Week 4 - CHT Analysis on Exhaust port
Aim:
1) To understand the concept of CHT (Conjugate Heat Transfer) analysis and its applications.
2) To perform a CHT analysis (setting up the case, meshing, solving, post-processing).
3) Validation of result.
CHT analysis - Theory
In real life simulations, we need to simulate a practical phenomenon. In most of the cases, instead of just free flowing, the fluid flows around a solid, exchanging energy with the surface. In such cases the heat transfer takes place due to conduction, convection and radiation.
When there are multiple modes of heat transfer in the simulation, we use CHT analysis. Conjugate heat transfer corresponds with the combination of heat transfer in solids and heat transfer in fluids. In solids, conduction often dominates whereas in fluids, convection usually dominates. Conjugate heat transfer is observed in many situations. For example, heat sinks are optimized to combine heat transfer by conduction in the heat sink with the convection in the surrounding fluid.
The CHT approach has an advantage over FE Thermal analysis in that wall heat transfer coefficients and their local variations on surfaces are directly calculated within the model rather than based on simplified empirical calculations. The CHT approach therefore has benefits for those applications where heat transfer is either non-uniform or difficult to calculate empirically.
(Image Source: Reference [3])
The objectives of CHT analysis mainly include:
1) Temperature distribution analysis.
2) Identification of localised ‘hot spots’ or heat sinks in checking against specified requirements.
3) Assessing insulation or heat shield effectiveness and optimising of material selections.
4) Coupling CHT with FE analysis to evaluate thermally induced stresses, expansion or fatigue.
5) Heat transfer coefficient analysis.
6) Heat transfer rate analysis.
(In this report, I have used CHT for heat transfer coefficient analysis.)
CHT analysis - Practical
Problem Statement:
Simulate a CHT analysis in exhaust port given below for inlet at 700 K and 5m/s and outlet at open air pressure. The open air has heat transfer coefficient = 20 W/m^2K and bulk temperature of 300 K. Also obtain the heat transfer coefficient of flow inside exhaust port.
Case 1: Baseline Mesh
A baseline mesh is created to check whether all boundary conditions are correct and to get a general flow pattern to understand the regions where mesh needs to refined.
1) Geometry and Meshing of Exhaust port:
Outlet Diameter = 150 mm
Wall thickness = 15 mm
Number of inlets = 4
Number of outlets = 1
This is the solid volume. The fluid volume is extracted and both volumes are made to share their topologies. This conformal mesh is important for CHT analysis because we want the heat to move from fluid to solid. A conformal mesh in where the edges and faces of two volumes do not meet each other.
Mesh Details:
Element size = 150 mm
Number of elements = 138057
2) Setup details:
Steady state analysis with pressure based solver.
Viscous model: Standard k - epsilon model
Fluid material = Air (Fluent database)
Solid material = Aluminium (Fluent database)
Inlet conditions = 5 m/s at 700 K
Outlet conditions = 0 Gauge pressure
Outer convection wall = bulk temperature = 300 K with h = 20 W/m^2 K
Number of iterations = 300
3) Results:
1) Temperature contour of outer wall
It is seen that wall temperature near outlet is higher than individual intakes. This is because of mass conservation. The velocity is higher near outlet and it causes more convective heat transfer to take place.
2) Velocity Contour:
The reason for higher outlet velocity is given above.
3) Velocity Contour in plane at z=0
The velocity plot near wall is not smooth. This region needs refinement.
4) Temperature plot
5) Pressure plot
Pressure goes below 0 value to balance the increase in velocity.
6) Wall heat transfer cooefficient
7) Wall heat Flux
The Wall Heat flux is negative. This happens due to the way ANSYS Fluent treats the heat flux direction. If heat is getting added to volume, the heat flux is represented as positive and vice versa.
Here, there are 2 volumes, solid and fluid. The heat flows from fluid to solid volume. So at the wall of fluid volume, the heat is removed and hence the value is negative. For solid wall, the heat flows inside so the value is positive.
Conclusion:
The tentative values are obtained but the mesh needs refinement at fluid-solid interface.
Case 2: Refinement (using inflation layers at fluid-solid interface)
The Mesh changes are:
Element size = 15 mm
Number of elements = 525751
Inflation layer type: Total thickness
Total Thickness = 5 mm
Number of layers = 5
Growth rate = 1.2
Inflation layers on both volumes
2) Results:
(The results are similar to what are obtained in case 1, so they are not explained here again. A final comparison of values is done at the end.)
1) Temperature contour:
2) Velocity contour
3) Velocity Contour at z=0
4) Temperature contour:
5) Pressure contour:
6) Wall Heat transfer Coefficient:
The coefficient is calculated at first cell along walls, so there is only one line visible. It is actually two lines, one for fluid volume and other for solid volume.
7) Wall heat flux
8) Temperature contour at a plane at x = 0.745 m
9) Velocity Contour:
Animation of temperature distribution
Result Comparison:
There is appreciable difference in values obtained after refinement.
Validation of h value
Methods of validation:
1) Theoretical verification using method given below
2) Theoretical verification using nusselt number.
(The relationship for turbulent internal flow needs to be used. Dittus Boelter equations is supposedly thought to be useful, but it isn't, as the flow regime is not of fully developed turbulent flow.)
3) Grid independence testing.
Here, I have selected a node and found the values using probe.
Properties:
By theoretical calculations:
So the value obtained by simulation is near to correct value. This error can be minimized by refining the mesh futher and choosing appropriate point for taking bulk temperature values.
Factors on which the results depend on:
1) Element size.
2) Correct application of boundary conditions.
3) Refinement at particular regions.
4) Appropriate solver and viscous models used.
References:
1) https://www.simscale.com/docs/content/simulation/analysis_types/OF_conjugateHeatTransfer.html
2) https://trivista.co.uk/design-and-analysis/cfd-overview/heat-transfer/
3) https://www.comsol.co.in/blogs/conjugate-heat-transfer