbulent flow in a vertical plane passage. International Journal of Heat and Fluid Flow 25, 420-430 (2004).


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