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In the present study, it is assumed that the how is turbulent, with exothermal hydrogen/air reaction inside the PAR unit. A numerical solution of the mean how, the chemical reaction and the thermal fields requires solving the Unsteady Reynolds Averaged Navier-Stokes (RANS) equations, as well as the energy and species equations.
The standard conservation equations within a URANS approach with the k-h model of turbulence are detailed in a previous publication by the authors  and not repeated here for the sake of conciseness.
It is nonetheless worth mentioning that the heat released by the hydrogen/air reaction in the PAR is implemented as a source term in the energy equation. In addition, gas the mixture is assumed to be an ideal gas whose density ? is computed according to the following:
Above P is the total pressure, Y the mole fraction of the kth species, T the temperature, R the ideal gas constant, and M the molecular weight.
The canalization process of hydrogen with oxygen taking place at the PAR catalyst plates can be approximated by the following exothermic reaction:
Above the heat released.
The volumetric heat source generated by the PAR is given as follow:
5 % ().
The PAR startup in the experiments has a stochastic nature. For this reason, it is difficult to fix a-priori the onset of recombination in the simulations. In this study, the starting point of the recombination has been set according to the experimental results at 1.5 % and 0.5 % of hydrogen concentration at the PAR inlet, respectively for test HR-48 and HR-49.
Some small amount of steam condensation takes place on the wall structures. To model this species sink using a CFD approach, it is referred to the work of Dehbi et al . The empirical correlation proposed by Uchida  is used to compute the condensation heat transfer coefficient as follows:
The THAI+ facility (TTV and PAD vessels) has been represented by a full 3D geometry mesh for CFD calculations as shown in Figure 4. The PAR unite is modelled by rectangular channel with thin walls, which has two open sides at the bottom and at the top (PAR inlet and PAR outlet). The PAR walls are considered as no-slip boundaries with conduction heat transfer. The PAR unite is subdivided into four parts, namely: a) an entrance zone where the mixture hydrogen/air content is calculated to judge whether or not the onset of reaction is reached; b) the catalytic plates section which presents the reaction part where it has been modeled by volumetric sources(steam)/sinks(hydrogen and oxygen) for species and heat released; c) the chimney zone; in this section the hot gases develops upward flow; and d) the exit zone: the second open section where the hot gas exhausts to the vessel atmosphere by two sides as schematic the Figure 1.
The sump free surface is considered as a wall surface with fixed temperature during the entire tests. The blower section is modeled by a fan sub-model, where a pressure jump is tuned to get the desired volume flow rate. The hydrogen and steam injections are presented as 2D surfaces with mass flow rate boundary conditions.
Conjugate heat transfer on wall structures is modeled since the wall sections are either heated or cooled to keep the thermodynamic conditions at saturation state. Thermal radiation is ignored owing to the low temperatures in most of the regions in the vessel.
The governing equations were solved using the ANSYS Fluent 16 software. The spatial and temporal discretization employed a second order accuracy scheme, while the SIMPLE solution procedure was chosen. A standard wall function approach was followed to model turbulence near the solid boundaries. Accordingly, mesh resolution in the near-wall region is constructed to obey best practice guidelines , .
Three different meshes with 300 K nodes, 640 K nodes and 920 K nodes were constructed to study grid independency. Spatial refinement is concentrated in locations where the flow is most dynamic (the fan zone and inner cylinder, the PAR region and the H2 injection ring). Figure 5 featuring PAR reaction rate versus time, one can see that the three grids give very similar profiles that are also close to the experimental data. Hereafter, the finest grid is selected to display the results for both tests.
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