Assessment of the GOTHIC code for prediction of hydrogen flame propagation in small scale experiments

Nuclear Engineering and Design 236 (2006) 63–76

Assessment of the GOTHIC code for prediction of hydrogen flame propagation in small scale experiments Jin-Yong Lee, Jung-Jae Lee, Goon-Cherl Park ∗ Department of Nuclear Engineering, Seoul National University San 56-1, Shinlim-dong, Kwanak-gu, Seoul 151-742, Republic of Korea Received 4 May 2004; received in revised form 25 June 2004; accepted 18 April 2005

Abstract With the rising concerns regarding the time and space dependent hydrogen behavior in severe accidents, the calculation for local hydrogen combustion in compartment has been attempted using CFD codes like GOTHIC. In particular, the space resolved hydrogen combustion analysis is essential to address certain safety issues such as the safety components survivability, and to determine proper positions for hydrogen control devices as e.q. recombiners or igniters. In the GOTHIC 6.1b code, there are many advanced features associated with the hydrogen burn models to enhance its calculation capability. In this study, we performed premixed hydrogen/air combustion experiments with an upright, rectangular shaped, combustion chamber of dimensions 1 m × 0.024 m × 1 m. The GOTHIC 6.1b code was used to simulate the hydrogen/air combustion experiments, and its prediction capability was assessed by comparing the experimental with multidimensional calculational results. Especially, the prediction capability of the GOTHIC 6.1b code for local hydrogen flame propagation phenomena was examined. For some cases, comparisons are also presented for lumped modeling of hydrogen combustion. By evaluating the effect of parametric simulations, we present some instructions for local hydrogen combustion analysis using the GOTHIC 6.1b code. From the analyses results, it is concluded that the modeling parameter of GOTHIC 6.1b code should be modified when applying the mechanistic burn model for hydrogen propagation analysis in small geometry. © 2005 Elsevier B.V. All rights reserved.

1. Introduction Since the TMI-2 accident in 1979, the prevention and mitigation of severe accidents have become critical issues for ensuring the ultimate safety of nuclear power plants (NPPs) (Henrie and Postma, 1987). ∗

Corresponding author. Tel.: +82 2 880 7210; fax: +82 2 889 2688. E-mail addresses: [email protected] (J.-Y. Lee), [email protected] (G.-C. Park). 0029-5493/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nucengdes.2005.04.007

During severe accidents in NPP, substantial amounts of hydrogen can be generated from a chemical reaction between zirconium cladding and steam as well as from the core-concrete interactions after a lower head failure of the vessel. Such generated hydrogen may be transported into the compartments in the containment building and after ignition has the potential to threaten the containment integrity by over-pressurization, either as hydrogen deflagration or detonation. Moreover, even local hydrogen burning, which is not a threat to

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Nomenclature Aff i k m ˙ Sl T Teff V Veff wl wt wt XH Yf YO

flame front area (m2 ) ratio of oxidizer mass required per unit mass of fuel burned turbulent kinetic energy (m2 /s2 ) hydrogen consumption rate (kg/s) laminar flame velocity (m/s) temperature (K) effective temperature (K) actual computational cell volume (m3 ) effective volume (m3 ) laminar hydrogen reaction rate (kg-H2 /m3 s) turbulent hydrogen reaction rate (kg-H2 /m3 s) turbulent hydrogen reaction rate containing the two quenching criteria (kg-H2 /m3 s) hydrogen mole fraction fuel mass fraction oxidizer mass fraction

Greek symbols δff flame thickness parameter (m) ε dissipation rate of turbulent kinetic energy (m/s) γj weighting parameter λ dimensionless ramp multiplier Λ dimensionless ramp multiplier ξ fraction of the gas mixture that is in the fine turbulent structure ρ gas mixture density (kg/m3 ) χ fraction of the smallest turbulent structures that can react the global containment integrity, may also threaten the survivability of safety-related equipment. Hence, various experimental activities have been performed around the world to investigate severe accident phenomena related to hydrogen combustion. These experimental investigations studied the characteristics of hydrogen combustion such as the flammability limit of hydrogen-steam mixture (SNL FITS) (Richards and Aragon, 1984), deflagration (SNL VGES) (Benedick et al., 1984), flame acceleration and DDT (SNL FLAME) (Sherman et al., 1989),

premixed combustion and continuous injection tests (NTS) (Ratzel, 1985). On the other hand, existing licenses related to hydrogen control, in Korea, have been issued based on estimations from lumped parameter models such as MAAP (Prior et al., 1991), HECTR (Dingman et al., 1986), CONTAIN or GOTHIC (George et al., 2001), which were verified with experimental data and which adopted correlations from single volume hydrogen combustion experiments. However, there are limitations in the appropriate simulation of the characteristics of hydrogen combustion in terms of local combustion phenomena such as flame front propagation and flame acceleration in complex geometry. Recently, with the rising concerns for local hydrogen control, numerical calculations for space resolved hydrogen distribution and combustion in the compartment have been attempted using 3-D codes such as GOTHIC-3D (George et al., 2001), HYCA-3D (Choi et al., 2001) or GASFLOW (Travis et al., 1998). However, the results suffer from the lack of experimental data of local hydrogen combustion and the limited validation work for local hydrogen combustion phenomena. The GOTHIC-3D code is a general-purpose, multi-dimensional, thermal hydraulics computer program that performs the design, licensing, safety and operating analysis of the nuclear containment, auxiliary building and related equipment. It presents practical containment analysis calculations using relatively coarse, spatial meshes for a large simple geometry. However, in principle, very fine meshes in relatively small and/or complex geometry may be needed to predict the local hydrogen combustion phenomena properly. Especially, in respect to local flame propagation, the use of the fine mesh analysis with GOTHIC has not been fully investigated yet. In spite of the fact that GOTHIC 6.1b has many burn model modifications compared with previous code versions, the assessment of the GOTHIC 6.1b burn models combined with fine mesh calculations still remains to be checked, before it can be used for multi-dimensional hydrogen combustion analysis in a relatively small geometry. Therefore, in this study, the experimental assessment of the GOTHIC 6.1b was performed with hydrogen combustion experiments executed at the Seoul National University (SNU). This paper focuses on

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investigating the capability of GOTHIC 6.1b to predict the local hydrogen combustion in a small or complex geometry. The SNU verification tests were conducted to investigate the effect of the igniter position and of an obstacle to local hydrogen flame propagation. This paper presents comparisons between the results from the SNU, premixed hydrogen/air, combustion experiments and those from the GOTHIC code analyses with lumped parameter and subdivided 2-D volumes. Also, some guidelines of the GOTHIC code on local hydrogen combustion analyses are presented by a review of burn models and parametric effect simulation results.

2. Premixed hydrogen combustion experiments 2.1. Experimental apparatus and instruments Figs. 1 and 2 show the combustion chamber and experimental apparatus, respectively. The combustion chamber had an upright, rectangular shape of dimensions 1 m × 0.024 m × 1 m. Because the chamber depth was very small compared to the width and height,

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the hydrogen flame propagation in the direction of depth could be ignored. Therefore, this chamber was sufficient to obtain 2-D flame propagation sequences. The chamber was made of transparent acrylic plates and an aluminum frame. For the sealing of the gas mixture, an inflammable rubber plate was inserted between the acrylic plates and the aluminum frame. Hydrogen gas was injected into the combustion chamber through a valve at the back of the plate and an electric igniter was installed to initiate combustion. The ignition system was composed of a capacity discharge igniter (CDI) and ignition coil. A high-speed CCD camera (motion analyzer) was used to visualize the hydrogen flame. Though the wavelength of the hydrogen flame light emission is not in the visible range, high-speed photographs of the hydrogen flame could be obtained because the high temperature steam generated at the hydrogen flame front emits red light wavelength series. Considering that the hydrogen and steam flames are generated at almost the same location, the steam flame can be regarded as the hydrogen flame. For the operation of the high-speed CCD camera, a simple circuit, synchronized photo-coupler was

Fig. 1. Pictures of the 2-D combustion chamber.

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Fig. 2. Apparatus for experiment control and data acquisition.

used. A mass flow controller compensated by wet test gas meter was equipped to precisely control the composition of the gas mixture. 2.2. Descriptions of experiments Table 1 summarizes the test conditions. Fig. 3 depicts a schematic of Tests FP1 to FP4 which were carried out to investigate the local hydrogen flame propagation phenomena in the rectangular combustion chamber and to produce the needed benchmark data. Because the gas mixture composition arising during severe accidents in NPP can be often around 10% hydrogen, an experimental gas mixture composed of

10% chemically pure hydrogen (>99%) and 90% dry air was used. No physical obstacle was installed in the combustion chamber in these tests. These tests examined the effect of the igniter position and the open boundary condition on local hydrogen flame propagation. The tests were therefore conducted with two different ignition positions (top center, top corner) and two boundary conditions (bottom full open, bottom right half open). Because the density of the gas mixture is smaller than that of the air, a homogeneous gas composition could be maintained in most of the chamber volume. Fig. 4 shows a schematic of Test FP5, which was conducted to investigate the effect of an obstacle on

Table 1 Experimental conditions of hydrogen combustion tests Test condition

H2 (%)

Boundary (bottom)

Ignition position

Obstacle

Test FP1 Test FP2 Test FP3 Test FP4 Test FP5

10 10 10 10 12

Full open Full open Half open Half open Half open

Top center Top corner Top center Top corner Top center

No No No No Yes

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Fig. 3. Scheme of combustion tests FP1-FP4.

hydrogen flame propagation. An obstacle of dimensions 0.02 m × 0.024 m × 0.5 m was placed vertically at the bottom of chamber. The igniter was located at the top center of the test chamber and the bottom left half was closed.

3. GOTHIC code analysis GOTHIC (Generation Of Thermal Hydraulic Information in Containments) is a general purpose, thermal hydraulics, computer program for the design, licensing, safety and operating analysis of NPP. Applications of GOTHIC analysis include hydrogen combustion phenomena in containment as well as overall thermal hydraulic phenomena such as high energy line break, containment heat-up calculations and so on. In this paper, the application of GOTHIC to predict local hydrogen flame propagation phenomena was examined. A review of GOTHIC combustion models and the modeling of SNU tests are described below.

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Fig. 4. Scheme of combustion test FP5.

3.1. A brief review of GOTHIC combustion models (George et al., 2001) The GOTHIC code includes hydrogen burn models for lumped parameter volumes and distributed (subdivided) volumes. The lumped parameter burn models are almost identical to the burn model in HECTR and CONTAIN, which consist of two separate models: discrete and continuous burn. The discrete burn model describes the hydrogen combustion within the volume, and the continuous burn model describes the hydrogen combustion flows into the volume through junctions. In the discrete burn model, the flame speed is calculated using built in functions of the steam, oxygen and hydrogen mole fractions in the volume. The time required to burn hydrogen within a volume is calculated by dividing the burn length by the flame speed. The mechanistic burn model is applicable to subdivided volumes. When this is specified, burning of hydrogen requires that certain mole fraction limits are satisfied. If the mole fraction limits are satisfied, then combustion of hydrogen is continuously calculated.

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The combustion rate of hydrogen is determined from the maximum of the laminar and turbulent combustion rates. Laminar combustion is preset to zero and is not calculated unless the effective temperature for combustion exceeds a user specified, lower temperature limit. The laminar burn model is given by the Lewis and von Elbe expression (Lewis and von Elbe, 1961). The turbulent burn model has two options. The first option is referred to as the eddy dissipation concept of Magnussen (1989) and Magnussen and Hjerthager (1976). In this model the turbulent reaction rate is given by
 ε YO wt = 11.08 ρξχ min Yf , (1) k i where ε is the dissipation of turbulent kinetic energy, k is the turbulent kinetic energy, ρ is the gas mixture density, Yf and YO are the fuel and oxidizer mass fractions, i is the ratio of oxidizer mass required per unit mass of fuel burned, ξ is the fraction of the gas mixture that is in the fine turbulent structure and χ is the fraction of the smallest turbulent structures that can react. The second option is the turbulent flame speed concept of Dahmkohler (1949). In this model the turbulent reaction rate is expressed as follows (Sl + k0.5 )ρH wt = δff

 Veff = Aff δff

(2)

(3)

where wl is the laminar burn rate, wt is the turbulent burn rate containing the two quenching criteria, λT is a temperature dependent multiplier, λ0 is a multiplier for stopping the burn process, and the effective burn volume Veff is approximated by   V      Veff = min (4) δ3ff     max  Veff

(5)

Aff = ANS max(γN , γS ) + AEW max(γE , γW ) +ATB max(γT , γB )

(6)

where ANS , AEW and ATB are the cell cross section areas perpendicular to the north-south, east-west, and topbottom directions, respectively. The weighting parameters are given by

min(Xj , Xi ) 4 (7) γj = 1 − max(Xj , Xi ) where the subscript, j, refers to one of the cell face designators, Xj is the hydrogen mole fraction in the adjacent cell across the cell face, j, and Xi is the hydrogen mole fraction in the cell under consideration. The effective temperature is used to modify the temperature diffusion at the flame front in a coarse mesh. The weighted average, effective temperature for cell i is calculated as Teff,i = max(Ti + λ4j Λ4i (Tj − Ti )),

where Sl is laminar flame velocity. In the model for the turbulent reaction rate, two empirically based limitations are imposed. The first condition is referred to as cold quenching and the second as high turbulence flame quenching. In the mechanistic burn model, the hydrogen consumption rate is given by m ˙ H = max (wl , wt )Veff λT λ0

where V is the actual computational cell volume, δff is  is calculated by the flame thickness parameter and Veff multiplying the flame front area and flame thickness parameter as

j ∈ Πi

(8)

where Π i is the set of cells that includes cell i and all cells j connected to cell i with velocity relations, and Λ and λ are the dimensionless ramp multipliers. 3.2. GOTHIC modeling The SNU premixed hydrogen combustion experiments (FP1-FP4) were simulated using the lumped parameter and the mechanistic burn model. In the analysis, the same conditions were adopted as those in the experiment. The initial temperature and pressure of the combustion chamber were set to room temperature (298 K) and atmospheric pressure (101.3 kPa), respectively. The gas mixture was composed of 10% hydrogen and 90% dry air. Because the GOTHIC code cannot directly use air as an oxidizer, it was assumed that the air consists of 21% oxygen and 79% nitrogen. Therefore, the calculations were performed with the premixed gas mixture composed of hydrogen, oxygen and nitrogen. The GOTHIC built-in physical properties were used for each gas.

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In the case of the lumped parameter analysis, the combustion chamber had only one volume of the dimension 1 m × 0.024 m × 1 m. The discrete burn model was applied to the volume and an igniter was assigned to the volume but the exact position of the igniter could not be set in the volume. The GOTHIC built-in igniter model was applied and other parameters related to hydrogen combustion criteria were used as default values. In the cases of subdivided volume analyses, the mechanistic burn model was applied. The above described eddy dissipation concept was used to simulate turbulent hydrogen combustion. The igniter was assigned to the experimental location. The combustion chamber was simulated with 1681 cells (41 cells × 1 cells × 41 cells). To simulate the boundary conditions, a large virtual volume was connected to the bottom of the control volume and an adiabatic wall condition was applied to the other parts of the walls. The FP5 test was simulated with the mechanistic burn model. Other analysis conditions adopted were identical to those of the tests FP1 to FP4, except the initial hydrogen fraction and the obstacle. The gas mixture was composed of 12% hydrogen and 88% air. The obstacle was simulated as null cells using a variation cell table. Finally, parametric simulations were performed for the propagation related parameters such as flame thickness and burn temperature limit.

4. Results and discussions 4.1. Experimental results Fig. 5 shows the high-speed CCD photograph images of premixed hydrogen combustion experiments (FP1-FP4). The time step between each image corresponds to 4 ms. The grid on top of each first image shows the chamber size and one block corresponds to 10 cm. Fig. 5(a) shows the result for test FP1, which is the case of top center ignition and fully opened bottom. After ignition, the hydrogen flame propagated concentrically. With the lapse of time, the shape of the hydrogen flame front became more and more wrinkled. Generally, in a lean mixture of a highly diffusive gas such as hydrogen, the generation and growth of the flame cell structure is highly affected by the diffusive

Fig. 5. Direct photograph images of 10% H2 /air premixed flame (250 fps) (a) FP1 test (b) FP2 test (c) FP3 test and (d) FP4 test.

thermal instability. It could be accepted that the observed wrinkled flame front shape reflected the effect of diffusive thermal instability. Fig. 5(b) shows the result for the case of top corner ignition and bottom full open (FP2). The characteristics of hydrogen flame propagation were similar to those of the previous case. The reason for the relatively weak flame intensity near the right wall was due to heat loss to the wall. Fig. 5(c) presents the result for the case of top center ignition

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and bottom half open, and Fig. 5(d) of top corner ignition and bottom half open. In comparison with the bottom full open cases, the results of the bottom half open cases showed faster flame propagation and slightly stronger flame intensity. Because of the

expansion of the burned gas, some unburned gas mixture was discharged through the bottom open end. In the bottom half open tests, the opened area was small compared to that of the full open tests. Thus, the amount of discharged gas mixture was decreased

Fig. 6. Flame front propagation sequences of 10% H2 /air premixed in 2-D combustion chamber, derived from photographs, t = 4 ms.

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and the combustion rate of the gas mixture was increased. Fig. 6 presents the sequence of hydrogen flame front shapes at every 4 ms. From this figure, we could confirm the effect of diffusive thermal instability on the generation and growth of the flame structure. With increasing time, the flame front shape apparently became more wrinkled. Also, the propagation

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characteristics of the hydrogen flame in the combustion chamber could be obtained clearly. In the early stage of combustion, the flame front propagated with almost equal velocity in each direction. Later time, however, the speed of the flame approaching the wall slowed down whereas the flame approaching the open end propagated more rapidly. Because the expansion of combusted gas generated a flow toward the open end, the flame had a tendency to rapidly propagate toward the open end of the chamber. On the other hand, the flame near the wall part was compressed by the wall. Fig. 6(d) shows this phenomenon clearly. In the bottom left wall part, the flame propagated slowly as time went by, whereas the flame in the bottom right part propagated rapidly toward the open end. Fig. 7 shows the image of the FP5 test at every 2 ms. Due to the obstacle, the velocity of the flame propagating to the closed end was remarkably slow. As the experiment proceeded, the flame was accelerated to the open end of the chamber and the flow generated by the expansion of burned gas led the gas mixture in the dead end region to the open end, causing the flame propagation to be bent around the obstacle. 4.2. Results of GOTHIC analyses Fig. 8 shows the result of the GOTHIC lumped parameter analysis. Because the location of the igniter could not affect the calculation in the lumped volume,

Fig. 7. Direct photograph images of 12% H2 /air premixed flame (500 fps); FP5 test (with obstacle).

Fig. 8. GOTHIC lumped parameter combustion analysis result.

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Fig. 9. GOTHIC analyses results of 10% H2 /air combustion.

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the results of analyses for tests FP1 to FP4 show only the same temporal trend of burning plotted in the average temperature in the node. The combustion of 10% hydrogen and air mixture was completed within 75 ms, which agreed well with the experimental result and indicated that the built-in flame velocity functions predicted the actual flame propagation velocity within a factor of 2. However, other information related to local combustion phenomena such as the effect of open boundary, hydrogen flame propagating sequence, and igniter position could not be obtained. The very obvious differences of the combustion process (in Fig. 5) cannot be addressed with such an approach. Fig. 9 represents the GOTHIC mechanistic analysis results for the tests FP1 to FP4. The analyses were performed with default values of propagation parameters, and this figure shows the contours of different

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hydrogen mole fractions. It was assumed that the highest hydrogen mole fraction boundary line depicts the flame front. The combustion progressed horizontally more rapidly than vertically. The rapid horizontal propagation could be explained by the following two reasons: the buoyancy effect of the hydrogen flame and the wall effect. The buoyancy force can lead the flame to move upward. In the early analysis stage, the dissipation term is increased near the top wall, and the additional dissipation term also increases the eddy dissipation turbulent reaction rate. As time continues, the flame front accelerates toward the open boundary. Although the results represented some characteristics of hydrogen flame propagation, they were not well matched with the experimental results for the flame propagation sequence and combustion time. In the experiments, the hydrogen combustion was finished in about 50 ms, whereas in the GOTHIC-3-D calculation,

Fig. 10. GOTHIC analyses results of 12% H2 /air combustion (FP5).

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the combustion was finished after more than 1 s, which means that the measured and calculated average flame speeds differ by more than a factor of 20. Moreover, the flame front shapes were quite different from the experimental results. Fig. 10 shows the mechanistic calculation result for the test FP5 with default propagation parameters. The propagation characteristics were qualitatively similar to those in the test results. The flame progressing to the open end propagated rapidly, whereas that progressing to the closed end became slow. The increased initial hydrogen mole fraction and the presence of the obstacle enhanced the turbulent reaction rate and the GOTHIC code predicted more rapid flame propagation

than the results of the FP3 test simulation. However, GOTHIC still predicted slower combustion factor 5 and quite different flame shapes than those of the experimental results. Fig. 11 presents the results of parametric simulations of the flame thickness, the burn temperature limit and the turbulent burn model options for test FP5. The cases (a), (b) and (c) were calculated to investigate the effect of flame thickness, (d) to assess the effect of burn temperature limit, and (e) and (f) to investigate the capability of the turbulent flame speed model. From the results, the flame propagation phenomena were highly affected by the flame thickness when the eddy dissipation concept was used. As the flame thickness parameter

Fig. 11. Parametric effect simulation results, test FP5.

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Fig. 11. (Continued ).

was set to a small value, the flame propagated rapidly, but the effect was relatively small when the flame thickness was set smaller than the cell size. By setting a small flame thickness compared with the cell size, we could get more reasonable analysis results for the flame propagation time sequences and flame front propagation shapes. However, these results could be validated only for test FP5 where a sufficient turbulence source exists in the combustion chamber. In the cases of the test FP1-FP4 analyses, in which the turbulent burn rate of eddy dissipation concept had a minor effect on hydrogen combustion, the flame thickness could not influence the flame propagation phenomena. In these cases, an appropriate, user-specified value was needed to adjust the hydrogen burn rate in order to

enable GOTHIC for combustion application in the small geometry. The burn temperature limit is the minimum local vapor temperature to initiate the hydrogen combustion. It is clear that a smaller value of burn temperature limit will promote the propagation of the hydrogen flame. From the analysis results for case (d), in which the default burn temperature of 175 ◦ C was replaced by 100 ◦ C, the hydrogen flame was greatly accelerated in the open end after the required time for the effective temperature of the adjacent cells to reach the specified value. The turbulent flame speed model is not affected by the flame thickness because the flame thickness parameter is cancelled out of the hydrogen consumption rate

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expression described in Section 3.1. From the analysis results for cases (e) and (f), the time dependent flame shapes were quite different from those of the experiment. It is concluded that the turbulent flame speed model is not applicable for the present local hydrogen flame propagation analysis.

5. Conclusions In this study, premixed, hydrogen flame propagation experiments were conducted and the performance of the GOTHIC code was assessed for lumped parameter and subdivided volumes modeling. The GOTHIC lumped parameter burn model produced a reasonable prediction of the time required to burn the hydrogen/air mixture in the case of experiments FP1-4, which represented empty volume. The most complicate test FP5, which involved an obstacle showed larger deviations. However, some other information such as flame propagation speed, flame position and boundary condition effect cannot be obtained with this approach. In the subdivided simulation using default propagation parameters, the GOTHIC code did not appropriately predict the time dependent flame propagation. However, in the parametric effect simulations, it was possible produce more agreement for the flame propagation sequence, when the flame thickness was set to 0.5 cm in the eddy dissipation burn model. When sufficient turbulence was generated by an obstacle or other turbulent sources and the eddy dissipation model was dominant, we could get more reasonable results by setting the flame thickness to a small value compared with the dimension of the cells. However, when a turbulent source does not exist in a volume, the GOTHIC code requires user-specified values to adjust the hydrogen burn rate for local combustion analyses. In conclusion, the modeling parameters of GOTHIC code should be modified appropriately when apply-

ing the GOTHIC code for space dependent and multidimensional hydrogen combustion analysis in small geometry. References George, T.L., Wiles, L.E., Claybrook, S.W., Wheeler, C.L., McElroy, J.D., 2001. GOTHIC-Containment Analysis Package: Technical Manual. Numerical Applications Inc. Benedick, W.B., Cummings, J.C., Prassinos, P.G., 1984. Combustion of hydrogen:air mixtures in the VGES cylindrical tank. NUREG/CR3273, Sandia National Laboratories. Choi, Y.S., Lee, U.J., Park, G.C., 2001. Study on local hydrogen behaviors in a subcompartment of the npp containment, Nuclear Engineering and Design, vol. 208, pp. 99–116. Dahmkohler, 1949. Z. Electrochem. 46, 601. Dingman, S.E., et al., 1986. HECTR Version 1.5 User’s manual, NUREG/CR-4507. Sandia National Laboratories, Albuquerque, NM. Henrie, J.O., Postma, A.K., 1987. Lessons learned from hydrogen generation and burning during the TMI-2 event. GEND-061, U.S. Department of Energy. Lewis, B., von Elbe, G., 1961. Combustion, Flames and Explosions of Gases. Academic Press, Inc., New York. Magnussen, B.F., 1989. Modeling of Nox and Soot Formation by the Dissipation Concept. IFRF Ist Topic Oriented Meeting. Ijmuiden, Netherlands. Magnussen, B.F., Hjerthager, B.H., 1976. On mathematical modeling of turbulent combustion with special emphasis on soot formation and combustion. In: Proceedings of the 16th International Symposium on Combustion. The Combustion Institute. Prior, R.P., Kirby, P.N., Lutz, R.J., Jr., 1991. Severe accident analysis of a 1300 Mwe PWR to address the hydrogen issue, Nuclear Engineering and Design, vol. 130, pp. 51–58. Ratzel, A.C., 1985. Data analyses for nevada test site (NTS) premixed combustion tests. NUREG-4138, Sandia National Laboratories. Richards, E.H., Aragon, J.J., 1984. Hydrogen-burn survival experiments at fully instrumented test site. NUREG/CR3521, Sandia National Laboratories. Sherman, M.P., Tieszen, S.R., Benedick, W.B., 1989. Flame facility—The effect of obstacles and transverse venting on flame acceleration and transition to detonation for hydrogen/air mixtures at large scale. NUREG/CR-5275, Sandia National Laboratories. Travis, J.R., Spore, J.W., Royl, P., et al., 1998. GASFLOW a computational fluid dynamics code for gases aerosols and combustion, FZKA-5994, vol. I–III, October.