DNS &fine LES versus RANS modelling of turbulent thermal mixing
for structural fatigue mitigation in power generation systems
University of Manchester, Modelling and Simulation Centre (UoM – MaSC)
Dominique.Laurence@manchester.ac.uk
As reported at UKTC 2013 while outlining our plans, modelling unsteady wall heat transfer is
essential to safety and longevity of power generation systems. Emergency cooling procedures can
involve several hundred degrees temperatures differences along steel walls of T junctions or vessels,
while years of exposure to smaller thermal fluctuations or radiation-induced brittling limit the lifespan
of the plant. Experimental data on thermal fluctuations penetration into solid walls (unsteady
conjugate heat transfer) is rare and coarse-grained. Unfortunately only RANS models, or hopefully
better, hybrid RANS-LES can reach the plant’s large Re numbers actual conditions but a Nusselt
number (heat exchange coefficient) RANS prediction within 30% is standard expectation and over- or
under- prediction by a factor of 2 not uncommon. DNS and fine LES run by Ryan Tunstall, Alex
Skillen & Zhao Wu complement this data scarcity (thanks to UKTC HPC resources and Incompact3D,
OpenFoam, CCM+ or Saturne codes) and improve our understanding and modelling for safer
designs.
The Jet in channel crossflow DNS of Zhao Wu has lower momentum than those in literature, to
represent power-plant conditions. The horseshoe vortex, shear layer vortices, near wall wake vortex
shedding, and shallow recirculation behind the jet are seen on Fig. 1. These structures strongly affect
the mixing of temperature in JICF. The roll-up of free shear-layer vortices induce unsteadiness of the
wall horseshoe vortices, leading to high rms wall T levels on the sides of the injection. Streamlines in
symmetry plane show a very shallow reciculation behind the jet, followed by what looks like a long
mass source due to converging flow from the sides. Fig. 2. Shows severe overestimation of
temperature variance,  2 by all RANS models, although the mean temperature prediction is
acceptable.
Ryan Tunstall is conducting several wall-resolved LES of the more industrial pipe flow with a small
secondary Tee junction injection relevant to safety cooling (most experimental data is for pipes of
same diameter and adiabatic walls). The low momentum ratio is similar to the channel DNS of Zhao.
For a straight pipe the T-rms maximum is found on the T sides and wake sides of the injection, Fig. 3.
However when a sharp bend precedes the junction, Dean vortices in the bend induce an unsteady
swirl-switching mechanism, whereby vortices in one half of the pipe will alternately dominate those in
the other, resulting in an unsteady secondary flow about the pipe axis. The LES shows that this
unsteadiness has the potential to introduce additional low frequency near-wall temperature
fluctuations at and downstream of a T-Junction with upstream pipe bend. In the industrial T-Junction
considered there are still strong interactions between the shear layer and the secondary motions
providing mixing in the region of elevated temperature.
Further downstream the effect of the bend’s secondary motions is far more pronounced, convecting
the region of hot fluid about the pipe axis in alternating directions resulting in large fluctuations in walltemperature. PSD of near-wall temperature fluctuations reveal that frequencies below 10Hz dominate,
which corresponds to the range of frequencies known to cause thermal fatigue damage in pipe walls.
Ryan is also developing hybrid RANS-LES whereby both simulations are running concurrently on
overlapping full-domain meshes and coupling is ensured by source terms based on finite-time
running averages. RANS drives the LES in the near wall layer and vice-versa away from walls. The
model with coupling timescales defined automatically is validated on channel flow so far but is a very
promising alternative to RANS and wall function models for high Re industrial thermal-hydraulics
studies.
The conjugate heat transfer channel flow DNS database of Cedric Flageul (see UKTC 2014, PhD
dissertation available this fall) has been used to show that one could economically replace full
coupled resolution of the thermal field in the solid by a Robin (mixed temperature – heat flux) fluidsolid boundary condition as far as 1-point statistics are concerned, see Fig. 4. Differences in 2-point
correlations are noted, but could be due to the predominance of streaks at this low Ret number of
150.
Fig. 1 DNS of a Jet in Cross Flow with passive scalar mixing (Wu, Laurence & Afgan). Clockwise:
DNS set-up; Temperature field; iso-Q coulured by T; wall temperature (line=DNS, symbols=RANS);
mean flow streamlines in symmetry plane.
Fig. 2 DNS and k-omega Nusselt number maps; Nusselt profile and mean temperature profile on the
axis (Line= DNS, Symbols=RANS).
Fig. 3. Large Eddy Simulation of a T-Junction with and without upstream elbow: The Role of Dean
Vortices in Thermal Fatigue (Tunstall, Laurence, Prosser).
Fig. 4. T fluctuation variance and its dissipation from heated channel flow DNS. Negative y+ values
correspond to points in the solid only resolved with the conjugate heat transfer simulation. A Robin
boundary condition at the interface, y+=0, seems acceptable (Flageul, Lambalais, Laurence,
Benhamadouche).