# A Hybrid Reduced Order Method for Modelling Turbulent Heat Transfer Problems

## TL;DR

This paper introduces a hybrid reduced order modeling approach combining Proper Orthogonal Decomposition and Radial Basis Function interpolation to efficiently simulate turbulent heat transfer in complex pipe flows.

## Contribution

It presents a novel parametric reduced order model that integrates POD, Galerkin projection, and RBF interpolation for turbulent heat transfer problems.

## Key findings

- The reduced order model accurately predicts turbulent mixing in a T-junction.
- The method significantly reduces computational cost compared to full order models.
- It effectively incorporates eddy viscosity and diffusivity at high Reynolds numbers.

## Abstract

A parametric, hybrid reduced order model approach based on the Proper Orthogonal Decomposition with both Galerkin projection and interpolation based on Radial Basis Functions method is presented. This method is tested against a case of turbulent non-isothermal mixing in a T-junction pipe, a common ow arrangement found in nuclear reactor cooling systems. The reduced order model is derived from the 3D unsteady, incompressible Navier-Stokes equations weakly coupled with the energy equation. For high Reynolds numbers, the eddy viscosity and eddy diffusivity are incorporated into the reduced order model with a Proper Orthogonal Decomposition (nested and standard) with Interpolation (PODI), where the interpolation is performed using Radial Basis Functions. The reduced order solver, obtained using a k-{\omega} SST URANS full order model, is tested against the full order solver in a 3D T-junction pipe with parametric velocity inlet boundary conditions.