In thermal simulations, most real world cases involve the transfer of heat between different states of matter, such as from solid to liquid. This is known as Conjugate Heat Transfer (CHT). Understanding the complex thermal interactions between these states allows us to enhance the thermal performance of electronics, engines, heat exchangers and much more.
However, accurately modelling this phenomena in Computational Fluid Dynamics (CFD) is particularly challenging. Multiple regions need to be effectively meshed to capture the relevant volumes and the interfaces between them. While each region is underpinned by complex physics models which need to be considered both separately and together at domain boundaries. In this article we will explore the concepts of conjugate heat transfer, its applications and how to simulate this process in HELYX with a case study of an Internal Combustion Engine (ICE).
Understanding Heat Transfer
When one area of an object is hotter than the other, the warmer molecules move faster than the cooler molecules and transfer a portion of this kinetic energy to the slower moving molecules. This flow of thermal energy heat transfer occurs via three types of transport phenomena: conduction, convection and radiation.
These heat transfer mechanisms can take place in any solid, liquid or gas that exhibits a difference in temperature. In solids, heat is typically transferred by conduction whereas liquids transfer heat via convection. However, in the majority of applications, heat is transferred across different states, such as from the liquid coolant jacket in an engine to the surrounding engine block.
What is Conjugate Heat Transfer?
CHT is the transfer of thermal energy between multiple fluid and solid regions. Instead of analysing the temperature fields of solids and liquids separately, this approach considers the heat transfer between solids and liquids simultaneously, as one unified system. This makes simulating CHT in thermal simulation software extremely challenging. Not only does the conduction in the solid region and the convection in the liquid region need to be modelled, but also radiation, energy transfer and contact resistance at the region boundaries.
Applications of Conjugate Heat Transfer Analysis
There are many real world applications where both conduction in solids and convection in fluids play significant roles in the transfer of heat. For example, in an ICE, heat transfers from components, such as the cylinder walls, head and piston, to the combustion chamber. By considering CHT, the boundary conditions of the cylinder walls are more representative, leading to more accurate predictions of combustion behaviour.
Heat exchangers used in refrigeration, air conditioning and electronics is another example. By definition, heat exchangers transmit thermal energy between two mediums. This can be to either cool a component down, or warm it up.
CHT helps to determine the rate of heat transfer between the coolant fluid and the solid walls. This has become particularly important in modern powertrains where batteries, motors and inverters need to be maintained within a specific temperature window to operate efficiently.
Case Study: Simulating CHT for a Thermal Analysis of an ICE Engine
ENGYS were tasked with performing a CHT analysis on an internal combustion engine for powertrain manufacturer, Aurobay. To accurately capture the thermal interactions between the fluid and solid regions, a total of four regions were modelled:
- Engine head
- Gasket
- Coolant Jacket
- Engine block
Multi Region Meshing
The CAD models for each of the four regions were provided by Aurobay, and once these were prepared for simulation, meshing could begin. ‘Traditionally to mesh this type of case you would create a separate computational grid for each part and then combine these into a single mesh,’ highlights Apostolos Krassas, CFD Engineer at ENGYS.
‘This can be time intensive, but with HELYX, you can mesh all these multi regions in one single process using a zoning approach. This involves locating one material point inside each region and then refining the mesh to capture all the details as well as ensure that the prism layers can grow,’ continues Krassas.
‘This particular project is one of the most geometrically challenging multi region cases we’ve run so far. So being able to accurately mesh it in a single execution with HELYX meant that meshing 19 million cells only took 12 minutes.’
Numerical Set-Up
The latest version of helyxSolve was used for this study which utilises the k-ω Shear Stress Transport (SST) turbulence model. This solver consists of a number of plug-ins which can be adjusted to solve the multi-physics and multi-regions required for CHT cases. It also takes a monolithic approach for solving the energy equation and so combines all the regions into a single matrix, as if it were solving for one region.
‘This monolithic approach helps to improve the stability of the simulation,’ explains Krassas. ‘CHT cases are typically prone to instabilities, especially when dealing with intricate geometries and complex interfaces. But by using this more robust setup we can reach the solution faster at a much cheaper computational cost. In some cases, the turnaround times can be as much as 100 times faster when compared to standard OpenFOAM solvers.’
There were a number of assumptions made for this study which were:
- Three solid regions: engine head, engine block and gasket
- One fluid region: coolant jacket
- Polynomial thermophysical properties to capture how thermal conductivity changes with temperature
- Coolant jacket material: 50% water and 50% ethylene glycol
Boundary Conditions
To model the initial temperature distribution of the solid regions such as the combustion chamber, cylinder head and exhaust manifold, data for all four combustion chambers, intakes and exhaust manifolds was supplied by Aurobay.
‘Modelling the average thermal load of the combustion chamber at the start would allow us to analyse the performance of the coolant jacket in lowering the temperature of the cylinders,’ says Krassas.
Results
Once all the boundary conditions were defined, the simulation ran on 128 cores and converged in only 300 iterations which took 7 minutes. This fast convergence rate is a result of the monolithic approach to solving the energy equation that underpins helyxSolve.
The results are shown below with the temperature distribution of the engine block on the left and velocity streamlines inside the coolant jacket on the right.
Conclusion
Overall, the different regions and interfaces involved in CHT make this type of CFD case extremely challenging to model accurately. Yet, CHT is utilised in such a wide variety of applications, that understanding its complexities is becoming more crucial to improving the efficiency of systems.
HELYX has been strategically developed to provide engineers with a versatile and efficient platform that allows them to accurately model CHT cases quickly and easily. This is achieved by HELYX’s hex-dominant automatic mesh algorithm which can mesh complex multi-regions in a single execution. While its monolithic approach leads to fewer iterations, higher stability and faster convergence rates. ‘Another benefit HELYX can bring to CFD simulations is flexibility,’ concludes Krassas. ‘Traditional OpenFOAM software typically has separate solvers and models for different cases, but with helyxSolve, everything is integrated into a single solver. This allows engineers to quickly shift from set-up to set-up and model say, an ICE engine one minute and a group of buildings the next. All they need to do is choose the right adjustments for the models they want to solve for.’
