Exhaust Port Challenge
- Give a brief description of why and where a CHT analysis is used.
- Maintain the y+ value according to the turbulence model and justify the results.
- Calculate the wall/surface heat transfer coefficient on the internal solid surface & show the velocity & temperature contours in appropriate areas.
- How to verify if the HTC predictions from the simulations are right? On what factors does the accuracy of the prediction depend on?
Solution:
1. Brief description of why and where a CHT analysis is used:
Conjugate heat transfer is a coupled problem involving heat transfer in a fluid domain as well as in the surrounding solid wall. Heat transfer by conduction and convection simultaneously occurs in the majority of engineering applications, such as heat exchangers and fins. Efficiently combining heat transfer in solids and fluids is the key to design effective coolers, heaters, or heat exchangers.
Conjugate heat transfer (CHT) analysis can accurately predict heat transfer by simultaneous solving all the relevant solid and flow field heat transfer processes, for example: conduction through solids, free and forced convection in the gases/fluids and thermal radiation.
The CHT approach has an advantage over FE Thermal Analyses 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.
Fig1 : Natural convection around a heat exchanger. Cold water enters in and gets heated due to hot air flowing opposite to it.
Given Exhaust Port Geometry:
The outer wall of the manifold is exchanging heat with the ambient through thermal convection.
Grid Independence Test and its significance:
A CFD simulation can never be trusted unless we check whether the result depends on the grid or not, or else we have any experimental data. The output result of a coarser mesh and finer mesh can neither be the same. So up to what extent, we need to vary the mesh to get the accepted level of tolerance, can be found out from Grid Independence test.
This is done by varying mesh size from coarse to fine and checking the output result of each mesh. When varying the mesh does not affect the result much then we can stop and select that minimum mesh size for our final solution attempt.
Grid dependency test is performed with multiple attempts (by refining mesh using local mesh refinement techniques).
Attempt 1 (with Baseline Meshing and K-Epsilon Model):
> Meshing Details:
- Mesh Type: Tetrahedral
- Element Size: 150 mm (Default)
- Mesh Statistics:
- Nodes: 27379
- Number of Elements: 137231
- Mesh Metrics:
> Setup:
- Solver: Pressure Based
- Algorithm: SIMPLE (Semi Implicit Method for Pressure Linked Equations)
- Time: Steady
- Fluid: Air
- Viscous Model: K-Epsilon
- K-Epsilon Model: Realizable
- Near Wall Treatment: Standard Wall Functions
- Boundary Conditions:
- Inlet Velocity: 5 m/s
- Temperature: 700 K
> Solution:
- Residuals Plot:
> Results:
- Temperature Contour Plot:
- Velocity Contour Plot:
> Velocity Streamline Contour:
-Wall Heat Transfer Coefficient:
In initial attempt, y+ value is not considered to get an overview of its effects and importance accordingly. The consideration of y+ value and its importance is dealt in further attempt.
Attempt 2 (with Refined Meshing and K-Epsilon Model):
> Meshing Details:
- Mesh Type: Tetrahedral
- Element Size: 100 mm
- Mesh Statistics:
- Nodes: 146933
- Number of Elements: 461635
Since academic version of Ansys is being used here, it is limited to cases with only 512000 cells and cannot exceed above 512000 cells while meshing.
- Body Sizing:
- Geometry Selected: Solid Volume of Exhaust Pipe
- Element Size: 100 mm
- Boundary Conditions and Setup are maintained same as in Attempt 1.
- Calculating First Layer Height or Near Wall Distance for given y+ :
Wall functions are useful in telling the solver how to approach the solution near wall. These are used to predict near-wall results accurately even at coarse grids. There are multiple wall functions for each turbulence model, but the most basic is the standard wall function.
The y+ value is a non-dimensional term that can be used to understand how coarse or fine our grid needs to be. It is given by,
We know that, for K-Epsilon model and standard wall function Y+ value range is 30 < y+ < 300. Here, we are aiming for y+ = 100
We know that,
y+ = `(rhou_tauy)/mu`
`=>`100 = `(1.225xx0.2193xxy)/(1.8xx10^-5)`
`=>`y = 6.7 mm
- Inflation Layers for Exhaust Port:
In ANSYS Fluent, cell/element stacking in the direction normal to the boundary can be achieved using a feature called Inflation. Essentially, the mesh with several layers can be inflated from the surface of the boundary until the boundary layer thickness is fully covered.
- Number of Layers: 5
- Growth Rate: 1.2
- First Layer Height: 6.7 mm
- Mesh Metrics:
- Histogram of Wall y+ :
> Fluid Volume:
> Solid Volume:
From the plot, it can be observed that most of the Exhaust Manifold Cells do not lie in y+ range 30-300 for K-Epsilon, Standard Wall Function. Hence, another attempt is carried out with K-Omega SST Model with its y+ consideration respectively.
> Results:
- Temperature Contour Plot:
- Velocity Contour Plot:
> Velocity Streamline Contour:
-Wall Heat Transfer Coefficient:
The smooth contour of Wall Heat Transfer Coefficient is obtained after using inflation layers along with consideration of y+.
Attempt 3 (with Refined Meshing and K-Omega SST Model):
> Meshing Details:
- Mesh Type: Tetrahedral
- Element Size: 200 mm
- Mesh Statistics:
- Nodes: 172515
- Number of Elements: 452708
Since academic version of Ansys is being used here, it is limited to cases with only 512000 cells and cannot exceed above 512000 cells while meshing.
- Body Sizing:
- Geometry Selected: Solid Volume of Exhaust Pipe
- Element Size: 200 mm
> Setup:
- Solver: Pressure Based
- Time: Steady
- Fluid: Air
- Viscous Model: K-Omega
- K-Omega Model: SST
- Boundary Conditions are maintained same as in Attempt 1.
- Calculating First Layer Height or Near Wall Distance for given y+ :
The y+ value is a non-dimensional term that can be used to understand how coarse or fine our grid needs to be. It is given by,
We know that, for K-Omega SST Model Y+ value range is y+ < 1. Here, we are aiming for y+ = 0.6
We know that,
y+ = `(rhou_tauy)/mu`
`=>`0.6 = `(1.225xx0.2193xxy)/(1.8xx10^-5)`
`=>`y = 0.0000402 mm
- Inflation Layers for Exhaust Port:
- Number of Layers: 8
- Growth Rate: 1.2
- First Layer Height: 0.0000402 mm
- Mesh Metrics:
- Histogram of Wall y+ :
> Fluid Volume:
> Solid Volume:
- Wall y+ vs Vector Direction in Airflow:
X-Axis Function: Turbulence, Wall y+
Y-Axis Function: Vector Direction in Air Flow
From the plot, it can be observed that most of the Exhaust Manifold Cells lie in y+ <1 for K-Omega, SST Model.
> Results:
- Temperature Contour Plots:
- Velocity Contour Plot:
> Velocity Streamline Contour:
-Wall Heat Transfer Coefficient:
- Verification of HTC predictions from simulation depends on following factors:
- Mesh quality and geometry
- Inflation layers
- Properties of material
- Turbulence models used
- It can also be verified with help of Dittus-Boelter correlation equation.
Under forced convection circumstances, heat transfer coefficient (h) can be determined and verified using Dittus-Boelter correlation equation. From Dittus-Boelter correlation, heat transfer coefficient can be calculated further using two dimensionless groups, the Reynolds Number and Prandtl Number.
h = `(k/D_H) * N_u`
where k is thermal conductivity of the liquid, `D_H` is the Hydraulic diameter and `N_u`is the Nusselt Number which is determined using following equation.
`N_u = 0.023*R_e^0.8*P_r^n`
where n = 0.4 when fluid is being heated and
n = 0.3 when fluid is being cooled
In the above equation Re is the Reynold's Number which is given by:
Re = `(mD_H) / mu`
where m = Mass flow rate
and Pr is the Prandtl Number:
Pr = `(C_p *mu)/k`
where Cp = Heat capacity
`mu` = Viscosity of the Fluid considered
In this way Heat Transfer Coefficient can be determined and verified using Dittus-Boelter correlation equation.
Conclusion:
- The quality of the contours and results are enhanced in attempt 2 and 3 by refining the mesh from coarser to finer. Accepted level of results are achieved from Grid Independence test.
- Computation time in second attempt is comparatively higher than in attempt 1, as mesh is refined further in attempt 2 and 3. This might not be economical at certain cases.
- It is important to get into habit of checking y+ values as a part of normal post processing, so that one can make sure to fall in the valid range for the flow physics and turbulence model selection.
- In attempt 3 better range of Wall Heat Transfer Coefficient is obtained when K-Omega SST Model is used because the BSL and SST variants combines two models into one model where we use the k-ω model in the inner portion of the boundary-layer then smoothly switch to the k-ε model when we move away from the wall and into the free stream area.
- The standard wall functions should not be used below the y+ limit of 11 as the solution's accuracy might deteriorate in an uncontrolled manner.
References:
[1] https://www.simscale.com/forum/t/what-is-y-yplus/82394
[2] https://skill-lync.com/knowledgebase/boundary-layer-y-plus-wall-functions-in-turbulent-flows-2