  This paper designs surrogate models with uncertainty quantification
capabilities to improve the thermal performance of rib-turbulated internal
cooling channels effectively. To construct the surrogate, we use the deep
operator network (DeepONet) framework, a novel class of neural networks
designed to approximate mappings between infinite-dimensional spaces using
relatively small datasets. The proposed DeepONet takes an arbitrary continuous
rib geometry with control points as input and outputs continuous detailed
information about the distribution of pressure and heat transfer around the
profiled ribs. The datasets needed to train and test the proposed DeepONet
framework were obtained by simulating a 2D rib-roughened internal cooling
channel. To accomplish this, we continuously modified the input rib geometry by
adjusting the control points according to a simple random distribution with
constraints, rather than following a predefined path or sampling method. The
studied channel has a hydraulic diameter, Dh, of 66.7 mm, and a
length-to-hydraulic diameter ratio, L/Dh, of 10. The ratio of rib center height
to hydraulic diameter (e/Dh), which was not changed during the rib profile
update, was maintained at a constant value of 0.048. The ribs were placed in
the channel with a pitch-to-height ratio (P/e) of 10. In addition, we provide
the proposed surrogates with effective uncertainty quantification capabilities.
This is achieved by converting the DeepONet framework into a Bayesian DeepONet
(B-DeepONet). B-DeepONet samples from the posterior distribution of DeepONet
parameters using the novel framework of stochastic gradient replica-exchange
MCMC.
