Week 4 - CHT Analysis on Exhaust port

Aim: Conjugate heat transfer (CHT) Analysis on Exhaust port.

Objective:

1. Give a brief description of why and where a CHT analysis is used.
2. Maintain the y+ value according to the turbulence model and justify the results.
3. Calculate the wall/surface heat transfer coefficient on the internal solid surface & show the velocity & temperature contours in appropriate areas.
4. How would you verify if the HTC predictions from the simulations are right? On what factors does the accuracy of the prediction depend?

1. Give a brief description of why and where a CHT analysis is used.

Computational fluid dynamic (CDF) and more specifically conjugate heat transfer (CHT) analysis can accurately predict heat transfer by simultaneously solving all the relevant solid and flow field heat transfer processes, such as conduction solids, free and forced convection in the gases/fluids, and thermal radiation.

The CHT approach has an advantage over FE thermal analysis. The wall heat transfer coefficients and their local variations on surfaces are directly calculated within the model rather than on simplified empirical calculations. THEREFORE, the CHT approach has benefits for those applications where heat transfer is either non-uniform or difficult to calculate empirically.

2. y+ value.
y+ is a non-dimensional distance. It is important in turbulence modeling to determine the proper size of the cells near domain
walls to check if the mesh is fine enough to catch the boundary layer near the walls. the value of y+ is different for different
turbulence models. for the k-epsilon standard turbulence model, the y+ value id ranges from 30 to 300, for the k-omega SST model
the y+ value is ranging from 0 to 5.
to determine the size of the cell at the boundary, that is first layer thickness we have to use below formulae
Firstly, we should calculate the Reynolds number for our model based on the characteristic scales of our geometry such that:

`Re = (ρ. U. L) /μ`

where and are the fluid density and viscosity respectively

U is the freestream velocity
L is the characteristic length (e.g. pipe diameter, body length, etc.).
The definition of the y+ value is such that:

`Y + = (ρ. Ut. Δ y1)/μ→ Δ y1 =Y + μ/(ρ. Ut)`

the frictional velocity, Ut is defined as:

`Ut = √((τw)/ρ)`

The wall shear stress can be calculated from the skin friction coefficient Cf such that:

`τw=1/2Cf. ρ. U^2`

for an external flow, the Cf value is defined as:

`Cf = 0.058 ⋅ (Re)^(−0.2)`

by using the above formulae we can calculate the first layer thickness. here we are taking air as fluid and we are going to take the
default values of air from Ansys fluent. I am going to use the k-epsilon standard turbulent model for the simulation. so I can take the
values of y+ in between 30 to 300.

3. Calculate the wall/surface heat transfer coefficient on the internal solid surface & show the velocity & temperature
contours inappropriate areas:

the geometry of the exhaust port:

solid part

fluid volume

final geometry

there are four inlets and one outlet in the exhaust port.

baseline mesh:

this is the mesh generated from the geometry by using default values from the mesh. the four inlets were named inlets and
the one outlet is named an outlet and the outer surface of the exhaust port is named as out wall convection. I have named it
because the mode of heat transfer from the outer surface to the air around the exhaust port is convection. so I have named the outer surface of the exhaust port as outer wall convection.

Setup:
here the inlet velocity of the fluid is 5m/s and the temperatures of inlet fluid are 700k. the pressure-based solver is used with steady-state conditions. k epsilon standard model is used here and the convective heat transfer coefficient at outer wall convection value
is 20 w/m^2.k. make the temperature contour at the outer wall convection. simulate 300 iterations.

final temperature contour:

here from the contour, we are seeing that the temperature at the outlet port is higher than the temperature of the inlet ports.
because as we know that the mass flow rate is the same at every cross-section of the exhaust port that is the mass flow rate at inlet
ports is equal to the mass flow rate at the outlet port. here the area of all inlet and outlet ports is the same with a diameter of 166 mm.
mass flow rate at inlet ports = mas flow rate at outlet port
a1.v1 + a2.v2 + a3.v3 + a4.v4 = a5.v5
where a1,a2,a3,a4,a5 are areas of inlet and outlet of the exhaust port, and v1,v2,v3,v4,v5 are the velocities of fluid in the exhaust
port at inlets and outlet port.
as the areas are almost equal then we can write the above equation as
v1+v2+v3+v4 = v5.
from this, we can say that the exhaust gases move out with high velocity. as we know that the temperature is a function of
velocity, so the temperature at the outlet is greater than the temperature at inlets.

residuals plot-

results:
velocity streamlines

as we discussed above, the velocity at the outer port is higher which is shown in the above figure.

velocity plane at the outer port

temperature plane at the outer port-

the exhaust port with refined mesh:

here the element size of the solid body is 15mm and the y+ value is taken here is 30 and the first layer thickness obtained
is 1.68027007449014E-03. the total number of elements produced is 495159.

residuals plot

surface heat transfer coefficient plot-

result:
velocity streamlines:

temperature plane at the outer port-

velocity plane at the outer port-

we can clearly visualize the increase of velocity at the bent portion of the outlet port. this is because of refining of mesh and
creating inflation layers at the wall boundary.
4.How would you verify if the HTC predictions from the simulations are right? On what factors does the accuracy of the
prediction depend?
the formula for nusselt number is the ratio of convective heat transfer to conductive heat transfer

Nasselt numberh=hL/K

where h is the convective heat transfer coefficient
L is the characteristic length
K is the conductive heat transfer coefficient
in the above problem characteristic length is the diameter of the exhaust port. we know that Reynolds number is a function of
characteristic length. so we can conclude here that nusselt number is a function of Reynolds number

Reynold number =ρ. v. L/μ

where v is the velocity of flow
is the absolute viscosity
is the density of the fluid in the exhaust port.
from the above conclusion and the above two formulae we can say that h is directly proportional to velocity, that is heat
transfer coefficient(htc) is directly proportional to the velocity of fluid inside the exhaust port.
in the above figures, we have clearly seen the velocity of the fluid in the outlet port using refined element size compared to baseline
elements. so we can also say that the heat transfer coefficient can be clearly visualized using the refined element size.
the factory considers for the accuracy of predictions are refining element size and providing inflation layers at the
boundaries of the exhaust fluid flow.