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Objectives Given: 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…
DARSHAN D G
updated on 01 May 2021
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 Statistics:
- Mesh Metrics:
> Setup:
- Boundary Conditions:
> 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 Statistics:
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:
- 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+ = ρuτyμ
⇒100 = 1.225×0.2193×y1.8×10-5
⇒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.
- 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 Statistics:
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:
> Setup:
- 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+ = ρuτyμ
⇒0.6 = 1.225×0.2193×y1.8×10-5
⇒y = 0.0000402 mm
- Inflation Layers for Exhaust Port:
- 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:
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 = (kDH)⋅Nu
where k is thermal conductivity of the liquid, DH is the Hydraulic diameter and Nuis the Nusselt Number which is determined using following equation.
Nu=0.023⋅R0.8e⋅Pnr
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 = mDHμ
where m = Mass flow rate
and Pr is the Prandtl Number:
Pr = Cp⋅μk
where Cp = Heat capacity
μ = Viscosity of the Fluid considered
In this way Heat Transfer Coefficient can be determined and verified using Dittus-Boelter correlation equation.
Conclusion:
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
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