Conjugate Heat Transfer Simulation-Converge Studio

Aim

It is a flow simulation through a pipe to understand super-cycling in a conjugate heat transfer problem.

Introduction

The analysis type Conjugate heat transfer (CHT) allows the simulation of the heat transfer between Solid and Fluid domains by exchanging thermal energy at the interfaces between them. It requires a multi-region mesh to have a clear definition of the interfaces in the computational domain. Such a mesh can be created with the Super cyclic operation in the mesh creator. Heat transfer problems are often analyzed using a conjugate, coupled, or adjoint formulation. These three equivalent terms correspond to the problems containing two or more subdomains with phenomena described by different types of differential equations. If the heat transfer in a solid body and a neighboring fluid is considered, the first is described by the Laplace equation and the latter by the Navier–Stokes equations. Thus, heat transfer through solid and fluid regions can always be considered as a conjugate problem.

The physical modeling of flows with heat transfer is based on conservation laws for mass, momentum, and energy.

The heat capacity of solids is way higher than fluids, and therefore the time required to heat a solid is several orders of magnitude higher than a fluid. If we run the simulation at the fluid time-scale, which is necessary to perceive the changes in the fluid, this would lead to an insignificant increase of temperature in the solid. Super cycling treats the heat transfer in the solid on a different time scale. It storages the information of this problem and updates the solid temperature in each time-step of this new scale, treating the problem as different steady-state cases in the fluid time scale.

Heat Transfer in a Solid

heat transfer in solids, if only due to conduction, is described by Fourier’s law defining the conductive heat flux, q, proportional to the temperature gradient:

q = -k(Delta T);

Heat Transfer in a Fluid

The transport of fluid implies energy transport too, which appears in the heat equation as the convective contribution. Depending on the thermal properties on the fluid and on the flow regime, either the convective or the conductive heat transfer can dominate. The viscous effects of the fluid flow produce fluid heating. This term is often neglected, nevertheless, its contribution is noticeable for fast flow in viscous fluids. As soon as a fluid density is temperature-dependent, a pressure work term contributes to the heat equation. This accounts for the well-known effect that, for example, compressing air produces heat.

Turbulence model

A turbulence model should be chosen in accordance to the flow regime. In a Laminar flow, associated with low Reynolds numbers, viscous effects dominate the flow and turbulence can be neglected. This flow regime is characterized by regular flow layers.

On the other hand, a Turbulent flow is characterized by chaotic and irregular patterns that are associated with high Reynolds numbers. In order to simulate turbulent fluid flow, an appropriate turbulence model should be chosen. Currently, these models are supported:

  • Laminar

Reynolds-Averaged Navier–Stokes (RANS)

  •  k-Epsilon
  •  k-Omega-SST

Grid dependence test

The grid independency check has been performed to investigate the modification of temperature with reference to the modification within the grid size.  The converge solver has been taken into consideration to watch the modification within the grid size and its output temperature.

1. Mesh Size 0.04

2. Mesh Size 0.03

3. Mesh Size 0.02

4. Mesh Size 0.01

Grid Comparison 

Effect of supercycle stage interval

In the previous calculations, the supercycle stage interval was set to 0.05 s, this is, the heat transfer problem in the solid was treated as a steady-state heat transfer problem every 0.05 s. In this part, the simulation will be run changing this interval to 0.03, 0.02 and 0.01 s.

1. Supercycle 0.01s Interval

2. Supercycle 0.05s Interval

From the above figure, we can see how the supercycle stage interval does not affect the final value of the fluid or solid temperatures. There is, as expected, a change in the "transient", as the solid heat transfer is computed as different steady states. However, note that the intermediate values at this simulation are not valid to determine the real transient state of the problem. In this case, where only the final steady solution is important, all of the different supercycles stages would be valid as they all reach the same solution.


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