Implementation and validation of the condensation

Nuclear Engineering and Design 270 (2014) 34–47

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Implementation and validation of the condensation model for containment hydrogen distribution studies Srinivasa Rao Ravva a,b,∗ , Kannan N. Iyer a , S.K. Gupta b,1 , Avinash J. Gaikwad b a b

Indian Institute of Technology-Bombay, Powai, Mumbai 400076, Maharashtra, India NSAD, Atomic Energy Regulatory Board, Mumbai 400094, Maharashtra, India

h i g h l i g h t s • • • •

A condensation model based on diffusion was implemented in FLUENT. Validation of a condensation model for the H2 distribution studies was performed. Multi-component diffusion is used in the present work. Appropriate grid and turbulence model were identified.

a r t i c l e

i n f o

Article history: Received 5 June 2013 Received in revised form 13 December 2013 Accepted 17 December 2013

a b s t r a c t This paper aims at the implementation details of a condensation model in the CFD code FLUENT and its validation so that it can be used in performing the containment hydrogen distribution studies. In such studies, computational fluid dynamics simulations are necessary for obtaining accurate predictions. While steam condensation plays an important role, commercial CFD codes such as FLUENT do not have an in-built condensation model. Therefore, a condensation model was developed and implemented in the FLUENT code through user defined functions (UDFs) for the sink terms in the mass, momentum, energy and species balance equations together with associated turbulence quantities viz., kinetic energy and dissipation rate. The implemented model was validated against the ISP-47 test of TOSQAN facility using the standard wall functions and enhanced wall treatment approaches. The best suitable grid size and the turbulence model for the low density gas (He) distribution studies are brought out in this paper. © 2014 Elsevier B.V. All rights reserved.

1. Introduction Large amounts of hydrogen could be generated and released into the containment during accident conditions in a typical nuclear power plant and its combustion may threaten the integrity of the containment. For the containment’s integrity assessment, it is imperative that a detailed knowledge of the local distribution of hydrogen, steam and air inside the containment is necessary. Detailed description of flow patterns and gas distributions can be obtained through the CFD analysis. Further, these codes also allow users to integrate different models for simulating the basic phenomena. Steam condensation controls the steam presence in the containment in the medium and long term which affects the

∗ Corresponding author at: NSAD, Atomic Energy Regulatory Board, Mumbai 400094, Maharashtra, India. Tel.: +91 22 25990468; fax: +91 22 25990499. E-mail addresses: [email protected] (S.R. Ravva), [email protected] (K.N. Iyer), [email protected] (S.K. Gupta), [email protected] (A.J. Gaikwad). 1 Formerly with Atomic Energy Regulatory Board. 0029-5493/$ – see front matter © 2014 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nucengdes.2013.12.047

mixing process and hence needs to be modeled. The commercial CFD codes do not have condensation models incorporated as a standard feature and this needs to be implemented before using it for hydrogen distribution analysis. The objective of this paper is to identify the best suited condensation model based on the available works and demonstrate that the chosen model is accurate and computationally efficient. In this direction, a best available condensation model was identified and implemented in the CFD code FLUENT. The condensation model implemented is based on Chilton–Bird formulations and is similar to the model presented by Arijit Ganguli et al. (2008) and Houkema et al. (2008). However, the validation details with regard to local behavior were not presented. This paper brings out the local behavior (temperature, velocities, species volume fractions, etc.) in addition to the global behavior. Houkema et al. (2008) used the diffusion coefficients which are determined for a constant temperature level and are kept constant during the calculation. The Fickian diffusion is valid when the mixture composition is not changing. Hence, the multi component diffusion treatment is used in this analysis. Malet et al. (2010) performed and compiled the

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35

Condensate film

Nomenclature A, B, C constants in Antoine equation wall surface area (m2 ) Awall Cp specific heat (J/kg-K) C1ε , C2ε , C3ε Constants D diffusion coefficient (m2 /s) F force vector (N)or user defined sources Generation of turbulence K.E. due to mean velocity Gk gradients Gb Generation of turbulence K.E. due to buoyancy Gω Generation of ␻ g gravitational acceleration (m/s2 ) gm mass transfer coefficient (kg/m2 s) species enthalpy (energy/mass) hj J diffusion flux of species k kinetic energy per unit mass (J/kg) turbulent kinetic energy (m2 /s2 ) k keff effective thermal conductivity (W/mK) ˙ mass flow rate (kg/s) m p pressure (Pa) heat flux (W/m2 ) q R net rate of production of species user defined source S t time (s) temperature (K) T u, v velocity (m/s) v overall velocity vector (m/s) w mass fraction steam mass fraction x Y dissipation YM fluctuating dilatation in compressible turbulence to the overall dissipation rate distance from the cell center to the wall (m) y y+ dimensionless distance to the wall Greek letters ε turbulence dissipation rate (m2 /s3 ) kinematic viscosity (m2 /s)   density (kg/m3 ) ¯¯ stress tensor (Pa)  turbulent Prandtl numbers for k and ε dynamic viscosity (Pa-s)  Subscripts cd condensation cell in the center of the cell contiguous to the wall cv convection condensate liquid film f i interface i, j species non-condensable gas g l liquid phase ref reference sat saturated condition wall w wall at the wall turbulence t h heat mass m k turbulent kinetic energy ε turbulent dissipation specific dissipation rate ω

Gaseous boundary layer Noncondensable concentration Steam concentration T TI Temperature Tw profile Fig. 1. Film condensation with non-condensables on a wall.

ISP-47 exercise on the validation of condensation models and recommended that the effect of mesh size (standard wall function and enhanced wall treatment) on the predictions should be studied for developing best practice guidelines. The present work deals with these two approaches and attempt to identify the best suited turbulence model and the grid for light gas distribution analysis. Such a model will be useful in formulating the best practice guidelines. Many previous authors attempted to address the condensation in the presence of non-condensables. If one needs to model this process from first principles using mechanistic approach of heat and mass transfer, very fine computational grid is necessary near the condensation surface, which leads to long computational times for containment simulations. To reduce the computational time, Klijenak et al. (2006) have directly employed experimental correlations for condensation that have been obtained by Uchida. Other experimental correlations of Dehbi, Liu, etc. are also cited by Rosa et al. (2009). These correlations have been obtained to characterize the average condensation. The applicability of such correlations to predict the local behavior in containment is questionable. Kudriakov et al. (2008) have used Chilton–Colburn correlation based on heat and mass transfer analogy to characterize the local condensation. Gido-Koestel, Herranz, Pieterson, Kim and Corradini correlations based on heat and mass transfer analogy are also cited in the literature by Arijit Ganguli et al. (2008), Houkema et al. (2008) and Malet et al. (2010). The models that are based on heat and mass transfer correlations which were developed from integral experiments do not have a strong fundamental base as the bulk flow parameters appear in these correlations have been assumed to be the value in the wall adjacent node and hence depends on the computation grid used for a particular problem. The cells should be coarser for appropriate bulk flow parameters at the cost of the other important phenomena. The authors of these models also have pointed out this deficiency. Film condensation process is shown schematically in Fig. 1, where condensation takes place on the gas–liquid interface. Gradients of steam and non-condensables develop across the gaseous boundary layer (Collier, 1972; Incropera and DeWitt, 1996). Martin-Valdepenas et al. (2005, 2007) developed a model in which liquid film resistance is considered. The liquid film heat transfer coefficient is obtained using Nusselt condensation model with correction factors for surface waviness (Terasaka and Makita, 1997). The heat flux due to condensation involves an empirical function obtained by fitting experimental data. The interface temperature is calculated iteratively. There are several effects that are not considered in the Nusselt liquid film theory which can affect the

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heat transfer through the liquid film; among them, the turbulence that can be established when the condensate length is high, or the momentum transfer from the condensate gas to the liquid that produces a shrinkage of the film (suction effect over the liquid). A model based on the diffusion and on the formulations of Chilton and Bird is an integral model. The modeling approach involves solving of the governing equations using CFD package and the simulation of wall condensation phenomena through boundary conditions which can be implemented through user defined functions (UDFs). This approach is likely to give better results as they are theoretically more general and they are applicable to all ranges of conditions and can capture all the factors influencing the condensation process in presence of non-condensable gases. Film may or may not be considered in this integral approach. 2. Present work From the above discussion, the approach followed for simulation of condensation behavior based on the diffusion and on the formulations of Chilton and Bird likely to give better results as they are theoretically more general and they are applicable to all ranges of conditions and can capture all the factors influencing the condensation process in presence of non-condensable gases. This approach involves solving of the governing equations using the CFD package. The wall condensation phenomenon is simulated through user defined functions (UDFs). The present problem deals with the single phase gas mixture involving species mixing and turbulence. Therefore the governing equations for conservation of mass, momentum, energy and species are solved. Additionally, transport equations for turbulence are solved. FLUENT CFD solver is used for solving these governing equations. Model sensitivity studies are carried out with three different turbulence models in the present work. The following are the governing equations for: Mass conservation: ∂ + ∇ · (v) = Sm ∂t Momentum conservation:

(1)

∂ (v) + ∇ · (vv) = −∇ p + ∇ · () + g + F ∂t Energy conservation:

(2)

 ∂ hj Jj + (¯¯ eff · v)) + Sh (E) + ∇ · (v(E + p)) = ∇ · (keff ∇ T − ∂t j (3) Species conservation: ∂ (Yi ) + ∇ · (vYi ) = ∇ · Ji + Ri + Si ∂t

(4)

Standard k–ε model Turbulent kinetic energy (k-equation):

 ∂

∂ ∂ (k) + (kui )= ∂t ∂xi ∂xj

+

  t ∂k k

∂xj

Turbulent dissipation rate (ε-equation):



− C2ε

+

t ε

ε2 + Sε k

 ∂ε  ∂xj

ε + C1ε (Gk + C3ε Gb ) k

t ε

 ∂ε  ∂xj

+ C1 Sε − C2

ε2 √ k + vε (7)

Shear stress transport k − ω model: Turbulent kinetic energy (k-equation): ∂ ∂ ∂ (k) + (kui ) = ∂t ∂xi ∂xj



+

t k

 ∂k  ∂xj

+ Gk − Yk + Sk

(8)

Specific dissipation rate (ω-equation): ∂ ∂ ∂ (ω) + (ωui ) = ∂t ∂xi ∂xj



t + ω

 ∂ω  ∂xj

+ Gω − Yω + Sω

(9)

The condensation model consists of sinks of steam, total mass, momentum, enthalpy and the turbulent quantities. These sinks are applied to grid cells contiguous to the walls. The condensation model incorporated in the FLUENT is as follows: The convective flow of gas occurs due to steam condensation at the wall. The mass balance of steam at the interface (subscript i) between gas and condensate film at the wall is: Condensation flux = Diffusive transport +Steam transported through bulk motion The condensate flux can then be represented at the interface by: mcond =

D (∂ω) + ωi (mcond )i ∂y

(10)

where ∂ω = ω − ωi , ω and ωi are the specie (vapour) mass fraction in the cells adjacent to the interface and at the interface respectively. Where,  is the density of the vapour and D is the diffusion coefficient. Since the interface is impervious to the noncondensables, the bulk motion of the gas to the interface mcond is equal to the condensation flux mcond . The Eq. (10) can be rearranged as mcond =

D (ω − ωi )

y 1 − ωi

(11)

The mass fraction ωi of steam at the interface of the condensate film is calculated from the vapour pressure at the interface. The Antoine equation is used for describing the vapour pressures as a function of the temperature: p



pref(pa)

=A+

B T +C

(12)

The coefficients A = 23.1512, B = −3788.02 K and C = −47.3018 K were fitted on data from steam tables. In the present work, the since the thermal resistance due to condensate film is neglected, the interface temperature is assumed as wall temperature. Therefore the boundary condition for mass fraction of steam at the wall is same as at the interface. The mass of the steam which condenses has to be removed through a mass sink (Sm ) at the interface.

(6)

Realizable k − ε model Turbulent kinetic energy (k-equation): k-equation is same as Eq. (5) except for the model constants.

+

ε + C1ε C3ε Gb + Sε k



+ Gk + Gb − ε − YM + Sk



∂ ∂ ∂ (ε) + (εuj ) = ∂t ∂xi ∂xj

ln

(5)

∂ ∂ ∂ (ε) + (εui ) = ∂t ∂xi ∂xj

Turbulent dissipation rate (ε-equation):

Sm =

mcond Af Vcell

(13)

Vcell is the cell volume (m3 ) and Af is the face area (m2 ). The associated enthalpy sink is required to remove the enthalpy associated

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37

with the mass of steam condensed. The enthalpy sink (Sh ) for each cell is calculated by: Sh =

mcond Af Cp (TCell − Tref )

(14)

Vcell

4.8 m

F =

mcond Af ∗ Velocity

2.391 2.1 m

Non-Condensing Zone

(16)

Vcell

Condensed water

Air /Steam / Helium 0.68 m

mcond Af kcell

Condensation Zone (2 m)

1.5 m 3.93 m

(15)

Vcell

The turbulent quantities associated with this mass are also to be removed. The sinks of the turbulent kinetic energy (k) sink is given by: Sk =

4.391

Oil in

Tref is the reference temperature (288.14 K) at which the enthalpy is zero. Cp is the specific heat at constant pressure for vapour. The  is obtained by multiplying the mass of the momentum sink (F) condensate with the velocity.

Non-Condensing Zone Oil Out

0.87 m

Turbulent energy dissipation rate (ε) sink is given by: Sε =

6

mcond Af εcell

(17)

Vcell

Fig. 2. TOSQAN experimental facility.

The above sink terms and species sink (steam sink) are modeled using UDFs and implemented in the CFD code FLUENT. The above model was validated for turbulent flows and has been reported in Srinivasa Rao et al. (2011) against the idealized version of the CONAN Test Facility (Ambrosini et al., 2006). The temperature jump in the film is generally less than 1 ◦ C and the liquid thermal resistance is lower than 5% of the total contribution for the conditions expected in the containment during the accident conditions (Rosa et al., 2009). Hence, interface temperature is assumed as wall temperature and the film thermal resistance is neglected in the present work. 3. Simulation of ISP-47 test conducted in TOSQAN facility The experimental facilities such as TOSQAN (France), MISTRA (Studer et al., 2007), ThAi (Martin Sonnenkalb and Gerhard Poss, 2009), PANDA (Michele et al., 2010) have been used for the containment thermal hydraulic studies. Most of these experimental facilities are equipped with instrumentation for measurement of local temperature, species concentration and velocities. This enables a better understanding of mixing and stratification processes. Besides, local data may be used to assess the validity of simulations performed by CFD codes. These experiments were conducted to assess the capability of CFD and lumped parameter codes in the area of containment thermal hydraulics. TOSQAN is one such facility and is devoted to the study of different basic phenomena especially for the validation of field codes. Wall condensation

3.1. TOSQAN facility The facility is of a cylindrical vessel with an internal volume of 7.0 m3 (Fig. 2) (Emmanuel et al., 2010). The total height of the facility is 4.80 m, and the diameter of the main cylindrical part is 1.50 m. Steam and other gases are injected through a vertical tube of 41 mm inner diameter located at the vessel center-line. The injection opening is located at the elevation 2.10 m with respect to the sump floor. The temperatures of the vessel walls are controlled to maintain the hot and cold zones (upper and lower zones are hot zones and middle zone is the cold zone). Steam gets condensed on the walls located in the cold zone. Instrumentation was provided for measuring temperature, pressure, mass flow-rates, volume fractions, etc. The condensate is drained continuously. The test is composed of a succession of different steady states obtained by varying the injection conditions in the vessel as shown in Fig. 3. Three steady states of air-steam mixture at two different

12g/s

Qsteam 1.4g/s

and buoyancy are addressed under well-controlled initial conditions in a simple geometry in the TOSQAN test facility. The experimental data of TOSQAN test facility and its benchmarking results are presented by Malet et al. (2010). The present study deals with the simulation of the ISP-47 test conducted in TOSQAN experimental facility using the CFD code FLUENT to evaluate the implemented condensation model and also to assess the behavior of non-condensable gases.

1.1g/s

1.1 g/s

0.9 g/s time

Qnc

Air 3g/s 10 min

Air 3g/s 10 min

He1 g/s 10 min

time Pressure

Steady State 1

Steady State 2

Steady State 3

Steady State 4 time

Fig. 3. Injection rates of species and pressure during the experiment.

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S.R. Ravva et al. / Nuclear Engineering and Design 270 (2014) 34–47

Table 1 Boundary conditions. Description

Calculation time (s)

Transient 1

0–1800

Transient 1 + short steady-state 1a Transient—air Steady-state 1 Transient 2 and steady-state 2 Transient 3 Steady-state 3 Transient—air Short steady-state 6b Transient 4

1800–5000 5000–5600 5600–6500 6500–9500 9500–12,000 12,000–13,000 13,000–13,600 13,600–14,000 14,000–14,600

Steady-state 4

14,600–18,000

Steam mass flow rate (g/s)

Injection mean temperature (◦ C)

Air mean flow rate (g/s)

Helium mean flow rate (g/s)

1.40–1.14, linear function of time 1.14 1.14 1.11 12.27 1.11 1.11 1.11 1.11 1.11–0.89, linear function of time 0.89

124

–

125 125 126 132 131 126 126 126 126

– 3.16 – – – – 3.16 – –

– – – – – – – – 1.03

101.8 101.8 101.8 107.8 101.8 101.8 101.8 101.8 101.8

138

–

–

101.8

Mean cond.-wall temp. (◦ C) 101.8

Fig. 4. Two-dimensional axi-symmetric model of TOSQAN.

pressures, and one steady state of air–steam–helium mixture were obtained. Each steady state is reached when condensation rate becomes equal to the steam injection flow rate. The objective of the first two steady states is to produce two different kinds of flows by changing the injection mass flow rate. Third steady state is similar to the first steady state except the differences in the initial conditions of the vessel and was performed to check the influence of initial conditions. The fourth steady state is obtained with the helium. The objective of this fourth steady state is to study the behavior of light gas (helium) on the mixing, the mass distribution and the condensation. 3.2. Simulation of boundary conditions Initial conditions of the facility, the injection flow rates of species viz. steam, air, helium and temperatures with time and the wall temperature characteristics for the condensing and noncondensing walls are obtained from the Malet et al. (2010). The facility is maintained at atmospheric pressure. The facility is initially filled with air at a temperature of 115.4 ◦ C and the condensing wall, upper and lower walls are maintained at 101.3 ◦ C, 122 ◦ C and 123.5 ◦ C respectively. Mass fraction of steam is computed based on the Antoine equation and no slip condition is assumed at the walls. Species Boundary conditions used in the simulation are given in Table 1.

User defined functions (UDFs) were developed for steam mass flow rate, air mass flow rate and helium mass flow rates as they are varying with the time. This was done by simulating the total mass flow rate of all species and mass fraction of individual species, i.e. separate UDFs for mass flow rate and species. Separate UDFs were developed for the condensing wall temperature and injection mean temperature as they are varied with time during the experiment. 3.3. Model The upper, lower and condensing wall temperatures were well controlled and the gases are injected centrally and hence 2-D axisymmetric model is used. Three different grids with 22, 32 and finer gird near the wall in the radial direction are used and are shown in Fig. 4. Total number of nodes in the axial direction considered is 163. The condensation zone from 2.391 m to 4.391 m includes 67 nodes in the axial direction. The air–steam and air–steam–helium atmospheres are treated as single phase gaseous mixtures. The compressible flow model and k − ε turbulent models are used for the simulation. The k–ε turbulence model is used with standard wall functions. The mixture diffusion coefficients are calculated from the user supplied constant binary diffusion coefficients obtained from the handbook of Vargaftik et al. (1981). The time step used in the simulations is 0.1 s

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39

for most part of the transient. However, smaller time step sizes were used in the beginning of the simulations to get convergence. 4. Results and discussion The grid sensitivity study with three different grids (20, 30 cells excluding the nozzle region and finer grid near the wall and at the axis) in the radial directions were carried out using the k–ε turbulence model. Standard wall function approach is used for the first two computational domains and whereas enhanced wall treatment approach is used for the refined grid near the wall and at the axis. The legend ‘TOSQAN’ is used for the experimental data and ‘Resolved’ is used for the finer grid with enhanced wall treatment approach in the following figures. 4.1. Global behavior Predictions and experimental pressure evolution during the test are shown in Fig. 5. The pressure increases with the steam injection and a short steady state is obtained at around 4000 s. Pressure increases further when air injected during 5000–5600 s along with the steam. The first steady state (SS1) is achieved when steam flow rate becomes equal to the condensation flow rate at around 5600 s. Subsequently, steam injected at higher rate and pressure rises suddenly. Again, the pressure remains constant when condensation rate becomes equal to the steam injection rate (SS2). Later, the injection flow rate of steam is reduced and pressure reduces. Again for the period between 12,000 and 13,000 s pressure remains constant (SS3). Later air, steam and helium (to simulate the effect of light gases) are injected and pressure increases again. Subsequently, pressure is predicted to be constant. The trends and magnitudes in general are in good agreement with the experimental values. However, there are slight differences in steady state magnitudes. The wall temperatures in the TOSQAN

Fig. 5. Pressure evolution during the test.

facility are controlled by adjusting oil flow rate. Since the details of oil flow rate, temperature, etc. are not available this could not be modeled. The under-prediction of steady state 2 and 4 may be due to use of isothermal boundary conditions in the computation. These have been seen when the system temperature is high. In the practical situation, as the system temperature increases, the wall temperature also increases due to convective resistance between the oil and steel vessel wall, thereby affecting the condensation. The performance can perhaps be improved by using more appropriate convective boundary condition. The grid size did not have any major influence on the global behavior with the considered grids. 4.2. Local behavior Parameters such as vertical and radial components of gas velocities, temperatures, mole/volume fractions of steam/helium for

Fig. 6. Steam mole fraction snap shots at (a) 1500 s, (b) 2000 s, (c) 3000 s, (d) 4500 s, (e) 5360 s, (f) 6360 s, (g) 8260 s, (h) 9760 s, (i) 12,760 s, (j) 13,760 s, (k) 16,760 s and (l) 18,260 s.

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S.R. Ravva et al. / Nuclear Engineering and Design 270 (2014) 34–47

Fig. 7. Helium mole fraction contours at 14,260 s, 14,760 sand 18,260 s.

Gas Temperature (oC)

130

Grid-20

SS-1

125

TOSQAN Grid-30

120

higher at the axis and decreases in the radial direction toward the walls. Radial profiles of the velocity at 2.8 m and 4.0 m are shown in Figs. 9 and 10 respectively and are over-predicted near the axis. This is due to the lower spreading rate of the plume in the computations as compared to experiments. Experimental data also shows scatter and uncertainty in the measurements. The gas temperature increases slightly toward the walls at the axial location of 1.47 m from the bottom in the non-condensing region (Fig. 11). However, the gas temperatures, at the axial locations 2.68 m and 3.93 m, in the condensing region decrease slightly or almost constant toward the walls (Figs. 12 and 13). The radial profiles of the temperature at 1.47 m, 2.68 m and 3.93 m are shown in Figs. 11–13 respectively and are slightly over-predicted for the grid sizes of 20 and 30 in the radial direction. Steady State 2: The vertical component of velocity (Fig. 14) at the injection location (2.1 m) is higher and gradually decreases along the height. Radial component of velocities (Figs. 15 and 16) at the center in the axial locations are predicted to be maximum and decreases toward the wall. It may be observed that in Figs. 15 and 16, the experimental results do not show symmetry. This may be due to some perturbations in the boundary conditions such as non-ideal cooling walls, disturbances caused by

0.5

Resolved

TOSQAN Grid-20 Grid-30 Resolved

0.4

Velocity (m/s)

steady states 1, 2 and 4 are compared with the experimental data. Since axi-symmetric model is used, the predictions of radial profiles for various parameters are available and plotted from 0 to 0.75 m against the experimental data of −0.75 to 0.75 m. Fig. 6 shows the snap shots of steam mole fraction contours covering the entire test duration. The snapshots from 1500 s to 6360 s indicate higher concentrations of steam in the top region including the condensation region compared to lower regions. Once the condensation reaches to the steam injection rates, the steam concentration in the upper region reduces compared to bottom regions of the vessel. A similar phenomenon occurs in the other steady states. This is also attributed to downward movement of colder non-condensables during the condensation. Fig. 7 shows the helium mole fraction contours during the helium injection, 160 s and 2260 s after completion of injection (during the steady state 4). Helium goes upwards during injection phase (at 14,160 s), and steam gets condensed and non-condensables including helium gets cooler and moves downward just after injection (14,760 s). Finally at 18,260 s, the light gas (helium) tends to move upward, the helium concentration is higher at the top compared to the bottom portion of the vessel. Steady State 1: The first steady state is referred to the time period between 5600 and 6500 s. The vertical profile of the gas temperature is in good agreement with the measured values as shown in Fig. 8 especially when refined grid is used. The gas temperature near the injection location is higher as hot steam enters through the nozzle and decreases along the height as it mixes with the remaining atmosphere. Radial velocities are predicted to be

0.3 0.2

SS-1, Z=2.8 m

0.1 0 -0.1

115 110 2

2.5

3

Elevaon (m) Fig. 8. Gas temperature during SS 1.

3.5

4

-0.2 -0.75

-0.5

-0.25 -2E-15 0.25

0.5

Radial distance (m) Fig. 9. Radial profile of velocity in SS-1 at 2.8 m.

0.75

0.4

Velocity (m/s)

0.3

TOSQAN Grid-20 Grid-30 Resolved

SS-1, Z=4.0m

0.2 0.1 0

Temperature (oC)

S.R. Ravva et al. / Nuclear Engineering and Design 270 (2014) 34–47

-0.1 -0.2 -0.75

120 118 116 114 112 110 108 106 104 -0.75

41

Grid-20 TOSQANSS-1, Z= 3.93 m Grid-30 Resolved

-0.5

-0.25 -2E-15 0.25

0.5

0.75

Radial distance (m) -0.5

-0.25 -2E-15 0.25

0.5

0.75

Fig. 13. Radial profile of temp. in SS 1 at 3.93 m.

Radial distance (m) 7

Temperature (oC)

124

Grid-20 TOSQAN Grid-30 Resolved

122 120 118

Velocity Uz (m/s)

Fig. 10. Radial profile of velocity inSS-1 at 4 m.

SS-1, Z=1.47m

116 114

5

TOSQAN Grid-20 Grid-30 Resolved

4 3 2 1 0

112

2

110 -0.75

-0.5

-0.25 -2E-15 0.25

0.5

3.5

4

4.5

Fig. 14. Vertical component of velocity in SS-2.

2.5

Grid-20 TOSQAN Grid-30 Resolved

Velocity (m/s)

2

Grid-20 TOSQAN Grid-30 Resolved

3

Elevaon (m)

Fig. 11. Radial profile of temp. in SS-1 at 1.47 m.

124 122 120 118 116 114 112 110 108 106 104 -0.75

2.5

0.75

Radial distance (m)

Temperature (oC)

SS-2

6

SS-1, Z=2.68 m

1.5

SS-2, Z=2.8 m

1 0.5 0 -0.5 -0.75

-0.5

-0.25 -2E-15 0.25

0.5

0.75

Radial distance (m) Fig. 12. Radial profile of temp. in SS-1 at 2.68 m.

instruments, etc. Although, the present model is 2-D, the predictions are in reasonable agreement with the experimental data. The vertical and radial components of gas velocity are in good agreement with the measured data especially for the case with the refined grid. Figs. 17–19 show the radial profiles of the steam volume fraction. Steam volume fraction at 1.35 m height, i.e. in the non-condensing zone and is below the injection nozzle remains almost constant in the radial direction. At 2.8 m and 3.93 m where condensation takes place on the walls, the steam volume fraction decreases in the radial direction toward the wall. The trends of the predictions for the radial profile of the steam volume fraction are in good agreement; however, the magnitudes are slightly

-0.5

-0.25 -5E-15 0.25

0.5

0.75

Radial distance (m) Fig. 15. Radial profile of velocity in SS-2 at 2.8 m.

under-predicted. The errors in the prediction of steam volume fractions are in the range of 4–8%. Steady State 4: The trends and magnitudes of the axial (3 cm from the wall) and radial profiles of gas temperature distributions are in agreement with the experimental data as shown in Figs. 20 and 21 respectively. Gas temperature up to the injection location from the bottom is higher and decreases suddenly (Fig. 20) in the condensation zone. Subsequently, temperature increases gradually along the height. Gas temperature remains almost constant in the radial direction at the axial location of 3.93 m. The radial profiles of the velocity at two different locations at 2.8 m and 4.0 m shown in Figs. 22 and 24 are in good agreement with the data except for the case with the refined grid. A closer observation of the contours shown in Fig. 23 suggests the existence of a recirculating

S.R. Ravva et al. / Nuclear Engineering and Design 270 (2014) 34–47

1.4 1.2 1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.75

Grid-20 TOSQAN Grid-30 Resolved

-0.5

0.7

SS-2, Z = 4.0 m

-0.25 -5E-15 0.25

Volume fracon

Velocity (m/s)

42

0.5

SS-2, Z=3.93m

0.65 0.6 0.55

0.45 0.4 -0.75

0.75

TOSQAN Grid-20 Grid-30 Resolved

0.5

-0.5

-0.25 -5E-15 0.25

0.5

0.75

Radial distance (m)

Radial distance (m)

Fig. 19. Steam volume fraction in SS-2 at 3.93 m. Fig. 16. Radial profile of velocity in SS-2 at 4 m.

Volume fracon

TOSQAN Grid-20 Grid-30 Resolved

0.65 0.6 0.55

Gas Temperature (0C)

135

0.7

SS-2, Z=1.35 m

0.5 0.45 0.4 -0.75

-0.5

-0.25 -2E-15 0.25

0.5

130

SS4 - 3cm from wall

TOSQAN Grid-20 Grid-30 Resolved

125 120 115 110 105

0.75

2

1

Radial distance (m)

3

4

Elevaon (m)

Fig. 17. Steam volume fraction in SS-2, at 1.35 m. Fig. 20. Gas temp. at 3 cm from the wall in SS-4.

0.65

SS-2, Z = 2.8m

0.6

TOSQAN Grid-20 Grid-30 Resolved

0.55 0.5 0.45 0.4 -0.75

-0.5

-0.25 -2E-15 0.25

0.5

0.75

116

Gas Temperature (OC)

Volume fracon

0.7

114

SS-4, Z=3.93 m

112 110

Grid-20 TOSQAN Grid-30 Resolved

108 106

104 -0.75 -0.5 -0.25 -2E-15 0.25

Radial distance (m)

0.5

0.75

Radial Distance (m)

Fig. 18. Steam volume fraction in SS 2 at 2.8 m.

Fig. 21. Gas temperature variation in SS-4.

cell captured by the resolved grid for the 2.8 m height, which was not captured by the coarser grids. Similarly at 4.0 m elevation, the observation point lies close to two circulating cells. A small change in the location of the cells would show a large variation in the profile. Hence the apparently deviating profile is due to the presence of the cells. Hence the relative better performance of the coarser grids is fortuitous. Further, it may be noted that the experimental data of velocity measurements also has a lot of scatter indicating the presence of cells, whose positions fluctuate with time. The axial profile of the steam mole fraction is shown in Fig. 25 at 0.375 m from the axis and is slightly under-predicted. The radial profiles of steam and helium volume fractions at three different locations are shown in Figs. 26 and 27 respectively. The steam

fraction and helium mole fractions are slightly under and overpredicted respectively. The parameters such as radial and axial profiles of gas temperatures and volume fractions are better predicted with the refined grid for all the steady states. However, the axial and radial profiles of velocities are better predicted with grid sizes of 20 and 30. Overall, grid size did not have significant impact on the predictions. 4.3. Model sensitivity Light gases mixing and distribution is characterized by turbulence and this makes flow complex, irregular and adds to complexity to the solution of governing equations fluid flow. There

S.R. Ravva et al. / Nuclear Engineering and Design 270 (2014) 34–47

0.3

SS-4, Z= 2.8m Velocity (m/s)

Velocity (m/s)

0.2 0.1 0

Grid-20 TOSQAN Grid - 30 Resolved

-0.1 -0.2 -0.3 -0.75

-0.5

-0.25 -5E-15 0.25

0.5

0.75

43

0.25 0.2 SS-4, Z=4 m 0.15 0.1 0.05 0 -0.05 Grid-20 -0.1 TOSQAN Grid - 30 -0.15 Resolved -0.2 -0.75 -0.5 -0.25 -5E-15 0.25

0.75

Radial distance (m)

Radial distance (m)

Fig. 24. Velocity variation in SS-4 at 4.0 m.

Fig. 22. Velocity variation in steady state 4 at 2.8 m.

0.4

Volume fracon

are many different turbulence models available in the literature. It is unfortunate that no single turbulence model is universally accepted as being superior for all classes of problems. The choice of turbulence models will depend on considerations such as the physics encompassed in the flow, the established practice for specific class of problem, the level of accuracy required, the available computational resources and the amount of time available for simulation. Different types of phenomena are encountered in the containment thermal hydraulics. For example, the buoyancy induced flow plays an important role in hydrogen distribution and mixing in the containment, whereas the low Reynolds number effects play a role in wall condensation phenomena. Therefore, it is imperative to select the best-suited model for the present applications. The objective of the turbulence models is to provide closure for the Reynolds stresses in the Reynolds Averaged Navier Stokes (RANS) equations. The two equation models provide not only for computation of kinetic energy but also for the turbulence length scale or equivalent. In the typical containment hydrogen distribution calculations two equation turbulence models such as the standard k–ε model, k–ω model, low Reynolds k–ε, shear stress transport (SST) model, etc. are widely used. In the present study, Standard k–ε, Realizable k–ε and shear stress transport k–ω models were used. The k–ε model is

0.5

0.35 0.3 0.25

SS-4 at 0.375 m

0.2

TOSQAN Grid-20 Grid-30 Resolved

0.15 0.1 0.05 0 0

1

2

3

4

5

Elevaon (m) Fig. 25. H2 O volume fraction at 0.375 m in SS-4.

implemented in many, if not all, general purpose CFD codes. For real scale simulations, it has been one of the most used models since it was proven to be stable and numerically robust and sufficiently accurate for a broad range of applications. In formulating the k–ε model, equations for k and ε are derived to find suitable closure approximations for the equations governing its behavior.

Fig. 23. Velocity contours for (a) fine grid, (b) Grid-30 and (c) Grid-20.

44

S.R. Ravva et al. / Nuclear Engineering and Design 270 (2014) 34–47

Steam Volume fraon

0.5

SS-4

0.4 0.3 0.2

TOSQAN - 3.93 m Grid-20-3.93 m Grid-30-1.9 m Resolved-1.9m

0.1 0 0

0.15

TOSQAN - 2.8 m Grid-20-2.8 m Grid-30-2.8 m Resolved-2.8m 0.3

0.45

TOSQAN - 1.9m Grid-20-1.9 m Grid-30-3.93 m Resolved-3.93m 0.6

0.75

Radial distance (m) Fig. 26. H2 O volume fraction in SS-4.

Helium volume fracon

0.3

SS-4

0.25 0.2 0.15

Grid-20-1.9 m TOSQAN - 1.9 m Grid-30-1.9 m Resolved-1.9m

0.1 0.05 0 0

0.15

Grid-20-2.8 m TOSQAN - 2.8 m Grid-30-2.8 m Resolved-2.8m 0.3

0.45

Grid-20-3.93 m TOSQAN - 3.93 m Grid-30-3.93 m Resolved-3.93m 0.6

0.75

Radial distance (m) Fig. 27. Helium volume fraction in SS-4.

In this model the coupling between the turbulent model and the Reynolds Average Navier Stokes (RANS) equations is via the turbulent viscosity. The values of k and ε are directly calculated from the differential transport equations for the turbulence kinetic energy and the turbulence dissipation rate. The SST model is a variation to the standard k–ω model called as SST k–ω model, so named because the definition of the turbulent viscosity is modified to account for the transport of the principal turbulent shear stress. This feature gives the SST k–ω model an advantage in terms of performance

Fig. 28. Model sensitivity of pressure evolution.

over both the standard k–ω model and the standard k–ε model (Wilkening et al., 2008). The realizable k–ε model is relatively a recent development and differs from the standard k–ε model and contains a new formulation for the turbulent viscosity. The

Fig. 29. Velocity contours during SS2 (a) k–ε, (b) Realizable k–ε and (c) SST k–ω.

S.R. Ravva et al. / Nuclear Engineering and Design 270 (2014) 34–47

45

130 Standard k-eps

Gas Temperature (oC)

TOSQAN - SS-1

TOSQAN

125

sstkw Realizable k-eps 120

115

110 2.5

2

3

3.5

4

Elevaon (m) Fig. 30. Gas temperature (SS1).

7

0.5

TOSQAN -2.8 m Standard k-eps - 2.8 m Realizable k-eps -2.8 m sstkw -2.8 m

Velocity (m/s)

0.3 0.2

6 Velocity Uz (m/s)

SS-1

0.4

0.1 0

SS-2

5

TOSQAN Standard k-eps Realizable k-eps

4

SSTkw

3 2 1

-0.1

0 2

-0.2 -0.3 -0.75

2.5

3 3.5 Elevaon (m)

4

4.5

Fig. 33. Vertical component of velocity (SS2).

-0.5

-0.25

-5E-15

0.25

0.5

0.75

Radial distance (m) Fig. 31. Radial profile of velocity at 2.8 m (SS1).

transport equation for the dissipation rate (ε), has been derived from an exact equation for the transport of the mean square vorticity fluctuation. This model accurately predicts the spreading of both planar and round jets. It is also likely to provide superior performance for flows involving rotation, boundary layers under strong adverse pressure gradients, separation and recirculation. As seen in the previous section, there are slight differences in predictions with the different grid sizes and slight improvement

in local behavior for the case with the refined grid. Overall, there is no major effect of the grid size on the predictions, therefore the computational domain with the grid size of 20 cells in the radial direction for the turbulence model sensitivity study was considered to save the computational time. The predictions of pressure evolution during the test by the three different turbulent models are similar (Fig. 28). Fig. 29 shows the velocity contours during the steady state 2. The vertical profile of gas temperature (Fig. 30), radial profiles of velocity at 2.8 m and 4.0 m (Figs. 31 and 32) predictions for the steady state 1(SS1) with three different turbulence models are compared with the experimental data. The predictions by all the three models are similar; however the predictions by standard k–ε and

0.4 TOSQAN -4.0 m

SS-1

0.3

Standard k-eps - 4.0 m 2.5 Standard-k-eps -2.8 m TOSQAN - 2.8 m Realizable k-eps - 2.8 m SSTkw -2.8 m

sstkw-4.0 m

0.2

2

0.1

Velocity (m/s)

Velocity (m/s)

Realizable k-eps - 4.0 m

0

1.5

SS-2

1 0.5

-0.1 0

-0.2 -0.75

-0.5

-0.25

-5E-15

0.25

0.5

Radial distance (m) Fig. 32. Radial profile of velocity at 4.0 m (SS1).

0.75

-0.5 -0.75

-0.5

-0.25

-5E-15

0.25

0.5

Radial distance (m) Fig. 34. Radial profile of velocity at 2.8 m (SS2).

0.75

46

S.R. Ravva et al. / Nuclear Engineering and Design 270 (2014) 34–47

1.4

1

SS-2

0.8 0.6 0.4 0.2

TOSQAN

SS-4

130 Gas Temperature (oC)

1.2

Velocity (m/s)

135

Standard-k-eps -4 m TOSQAN - 4 m Realizable k-eps - 4 m SSTkw - 4 m

Standard k-eps Realizable k-eps

125

SSTkw

120 115

0

110

-0.2

105

-0.4 -0.75

-0.5

-0.25

-5E-15

0.25

0.5

1

0.75

Radial distance (m)

2

3 Elevaon (m)

4

5

Fig. 38. Gas temperature at 3 cm from the wall (SS4) at 3.93 m (SS2).

Fig. 35. Radial profile of velocity at 4 m (SS2).

0.6

0.8

0.65

Realizable k-eps - 2.8 m

Volume fracon

Standard k-eps - 2.8 m SSTkw - 2.8 m

0.6

SS-2 at 0.375 m

0.5

0.7

0.55 0.5

0.4 0.3 0.2

TOSQAN Standard k-eps Realizable k-eps SSTkw

0.45 0.1

0.4 0.35

0

0.3 -0.75

1

0 -0.5

-0.25

-5E-15

0.25

0.5

2 3 Elevaon (m)

0.75

Radial distance (m)

4

5

Fig. 39. Steam volume fraction (SS4).

Fig. 36. Radial profile of H2 O volume fraction at 2.8 m (SS2).

0.5

0.8

SS-2

0.7

Standard k-eps - 2.8 m TOSQAN - 2.8 m Realizable k-eps - 2.8 m SSTkw - 2.8 m

SS-4

0.4 0.3 Velocity (m/s)

0.6 0.5 0.4 0.3

TOSQAN - 3.93 m Standard k-eps - 3.93 m

0.2

Realizable k-eps - 3.93 m SSTkw -3.93 m

0.1 -0.75

-0.5

-0.25

-5E-15

0.2 0.1 0 -0.1 -0.2

0.25

0.5

-0.3 -0.75

0.75

Radial distance (m)

-0.5

-0.25

-5E-15

0.25

0.5

Radial distance (m)

Fig. 37. Radial profile of H2 O volume fraction.

Fig. 40. Radial profile of velocity at 2.8 m (SS4).

0.4

SS-4

0.35 Steam Volume fraon

Volume fracon

Volume fracon

TOSQAN - 2.8 m

SS-2

0.75

0.3 0.25

TOSQAN - 3.93 m

TOSQAN - 2.8 m

TOSQAN - 1.9m

0.2

Standard k-eps - 3.93 m

Standard k-eps - 2.8 m

Standard k-eps - 1.9 m

0.15

Realizable k-eps - 1.9 m

Realizable k-eps - 2.8 m

Realizable k-eps - 3.93 m

SSTkw - 1.9 m

SSTkw - 2.8 m

SSTkw - 3.93 m

0.1 0.05 0 0

0.15

0.3

0.45 Radial distance (m)

Fig. 41. Steam volume fraction (SS4).

0.6

0.75

0.75

S.R. Ravva et al. / Nuclear Engineering and Design 270 (2014) 34–47

47

Helium volume fracon

0.3

SS-4

0.25 0.2 0.15 0.1 0.05

Standard k-eps - 1.9 m

Standard k-eps - 2.8 m

Standard k-eps - 3.93 m

TOSQAN - 1.9 m

TOSQAN - 2.8 m

TOSQAN - 3.93 m

Realizable k-eps - 1.9 m

Realizable k-eps - 2.8 m

Realizable k-eps - 3.93 m

SSTkw - 1.9 m

SSTkw - 2.8 m

SSTkw - 3.93 m

0 0

0.15

0.3

0.45

0.6

0.75

Radial distance (m) Fig. 42. Model sensitivity of helium volume fraction (SS4).

realizable k–ε are in better agreement with the experimental data for the SS1. Figs. 33–37 show the vertical component of velocity, radial profiles of the velocities at 4 m and radial profiles of steam volume fractions at 2.8 m and 3.93 m respectively. In general, the predictions by turbulence models standard k–ε and SST k–ω are in close agreement with the experimental data for the steady state 2. Figs. 38–42 show the gas temperature 3 cm from the wall, steam volume fraction, radial profiles of the velocity at 2.8 m, gas temperature, steam and helium mole fractions respectively. The predictions by turbulence models standard k–ε and SST k–ω are in close agreement with the experimental data except for the velocities, where predictions with standard k–ε are only in good agreement. The SST k–ω predictions for velocities are over-predicted. 5. Conclusion A condensation model based on diffusion (Chilton and Bird) was incorporated in the FLUENT CFD code through user defined functions for containment hydrogen distribution analysis. This model was benchmarked against the ISP-47 test of TOSQAN test facility. Grid and turbulence model sensitivity studies were carried out to check the influence on various local parameters. The standard k–ε and realizable k–ε model predictions were in good agreement with the experimental data for the steady state 1. Whereas, the standard k–ε and SST k–ω models predicted well for the steady states 2 and 4 except minor variations. The parameters such as radial and axial profiles of gas temperatures and volume fractions are better predicted with the refined grid for all the steady states. However, the axial and radial profiles of velocities are better predicted with grid sizes of 20 and 30 in the radial direction. Overall, grid size did not have significant impact on the predictions. Therefore, the standard k–ε model can be used for the for the containment hydrogen distribution studies involving condensation phenomena and non-condensable gases with the suitable grid. References Ambrosini, W., Forgione, N., Manfredini, A., Oriolo, F., 2006. On various forms of the heat and mass transfer analogy: discussion and application to condensation experiments. Nuclear Engineering and Design 236, 1013–1027.

Arijit Ganguli, Patel, A.G., Maheshwari, N.K., Pandit, A.B., 2008. Theoretical modeling of condensation of steam outside different vertical geometries (tube, flat plates) in the presence of noncondensable gases like air and helium. Nuclear Engineering and Design 238, 2328–2340. Collier, J.G., 1972. Convective Boiling and Condensation. McGraw-Hill, UK, pp. 314–359. Houkema, M., Siccama, N.M., Lycklama a Nijeholt, J.A., Comer, E.M.T., 2008. Validation of the CFX4 CFD code for containment thermal hydraulics. Nuclear Engineering and Design 238, 590–599. Incropera, F.P., DeWitt, D., 1996. Fundamental of Heat and Mass Transfer, 4th ed. John Wiley & Sons, New York, pp. 556–564. Klijenak, I., Babic, M., Mavko, B., Bajsic, I., 2006. Modelling of containment atmosphere mixing and stratification experiment using a CFD approach. Nuclear Engineering and Design 236, 1682–1692. Kudriakov, S., Dabbenea, F., Studer, E., Beccantinia, A., Magnauda, J.P., Paillèrea, H., Bentaibb, A., Bleyerb, A., Malet, J., Porcheron, E., Caroli, C., 2008. The TONUS CFD code for hydrogen risk analysis: physical model, numerical scheme and validation matrix. Nuclear Engineering and Design 238, 551–565. Malet, J., Porcheron, E., Vendel, J., 2010. OECD international standard problem ISP-47 on containment thermal-hydraulics – conclusions of the TOSQAN part. Nuclear Engineering and Design 240, 3209–3220. Sonnenkalb, M., Poss, G., 2009. The International Test Programme in the THAI Facility and its Use for Code Validation. Eurosafe Conference, Brussels, Belgium. Martin-Valdepenas, J.M., Jimenez, M.A., Martin-Fuertes, F., Fernadez, J.A., 2007. Improvements in a CFD code for analysis of hydrogen behaviour within containment. Nuclear Engineering and Design 237, 627–647. Martin-Valdepenas, J.M., Jimenez, M.A., Martin-Fuertes, F., Fernadez, J.A., 2005. Comparison of film condensation models in presence of non-condensable gases implemented in a CFD code. Heat Mass Transfer 41 (11), 961–976. Andreania, M., Paladinoa, D., George, T., 2010. Simulation of basic gas mixing tests with condensation in the PANDA facility using the GOTHIC code. Nuclear Engineering and Design 240, 1528–1547. Emmanuel, P., Lemaitre, M., Marchand, D., Plumecocq, W., Nuboer, A., Vendel, J., 2010. Experimental and numerical approaches of aerosol removal in spray conditions for containment application. Nuclear Engineering and Design 240, 336–346. de la Rosa, J.C., Escriva, A., Herranz, L.E., Cicero, T., Munoz-Cobo, J.L., 2009. Review on the condensation on the containment structures. Progress in Nuclear Energy 51, 32–66. Srinivasa Rao, R., Thomas, T., Iyer, K.N., Gupta, S.K., 2011. Development of Condensation Model and Implementation in CFD Code for Hydrogen Distribution Calculations, Transactions. SMiRT 21, New Delhi, India. Studer, E., Magnaud, J.P., Dabbene, F., Tkatschenko, I., 2007. International standard problem on containment thermal–hydraulics ISP47. Step 1—Results from the MISTRA exercise. Nuclear Engineering and Design 237, 536–551. Terasaka, H., Makita, A., 1997. Numerical analysis of the PHEBUS containment thermal hydraulics. Journal of Nuclear Science and Technology 34 (7), 666–678. Vargaftik, N.B., Vinogradov, Y.K., Yargin, V.S., 1981. Handbook of Physical Properties of Liquids and Gases, 2nd ed. Hemisphere Publishing Corporation, New York. Wilkening, H., Daniele, B., Matthias, H., 2008. CFD simulations of light gas release and mixing in the Battelle model containment with CFX. Nuclear Engineering and Design 238, 618–626.