Surrogate modelling of transient stratified flow in a u-shaped pipe

In this work, we compute the mixed convection flow through a u-shaped bend, where transient thermal boundary conditions are applied at the inlet. The flow is governed by the Unsteady Reynolds Averaged Navier-Stokes equations. The Reynolds number is set to 10 000, while the Prandtl number is 6 (water). Polynomial chaos with parametric space discretisation is employed to assess the influence of Froude number (Fr), related to the magnitude of the thermal transient, uniformly distributed over a range of Fr=0.402 to 0.938. Skewed and bi-modal responses in the strength of the stratification were observed, which are related to the flow being at locally sub-critical or supercritical Fr.

The application of polynomial expansion enables wider exploration of parameter space to gain better understanding of flow behaviour. For Fr<0.67, we observe a more persistent thermal stratification as the secondary flow motion confines the hotter core fluid to the centres of the two counter-rotating vortices away from the pipe wall.