Conjugate Heat Transfer Simulation

Grid dependency test is necessary to have confidence on the accuray of simulated results.

1) Firstly, you can try to compare your simulated restuls with experimental resutls (your own or availabe from other) or results from analytical equations. If the error is in the tolerable range (according your criterion), you don\'t need to waste your time on grid dependency.

2) If you are looking for the best mesh which can give the smallest error, you need to work on grid dependency.

In this simulation, we have tried three different mesh sizes 0.004, 0.003 and 0.002 mm.

we will compare the results of these meshes using graphs of different parameters and time they have taken to converge.

mesh=0.002

mesh=0.003

mesh=0.004

by this images of time taken by the different meshes tell us that there is an exponential increase in the time taken by the 0.002 mesh. where as other meshes have taken very less time.

Apart from knowing the time of convergence we will not know how the results are affected by the meshes sizes so we will observe the other parameter results to understand the mesh effects.

velocity profiles

Eventhough there are difference at the begining of the simulation, finally after complete three lenght flows velocities of the meshes at the outlet got settled to around 6.8 m/s. we did not find much of the difference. As this is a CHT simulation we will find the variation among meshes in the temperatures plots of fluid and solid.

Temperature plots

outlet fluid temperature plot

Solid domain temperature plot

From this graph it is quite evident that there is not much of the mesh size effect on the fluid domain. There is very small difference in the temperature of the outlet fluid temperature However there is a huge difference of almost all hundred degrees in the solid domain between each mesh size. Although there is huge differences we can pick 0.003m mesh to be optimum grid size since all the cases in plots have mean values closer to this mesh. The runtime or simulation time of the case is very low and the results are acceptable.

It would be great to compare the results with 0.001m grid but the time taken for the convergence will be very high. Actually I have initialed the simulation but it did not even reached half way in two hours so I gave up on it.

temperature flow can be seen from the screenshots of the meshes of temperatue contours.

0.002 temp

0.003

0.004

From this contour we can clearly say that the size of the cell has an huge impact on the effective calculation of the temperatures near the wall.

y+ is a non-dimensional distance from the wall of the domain. It is often used to describe how coarse or fine a mesh is for a particular flow pattern. It is important in turbulence modeling to determine the proper size of the cells near domain walls. The turbulence model wall laws have restrictions on the y+ value at the wall. For instance, the standard K-epsilon model requires a wall y+ value between approximatly 300 and 100. A faster flow near the wall will produce higher values of y+, so the grid size near the wall must be reduced.

The definition of y+ for the K-e model is:

y+ = (((density^2 * Cmu^(1/2) * K)^(1/2))/viscosity) * (distance from wall)

where Cmu is the constant 0.09 and K is the kinetic energy.

Meshes contours are below

0.002

0.003

0.004

Velocity contours

0.002

0.003

0.004

Velocity over all the grids is almost same.

you could simulate fluid flow and assume that the walls of the container were at a constant temperature or even adiabatic. In reality, however, there may be significant heat transfer between the fluid and its container. The internal combustion engine is one example of such an application.

The internal combustion engine industry is moving toward simulating the entire system rather than independent components. Conjugate heat transfer (CHT)—the simultaneous prediction of heat transfer in both the fluid and solid portions of the domain—is of critical importance in a full-engine simulation. The accuracy of the predicted combustion in the cylinder is dependent on the temperature boundary conditions in the cylinder. By considering heat transfer in the metal components (e.g., the cylinder head, liner, piston, etc.) in the simulation, the cylinder wall no longer has a user-specified temperature, but instead has temperatures predicted as part of the system simulation. This makes the overall simulation results more predictive by reducing the dependence on boundary conditions.

There are several challenges when solving the fluid and solid domains together. The largest challenge to overcome is the difference in time-scales associated with the fluid and solid. In general, the heat transfer in the solid occurs more slowly than the convective and diffusive time-scales dictated by the fluid flow in the cylinder. For example, when you start a car in cold temperatures, combustion occurs almost instantly while the coolant takes minutes (thousands of cycles) to reach a steady-state temperature. This disparity in time-scales is problematic for CFD simulation because each cycle can be computationally expensive.

Converge offers an alternative approach called super-cycling for overcoming the time-scale disparity. In super-cycling, the fluid solver is frozen periodically while the heat transfer in the solid is allowed to progress to steady-state. Converge solves the fluid and solid phases in the same simulation without requiring you to stop and restart the simulation. Super-cycling significantly reduces the computational cost of the CHT simulation.

In order to understand the effect of super cycling in the context of the challenge we will present the images down below which are of various super cycling stage intervals like starting with the base value of 0.05 and 0.03,0.02,0.01. Suoer cycling takes place after 0.05 secs. Base grid is 0.004

Temperatue profile of solid region that got updated in respective intervals

Temperatue profile of fluid region that got updated in respective intervals

From two graphs we can say that the plots in the solid regions got updated at different intervals but eventually converged at the end towards a point. Here the main intension is to get the solution to a very faster convergence rate. Inorder to know that we will see the pics of the simulation time taken by each super cycle interval.

0.01

0.02

003

0.05

Here we can witness that 0.01 and 0.05 interval has very less convergence time were as 0.02 and 0.03 has taken more time. this is a weird phenomenon which is out of convention.

so by this results we can use 0.01 or 0.05 as super cycling interval for faster results.

Here are the animations of temperature and velocity animations.