Recommendation for maximum allowable mesh size for plant combustion analyses with CFD codes

The selection of the maximum allowable mesh size for a fluid dynamic calculation with Computational Fluid Dynamic (CFD) codes is essential for the reliability of the results assuming suitable physical and numerical models are used. Calculations with CFD codes are necessary for the assessment of the consequences of pressure loads on containment structures due to possible hydrogen combustion in nuclear power plants in a severe accident and on piping system due to pressure wave propagation in case of a pipe break accident or fast closing of a valve in a pipe with forced flow.CFD simulations of the transport and distribution of the released hydrogen/steam as well as the possible combustion during the transient in the containment require an appropriate mesh size to resolve the relevant phenomena and loads.The determination of the mesh size has to take into account:
• adequate delineation of the containment geometry for accurate hydrogen distribution calculations,
• sufficient conservative resolution of the combustion phenomena for the determination of pressure wave propagation and pressure loads,
• no loss of pressure wave loads with relevant frequencies for the structural response analysis of the containment during the combustion calculation.In this paper, it is found that the accuracy of the calculated pressure wave associated with its frequency depends on the mesh size and a simple and easily useable analytical formula for the determination of the maximum allowable mesh size is derived. This formula can be used as a criterion to find out easily and simply the appropriate mesh size for accurate determination of the pressure wave load function with sufficient resolved frequencies relevant for structural response analyses. This criterion in form of a relation is deduced in this theoretical treatment from the connection between the structural characteristic associated with the relevant frequency and fluid property associated with mixture quality and gas temperature as well as numerical determination of the pressure wave load function associated with the accuracy of the approximation.This criterion gives the CFD code users the ability to determine the upper limit of the mesh size during the preparing of the geometry simulation specially for performing a combustion calculation.Applying the criterion presupposes that the used CFD code can calculate correctly the turbulent combustion, flame and pressure wave propagation for the predicted maximum allowable mesh size.The mesh size can be calculated from the analytical formula using:
• the mixture quality and temperature in the cloud surrounded by structures (containment),
• the highest relevant frequency for the structural analysis of the containment and
• the number of points for the accurate approximation of the pressure wave function.The methodology can be applied also for the assessment of the frequency content of the determined pressure wave load function for the response analysis of a piping system like main coolant or steam lines in case of a break accident or other accidents with occurrence of pressure waves.

► Used mesh size has to be small enough to resolve all pressure waves relevant for the structural response analyses.
► Maximum allowable mesh size for a combustion pressure load calculation decreases with increasing relevant natural frequency of the structure.
► Maximum allowable mesh size for a combustion pressure load calculation increases with increasing of the speed of the sound in the gas mixture.
► Maximum allowable mesh size can be calculated from the developed analytical formula.