FR0200503 NUMERICAL SIMULATION OF HYDROGEN COMBUSTION Jan-patrice SIMONEAU, FRAMATOME - FRANCE Novatome - 10, rue Juliette Recamier- F 69456 LYON cedexo6 - France Ph : +33 4 72 74 73 75 - Facs : +33 4 72 74 73 75 E-mail: jpsimoneau@framatome.fr Jean-philippe PIRUS, FRAMATOME - FRANCE Novatome - 10, rue Juliette Recamier- F 69456 LYON cedexo6 - France Ph : +33 4 72 74 72 64 - Facs : +33 4 72 74 73 75 E-mail: jppirus@framatome.fr Key Words : Fluid dynamics - combustion - hydrogen. Summary: The aim of this paper is to present a combustion model of hydrogen developed using the Star-cd fluid mechanics code. The model involves a detailed reaction process (11 elementary reactions and 4 intermediate elements) and a procedure is developed to solve the set of fully coupled reactions. Then, a preliminary study allowed to determine ignition conditions needed to numerically trigger a detonation phenomenon. The detonation phenomenon is computed on a first test case and the comparison with literature and another code shows a good agreement (temperature, pressure and velocity of the reaction front). The validation process is still in progress by comparison with other available results. Furthermore, combustion calculations including the prior hydrogen diffusion process can be foreseen. Introduction : In case of severe accidents in nuclear reactors, notably for liquid sodium cooled ones, hydrogen may be potentially produced. A possible combustion and subsequent detonation could occur and induce high dynamic pressure load on neighbouring structures. Some devices are investigated to control the hydrogen concentration (ref. 1, 2), but the study of hydrogen combustion remains of great interest (ref. 3). The objective of this paper is to present a combustion model of hydrogen developed using the Star-cd fluid mechanics code. The general purpose code Star-cd is first described. The combustion process and its implementation in the code is then detailed. This process involves several intermediate reactions. 33/11
OGOO Hydrogen combustion can lead to either deflagration or detonation depending on the surrounding and concentration conditions. The objective is to simulate severe consequences of hydrogen combustion, i.e. the detonation phenomenon. A preliminary test case has been studied first to set up the ignition condition of the reaction, in order to observe a detonation transient. A more realistic test case has then been performed : the detonation of a stoichiometric mix of air and hydrogen in a tall building is computed with the previous combustion model. Results are compared with those obtained with another fast dynamics code. The Star-cd code : The general purpose code Star-cd for fluid mechanics and thermics (ref. 4) is used. The main characteristics of this software are listed below: > 3 dimensional code > a finite volume formulation > unstructured grid capabilities including advanced features : local refinement, non-conformant grids with arbitrary interfaces. Meshes are mainly hexahedrons and prisms. > Matrices inverted by bi-conjugate gradient method with preconditioning > PISO algorithm for pressure linked equations (the pressure solver is semiimplicit : pressure fields are corrected at every iteration in order to achieve both momentum and continuity balances > Numerical schemes up to third order The Navier-Stokes and energy equations are solved in primary variables (velocity, pressure and temperature). For this specific study, computations are run in transient regime. Species concentrations are solved : either via transport-equations (using the Fick law for diffusion): Fixj = -D ddldxj (1) and with appropriate source / sink terms, or via algebraic equations (from chemical reaction balance). The combustion reaction : The general reaction of hydrogen combustion 2H 2 + O 2 -> 2H 2 O (2) does not occur directly, even at high temperature. The transformation of hydrogen and oxygen molecules into water ones is performed thanks to free radicals. First initialisation reactions produce free radicals from hydrogen and oxygen. Then, other free radicals come from propagation reactions. At last, termination reaction makes water molecules. Some reactions are collision ones : they involve an extra element M which is not modified by the reaction but which is necessary. The element M is in fact any of the elements surrounding the reactants and which can be in collision with them. Some other reactions, due to gas - wall interaction, are neglected.
oooe The final set of reactions is the following : 1. Initialisation: H 2 + O 2 -> 2OH H 2 + O 2 ->HO 2 + I H 2 + M ->2H+M 2. Propagation O + H 2 ->OH + H H + O 2 ->OH+O HO 2 +H 2 ->H 2 O + H + O 2 + M -> HO 2 + M OH + H 2 ->H 2 O + M 3. Termination H + H + M ->H 2 + M OH + H + M->H 2 O+M The overall reaction in exothermic. (R1) (R2) (R3) (R4) (R5) (R6) (R7) (R8) (R9) (R10) (R11) Numerical modelling : The combustion model: The combustion model has to determine the concentration evolution of each species. For each reaction, a combustion rate W must be calculated (moles reacting per second). W is approximated as W=k(T)[A][B] (3) Where [A] ([B]) is the molecular concentration of the reactants (of the products) and k is the Arrhenius constant. The Arrhenius constants have been available for only initialisation and propagation reactions. The Arrhenius constant expressed as : k - a 7* exp(-clt) (4) The values of a, b and c constants are reported here after [5]: Reaction # 1 2 3 4 5 6 7 8 9 10 11 Arrhenius constant parameters B 0.5 0.5 0.5 0.5 1. 0. 0. 0. 1.3 A 2.2 10 13 7.6 10 13 2.2 10 12 1.8 10" 1.81 1O 1U 1.44 10 14 6.02 10" 7.25 10 15 1.14 10 9 Not available Not available C 21500. 29500. 46600. 48100. 4480 8250. 9400. 500. 1825. Table 1 - Arrhenius parameters
oooe For reactions 10 and 11, k is obtained from enthalpy and entropy of the different species involved. k is obtained from free enthalpy variation AG of the reactants and products. AG = AH-TAS (5) AH and AS are enthalpy and entropy variations during the reaction (Sreactants - ^products). k-exp(-agirt) (6) The 11 reactions are highly coupled and non linear. The reactions are processed sequentially. At each time step a procedure sorts the reactions according to their velocity, i.e. the value of the Arrhenius constant of the reaction. The reaction are then processed from the fastest (high k) to the slowest (low k). Physical properties of gas: The fluid is considered as a mix of perfect gases obeying to the Dalton law: p = PI RT(ZCiMi) (7) Gravity acceleration is not taken into account in the present case. The other physical properties : > Specific heat: mass weighted average of components > Viscosity : mass weighted average of hydrogen and air concentrations > Thermal conductivity : same as for viscosity One needs to know the diffusion coefficients of each species in the mix. Only steam, hydrogen and oxygen values are available. For free radicals, values of hydrogen, oxygen or steam diffusion are used. In fact, those components are only present in the flame front and the diffusion process is not significant. The following table gives the diffusion coefficient of oxygen, hydrogen, steam and nitrogen in air. It gives also values used for free radicals : oxygen values are used for radicals containing O and hydrogen values for H radical. Values are at 1000 C if available. For the specific heat, polynomial expressions are used [6]. Element Oxygen Hydrogen Steam Nitrogen H 0 OH HO2 Molecular weight M (g) 32 2 18 28 1 16 17 33 Mass diffusion coefficient D (m 2 ls) 20 C 0.202 10" 4 1OO C 0.307 10" 4 400 C 0.849 10" 4 20 C 0.627 10" 4 1OO C 1.153 10" 4 400 C 3.238 10" 4 20 C 0.242 10" 4 1OO C 0.399 10" 4 400 C 1.135 10~ 4 20 C 0.20210" 4 100"C 0.307 10" 4 400"C 0.849 10" 4 Dynamic viscosity n PI 55.9 10" b 22.5 10" e 37 10* 45.8 10" b Specific heat Cp J/kg/K 1123 1215 Same as H2 values Same as 02 values 15500 2300 Conductivity X W/m/K 0.035 (15O C) 0.593 0.094 (700 C) 0.047 (500 C) Table 1 - Physical characteristics of species.
oooo Turbulence modelling: The turbulence is represented by the standard k-e model, introducing two additional transport-diffusion equations, coupled with momentum via an eddy viscosity v t. The turbulent viscosity is also introduced in the energy and species equations via an eddy thermal diffusivity and a turbulent Prandtl number a t = v t / Pr t and an eddy species diffusivity and a turbulent Schmidt number D t = vt / SQ. Pr t and Sc t are both set to the value 0.9. Results: Preliminary cases: The objective is to model the detonation phenomenon. The initialisation of the detonation is not a well known phenomena. Preliminary test cases have therefore been performed to determine how to numerically trigger the reaction process. The domain is a tube with one side open, and filled with stoichiometric mix of H2 and air. The ignition is set in a small part of the domain (see figure 1). Table 2 shows two ignition conditions for the same problem. For case B, the conditions in the ignition zone are more "severe". Figure 2 presents the temperature history at the point P (near tube outlet). In case B, the reaction propagates much faster than for case A. The other main characteristics of the reaction are displayed in table 2 and allow to conclude that for case A, the reaction propagation becomes similar to deflagration while case B has detonation features. We conclude that a precise reaction model is not sufficient to simulate detonation, appropriate initial conditions are also needed. v_ Ignition zone Figure 1 - configuration Figure 2 presents the time evolution of the temperature at the point P for both cases. Temperature at point P = f (time) (K) IW 2500 2000 1500 1000 - Case B - Case A - A 500 1.00E-05 1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 Time (second) Figure 2 - temperature = f(t)
Pressure field (scale from 0 to 18 bar): Figure 3 - Pressure field (detonation) Case A B Ignition conditions 2 bar-2000 K 20 bar 3500 K Pressure wave Subsonic Supersonic Pressure level (bar) <2 15-25 Reaction Temperature 2750 2800 Combustion wave velocity 80 1300 Literature results Deflagration (ref 7) Detonation (ref 8) Pressure wave Subsonic Sonic or supersonic Pressure level 1.1 15.8 Reaction Temperature 2950 Combustion wave velocity 80 1900 Table 2 - Preliminary test case - results and comparison Test case : Geometry : This test case is a two-dimensional one. It represents a large tall building 20m x 70m. This cavity is filled as : > Stoichiometric mix of hydrogen and air in its upper part, > Pure air in its lower part (see figure below) 20 m 70 m air + h2 stoichiometric mix of h2 and o2 ignition zone 20 bar, 3500 K air Figure 4 - Test case geometry
oooo The ignition point is set at a vertical wall and at the interface pure air - (mix air + H2). The initial temperature is 20 C and the four lateral walls are adiabatic. In order to trigger the reaction, temperature and pressure are prescribed to high values Tj and Pi in a small region around the prescribed ignition point. Pi = 20 bar Ti = 3500 K (the mass of gas is therefore not significantly modified by this artificial condition). Computational grid : The grid is made of 18000 hexahedral meshes. The two-dimensional problem is represented by using a single layer of meshes. Results : The computation is run along 80 ms. The figure 5 shows the evolution of the pressure field. An over pressure front moves upwards from the ignition point. The value of this pressure reaches first 14 bar at 8ms and then stabilises at 17 bar. Near the walls, the friction implies an over pressure which propagates also transversally in the reaction front. The temperature field is presented on figure 6. The temperature in the ignition region is not significant, but in the reaction front, the temperature reaches about 2400 K. The reaction front propagates at a supersonic velocity of about 1500 m/s (the sound velocity at the local conditions is about 900 m/s). Those results show a detonation process. Pressure, temperature and reaction front velocity are comparable to literature results obtained for detonation in an open domain (see table 3). Furthermore, a comparison was also performed with results obtained from another validated fast dynamics code on the same test case (results not given in the present paper) : the agreement is good especially on the reaction front displacement. Reaction (detonation) occurs only in the upper part of the domain (see figure 4). Downwards, the pressure front is only the pressure wave moving (slower) at sound velocity, and temperature increase is due to compression. At 8 ms, the reaction front reaches the opposite wall and produces an over-pressure, the same phenomenon occurs at about 35 ms at the top wall. The over-pressure is found to be slightly higher than twice the reaction front pressure. After about 30 ms, the combustion of all hydrogen is obtained, and the pressure is now due to wave reflection against walls. Pressure waves move at sound velocity, interfere and finally damp down slowly. Free radicals : Figure 7 shows the field concentration of the reactants (02, H2), the product (H2O) and of the free radical OH at 7 ms. We check that after reaction front, hydrogen and oxygen are fully consumed while water (steam) is produced. We note also that free radical are produced and consumed in the reaction front zone. Other computations : A comparison between coarse and fine grids has also been performed. The previous test case has been computed on a coarser grid (4 times less meshes). The results are not detailed here but the main point highlighted are : About same temperature in the reaction front Pressure in the reaction front: 4 bars below fine grid results. Detonation obtained with same ignition conditions.
oooo PROSTAR3.10 g-jan-** PRESSURE ABSOLUTE PA TIME = 0.300000E-02 LOCAL MX= 0.2812E+07 LOCAL MN= 0.2000E+06 t\ ' : 'I \ 30 ms 40 ms 1 ms 0.4000E+07 0.3714E+07 0.3429E+07 0.3143E+07 0.2857E+07 0.2571 E+07 0.2286E+07 0.2000E+07 0.1714E+07 0.1429E+07 0.1143E+07 0.8571 E+06 0.5714E+06 0.2857E+06 0. Y! -. Figure 5 - Pressure fields Pressure in the reaction front (bar) Temperature in the reaction front (K) Reaction front velocity (m/s) Present computation 15-25 2400 1625 Literature (open domain) 16 2950 1900 Table 3 - Main computation results compared to the literature
OGOO PROSTAR3.10 10-JAN-** TEMPERATURE ABSOLUTE KELVIN TIME = 0.300000E-0Z Figure 6 - Temperature fields H2 02 OH HO2 H2O C:Oto 0.028 C:0to0.233 C:0to0.095 C:Oto 0.038 C:0to0.26 Figure 7 - Mass concentrations of species at 7 ms.
oooe Conclusion : A combustion model of hydrogen has been developed, involving a detailed reaction process (11 elementary reactions and 4 intermediate elements, procedure developed to solve the fully coupled reactions). The detonation phenomenon is observed on first test cases and the comparison with literature and another code shows a good agreement (pressure, temperature and velocity of the reaction front), but the ignition conditions must be properly set to trigger the detonation phenomenon. The validation process is still in progress by comparison with other experimental of numerical results. Furthermore, reaction parameters (e.g. Arrhenius constants) could be adapted to improve the model. Three dimensional computations are also needed to evaluate the model. Finally, the calculation of the complete behaviour process of hydrogen : source, diffusion and convection, combustion can now be foreseen. References 1. M. Manninen, R. Huhtanen, I. Lindholm, H. Sjovall. "Hydrogen in BWR reactor building". Proceedings of ICONE-8 conference, paper #8155. Baltimore, April 2000. 2. JP. Simoneau. "Simulation of hydrogen behavior in large cells". Proceedings of ICONE-8 conference, paper #8549. Baltimore, April 2000. 3. O. Kawabota, M. Kajimoto, N. Tanaka. "Hydrogen detonation and dynamic structural response analyses for large dry containment vessels of steel and prestressed concrete types". Proceedings of ICONE-8 conference, paper #8030 Baltimore, April 2000. 4. Star-cd manuals, version 3.100. Computational dynamics limited, London, 2000. 5. Lide, D., R. "Handbook of chemistry and physics". 1995. 6. Aide memoire du thermicien (heat engineer memorandum), Editions europeennes thermique et industrie, 1987. Nomenclature : FjXj mass flux of species i in dir. j D, D t molecular, turbulent diffusion coefficient (m 2 /s) c. mass concentration of species i M surrounding element in chemical reactions W combustion rate k Arrhenius constant [A],, [B] mole fractions of a,t T G H S reactants, products D, c parameters of Arrhenius constant temperature (K) free enthalpy enthalpy entropy R ideal gas constant Mj molecular weight (g) p density (kg/m 3 ) X conductivity (W/m/K) (j, dynamic molecular viscosity (Pa.s) v t turbulent viscosity (m 2 /s) Pr t turbulent Prandtl number Set turbulent Schmidt number a t turbulent thermal diffusivity (m 2 /s) D t turbulent mass diffusivity (m 2 /s) Pi Pressure in ignition zone (Pa) Tj temperature in ignition zone (K) k turbulent kinetic energy (m 2 /s 2 ) e rate of dissipation of k (m 2 /s 3 ) 10