DIRECT NUMERICAL-SIMULATION OF TURBULENCE IN AN INTERNALLY HEATED CONVECTIVE FLUID LAYER AND IMPLICATIONS FOR STATISTICAL MODELING

Direct numerical simulations (DNS) are reported for the convection in an internally heated convective fluid layer which is bounded by rigid isothermal horizontal walls at equal temperature. The simulations for a fluid Prandtl number of seven cover seven distinct internal Rayleigh numbers in the range 10(5) less than or equal to Ra-I less than or eq ual to 10(9). From the numerical database the changes of convective pa tterns and dynamics for increasing Ra-I i.e. increasing turbulence int ensity, are analysed. To support the development and improvement of st atistical turbulence models for this special type of convection, turbu lence data for mean and fluctuating temperature and velocities are pro vided. For the simulation with Ra-I = 10(8) budgets of turbulence kine tic energy k and vertical turbulent heat flux <(u'T-3)over bar> are pr esented. In addition, closure assumptions commonly used in statistical turbulence models are tested against the DNS data. It is found that t he turbulent diffusive transport of k and <(u'T-3)over bar> is strongl y underestimated by standard models. The modelling of the turbulent he at fluxes by a turbulent Prandtl number approach is totally inadequate for internally heated convection. Instead, a second moment closure fo r <(u'T-i)over bar> is required.