Propagation of temperature oscillations

This benchmark, designed for incompressible flows, tests the capability of the code to advect oscillations of primitive variables like temperature along the main flow inside a pipe.

It was proposed by Hu in the frame of thermal-hydraulics systems, that is one of the major disciplines essential for the design and operation of nuclear systems.

The inlet temperature of a one-meter pipe oscillates following a sinusoidal distribution,

T(t) = 628 + 100 x sin(𝜋 t);

the inlet velocity is fixed, u(t) = 0.5 m/s;

and the initial pipe temperate is at 628 K.

The material is incompressible water.

The diagonal tau of 2014 is employed, while the grid has uniform resolution of 0.05 m, and the time step is 1e-3 s.

All the settings of this problem are specified in files props.txt, setup.txt, fluid_ic_bc.hpp and mesh.geo.

The transient responses of the wave propagation are shown in Figures below, where the code predictions agrees very well with the analytical solutions.

Reference

Rui Hu “An Advanced One-Dimensional Finite Element Model for Incompressible Thermally Expandable Flow”, Argonne National Laboratory, USA