Direct simulation of conjugate heat transfer of jet in channel crossflow

We present a DNS study of a hot, low momentum laminar water jet discharged into a cold turbulent channel stream through a circular orifice in one of the steel channel walls. The channel wall has a finite thickness and its outer side is cooled under Robin type thermal boundary conditions for a realistic external environment, leading to a conjugate heat transfer system. Nusselt number and r.m.s temperature fluctuations on the wall are compared with our earlier DNS results for the simpler iso-thermal and adiabatic conditions at the channel inner surface. Temperature fluctuations inside the channel wall are resolved to provide data for a conjugate heat transfer (CHT) thermal fatigue test case related to the ageing of pipe walls and welds studies, as found, for example, in power plant piping T-junctions. The crossflow Reynolds number is Re=3333, jet-to-crossflow velocity ratio is R=1/6 and fluid-to-solid conductivity ratio is 1/64. The near-wall mean flow structures, a horseshoe vortex ahead and on the sides of the jet orifice, a shallow recirculation behind the discharge and a counter-rotating vortex pair drawing in a blanket of cooler cross-flow, lead to a complex convective and turbulent wall heat transfer pattern around the orifice. The main findings are: (i) Wall maps of Nusselt number and r.m.s temperature, θ_r.m.s, for conjugate heat transfer are only qualitatively similar to the iso-thermal and adiabatic wall cases.(ii) Inside the solid θ_r.m.s and its dissipation, analysed from RANS modelling perspective, show that predicted thermal spot length scales are discontinuous on the interface, at variance with the 2-point spectrum-derived scales.(iii) At the high wavenumber range, the spanwise temperature spectra decrease according to exponential-decay spectral models for the fluid turbulence in the Kolmogorov range, but with large exponential coefficients increasing with depth inside the solid.