Density stratification breakup by a vertical jet: Experimental and numerical investigation on the effect of dynamic change of turbulent schmidt number

The hydrogen behavior in a nuclear containment vessel is one of the significant issues raised when discussing the potential of hydrogen combustion during a severe accident. Computational Fluid Dynamics (CFD) is a powerful tool for better understanding the turbulence transport behavior of a gas mixture, including hydrogen.

Nuclear Engineering and Design 368 (2020) 110785 Contents lists available at ScienceDirect Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes Density stratification breakup by a vertical jet: Experimental and numerical investigation on the effect of dynamic change of turbulent schmidt number T Satoshi Abea, , Etienne Studerb, Masahiro Ishigakia, Yasuteru Sibamotoa, Taisuke Yonomotoa ⁎ a b Thermohydraulic Safety Research Group, Nuclear Safety Research Center, Japan Atomic Energy Agency, 2-4, Shirakata-Shirane, Tokai, Ibaraki 319-1195, Japan DEN-STMF, CEA, Université Paris-Saclay, F-91191 Gif-sur-Yvette, France ARTICLE INFO ABSTRACT Keywords: Density stratification Nuclear containment vessel RANS Turbulent Schmidt number The hydrogen behavior in a nuclear containment vessel is one of the significant issues raised when discussing the potential of hydrogen combustion during a severe accident Computational Fluid Dynamics (CFD) is a powerful tool for better understanding the turbulence transport behavior of a gas mixture, including hydrogen Reynoldsaveraged Navier–Stokes (RANS) is a practical-use approach for simulating the averaged gaseous behavior in a large and complicated geometry, such as a nuclear containment vessel; however, some improvements are re­ quired In this paper, we focused on the turbulent Schmidt number Sct for improving the RANS accuracy Some previous studies on ocean engineering mentioned that the Sct value gradually increases with the increasing stratification strength We implemented the dynamic modeling for Sct based on the previous studies into the OpenFOAM ver 2.3.1 package The experimental data obtained by using a small scale test apparatus at Japan Atomic Energy Agency (JAEA) was used to validate the RANS methodology In the experiment, we measured the velocity field around the interaction region between vertical jet and stratification by using the Particle Image Velocimetry (PIV) system and time transient of gas concentration by using the Quadrupole Mass Spectrometer (QMS) system Moreover, Large-Eddy Simulation (LES) was performed to phenomenologically discuss the in­ teraction behavior The comparison study indicated that the turbulence production ratio by shear stress and buoyancy force predicted by the RANS with the dynamic modeling for Sct was a better agreement with the LES result, and the gradual decay of the turbulence fluctuation in the stratification was predicted accurately The time transient of the helium molar fraction in the case with the dynamic modeling was very closed to the VIMES experimental data The improvement on the RANS accuracy was produced by the accurate prediction of the turbulent mixing region, which was explained with the turbulent helium mass flux in the interaction region Moreover, the parametric study on the jet velocity indicates the good performance of the RANS with the dynamic modeling for Sct on the slower erosive process This study concludes that the dynamic modeling for Sct is a useful and practical approach to improve the prediction accuracy Introduction As emphasized in the Fukushima–Daiichi accident, the hydrogen behavior raises concern for the safety of a light water reactor (LWR) ( Breitung and Royl, 2000; Lopez-Alonso et al., 2017, OECD/NEA, 1999) During a severe accident in an LWR, a large amount of hydrogen gas can be produced by the metal/steam reaction and released in a nuclear containment vessel To understand the mechanism underlying these hydrogen transport phenomena, nuclear research groups have per­ formed experimental and numerical studies on the stratification breakup behavior using several types of jets Computational fluid dynamics (CFD) analysis is a powerful tool for better understanding the hydrogen transport behavior in a nuclear ⁎ containment vessel Thus, many CFD benchmark tests have been con­ ducted under the auspices of Organisation for Economic Co-operation and Development/Nuclear Energy Agency (e.g., international standard problem No 47 (ISP-47) (Allelein et al., 2007; Studer et al., 2007), the SETH project (Auban et al., 2007), the SETH-2 project (OECD/NEA Committee on the Safety of Nuclear Installations, 2012), and the third international benchmark exercise (IBE-3) (Andreani et al., 2016)) The experimental condition for the IBE-3 conducted in the PANDA facility (Paladino and Dreier, 2012) was designed to investigate the stratifica­ tion erosion by a vertical jet from below These benchmark tests in­ dicated that the turbulence model is an important factor in the accurate prediction of hydrogen transport and distribution (Kelm et al., 2019) Considering the computational cost and time, the Reynolds- Corresponding author E-mail address: abe.satoshi@jaea.go.jp (S Abe) https://doi.org/10.1016/j.nucengdes.2020.110785 Received 10 February 2020; Received in revised form 15 May 2020; Accepted 28 July 2020 Available online 02 September 2020 0029-5493/ © 2020 The Author(s) Published by Elsevier B.V This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Nuclear Engineering and Design 368 (2020) 110785 S Abe, et al Fig Schematic of the VIMES apparatus (a) schematic of gas line and test vessel and (b) photograph of test vessel averaged Navier–Stokes (RANS) approach is a practical tool for simu­ lating the averaged gaseous behavior in a large and complicated geo­ metry, such as a real nuclear containment vessel In the OECD/NEA HYMERES (Hydrogen Mitigation Experiments for Reactor Safety) pro­ ject, the k–ε model (Launder and Spalding, 1974) was used as a “common model” (Studer et al., 2018; Andreani et al., 2019) because of its low computational cost and good numerical stability The buoyancy effect on the turbulence property must be accurately estimated to im­ prove the accuracy of RANS modeling on the stratification behavior (Kelm et al., 2019; Abe et al., 2015) In a collaboration research activity of the Commissariat l'énergie atomique et aux énergies alternatives (CEA) and the Japan Atomic Energy Agency (JAEA), we performed a CFD simulation on the HM1-1 benchmark in the OECD/NEA HYMERES project (Studer et al., 2018) In this benchmark test, we focused on the change of the turbulent Schmidt number Sct and Prandtl number Prt in the stratification, which are usually set to constant values of less than unity (Ishay et al., 2015; Tominaga and Stathopoulos, 2007) and di­ rectly affect the turbulence production and turbulence transport beha­ vior However, some recent studies on ocean engineering (Venayagamoorthy and Stretch, 2010; Elliott and Venayagamoorthy, 2011; Strang and Fernando, 2001) mentioned that these numbers dy­ namically change with the increase of the stratification strength We implemented the dynamic modeling for the turbulent Schmidt number Sct and Prandtl number Prt based on the formulation developed by Venayagamoorthy and Stretch (2010) Consequently, the CFD result was in a good agreement with the MISTRA experimental data, in­ dicating that the accuracy was improved by changing Sct and Prt (Abe et al., 2018a,b) Additionally, our study mentioned that a further vali­ dation with detailed experimental data on a simpler condition is re­ quired A small-scale experiment is one useful approach for obtaining the detailed experimental data for the CFD validation Deri et al (2010) measured the velocity field around the interaction region between a vertical jet and stratification in a small-sized rectangular vessel We at the JAEA also constructed a small experimental apparatus, called the VIsualization and MEasurement system on Stratification behavior (VIMES), to observe the gaseous mixture behavior in a rectangular vessel (Abe et al., 2016) The objectives of the VIMES experiment is to visualize the flow field with the Particle Image Velocimetry (PIV) system and measure the time transient of the helium concentration at several locations Several types of obstacles were installed in the test vessel, and the interaction behavior between the complicated flow and stratification was investigated (Abe et al., 2018a,b) In this study, the data from the VIMES test are used for the dynamic modeling for Sct Combined with experimental research, the Large -Eddy Simulation (LES) can provide more insights into the turbulence phenomena; however, it is not realistic to apply it for simulating the gaseous be­ havior in a real containment vessel because of the necessity of high computational cost and time Röhrig et al (2016) performed the LES and RANS on a light gas stratification breakup by a vertical jet in the small-scale vessel conducted by Deri et al (2010) at the CEA This re­ search concluded that the LES yields a decent prediction of the char­ acteristic erosion process Moreover, they mentioned that the RANS approaches manage to capture the overall behavior though with a no­ table lack in accuracy, indicating the improvement of the RANS accu­ racy is required Sarikurt and Hassan (2017) used the LES methodology on the IBE-3 in the PANDA facility and investigated the flow structures for the interaction of a buoyant jet and a stratified layer The research summarized that understanding the interaction mechanism will help quantify the turbulent mass transfer of the gas component In this study, we performed the LES to obtain detailed turbulence properties in the interaction region, such as turbulence fluctuation and turbulent mass flux This paper phenomenologically discusses the interaction behavior between a vertical jet and stratification The capability of the dynamic modeling for Sct in RANS is shown based on a phenomenological un­ derstanding The VIMES experimental data are used to validate the LES and RANS The remainder of the paper is organized as follows: Section describes the VIMES apparatus with the initial and boundary condi­ tions and the brief experimental results; Section presents the nu­ merical and boundary conditions, including the turbulence model, mesh, and discretization schemes, and explains the validity confirmed by various perspectives (i.e., mean and turbulence profiles, velocity spectra, and mesh convergency); Section shows a comparison of the simulation result with the experimental results, and turbulence pro­ duction phenomena obtained by the LES and RANS; Section presents the turbulence mixing behavior in the interaction region between the vertical jet and stratification, and a parametric study to evaluate the capability of dynamic modeling for Sct; and Section summarizes the main conclusions VIMES apparatus The VIMES apparatus had a rectangular acrylic vessel with 1.5 m width, 1.5 m length, and 1.8 m height (Fig 1) Two horizontal nozzles with 0.03 m diameter were inserted for injecting the binary gas of air and helium (as a mimic gas of hydrogen) controlled with two mass flow controllers An upward nozzle with 0.03 m diameter was equipped to Nuclear Engineering and Design 368 (2020) 110785 S Abe, et al inject a vertical jet from the bottom of the test vessel The insert length Hinj was 0.1 m The flow field was visualized with a two-dimensional Particle Image Velocimetry (PIV) This system consisted of 135 mJ Pulsed Nd:Yag laser and a black and white Andor NEO 5.5 camera with a resolution of 2560 × 2160 px and Nikon 50 mm f/1.2 s The PIV system measured with an error of less than 4% on the total momentum flux of a jet at any downstream location The size of the field-of-view (FOV) achieved approximately 500 mm height and 600 mm wide The FOV was set to z = 1.0 to 1.5 m (z/D = 33.3 to 50) to observe the interaction behavior between the jet and stratification The acquisition rate of the PIV system was set to Hz The gas concentration was measured using the Quadrupole Mass Spectrometer (QMS) system with a multiport rotating valve for multipoint measurement The capillary tubes with 1.0 mm inner diameter were connected to the rotating valve The pipe ends were placed at the near corner of the test vessel (Fig 1) The measurement system was validated based on multiple experiments, as mentioned in detail below each parametric case to assess the reproducibility of the VIMES ex­ periments The error bars shown in the figures below are the standard deviations from the independent measurements Studer et al defined the interaction Froude number Fri to express the interaction behavior between the jet and stratification (Studer et al., 2012) Fri = W NL (1) where the W and L are the velocity and the diameter of the jet in the impingement region, respectively (Rodi, 1982), and the N is the char­ acteristic pulsation of the stratification These values are defined as follows: W = 6.2Winj z L = 0.068(z 2.1 Initial and boundary conditions N= All experiments in this paper were performed under the condition of iso-thermal Gas temperature in the initial and inlet conditions was approximately 288.15 (± 5.0 ) deg-K The binary gas of air and helium was injected to build up the initial density stratification, as shown in Fig 2(a) The injection flow rate was 105( ±6.0) L/min The molar fractions of helium and air were 70% and 30%, respectively The in­ jection duration was 420 s Consequently, the density stratification was formed above 1.0 m The maximum value of the helium molar fraction reached approximately 60% at the top of the test vessel A horizontal bar attached to each data point in Fig 2(a) indicates the standard de­ viation taken from nine experiments conducted with the same initial conditions, showing that the helium molar fraction was measured with an error of less than 3% Fig 2(b) compares the time history of the integrated injection volumetric flow rate derived from the mass flow rate and the air–helium mixture volumes estimated from the QMS measurements A good agreement indicates a one-dimensional vertical distribution of helium gas At 120 s from the end of the horizontal injection for the stratifica­ tion buildup, the vertical air jet was initiated with the upward nozzle (Fig 1) to produce the stratification breakup The start time of the jet injection was defined as Time = s in this paper Table shows the experimental case The jet velocity was 5.0( ±0.15) m/s in the base case (Case 1) and 2.5 and 3.8 m/s in the parametric cases (cases and 3, respectively) We performed five tests for the base case and twice for 2g Hinj ) ( D Hinj + (2) (3) s s ) Hs (4) where Winj in Eq (2) is the velocity magnitude at the nozzle exit, and s and Hs are the density and the height of the initial stratified layer, re­ spectively In the VIMES experimental condition, the value of Hs was 0.65 m, where the nominal bottom of the initial stratification was as­ sumed to z = 1.0 m as shown in Fig Table shows the value of Fri in each case 2.2 Main experimental result in case Fig shows the visualized flow field with the PIV system in Case at 46 s The color contour shows the velocity magnitude based on radial and vertical components ur2 + w This figure indicates the upward jet impingement on the stratification and the rebounding flow surrounding this The occurrence of a strong turbulence mixing was estimated from Fig 4, showing the time transients of the helium gas molar fraction at heights of 0.1, 1.3 1.5, and 1.7 m from the bottom of the test vessel The vertical jet achieved approximately z = 1.3 m (Fig 3); hence, the sharp decay of the helium fraction occurred in the lower region of the initial stratification (line for z = 1.3 m, Fig 4) In the upper region, the slow erosive process was kept before the jet achievement The decrease rate then became faster induced by the strong turbulence mixing Fig shows the vertical distribution of the helium molar fraction The bottom of the stratification was pushed up, and the volume of the stratification Fig (a) Vertical distribution of the helium molar fraction at s and (b) time history of the integrated flow of the helium component rate during the stratification buildup with air–helium gas mixture injection The vertical jet was started at time = s Nuclear Engineering and Design 368 (2020) 110785 S Abe, et al Table VIMES experimental and simulation cases VIMES test CFD analysis Initial Stratification Case See Fig Hs=0.65 m ρs=0.56 kg/m3 Case Case Vertical jet D = 0.03 m, Hinj = 0.1 m, ρ0 = 1.17 kg/m3 Fri 5.0 (m/s) 2.0 2.5 (m/s) 1.0 3.8 (m/s) 1.5 Number of test RANS LES Constant Sct Dynamic Sct Performed with Sct=0.85, Sct=8.5 Performed with Sct=0.85 Performed with Sct=0.85 Performed Performed Performed - Performed - region gradually decreased This behavior also indicated that the strong turbulence mixing appeared at the interaction region between the jet and stratification, and the height of the jet achievement gradually rose CFD simulation The CFD simulation was performed with the rhoReactingFoam in OpenFOAM ver 2.3.1 package, an open source code developed by the OpenFOAM® Foundation The governing equation system in this solver consists of the continuity, momentum, and transport equations for mass fraction and enthalpy The detailed description of the momentum and mass transfer equations is shown below 3.1 LES Fig Time transients of the helium molar fraction (%) in the VIMES experi­ ment at z = 0.1 m, 1.3 m, 1.5 m, and 1.7 m in Case The error bars are the standard deviation from five independent experiments The equation governing momentum transport for compressible flow in the LES is t ( u~i ) + xj ( u~i u~j ) = p~ µ + xi xj u~j u~i + xj xi ij xj + cube root of the computational cell volume as follows: gi (5) = where ui, , p, and µ are the velocity component in the ith direction, fluid density, pressure, and molecular viscosity, respectively µ is cal­ culated with the Sutherland equation, consequently corresponding to approximately 1.8e−05 Pa∙s under the condition of 288.15 deg-K in the ambient pressure The fourth term at the right-hand side is the buoy­ ancy term gi is the gravity accelation The overline denotes a threedimensional space filter operation with a filter width Δ derived with the x y z (6) where x , y , and z represent the cell size in the respective coordinate direction The Favre density filtering was employed to reduce the complexity of the compressible equation for the LES This operation is expressed with a tilde The subgrid-scale (SGS) tensor ij must be modeled to close the equation system The Boussinesq approximation, assuming a linear correlation between the SGS tensor and the filtered Fig Instantaneous flow field in the interaction region of the jet and stratification obtained with the PIV measurement in Case The color contour shows the velocity magnitude based on rdial and vertical components ur2 + w (m/s) Nuclear Engineering and Design 368 (2020) 110785 S Abe, et al Table Model constants in the standard k–ε model 0.09 Cµ 1.00 1.30 1.44 1.92 (in stable layer Gk < 0), (in unstable layer Gk k C1 C2 C3 0) (Viollet, 1987) model (Launder and Spalding, 1974) as µt = Cµ k2 (14) Cμ is the model constant generally set to the value of 0.09 The RANS model requires transport equations for the turbulent kinetic en­ ergy k and its rate of dissipation ε to estimate the value of μt: k Fig Time transient of the vertical distribution of the helium molar fraction (%) in Case 1in the VIMES experiment strain rate tensor s~ij = ij = 2µSGS s~ij + ( u~i xj u~j + xi ) t , is utilized as follows: t In the Smagorinsky model [Smagorinsky, 1963], the SGS viscosity µSGS is modeled as µSGS = Cs |s~ij | (8) t xi ~ ( u~i Yk ) = D xi ~ ~ µ Yk Y + SGS k xi ScSGS x i Gk = (9) Gk = = t ( xj ( [ui ][uj]) p + µ xi xj [Yk ]) + xi ( [uj ] [ui ] + xj [u'i u' j] xi [ui ][Yk ]) = [Yk ] xi D xi + p gi [u'i Y 'k ] [u'i Y 'k ] = µt [ui ] + xj Dt [uj ] [Yk ] = xi xi + µt [Yk ] Sct x i k ij ] k + k xi k µ+ xi (15) µt xi (16) (17) gi [u' j '] µt gi Sct (18) (19) xj Rig Sct = Scto exp (10) Scto C1 + Ri g (20) C2 where Sct0 is the turbulent Schmidt number under the neutral condition usually set to less than unity The stratification strength is characterized by the gradient Richardson number Ri g derived with the square ratios of (11) The brackets [ ] denots Reynolds-averaging operation, and the angle brakets < > is expressed the Favre density averaging The terms with a fluctuation component expressed with the prime mark are modeled with a simple gradient diffusion hypothesis as [u'i u' j] = µt 3.2.1 Dynamic modeling for the turbulent Schmidt number Sct The Sct value is generally set to the constant value of less than unity (Ishay et al., 2015; Tominaga and Stathopoulos, 2007) Some studies on ocean engineering mentioned that the Sct value gradually increases with the increasing stratification strength Venayagamoorthy and Stretch (2010) proposed the following formulation: The unsteady Reynolds-averaged equations for momentum and mass fraction transports are described as [ui]) + µ+ To close the equation system, Pk is modeled with the Eq (12) Gk, which is one of the most important factors in this study, is simply ex­ pressed as 3.2 RANS ( C2 [ui ] xj [u'i u' j ] Pk = where Yk means the mass fraction of kth gas, helium, and air in this study D denotes the diffusion coefficients of mass fraction, which is set to the constant value of 6.7e−05 m2/s based on the literature (Fuller et al., 1966) The SGS Schmidt number ScSGS was set to 1.0 t xi where σk, σε, Cε1, Cε2, and Cε3 are model constants Table summarizes these model constants (Launder and Spalding, 1974; Viollet, 1987) Pk and Gk are the production terms of the turbulent kinetic energy by shear stress and buoyancy force, respectively In this study, the model constant Cs was set to 0.1 based on the literature (Wang et al., 2006; ANSYS, 2009) The Favre-filtered trans­ port equation of mass fraction is expressed as ~ ( Yk ) + + [ui ] xi + = [C (Pk + C Gk ) (7) ii ij [ui ] k = Pk + Gk xi + the Brunt–Väisälä frequency Nu = rate S = ( [ui ] xj + ) [uj ] xi g z and the mean shear flow in this paper This formulation was de­ veloped in terms of scalar time scale ratio TL/ T ; TL = k/ is the turbu­ lent kinetic energy decay time scale, and T = ((1/2) < '>2 )/ is the scalar decay time scale, where is the dissipation ratio of scalar fluc­ tuation The DNS results of Shih et al (2000) indicated values of C1 = 1/3 and C2 = 1/4 However, this formulation was validated with the DNS data of Rig = to 0.6, which seems a much smaller range than that in the VIMES experiment Strang and Fernando (2001) proposed a formulation of Sct based on the measurement data of the temperature and velocity at the Pacific (12) (13) where μt and Dt are the turbulent viscosity and the diffusion coefficient, respectively The turbulent Schmidt number Sct is the ratio of μt and Dt μt is calculated with the formulation according to the standard k–ε Nuclear Engineering and Design 368 (2020) 110785 S Abe, et al Ocean near the equator by Peters et al (1988) The proposed for­ mulation indicated that Sct asymptotes the value of 20 as Ri g , although in the above model of Venayagamoorthy and Stretch Sct, it becomes the value of infinity when Ri g The formulation of Ve­ nayagamoorthy and Stretch with the threshold value of 20 was applied in our previous study on the MISTRA HM1-1 test (Abe et al., 2018a,b), and the CFD simulation predicted well the breakup behavior of the density stratification The following formulation was applied herein as the dynamic modeling for Sct: Sct = max Scto, Scto exp Ri g Scto C1 + Rig C2 , 20 Wmean at z = 1.2 m (z/D = 40) from the bottom of the test vessel was then compared with the experimental results and literature (Panchapakesan and Lumley, 1993) (Fig 7(a)) The simulated profile was in a good agreement with the experimental data Fig 7(b) shows the radial profiles of the turbulence fluctuation ( [ui ui] [ui ][ui] ) in the vertical component wr.m.s The overall shape (e.g., flat shape in the jet inner region) was in a good agreement with the experimental data The axial variation of the axial mean velocity Winj / Wmean along the jet centerline in the LES was also close to Eq (2) and literature (Panchapakesan and Lumley, 1993) (Fig 8(a)) Moreover, the axial variation of the normalized turbulence fluctuation wr m s /Wmean along the jet centerline in the LES was in a good agreement with the data of Panchapakesan and Lumley (1993) exhibiting wr m s /Wmean 0.24 (Fig 8(b)) This comparison indicated that the general jet behavior was reasonably simulated Fig 9(a) shows the axial velocity spectrum at z = 1.2 m (z/D = 40) from the bottom of the test vessel in the LES The spectra were normalized with the Kolmogorov length scale 1/4 , where = sij sij and are the dissipation ratio and the k = ( / ) kinematic viscosity, respectively, and the Kolmogorov velocity scaleuk = ( )1/4 The figure confirms the region corresponding to the slope of 5/3 shown in a dashed line The extent of the −5/3 range w generally increases with the Taylor Reynolds number Re = k r m s , which is approximately 330 in this case Compared with the previous study of Saddoughi and Veeravalli (1994), who assembled data of several flows for Re = 23 3180 , the −5/3 range in this simulation was considered reasonable In other words, the energy cascade by in­ ertial transfer was adequately simulated Fig 9(b) also provides the compensated velocity spectrum defined as 2/3 5/3E ( ) In the inertial subrange (−5/3 range), the spectra should be independent of the wa­ venumber and equal to the Kolmogorov constant of approximately 0.491 The smoothed data shown by the red solid line was close to this value, although the plots largely fluctuated This result shows that the numerical mesh was sufficient for simulating the turbulent jet behavior The simulation on the stratification breakup by a vertical jet showed no clear criterion for determining whether the numerical mesh was suffi­ cient for simulating the interaction behavior Therefore, in this study, the µSGS value was used as the criteria for mesh sufficiency The result for Case showed that the maximum value of µSGS at the interaction region between the vertical jet and stratification achieved approxi­ mately 2.9e−06 Pa⋅s, corresponding to approximately 16% of the molecular viscosity We consider this value to be small enough for (21) The minimum value of Scto was implemented for the neutral and unstratified conditions 3.3 Simulation case This section presents the numerical and boundary conditions The numerical model was validated with respect to the VIMES experiment To simulate the turbulent behavior in the near-wall region in the LES, the Van Driest damping function Fd = y+ A exp (22) was used with A = 25 (Van Driest, 1956) That is, the filter width in Eq (8) was replaced with Fd y+ is a non-dimensional wall distance from a wall In the RANS cases, µt was damped with the following formulation: 0(y+ µt = µ ( y+ ln (9.8y+) 11) ) (y+ > 11) (23) where is the von Karman constant of 0.41 Table summarizes other details of the LES and RANS The grid system for the LES was composed of approximately 22.4 million hexahedral elements (Fig 6(a)) The jet inlet face was filled with 320 surfaces The grid system for the interaction region between an upward jet and stratification is refined We checked the mesh suf­ ficiency by first performing the simulation on an upward jet with the Winj D 10000) in injected velocity of 5.0 m/s (Reynolds number Re = µ the VIMES test vessel The radial profile of the axial mean velocity Table Numerical and boundary conditions of the simulations Numerical Space discretization Time discretization Time marching Boundary Inlet B.C Outlet B.C Wall B.C 2nd-order central difference TVD (Total variation diminishing) scheme for advection terms Euler-implicit PIMPLE, Combination of PISO(Pressure Implicit with Splitting of Operator) and SIMPLE (Semi-Implicit Method for Pressure Linked Equations) Velocity LES RANS Mass fraction Temperature Turbulent kinetic energy (k) in the RANS Turbulent dissipation rate (ε) in the RANS Gradient-zero Velocity Mass fraction Temperature Turbulent kinetic energy (k) in the RANS Turbulent dissipation rate (ε) in the RANS Uniform velocity and random fluctuation of 5%(z) and 3% (x, y) of the axis velocity Uniform velocity Constant (Air=100%, He=0%) Constant (288.15 deg-K) Gradient-zero Gradient-zero Constant (0, 0, 0) Gradient-zero Gradient-zero Gradient-zero p = 3/4 k3/2 Cµ p p yp is the value of turbulence dissipation rate at the nearest cell center to wall yp and kp mean distance from the wall to the cell center and turbulent kinetic energy at the cell center, respectively Nuclear Engineering and Design 368 (2020) 110785 S Abe, et al Fig Numerical meshes: (a) overall domain in the LES (1: jet injection region; 2: interaction region); and (b) overall domain in RANS (1: coarse mesh with 0.31 million elements; 2: medium mesh with 0.46 million elements; 3: fine mesh with 0.88 million elements) Mesh_03 with approximately 0.88 million elements, the overall simu­ lation domain was refined from Mesh_02 First, we performed the si­ mulation on an upward jet with an injected velocity of 5.0 m/s Fig 10(a) compares the radial profiles of the axial mean velocity Wmean at z = 1.2 m (z/D = 40) among the RANS results using the three re­ solutions Furthermore, Figs and compare the axial mean velocity Wmean and turbulence fluctuation wr.m.s on the upward jet in the case with Mesh_02 with the LES and experimental results The vertical jet was reasonably simulated Second, the convergency on the time simulating the flow and mass transport behavior using the LES meth­ odology Regarding the numerical mesh for the RANS, we confirmed the mesh convergency by comparing three different resolutions (Fig 6(b)) Mesh_01 was composed of approximately 0.31 million hexahedral ele­ ments The inlet face was filled with 48 surfaces The region above the inlet boundary was refined to suppress the excessive flow spreading The jet impingement region to the stratification was refined in Mesh_02, which was composed of approximately 0.46 million elements In Nuclear Engineering and Design 368 (2020) 110785 S Abe, et al Fig Radial profiles of the (a) axial mean velocity Wmean (m/s) and (b) turbulence fluctuation of the axial velocity component wr.m.s (m/s) at z = 1.2 m (z/D = 40) from the bottom of the test vessel The error bars are the standard deviations from five independent measurements Fig Axial variations of (a) the axial mean velocity Winj/Wmean and (b) turbulence fluctuation Wr.m.s./Wmean at the jet centerline transient of the helium fraction in Case was confirmed (Fig 10(b)) These figures not indicate dependence on the numerical mesh The RANS results with Mesh_02 are shown herein Ishay et al., 2015) The second one was set to validate the effect of the forcible suppression of the turbulent mixing The Sct value for the other cases was set only to 0.85 The dynamic modeling for Sct given by Eq (21) with Sct0 = 0.85 was applied in all experimental cases CFD result 4.1 Flow and gas concentration fields in the interaction region in case Table summarizes the simulation case in this study The LES was performed only for Case The calculated period was limited only to 62 s from the start of the upward jet injection to save computational cost and time The statistical processing was performed with the data of 30 s to 62 s, which corresponded to the period of the PIV measurement in the VIMES experiment For RANS in Case 1, the constant value of Sct was set to 0.85 and 8.5 The first value was decided based on the pre­ vious studies that simulated the same kind of stratification erosion process by several jet types (Kelm et al., 2019, Studer et al., 2018, and Fig 11 shows the LES-simulated instantaneous flow field in the interaction region between the upward jet and stratification at 46 s in Case Two interesting flow patterns were seen: a large meandering flow and a small eddy structure at the upper part (z > 1.3 m, Fig 11(b)) The first behavior is presumed to result from the jet rapid deceleration and rebounding flow At the upper part of the impinge­ ment region (z > 1.3 m), the upward jet was changed to the flow direction horizontally, and a large velocity gradient existed across the Nuclear Engineering and Design 368 (2020) 110785 S Abe, et al The spatial gradient of the helium gas concentration at the inter­ action region is very important because the turbulence transport quantity and the production term Gk are modeled with Eqs (13) and (19), respectively Fig 13 shows the time-averaged gradient of the helium mass fraction in the vertical direction along the jet centerline from the LES and RANS results The stratification interface was pushed up (Fig 12(b) to (e)); hence, the gradient became steep The vertical distribution in the RANS result with the dynamic modeling for Sct was similar to that of the LES result Regarding the turbulence fluctuation in the vertical component wr.m.s., the LES result indicated a similar spatial distribution to the VIMES result (Fig 14(a), (b), and (f)) These results imply the gradual decay of wr.m.s above the jet impingement region (z > 1.3 m) In contrast, RANS in the case with Sct = 0.85 predicted the rapid decay in this region (Fig 14(c) and (f)) The discrepancy was from the turbu­ lence production term shown by Eq (17), (18), and (19) Fig 15(a) shows the vertical profiles of the Pk and Gk terms along the jet center­ line The negative value in this figure means the damping on the tur­ bulence kinetic energy, while the positive value denotes the activation The magnitude of Gk in the RANS with Sct = 0.85 was larger than that in the LES, and the peak value of the Pk term was lower In other words, the mechanism of the turbulence production was not adequately si­ mulated In the case with Sct = 8.5, the turbulence fluctuation in the upper part gradually decreased This result was seemingly close to the VIMES experimental and LES results (Fig 14(d) and (f)) Moreover, RANS with the dynamic modeling for Sct predicted the gradual decay behavior (Fig 14(e) and (f)) Focusing on the turbulence production in the interaction region, the Gk profile in the case with Sct = 8.5 was smaller than that in the LES, and the Pk profile was larger (Fig 15(a)) Meanwhile, the profiles of Gk, Pk, and the total balance of the turbulent kinetic energy production Gk + Pk predicted by using the dynamic modeling for Sct was very close to that in the LES Figs 16 and 17 show the radial profiles of Gk and Pk The heights were selected based on the peak value at the jet centerline These figures reveal the good perfor­ mance of the dynamic modeling for Sct Both distributions were similar to those in the LES Fig 15(c), Fig 16(b), and Fig 17(b) show the vertical and radial profiles of Sct to clarify the effect of the dynamic modeling in detail The Sct at the inner jet region (z < 1.3, r < 0.1 m) was a constant value of approximately 0.85 to In the stratification and side of the vertical jet, the Sct value gradually increased, demon­ strating that the change of the Sct value plays a key role in predicting the turbulence properties in the density stratification Fig (a) Velocity spectra of the axial velocity component at z = 1.2 m (z/ D = 40) from the bottom of the test vessel in the LES k is the Kolmogorov length scale uk is the Kolomogorov velocity scale The solid line is from the LES, and (b) Compensated velocity spectra of the axial velocity component at z = 1.2 m (z/D = 40) from the bottom of the test vessel Black circle is the compensate velocity spectra in the LES, and the red line is the smoothed data density interface Therefore, the small eddy structure was generated We consider that the LES simulated a reasonable flow behavior in the interaction region The time-averaged flow field in the LES showed that the upward jet arrived at approximately z = 1.3 m (Fig 12(b)) The penetration depth was close to that in the VIMES experiment Furthermore, some im­ portant flow patterns (i.e., upward jet spreading and magnitudes of the upward jet and rebounding flow) were similar to those of the experi­ mental result The general flow patterns in all RANS results were in accordance with the experimental result (Fig 12(c) to (e)), although a slight difference was found among the RANS results (i.e., the upward jet arrival point in the case with Sct = 0.85 was higher than those in the other cases, while that in the case with Sct = 8.5 was lower than the others) This small difference influenced the stratification erosive pro­ cess 4.2 Time transient of the helium molar fraction in case In all RANS, the time transients of the helium molar fraction were qualitatively predicted well (Fig 18) In the lower part of the initial stratification, the molar fraction immediately decreased after the start of the vertical jet injection This rapid decay was induced by the jet Fig 10 Comparison of the RANS results using three numerical resolutions: (a) radial profile of the axial velocity component Wmean (m/s) at 1.2 m (z/D = 40) and (b) time transient of the helium molar fraction (%) in Case Nuclear Engineering and Design 368 (2020) 110785 S Abe, et al Fig 11 Instantaneous flow field obtained by the LES in Case 1: (a) overall interaction region between the vertical jet and stratification and (b) focusing on the small eddy structure at the stratification interface The color contour shows the velocity magnitude based on rdial and vertical components ur2 + w (m/s) impingement into the stratification The small difference at z = 1.3 m among the RANS results was produced by the change of the jet pene­ tration depth (Fig 12) The decay of the helium molar fraction in the upper part of the stratification was also qualitatively predicted (i.e., slow erosive process before the jet achievement and the rapid decrease induced by the strong turbulence mixing) Quantitatively, the RANS result with the constant value of Sct = 0.85 showed a faster breakup transient, indicating that the turbulence mixing was overpredicted In the case with the constant value of Sct = 8.5, the turbulence mixing in the jet impingement region was forcibly suppressed, and the time transients were closer to the experimental data In the case with the dynamic modeling for Sct, the time transients of the helium molar fraction were in a good agreement with the experimental result, in­ dicating that the turbulence mixing in the impingement region was accurately simulated Discussion 5.1 Turbulence transport phenomena in the interaction region Hereafter, we focused on the turbulence mixing phenomena with the spatial visualization of the turbulence helium mass flux obtained with the CFD simulation Fig 19 shows the turbulent helium mass flux [w'Y ' He ] and the horizontal integral value of in the vertical direction this turbulent flux In the LES, this turbulent flux was directly derived from statistical processing The LES result showed negative values in the interaction region between the jet and stratification This negative value meant that the helium gas was transported downwardly by the turbulence mixing Incidentally, the positive value of the turbulence flux was seen surrounding this region, showing the counter-gradient diffusion (Komori et al., 1983), which was a buoyancy-driven motion in the stratified layer (Komori and Nagata, 1996) This behavior demon­ strates that a part of the light gas mixture returned to its original level In RANS, the turbulent mass flux was modeled by Eq (13) with the positive diffusion coefficient of µt / Sct ; thus, the counter-gradient dif­ fusion was not simulated Focusing on the interaction region, where the Fig 13 Time-averaged gradient of the helium mass fraction in the vertical direction (m−1) along the jet centerline in Case obtained from the LES and RANS results strong turbulence mixing was seen, the simulation result in the case with Sct = 0.85 indicates a distribution larger than that in the LES result The RANS result in the case with Sct = 8.5 showed that the overall mixing capability seemed lower than that in the case with Sct = 0.85 in Fig 19(e) However, the spatial distribution was far from that of the LES result, as shown by the comparison between Fig 19(a) and (c), indicating that the turbulence mixing behavior was different That is, a better agreement, as mentioned in Section 4, was not pro­ duced by the reasonable improvement In the case with the dynamic modeling for Sct, turbulence mixing was adequately suppressed The Fig 12 Averaged velocity field in Case 1: (a) VIMES, averaged flow field with line contour of the helium molar fraction in Case 1; (b) LES; (c) RANS (Sct = 0.85); (d) RANS (Sct = 8.5); and (e) RANS (dynamic Sct) The color contour shows the velocity magnitude based on rdial and vertical components 10 ur2 + w (m/s) Nuclear Engineering and Design 368 (2020) 110785 S Abe, et al Fig 14 Spatial distribution of the turbulence fluctuation of the axial velocity component wr.m.s (m/s) in the interaction region in Case 1: (a) VIMES; (b) LES; (c) RANS (Sct = 0.85); (d) RANS (Sct = 8.5); (e) RANS (dynamic Sct); and (f) axial variation of at the jet centerline The error bars in (f) are the standard deviation from five independents measurements Fig 15 Axial variation of (a) Gk and Pk, (b) Gk + Pk (kg/m2/s3) in the LES and RANS, and (c) turbulent Schmidt number Sct in the RANS predicted mixing region was narrower than those in the other RANS cases and much closer to the LES result That is, the mixing behavior in the case with the dynamic modeling was similar to that of the LES As mentioned earlier, in the case with the dynamic modeling for Sct, the improvement of the CFD accuracy was confirmed in terms of the tur­ bulence fluctuation (Fig 14), turbulence production (Figs 15–17), time transient (Fig 18), and turbulent mixing behavior (Fig 19) 5.1.1 Parametric study We performed a parametric study on the stratification breakup to evaluate the capability of the dynamic modeling for Sct In Case de­ scribed in Table 1, the upward jet was injected with 2.5 m/s, and the Fig 16 Radial distributions of (a) Gk (kg/m2/s3) in the LES and RANS and (b) Sct in the RANS 11 Nuclear Engineering and Design 368 (2020) 110785 S Abe, et al Fig 17 Radial distributions of (a) Pk (kg/m2/s3) in the LES and RANS and (b) Sct in the RANS Fig 20 Time transient of the helium molar fraction (%) at z = 0.1 m, 1.3 m, 1.5 m, and 1.7 m in Case in VIMES experiment and RANS The error bars are the standard deviation from two independent measurements Fig 18 Time transient of the helium molar fraction (%) at z = 0.1 m, 1.3 m, 1.5 m, and 1.7 m in Case in VIMES experiment and RANS The error bars are the standard deviation from five independent measurements slower erosive processes, such as in cases and (Figs 20 and 21) Conclusion interaction Froude number (Fri) was limited to approximately 1.0 Thus, the time transient of the helium fraction was quite slow (Fig 20) The fraction at the top of the test vessel decreased, while that at the bottom of the test vessel gradually increased Consequently, it took more than 7000 s to complete the stratification breakup, indicating that the strong turbulence mixing was not induced In Case of Fri = 1.5, the erosion rate of the stratification was faster than that in Case (Fig 21) The helium fraction at the upper part linearly decreased, although we did not see the sharp decay being induced by strong turbulence mixing as seen in Case (i.e., intermediate erosion behavior between cases and 2) The dynamic modeling for Sct improved the CFD accuracy for the We phenomenologically discussed herein the interaction behavior between a vertical jet and density stratification by investigating the turbulence properties obtained with the LES For RANS, we focused on the turbulent Schmidt number Sct because the change of Sct directly operates on the turbulent diffusion coefficient Dt and the production term in the transport equations of the turbulent kinetic energy and its dissipation ratio by buoyancy force We applied the constant Sct values of 0.85 and 8.5 The first value was selected based on the previous studies, while the second value was for forcibly suppressing the tur­ bulence mixing The dynamic modeling for Sct was applied The ex­ perimental data obtained with the VIMES apparatus were utilized as the [w'Y ' He ] (kg/s/m2) in Case obtained with the LES and RANS: (a) LES; (b) RANS (Sct = 0.85); (c) Fig 19 Turbulent helium mass flux in the vertical direction RANS (Sct = 8.5); (d) RANS (dynamic Sct); and (e) horizontal integral value of the turbulent helium mass flux (kg/s) 12 Nuclear Engineering and Design 368 (2020) 110785 S Abe, et al Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influ­ ence the work reported in this paper Acknowledgments The authors acknowledge Mr Wakayama, Mr Kurosawa, Mr Yanai, Mr Kawakami, Mr Yamaki of Nuclear Engineering Co (NECO), and Mr Ohmiya of KCS corporation for performing the experiment to­ gether The experimental data used to validate the CFD analysis were acquired with the support of the Nuclear Regulation Authority (NRA), Japan References Fig 21 Time transient of the helium molar fraction (%) at z = 0.1 m, 1.3 m, 1.5 m, and 1.7 m in Case in VIMES experiment and RANS The error bars are the standard deviation from two independent measurements Abe, S., Ishigaki, M., Sibamoto, Y., Yonomoto, T., 2015 RANS analyzes on erosion be­ havior of density stratification consisted of helium–air mixture gas by a low mo­ mentum vertical buoyant jet in the PANDA test facility, the third international benchmark exercise (IBE-3) Nucl Eng Des 289, 231–239 Abe, S., Ishigaki, M., Sibamoto, Y., Yonomoto, T., 2016 Experimental and numerical study on density stratification erosion phenomena with a vertical buoyant jet in a small vessel Nucl Eng Des 303, 203–213 Abe, S., Ishigaki, M., Sibamoto, Y., and Yonomoto, T., 2018 Influence of grating type obstacle on stratification breakup by a vertical jet The 12th International Topical Meeting on Nuclear Reactor Thermal Hydraulics, Operation and Safety, Qingdao, China, October Abe, S., Studer, E., Ishigaki, M., Sibamoto, Y., Yonomoto, T., 2018b Stratification breakup by a diffuse buoyant jet: The MISTRA HM1-1 and 1–1bis experiments and their CFD analysis Nucl Eng Des 331, 162–175 Allelein, H., Fischer, K., Vendel, J., Malet, J., Studer, E., Schwarz, S., Houkema, M., Paillere, H., Bentaib, A., 2007 International standard problem (ISP-47) on contain­ ment thermal hydraulics, Report NEA/CSNI/R(2007) 10 Andreani, M., Badillo, A., Kapulla, R., 2016 Synthesis of the OECD/NEA-PSI CFD benchmark exercise Nucl Eng Des 299, 59–80 Andreani, M., Gaikwad, A.J., Ganju, S., Gera, B., Grigoryev, S., Herranz, L.E., Huhtanen, R., Kale, V., Kanaev, A., Kapulla, R., Kelm, S., Kim, J., Nishimura, T., Paladino, D., Paranjape, S., Schramm, B., Sharabi, M., Shen, F., Wei, B., Yan, 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the upward jet and stratification is adequately simulated - In RANS with the constant Sct value of 8.5 and the dynamic mod­ eling for Sct, the predicted turbulence fluctuation around the inter­ action region agrees with the experimental data of the VIMES ex­ periment and LES result Moreover, the profiles of turbulence production by shear stress and buoyancy force (Pk and Gk, respec­ tively) predicted by using the dynamic modeling for Sct is very closed to that in the LES In other words, the change of the Sct value plays a key role in simulating the turbulence behavior in the density stratification comprising the multicomponent gas mixture - The comparison of the time transient of the helium molar fraction with that in the VIMES data indicates that the consistency between the experiment and RANS results is improved by the change of the Sct value In the case with the constant value of Sct = 0.85, the stratification erosion rate is faster than that of the VIMES experi­ ment Meanwhile, in the case with Sct = 8.5, the time transient is closer to the experimental data because of the forcible suppression of the turbulence scalar transport Furthermore, in the dynamic modeling for Sct, the time transient is in a good agreement with the experimental data - The spatial distribution of the turbulent helium mass flux in the vertical direction around the interaction region implies that the turbulence mixing is not adequately simulated in the case with Sct = 8.5 In other words, the better agreement of the time transient of the helium molar fraction as mentioned earlier is not produced by the reasonable improvement Meanwhile, the mixing behavior in the case with the dynamic modeling for Sct is similar to that in the LES result - The parametric study indicates the good performance of RANS with the dynamic modeling for Sct on the slower erosive process by a lower momentum jet In conclusion, the dynamic modeling for Sct is a useful and practical approach to improve the prediction accuracy on the stratification breakup behavior by a vertical jet Although we have directly applied herein the model formulation developed in research on ocean en­ gineering, further works for more types of flow behavior are needed to optimize the model formulation for the multicomponent gas behavior 13 Nuclear Engineering and Design 368 (2020) 110785 S Abe, et al Peters, H., Gregg, M.C., Toole, J.M., 1988 On the parameterization of equatorial tur­ bulence J Geophys Res 93, 1199–1218 Rodi, W (Ed.), 1982 HMT the science & applications of heat and mass transfer in: Turbulent Buoyant Jets and Plumes, vol 6., 1st edition Pergamon Press Röhrig, R., Jakirlic, S., Tropea, C., 2016 Large eddy simulation of a light gas stratification breakup by an entraining turbulent fountain J Turbl 17 (9), 878–899 Sarikurt, F.S., Hassan, Y.A., 2017 Large-eddy simulations of erosin of a stratified layer by a buoyant jet Int J Heat Mass Trans 112, 354–365 Saddoughi, S.G., Veeravalli, S.V., 1994 Local isotropy 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stratification in a small-sized rectangular vessel We at the JAEA also constructed a small experimental apparatus, called the VIsualization and MEasurement system on Stratification. .. region between the vertical jet and stratification, and a parametric study to evaluate the capability of dynamic modeling for Sct; and Section summarizes the main conclusions VIMES apparatus The. .. m) was a constant value of approximately 0.85 to In the stratification and side of the vertical jet, the Sct value gradually increased, demon­ strating that the change of the Sct value plays a