The role of CFD combustion modelling in hydrogen safety management – VI: Validation for slow deflagration in homogeneous hydrogen-air-steam experiments

Nuclear Engineering and Design 311 (2017) 142–155

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The role of CFD combustion modelling in hydrogen safety management – VI: Validation for slow deflagration in homogeneous hydrogen-air-steam experiments A. Cutrono Rakhimov a,⇑, D.C. Visser a, T. Holler b, E.M.J. Komen a a b

Nuclear Research and Consultancy Group (NRG), Westerduinweg 3, 1755 ZG Petten, The Netherlands Jozˇef Stefan Institute (JSI), Jamova cesta 39, 1000 Ljubljana, Slovenia

h i g h l i g h t s
Deflagration of hydrogen-air-steam homogeneous mixtures is modeled in a medium-scale containment.
Adaptive mesh refinement is applied on flame front positions.
Steam effect influence on combustion modeling capabilities is investigated.
Mean pressure rise is predicted with 18% under-prediction when steam is involved.
Peak pressure is evaluated with 5% accuracy when steam is involved.

a r t i c l e

i n f o

Article history: Received 16 July 2016 Received in revised form 18 October 2016 Accepted 28 November 2016 Available online 7 December 2016 Keywords: Turbulent premixed flame propagation Hydrogen deflagration Code validation Hydrogen-air-steam mixture

a b s t r a c t Large quantities of hydrogen can be generated during a severe accident in a water-cooled nuclear reactor. When released in the containment, the hydrogen can create a potential deflagration risk. The dynamic pressure loads resulting from hydrogen combustion can be detrimental to the structural integrity of the reactor. Therefore, accurate prediction of these pressure loads is an important safety issue. In previous papers, we validated a Computational Fluid Dynamics (CFD) based method to determine the pressure loads from a fast deflagration. The combustion model applied in the CFD method is based on the Turbulent Flame Speed Closure (TFC). In our last paper, we presented the extension of this combustion model, Extended Turbulent Flame Speed Closure (ETFC), and its validation against hydrogen deflagration experiments in the slow deflagration regime. During a severe accident, cooling water will enter the containment as steam. Therefore, the effect of steam on hydrogen deflagration is important to capture in a CFD model. The primary objectives of the present paper are to further validate the TFC and ETFC combustion models, and investigate their capability to predict the effect of steam. The peak pressures, the trends of the flame velocity, and the pressure rise with an increase in the initial steam dilution are captured reasonably well by both combustion models. In addition, the ETFC model appeared to be more robust to mesh resolution changes. The mean pressure rise is evaluated with 18% under-prediction and the peak pressure is evaluated with 5% accuracy, when steam is involved. Ó 2016 Elsevier B.V. All rights reserved.

1. Introduction The risks of hydrogen release and combustion during a severe accident in a Light Water Reactor (LWR) have received considerable attention after the accidents at Three Mile Island, USA in ⇑ Corresponding author. E-mail addresses: [email protected], [email protected] (A. Cutrono Rakhimov), [email protected] (D.C. Visser), [email protected] (T. Holler), komen@nrg. eu (E.M.J. Komen). http://dx.doi.org/10.1016/j.nucengdes.2016.11.034 0029-5493/Ó 2016 Elsevier B.V. All rights reserved.

1979 (Alvares et al., 1982) and at Fukushima, Japan in 2011 (ANS Committee, 2012). When mixed with air in the containment, the hydrogen can form a flammable or even explosive gas mixture. After ignition, a combustion process is initiated that may damage relevant safety systems and may even compromise the integrity of the containment walls. The recent accident in Fukushima confirmed the destructive power of a hydrogen deflagration and therewith the importance of hydrogen control. Hydrogen mitigation systems, such as Passive Autocatalytic Recombiners (PARs) and igniters, can be designed and installed

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to reduce the risk of hydrogen combustion. Despite the installation of PARs, it has been generally recognized that the temporary existence of flammable gas clouds cannot be fully excluded during certain postulated accident scenarios (Bentaib et al., 2010). Therefore, reliable numerical modelling is needed to assess the associated residual risk of possible hydrogen deflagrations. In addition, numerical models can be employed to optimize the design of the hydrogen mitigation systems in order to reduce this residual risk as far as possible. Traditionally, lumped parameter (LP) codes are used to analyse the hydrogen distribution inside the containment. In a more detailed approach, complementary Computational Fluid Dynamics (CFD) codes are also used for the analysis of some selected most critical scenarios. The main reasons for the need of complementary CFD analyses are explained by Komen et al. (2015). The presented CFD-based model for hydrogen deflagration analyses (Sathiah et al., 2012a) is based on (a) a density-based coupled solver (ANSYS Fluent, 2008) for accurate tracking of the induced pressure wave phenomena, (b) the application of an advanced Turbulent Flame Speed Closure (TFC) combustion model based on the Zimont model (Zimont, 1979) via user defined functions and (c) the application of Adaptive Mesh Refinement (AMR) for accurate and efficient tracking of the turbulent flame propagation (Sathiah et al., 2012b). The TFC combustion model has been validated against fast deflagration experiments from the ENACCEF experimental facility operated by CNRS (Centre National de la Recherché Scientifique, France) (Bleyer et al., 2012; Chaumeix and Bentaib, 2010, 2011; ISP-49, 2011), for the following mixtures: (a) homogeneous hydrogen-air mixtures (Sathiah et al., 2012b); (b) homogeneous hydrogen-air-steam mixtures (Sathiah et al., 2015); and (c) nonhomogeneous hydrogen-air mixtures (Sathiah et al., 2016). The general conclusion was that the applied CFD model predicted all the considered ENACCEF experiments reasonably well. That means, for example, the maximum pressure was predicted within 12–15% accuracy for the considered tests. Recently, Sathiah et al. (2016b) presented an extension of the TFC combustion model that was validated for slow deflagrations in homogeneous hydrogen-air experiments conducted in a medium-scale Thermal-Hydraulics Hydrogen Aerosols and Iodine (THAI) test facility (Kanzleiter and Langer, 2010; ISP-49, 2011). This model, referred to as the Extended TFC (ETFC), is based on the improvements made by Lipatnikov and Chomiak (2002) to the Zimont model. It was concluded that the ETFC model shows improvement in the initial laminar-like regime of slow deflagration compared to the TFC model. In order to continue the validation study for both the TFC model and the ETFC model within the slow deflagration regime, this paper studies the steam dilution effect for slow deflagrations in homogeneous mixtures. For that purpose, the experimental data from the THAI facility are used again. Three THAI hydrogen deflagration (HD) experiments with different initial steam concentrations are considered, namely THAI HD-15 with no steam, THAI HD-22 with 25 vol.% steam, and THAI HD-24 with 48 vol.% steam. The objectives of the current paper are defined as follows: (a) to further validate the TFC model from Zimont (1979) and the ETFC model from Lipatnikov and Chomiak (2002) against three slow deflagration experiments performed in the THAI facility, with different initial steam amount; (b) to investigate if the combustion models are able to predict the effect of steam on hydrogen deflagration; (c) and to perform grid sensitivity of the aforementioned combustion models. The paper is structured as follows: First, the experimental facility and the experiments used for the validation are described in Section 2. The applied CFD models, with all the issues concerning the hydrogen-air-steam uniform mixture is described in Section 3. Next, the validation results are presented and discussed in

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Section 4. The summary and conclusions are then presented in Section 5, including future steps for further validation of the presented CFD-based combustion modelling approach.

2. THAI HD experiments 2.1. THAI facility A large number of hydrogen deflagration (HD) experiments have been executed in the Thermal-Hydraulics Hydrogen Aerosols and Iodine (THAI) test facility (Kanzleiter and Langer, 2010; ISP-49, 2011) located in Eschborn, Germany. The measurements were performed by Becker Technologies GmbH under the sponsorship of the German Federal Ministry of Economics and Technology. The THAI test facility is a cylindrical stainless steel vessel. The vessel is 9.2 m high and has an internal diameter of 3.2 m with a total volume of 60 m3. During the HD experiments there are no internal structures present in the THAI vessel that can generate extra turbulence. The setup of the THAI facility during the deflagration experiments is shown in Fig. 1. A hydrogen distributor located in the sump was used to inject the hydrogen in the cylindrical vessel before each experiment started. An axial fan located near the hydrogen distributor was used to create a homogeneous mixture before it was ignited. The ignition is located 0.5 m from the bottom of the facility and the mixture was ignited using a spark igniter, about 10–15 min after the end of fan operation. A grid of 43 fast sheathed thermocouples (outer diameter 0.25 mm), is installed at different elevations and radial positions in the vessel to monitor flame propagation (‘‘flame front arrival”) and flame temperature during hydrogen combustion. The flame position was determined by the arrival of the flame at the locations of the fast thermocouples by measuring a steep temporal increase of the temperature. Only measurements of ‘‘first arrival” were used in order to exclude the influence of hot burnt gas and to minimize the influence of thermal radiation. The pressure signal was measured using four fast pressure transducers of the strain gauge type which are mounted at the inner wall of the vessel. Further details about instrumentation accuracy and the repeatability of the experiments are available in the technical report (Kanzleiter and Langer, 2010). Access into the vessel for installation of components and instrumentation is provided by the top flange (1540 mm wide) and by a lower and an upper man hole. Supporting structure for instrumentation can be assumed not to have any significant effect on turbulence generation and thus on the deflagration phenomena and flame propagation. It is worth stressing here that initial turbulence levels were not measured in these experiments, and heat losses from the domain boundary are also not specified. However, from the gradual decrease in the pressure after complete burning in the experimental results, it is evident that some heat loss occurred.

2.2. THAI HD experiments selected for code validation In total, 29 hydrogen-air and hydrogen-air-steam flame propagation experiments have been performed in the THAI facility within the OECD THAI project (2007–2009): (a) HD-1R through HD-14 (15 experiments) correspond to deflagrations in homogeneous hydrogen-air mixtures at ambient temperature; (b) HD-15 through HD-21 (6 experiments) correspond to deflagrations in homogeneous hydrogen-air mixtures at elevated temperature; (c) HD-22 through HD-24 (3 experiments) correspond to deflagrations in homogeneous hydrogen-air-steam mixtures at superheated and saturated conditions; (d) HD-25 through HD-29 (5 experiments)

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Fig. 1. Schematic representation of the THAI facility (Kanzleiter and Langer, 2010).

correspond to deflagrations in non-uniform hydrogen-air-steam mixtures. In the previous paper, the THAI tests HD-12, HD-7 and HD-3 have been used to validate the CFD model in the slow hydrogen deflagration regime for different uniform hydrogen-air mixtures. In this paper, uniform hydrogen-air-steam mixtures in the slow deflagration regime are considered. In order to investigate the steam effect, three experiments with upward propagation and similar initial conditions but different steam concentrations (at saturated state) were selected, namely: HD-15 with no steam, HD-22 with 25 vol.% steam, and HD-24 with 48 vol.% steam. In these experiments, the initial temperatures, the initial pressures, and

the initial hydrogen concentrations are very similar. The details of experiments HD-15, HD-22 and HD-24 are summarized in Table 1. Figs. 3 and 4, show the measured pressure evolution and the axial flame front positions during experiments HD-15, HD-22 and HD-24. Scattered clouds with all experimental points are represented in Fig. 3 and the corresponding moving averaged pressure profiles. The window for the moving average is 0.1 s and it is applied for the quantitative analysis as well. In all the following figures in this paper, a reduced number of experimental points will be used in order to have better overall visibility. Clearly, the peak pressure is the highest for test HD-15 without steam and decreases

Table 1 THAI HD experiments considered for validation (Kanzleiter and Langer, 2010; ISP-49, 2011). RUN

P0 [bar]

T0 [K]

H2 [vol.%]

Steam [vol.%]

Burn direction

Mixture

HD-15 HD-22 HD-24

1.504 1.487 1.472

366.0 365.0 363.5

9.9 9.9 9.8

0 25 48

Upward Upward Upward

Uniform Uniform Uniform

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Fig. 2. Flame front propagation as timelines, test HD-15, HD-22 and HD-24 (Kanzleiter and Langer, 2010).

Fig. 3. Measured pressure evolution during THAI experiments HD-15, HD-22 and HD-24 (Kanzleiter and Langer, 2010). The symbols represent the raw experimental data and the lines the corresponding moving average.

with increasing steam content. In test HD-15, the peak pressure is also reached faster. The effect of increasing steam content is also evident in the graph of flame front position. A slower flame propagation is observed at higher steam concentration. As stated in the technical report (Kanzleiter and Langer, 2010), an increased combustion time means enhanced heat transfer to the vessel walls, resulting in lower peak temperatures and peak pressures for the experiments with steam. Apart from this, replacing air by steam means an increased heat capacity of the gas

(cv ;H2 O ¼ 1:4 kJ=kg K; cv ;air ¼ 0:72 kJ=kg K) which will also result in a lower peak temperature and peak pressure for the same amount of energy released as has been the case for the three selected experiments. The mass difference of steam and air compensates this effect only partially. In Fig. 3, scattered clouds of experimental data are the consequence of acoustic effects (high frequency pressure waves). This effect can be observed in tests HD-15 and HD-22, but not in test HD-24 with high steam content. The reason for this is not known

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Fig. 4. Experimentally measured axial flame front positions during THAI experiments HD-15, HD-22 and HD-24 (Kanzleiter and Langer, 2010). The symbols represent the first flame front arrival at elevation and the lines the corresponding moving average.

from the technical report, either it is due to the longer combustion time, or the steam changes the acoustic properties, e.g. the damping behaviour and/or resonance frequency of the system. The relative low steam content in the test HD-22 reduces flame front velocity, but not as significant as for the test HD-24. Combustion is erratic and slow in test HD-24 with the flame front bypassing the vessel centreline, leaving there portions of unburned gas, which are ignited later during the deflagration. This high steam content brings the mixture relatively close to the flammability limit, and this apparently results in an unsteady combustion. As shown in Fig. 2, the flame propagates rather steady in tests HD-15 and HD-22, but extremely chaotic in test HD-24 where it burns in a kind of ‘‘hoses”, producing separated fire balls. However, at the end, combustion was also complete in this test (as in test HD-15 and HD-22), indicating that the mixture was ignitable throughout the vessel.


 @ @ @ @ ~c ~ j ~cÞ ¼ þ qu U t jr~cj: ðq~cÞ þ ðqu qðju þ Dt Þ @t @xj @xj @xj

Here ju and Dt are the thermal diffusivity of the unburned mixture and the turbulent diffusivity respectively, U t is the turbulent flame speed, and qu is the unburned gas density. In our simulations, it is assumed that counter-gradient transport has negligible effects on the results. This is true for flame propagation in closed vessels as indicated by Cant and Bray (1989). For non-unity Lewis number, as for hydrogen-air mixtures, the progress variable ~c is defined as follows:

~c ¼

Y~ f  Y f ;u Y f ;b  Y f ;u

3.1. TFC combustion model The Turbulent Flame Speed Closure (TFC) combustion model based on Zimont model (Zimont, 1979) solves the following progress variable equation:

ð2Þ

where Y f represents the fuel mass fraction, and indexes u and b stand for unburned and burned state of the mixture, respectively. The turbulent diffusivity is evaluated as:

3. Numerical methodology The presented hydrogen deflagration model is implemented in the commercial CFD code ANSYS Fluent (2008). The unsteady Favre averaged (density-weighted) Navier-Stokes equations are solved. Within the CFD code, the equations for the conservation of mass, momentum, energy and a combustion progress variable are solved. These equations are described in detail by Sathiah et al. (2012a). Here, only the combustion model is discussed. First, the differences between the TFC model based on Zimont (1979), and the ETFC model based on Lipatnikov and Chomiak (2002) will be explained. Next, combustion sub-models for preferential diffusion and compression effects on the laminar flame speed are described. Finally, the laminar flame speed, additional models, the mesh, boundary conditions, and the numerics applied in the CFD model are described.

ð1Þ

Dt ¼

mt Sct

ð3Þ

Here, mt is the turbulent kinematic viscosity and Sct the turbulent Schmidt number. The turbulent kinematic viscosity is calculated using the standard k  e turbulence model. Although widely validated and used, the Zimont model has limitations discussed and addressed by Lipatnikov and Chomiak (2002). These relate to the fact that turbulent combustion can appear in several regimes and it is difficult to cover all of them efficiently in one model. More specifically, limitations of the Zimont model are, first, the TFC model simplifies the flame development process to the growth of a mean flame brush thickness, dt , fully determined by the turbulent diffusion law. This is a reasonable zero-level approximation, employing Dt , which offers the opportunity to account for the effective turbulent diffusivity increase with flame development time. Second, the TFC model assumes a steady turbulent burning velocity in a flame of a growing thickness. Again, this is a reasonable zero-level approximation where the burning velocity tends to approach an Asymptotically Steady (AS) limit faster than dt , because U t is mainly controlled by small-scale eddies. Moreover, large-scale eddies, which increase dt , also increase

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instantaneous flame surface area and therewith the burning velocity. Thus, a first-order approximation for U t must depend, although weakly, on time when the thickness grows and has to account for a weak growth of U t when approaching the AS regime (t > st turbulent time scale). Third, at small and moderate u0 =U l , effects of the laminar flame speed U l and mixture properties on the development of dt are possible, mostly for expanding flames. Fourth, in case of weak turbulence, when u0 ! 0, the model predicts zero flame speed rather than U t ! U l . The ETFC model addresses the aforementioned limitations.

where t fd represents the flame development time, which is simply equal to the time counted from spark ignition for expanding flames. For typical stationary flames stabilized in parabolic flows, t fd should R be replaced by dx=u1 where u1 is the mean gas flow velocity and x is the axial distance from the flame holder. Thus, for these flows the development of dt with time is equivalent to the increase in dt with distance from the flame holder. The Lagrangian time scale sL is estimated as:

3.2. ETFC combustion model

where u0 is the turbulent intensity, according to Taylor’s theory of turbulent diffusion (Brodkey, 1967) and Dt;1 the fully developed turbulent diffusivity, given by:

To overcome the Zimont model limitations, Lipatnikov and Chomiak have applied the following modifications. First, the insertion of an additional laminar-like source term (Ls ) and second, the insertion of time-dependent expressions for the turbulent diffusivity (Dt;t ) and the turbulent flame speed (U t;t ). The Extended Turbulent Flame Speed Closure (ETFC) combustion model based on Lipatnikov and Chomiak (2002), solves the following progress variable equation:


 @ @ @ @ ~c ~ j ~cÞ ¼ þ Ls þ qu U t;t jr~cj; ðq~cÞ þ ðqu qðju þ Dt;t Þ @t @xj @xj @xj

ð4Þ

where the additional laminar-like source term Ls on the right-handside is given by:




Ls ¼

qð1  ~cÞ h exp  t r ð1 þ Dt;t =jb Þ T~



ð5Þ

The activation temperature is h, and t r is the reaction time scale. As shown by Lipatnikov and Chomiak (2002), this formulation gives the correct burning velocity in the limit of weak turbulence, namely U t ! U l , rather than U t ! 0 as for TFC model. However, the model requires the evaluation of the reaction time scale tr , which is not straight forward. Therefore, we rely on an alternative formulation, from the quoted authors, for the laminar-like source term. The alternative progress variable equation has a slightly different laminar source term, namely:

Ls ¼

U 2l q ~cð1  ~cÞ 4ðju þ Dt;t Þ u

ð6Þ

This formulation is computationally somewhat less demanding and does not require evaluation of the reaction time scale. It is worth mentioning that the turbulent flame speed does not exactly converge to the laminar flame speed in the limit of weak turbulence using the proposed alternative equation. The first model modification discussed, namely the Ls insertion, offers the opportunity to obtain the steady mean flame brush thickness in the fully developed case instead of a growing dt as for the TFC model. It includes neither new constants nor unknown parameters. When u0  U l , the laminar-like source term dominates and controls the mean burning rate and thereby directly U t . When u0 is markedly higher than U l , the laminar-like source term is strongly reduced and its effects on the burning rate are negligible. Moreover, the flame speed dependency on flame thickness by numerical errors should be reduced to a minimum thanks to an adaptive mesh refinement applied in the flame front region. The time-dependent turbulent diffusivity Dt;t in Eqs. (4)–(6) and the time-dependent turbulent burning velocity U t;t in Eq. (4) follow from Lipatnikov and Chomiak (2002):



Dt;t ¼ Dt;1


 tfd 1  exp 

sL

 U t;t ¼ U t;1 1 þ

sL t fd


 1=2 tfd 1 exp 

sL

ð7Þ

sL ¼

Dt;1 ; u02

Dt  Dt;1 ¼

ð9Þ

~2 Cl k : Sct ~e

ð10Þ

~ and ~e are the FavreHere, C l is a turbulence model constant, k averaged turbulent kinetic energy and turbulent dissipation rate, respectively. This definition is analogous to Dt ¼ mt =Sct previously showed for the TFC model. The same analogy is valid for U t;1 from ETFC and U t from TFC. The closure for this turbulent flame speed will be explained in the following section. The second model modification discussed, namely the Dt;t and U t;t insertion, offers the opportunity to simulate the transition from a laminar to a turbulent flame kernel, as well as the turbulent flame development. The modification includes neither new constants nor unknown parameters. The time-dependence of turbulent diffusivity accounts for the fact that, initially, only small fast scales can participate in the dispersion of an admixture cloud, whereas larger, slow scales are effective with a delay characterized by their time scales. Then, the effective turbulent diffusivity increases with time. From a physical perspective, the growth of Dt;t and U t;t is associated with the concept that the larger eddies wrinkle the instantaneous flame surface as the turbulent flame brush grows. It is worth emphasizing that Eq. (8) is consistent with other parts (Eqs. (11) and (7)) of the whole model. Finally, thanks to the aforementioned extensions that include the laminar-like source term and address the time-dependence of the turbulent flame speed and turbulent diffusivity, we can expect this ETFC model to be more suitable for simulating slow deflagrations, especially in the initial phase following ignition. It is worth reminding that the aim of this paper is to investigate the steam effect prediction capabilities of the codes as well. Indeed, the ETFC model includes differentiation of U l due to steam dilution, according to the different experiments from Table 1. Hence, this model is expected to be more capable for predicting the steam effect. Therefore, the TFC and the ETFC model will be tested and compared in this paper for the slow deflagration regime with steam diluted mixtures. 3.3. Turbulent flame speed closure In order to close the progress variable equation for both combustion models, an expression for the turbulent flame speed U t and U t;1 is needed. Zimont (1979), has theoretically derived the following formulation:

U t  U t;1 ¼ Au0 Da1=4 ¼ Au0




l

u0

sc

1=4

¼ Au0


1=4

st sc

ð11Þ

where A is a constant, Da the Damkohler number, u0 and l the turbulent intensity and integral length scale respectively, and

sc ¼ ju =U 2l the chemical time scale of a corresponding laminar ð8Þ

flame. Here, U l represents the unperturbed laminar flame speed, and ju the thermal diffusivity of the unburned mixture. The

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turbulent flame speed closure was later improved by Lipatnikov and Chomiak (2002) to account for local combustion quenching by strong turbulent stretching, local variations in temperature and mixture composition due to the difference in molecular heat and mass diffusivities. This improved turbulent flame speed model is given as:

U t  U t;1 ¼ Au0


1=4

st sc

FðLeÞGðg cr sg Þ

ð12Þ

Here, the functions FðLeÞ and Gðg cr sg Þ are accounting for preferential diffusion effects and quenching due to stretching effects, respectively. The Lewis number, Le ¼ ju =D, is the ratio of thermal diffusivity of the mixture to mass diffusivity of the deficient reactant. In our case, hydrogen is the deficient reactant. Effects of stretching on flame propagation were not considered in our simulations, which means that the function G is set to unity. Preferential diffusion thermal instability (PDT) effects are important in deflagrations of lean hydrogen-air and hydrogen-air-steam mixtures (Sathiah et al., 2012b). The turbulent burning velocity depends substantially on the Lewis number. The local composition, combustion rate, and temperature inside the flamelets perturbed by turbulent eddies can vary substantially. This is due to the differences between heat losses via molecular thermal conductivity and the reactant supply via molecular diffusion. Recently, preferential diffusion and Lewis number effects were reviewed in detail by Lipatnikov and Chomiak (2005). The function FðLeÞ is defined to address preferential diffusion effects as follows:


FðLeÞ ¼

sc scr

1=4 ð13Þ

where scr is the critical chemical time scale defined by Lipatnikov and Chomiak (2005). This time scale is based on the assumption that a critically curved laminar flamelet is the structure of the leading edge flamelet. The expression for spherical flames is the following:

scr ¼ sc Le1


3=2   Tb hðT b  T r Þ exp 2T b T r Tr

ð14Þ

Here T b is the adiabatic flame temperature of the burned state, h is the activation temperature, and T r is the inner layer temperature given as:

Tr ¼ Tu þ

Tb  Tu Le

ð15Þ

with T u the temperature of the unburned state. A detailed description on this topic can be found in the paper of Sathiah et al. (2012b). 3.4. Laminar flame speed The laminar flame speed of a fuel-air mixture is an important physical-chemical property, which depends on the pressure, temperature, equivalence ratio, and type of the mixture. More details can be found from Sathiah et al. (2012b, 2015). Laminar flame speed measurements for hydrogen-air-diluent mixtures were performed by Liu and MacFarlane (1983) and Bentaib and Chaumeix (2012). In this paper, we rely on the latter more complete correlation from Bentaib and Chaumeix (2012):

U l;0 ¼ ð1:44/2 þ 1:07/  0:29Þð1  wÞ4

ð16Þ

where / is the equivalence ratio and w is the mole fraction of the diluent such as steam. The very same correlation can be also used for lean hydrogen-air mixtures. Here, U l;0 is the laminar flame speed at the reference temperature T ref ¼ 298 K and reference pressure pref ¼ 101325 Pa. It is worth emphasizing that lower U l;0 values

are associated with more diluted mixtures and this effect is explicitly included in ETFC modelling, in the laminar-like source term. 3.5. Effects of compression on flame propagation As a flame propagates in a closed vessel, the unburned gas ahead of the flame is compressed. This leads to an increase in pressure and temperature. Typically, the laminar flame speed is a function of pressure and temperature, which should be properly accounted for. The following equation is used to modify the laminar flame speed as a function of pressure and temperature:

U l ¼ U l;0

p pref

!m


T T ref

n ¼ U l;0

p pref

!a ð17Þ

Here, m and n are the pressure and temperature coefficients, while a is the overall thermokinetic index. For hydrogen-air mixtures, a is used, and the values for lean hydrogen-air mixtures (less than 15 vol.% of hydrogen) are not available. Hence, these value must be obtained by extrapolation. For hydrogen-air-steam mixtures, m and n are used, namely m ¼ 0:5 and n ¼ 2:2 (Sathiah et al., 2015). The unburned density, thermal diffusivity, and molecular mass diffusivity are also modified in the same way as the laminar flame speed to account for compression effects (Sathiah et al., 2012b). 3.6. Ignition method and flame position For the progress variable based models, the procedure is to patch a certain region corresponding to an ignition radius, r k , in the domain with progress variable value equal to one i.e., ~c ¼ 1, which indicates the presence of burned products only. An ignition radius of 8 mm is used in the analyses. As demonstrated by Sathiah et al. (2012a), an increase in the ignition radius leads to a time shift of the results. The flame position obtained from the simulations was extracted from the axial coordinate corresponding to an iso-surface value of ~c ¼ 0:5, as done by Gubba et al. (2009). This method is also used in our previous validation works (Sathiah et al., 2012b, 2015, 2016a, 2016b). 3.7. CFD solution method As described by Sathiah et al. (2012b), a dynamic grid adaptation, or an adaptive mesh refinement (AMR) method is used to resolve the flame brush thickness with different levels of refinement. Adaptive mesh refinement is an efficient method for computing flame propagation in large and complex geometries, since very high grid resolution is required only in the flame front region, while away from the flame, coarser cells can be used without any significant loss of accuracy. The base grid used in the simulations was 4 cm by 4 cm. However, the grid around the ignition region was additionally refined to much smaller size, i.e. approximately 1 mm, to retain the circular shape of the ignition region and to reduce the initial spatial discretization errors. The time step is selected corresponding to a maximum Courant number CFL ¼ 0:8 (Sathiah et al., 2012b). Heat transport to the vessel walls by means of convection and radiation were accounted for in the simulation. The applied discrete ordinates (DO) radiation model uses a steam absorption coefficient evaluated via a user defined function in order to account for different steam concentrations. Stagnant flow conditions were applied as initial conditions. Since the initial turbulence parameters have not been measured in the THAI experiments, best guess values of 1.5e-04 m2 s2 and 4.8e-05 m2 s3 were assumed for the turbulent kinetic energy and the turbulent dissipation rate respectively. The corresponding values of the

A. Cutrono Rakhimov et al. / Nuclear Engineering and Design 311 (2017) 142–155 Table 2 General features of the CFD analyses. Solver Numerical scheme Turbulence approach Turbulence model Spatial discretization Time integration

2D axisymmetric, density based, coupled Explicit, CFL = 0.8 URANS Standard k-e with buoyancy effect 2nd Order Upwind 4th Order Runge Kutta

Walls Near-wall treatment

No slip Enhanced wall treatment

Fluid properties

Composition and temperature dependent ideal gas

Radiation Convective flux

Discrete ordinates uncoupled (DO) Flux difference splitting (FDS)

turbulent length scale and turbulent intensity are 0.006 m and 0.01 m/s. These values were also used for the validation process of the experiments considered in previous papers of this series. It is worth stressing that our best guess values for initial turbulence are not tuned to match any of the experimental results and are applied to each simulation, which is consistent with our previous works (Sathiah et al. 2012a, 2012b, 2015, 2016a, 2016b). The applied numerical schemes and general features are listed in Table 2.

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(u0 =U l;0 ) versus the normalized integral length scale (l=lf ). The simulated THAI experiments cover the flame regimes expected in a nuclear reactor containment during severe accident conditions. The CFD model presented in Section 3 is validated against slow deflagration experiments presented in Table 1. The experimental data and the CFD results are compared for the following most important parameters: the maximum pressure, the pressure rise (dp/dt), and the associated flame front propagation in axial direction. Detailed sensitivity studies were performed to guarantee grid and time step independent results. From experimental data, no clear time has been specified for the ignition, since the activation of the spark igniter does not mean in every case the immediate initiation of the deflagration at the same time. Particularly in lean mixtures, there is sometimes a considerable time delay between activation of the igniter and the beginning of observable deflagration phenomena, which can be clearly observed for test HD-24 (Kanzleiter and Langer, 2010; ISP-49, 2011). Indeed, for test HD24, deflagration is observed from 3 s after ignition (Fig. 3). On the other hand, the current simulations are not able to represent the same time delay from ignition to observable deflagration phenomena as the experimental ones. The TFC results are presented on the left side of the figures and the ETFC results are presented on the right side. 4.1. RUN HD-15

4. Results and discussion Borghi (1985) proposed a classification of the different regimes of combustion based on the turbulent Reynolds number (Ret ), the Karlovitz number (Ka), and the Damkohler number (Da). Considering lean hydrogen-air mixtures, the regimes of combustion that would be the most relevant to nuclear power plants, are shown in Fig. 5a: the wrinkled flamelet regime, for which the Ret > 1, and u0 =U l;0 < 1, the corrugated flamelet regime, for which u0 =U l;0 > 1 and Ka < 1, the thickened flame regime (or thin reaction zone) Ka > 1 and Da > 1. Relevant regimes of turbulent combustion to nuclear power plants are covered in a recent experimental study on the effect of turbulence on the propagation speed of hydrogen-air flames. These experiments are performed by CNRS in a spherical bomb and reported in NURETH-16 Paper (Goulier et al., 2016). In order to report simulated flame propagations on the Borghi diagram, turbulent quantities have been evaluated from some selected flame front positions, which cover a range from 1 m height to the top of the THAI facility. Runs using the ETFC model are represented in Fig. 5b, where the different turbulent regimes are identified by plotting the normalized turbulent intensity

The HD-15 experiment is the reference case for the steam effect investigation. It has no steam content, 9.9 vol.% H2, while the initial temperature and pressure were 366 K and 1.504 bar respectively. The TFC and the ETFC combustion models are compared using the standard k  e turbulence model and three different levels of AMR. From Figs. 6 and 7, it can be concluded that: (a) the TFC combustion model is more mesh sensitive, and at least two AMR levels are recommended, while the ETFC combustion model is more robust regarding mesh resolution; (b) the peak pressure is slightly under-predicted with both combustion models; (c) the pressure rise is predicted very well by the ETFC model, while the TFC model shows a slight deviation from experimental results; (d) the flame front propagation is captured better by the ETFC model as well, but for both models, a higher mesh refinement leads to an earlier arrival of the flame front. In the relatively large test vessel, combustion produces large scale convection which displaces and mixes burned and unburned mixture and thus increases flame speed during the ongoing deflagration process. This effect can be observed only in large scale test facilities (Kanzleiter and Langer, 2010; ISP-49, 2011). While

Fig. 5. (a) Borghi diagram with the domain of possible regimes in case of a nuclear power plant accident (Goulier et al., 2016). (b) Borghi diagram for the simulated THAI experiments using ETFC model.

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Fig. 6. Comparison of the measured (symbols) and predicted (lines) pressure evolution for THAI HD-15.

Fig. 7. Comparison of the measured (symbols) and predicted (lines) flame front position for THAI HD-15.

acoustic effects (high frequency pressure waves) can be observed in test HD-15, this effect is not captured in the simulations. Combustion simulations are characterized by a strong coupling between large scale convection and the shape of the flame front resulting from the combustion modelling. As observed in Fig. 7, the flame front predicted by the ETFC model matches the measurements very well up to 6 m. After 6 m, the models start to under-predict the propagation. The reason might be that large scale convection is no longer captured well, either due to some problems with the convection modelling, or due to combustion modelling limitations. More details might be obtained from 3D simulations. In addition, the flame front deviation after 6 m can be to some extent the result of the acoustic wave effect and its interaction with the flame front not being captured. Indeed, the flame front reaches 6 m axial position in the vessel at 1.5 s, which is where the acoustic effect starts to be noticeable based on the scatter in the experimental pressure values.

4.2. RUN HD-22 The HD-22 experiment uses a mixture of 25 vol.% steam content, and 9.9 vol.% H2, while the initial temperature and pressure were 365 K and 1.487 bar respectively. From Figs. 8 and 9, it can be concluded that: (a) the TFC combustion model is again more mesh sensitive and at least two AMR levels are recommended, while the ETFC combustion model is more robust; (b) the peak pressure is predicted better using the ETFC combustion model; (c) the overall pressure rise is predicted qualitatively well with both models, most of all close to the peak pressure; (d) the flame front propagation is captured better with the ETFC model, but again, for both models a higher mesh refinement leads to faster flame propagation. As observed in Fig. 9, both models slightly under-predict the final stage of the flame front propagation after 8 m. Again, the

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Fig. 8. Comparison of the measured (symbols) and predicted (lines) pressure evolution for THAI HD-22.

Fig. 9. Comparison of the measured (symbols) and predicted (lines) flame front position for THAI HD-22.

reason might be that large scale convection is no longer captured well, as previously discussed for the HD-15 case. Compared to the HD-15 test, acoustic effects on the experimental data are observed after the flame reaches the top of the vessel (from 3 s on), influencing the pressure rise. The acoustic effect is not included in the simulations, thus a smooth pressure built-up is obtained. In order to capture those weak acoustic effects, higher than 2nd order spatial discretization schemes may be required. 4.3. RUN HD-24 The HD-24 experiment has 48 vol.% steam content, and 9.8 vol.% H2, while initial temperature and pressure were 363.5 K and 1.472 bar respectively. As observed on the right side of Fig. 10, a pressure flattening was observed for two and three AMR with the ETFC combustion model. This peak pressure flattening is due to a

source term drop in the simulations when the flame reaches the top of the facility, which we have not been able to explain thus far. From Figs. 10 and 11, it can be concluded that: (a) the TFC combustion model is again more mesh sensitive and at least two AMR levels are recommended; (b) the peak pressure is over-predicted with both combustion models using one level of adaptive mesh refinement; (c) regardless the time shift, the pressure rise is predicted quite well with both models, with slight over-prediction for the TFC model in the second half of the rise. Overall, no significant improvement can be achieved using the ETFC model for case HD-24. The flame front propagation is over-predicted during the first 2–3 m. As observed from experimental points in Fig. 11 and flame propagations in Fig. 2, combustion is erratic and slow in test HD24. The flame front propagates chaotic which makes it difficult to compare the flame propagation results. Acoustic effects on the pressure transient are not observed for HD-24.

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Fig. 10. Comparison of the measured (symbols) and predicted (lines) pressure evolution for THAI HD-24.

Fig. 11. Comparison of the measured (symbols) and predicted (lines) flame front position for THAI HD-24.

4.4. Effect of steam on slow deflagration

4.5. Quantitative comparison

The qualitative prediction of the steam effect by the TFC and the ETFC model using three levels of adaptive mesh refinement is presented in Figs. 12 and 13, since completely mesh independent results were not yet achieved. Overall, the steam effect is predicted qualitatively well with both combustion models, but the ETFC model appears to be more accurate for the pressure rise prediction than the TFC combustion model. Moreover, the peak pressure as well as the reduction of peak pressure with increasing steam concentration is better captured with the ETFC model. This better capability is most likely obtained thanks to the laminar flame speed inclusion in the ETFC modelling as an additional input characterizing the mixture properties and therefore lower U l values with increasing steam content, as explained in Section 3.4.

In case of a hydrogen deflagration, the prediction of the pressure dynamics is important. Typically, two important parameters are used to define pressure dynamics. These are the peak value of the pressure and the rate of pressure rise, which can be used in the design of a vessel or containment against deflagration damage. The experimental pressure profiles were filtered using 0.1 s window for the moving averaging, and analysed in order to obtain a relevant maximum values. From Table 3, we can conclude that the ETFC model is more accurate than the TFC model concerning the computation of the effect of the steam on the peak pressure and the decreasing pressure values with increasing steam amount, regardless of the of AMR level used. This effect is due to the laminar flame speed computed with the correlation (Eq. (20)) from Bentaib

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Fig. 12. Comparison of the measured (symbols) and predicted (lines) pressure evolution for THAI HD-15, HD-22 and HD-24. Predictions by the TFC model.

Fig. 13. Comparison of the measured (symbols) and predicted (lines) pressure evolution for THAI HD-15, HD-22 and HD-24. Predictions by the ETFC model.

and Chaumeix (2012), which eventually affects the pressure history. The over-prediction of the flame front propagation as observed in Section 4.3 is slightly affecting the peak pressure for the run HD-24. Hence, a small correlated over-prediction of the peak pressure is observed (4.8–8.6%). A slight under-prediction is reported for the case HD-24 using the ETFC model and higher AMR levels due to flattening of the computed pressure history before the peak pressure is reached, as shown in Fig. 10. The experimental pressure rises dp/dt were filtered and analysed, as for the peak pressure analysis, in order to obtain relevant maximum values. First, a local maximum dp/dt was evaluated. From Table 4, we conclude that the ETFC model is somewhat more accurate concerning the prediction of the effect of steam on the maximum local pressure rise values by means of decreasing values with increasing steam amount, regardless the AMR level used.

Given the difficulties in simulating HD-24 case with ETFC model and higher levels of AMR, results of the pressure rise should be taken with caution. On the other hand, the slope of the computed pressure rise with the ETFC model is more in accordance with the experimental slope, compared to the TFC model’s over-prediction in pressure rise, as shown in Fig. 10. Both models show larger under-prediction if there is no steam in the mixture, which is in agreement with conclusions of previous papers of this series. Secondly, an average significant dp/dt was evaluated for eventual structural analysis. For this purpose, values corresponding to a rise greater than 0.1 MPa/s are selected for averaging before the peak pressure is reached. From Table 5, we conclude that the ETFC model is somewhat more accurate concerning the prediction of the effect of steam on the overall average pressure rise value, regardless the AMR levels used.

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Table 3 Peak pressure. Experiment [Pa]

HD15

5.005E+05

HD22

4.761E+05

HD24

4.245E+05

TFC [Pa] (dev%)

ETFC [Pa] (dev%)

1 AMR

2 AMR

3 AMR

1 AMR

2 AMR

3 AMR

4.844E+05 3.2% 4.900E+05 +2.9% 4.583E+05 +8.0%

4.819E+05 3.7% 4.896E+05 +2.8% 4.610E+05 +8.6%

4.776E+05 4.6% 4.910E+05 +3.1% 4.545E+05 +7.1%

4.886E+05 2.4% 4.812E+05 +1.1% 4.446E+05 +4.8%

4.886E+05 2.4% 4.785E+05 +0.5% 4.211E+05 0.8%

4.866E+05 2.8% 4.809E+05 +1.0% 4.162E+05 1.9%

Table 4 Maximum local pressure rise dp/dt. Experiment [Pa/s]

HD15

3.701E+05

HD22

2.613E+05

HD24

1.850E+05

TFC [Pa/s] (dev%)

ETFC [Pa/s] (dev%)

1 AMR

2 AMR

3 AMR

1 AMR

2 AMR

3 AMR

2.435E+05 34.2% 2.196E+05 16.0% 2.239E+05 +21.0%

2.233E+05 39.7% 2.120E+05 18.9% 2.486E+05 +34.4%

1.688E+05 54.4% 2.224E+05 14.9% 2.298E+05 +24.2%

2.607E+05 29.6% 2.446E+05 6.4% 1.725E+05 6.8%

2.626E+05 29.0% 2.466E+05 5.6% 1.500E+05 18.9%

3.103E+05 16.2% 2.385E+05 8.7% 1.527E+05 17.5%

1 AMR

2 AMR

3 AMR

1 AMR

Table 5 Mean pressure rise. Experiment [Pa/s]

TFC [Pa/s] (dev%)

ETFC [Pa/s] (dev%) 2 AMR

3 AMR

HD15

2.245E+05

1.702E+05 24.2%

1.568E+05 30.1%

1.907E+05 15.0%

1.929E+05 14.0%

1.853E+05 17.4%

2.001E+05 10.9%

HD22

2.087E+05

1.726E+05 17.3%

1.677E+05 19.7%

1.696E+05 18.7%

1.769E+05 15.3%

1.771E+05 15.1%

1.710E+05 18.0%

HD24

1.384E+05

1.577E+05 +14.0%

1.666E+05 +20.4%

1.597E+05 +15.4%

1.304E+05 5.8%

1.255E+05 9.3%

1.326E+05 4.2%

5. Summary and conclusions The presented CFD-based method is applied to simulate turbulent flame propagation in the slow deflagration regime in hydrogen-air-steam mixtures. The method consists of solving the Navier-Stokes equations using a density-based coupled solver together with the standard k  e turbulence model and two combustion models, namely the Turbulent Flame Speed Closure (TFC) based on Zimont model (Zimont, 1979) and an Extended Turbulent Flame Speed Closure (ETFC) model of Lipatnikov and Chomiak (2002). Validation of these combustion models together with adaptive mesh refinement has been executed using three experiments performed in the medium-scale THAI facility, as presented in Table 1. For each validation case, a detailed mesh sensitivity study was performed by changing the levels of adaptive mesh refinement. The selected experiments show a reduction of the maximum pressure, the rate of pressure rise, and the flame front propagation speed, while increasing the initial steam concentrations in the mixtures. The implemented combustion models were able to reproduce these trends qualitatively well in almost all of the conducted simulations. Furthermore, quantitative analyses indicate a prediction of the peak pressure within 9% accuracy, while both the maximum and the mean pressure rises were predicted within about 4–55% accuracy. The TFC model is based on the gradient of the progress variable jr~cj in the turbulent source term. On the other hand, the ETFC model is based on ~cð1  ~cÞ in the laminar-like source term, which dominates during initial flame propagation. As a result, the TFC model needs higher mesh resolu-

tion and the current tests showed how mesh refinement has more influence on the TFC model results. Hence, the ETFC model is somewhat more robust. Indeed, the pressure development in the simulations of HD-15 and HD-22 with the ETFC model show only minor differences and one level of AMR appears to be sufficient. However, grid independent solutions are not completely achieved so far, due to both a pressure profile flattening for case HD-24, and flame front positions which still show some deviations using more AMR levels. For all current tests, a finer mesh leads to an earlier arrival of the flame at a given axial position. Any grid refinements above three levels of AMR are considered computationally too demanding for the considered cases. For the current tests, the effect of steam on the experimental peak pressure is captured somewhat better by the ETFC model than the TFC model. More specifically, the ETFC model captures the lower peak pressure with increasing steam content somewhat better. Finally, the ETFC model qualitatively represents the experimental pressure rise for the current tests in a better way as well. From quantitative point of view, regarding the TFC model, we conclude that: (a) the model is more mesh sensitive and two levels of AMR were at least needed for the current tests; (b) the maximum dp/dt is computed with less than 19% under-prediction for run HD22 and less than 35% over-prediction for run HD-24; (c) the mean dp/dt is computed with less than 20% under-prediction for run HD22 and less than 21% over-prediction for run HD-24; (d) the peak pressure is computed with less than 9% over-prediction when steam is involved. Regarding the ETFC model, we conclude that: (a) the model gives almost consistent results among the increasing levels of adaptive mesh refinement, despite the fact that

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completely grid independent solutions were not yet achieved; (b) the maximum dp/dt is adequately evaluated for the current tests, with less than 9% under-prediction for run HD-22 and less than 19% under-prediction for run HD-24; (c) the mean dp/dt is computed with less than 18% under-prediction for run HD-22 and less than 10% under-prediction for run HD-24; (d) the peak pressure is evaluated with less than 5% accuracy when steam is involved. For case HD-24, the ETFC model produces a significant change in the shape of the pressure development with two and even three levels of AMR, which we have not been able to explain so far. Overall, no strong improvement can be observed using the ETFC model for case HD-24. In order to apply the presented CFD-based combustion modelling to real-scale containment applications, further validation is needed to simulate uniform and non-uniform hydrogen-airsteam mixtures in the slow deflagration regime. Conflict of interest The authors declare that they have no conflict of interest. Acknowledgments The authors would like to thank the Dutch Ministry of Economic Affairs for financial support and the Slovenian Research Agency (ARRS). All participants to the OECD-NEA THAI project are appreciated for their collaboration and contributions. A special thanks is addressed to Becker Technologies for producing the valuable experimental data. References Alvares, N.J., Beason, D.G., Eidem, G.R., 1982. Investigation of Hydrogen Burn Damage in The Three Mile Island Unit 2 Reactor Building. Tech. Rep., Nuclear Regulatory Commission (NRC), USA. ANS Committee, 2012. Fukushima Daiichi: ANS Committee Report. Tech. rep., American Nuclear Society Special Committee, Illinois, USA. ANSYS Fluent, 2008. ANSYS-Fluent Inc. Bentaib, A., Chaumeix, N., 2012. SARNET H2 Combustion Benchmark Diluent Effect on Flame Propagation Blind Phase Results. Tech. Rep., IRSN. Bentaib, A., Caroli, C., Chaumont, B., Chevalier-Jabet, K., 2010. Evaluation of the Impact that Pars have on the Hydrogen Risk in the Reactor Containment:

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