Week 4 - CHT Analysis on Exhaust port

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 on?

1. Conjugate heat transfer (CHT):

The Conjugate Heat Transfer (CHT) analysis type allows for the simulation of heat transfer between solid and fluid domains by exchanging thermal energy at the interfaces between them. Typical applications of this analysis type exist as, but are not limited to, the simulation of heat exchangers, cooling of electronic equipment, and general-purpose cooling and heating systems.

The contemporary conjugate convective heat transfer model was developed after computers came into wide use in order to substitute the empirical relation of proportionality of heat flux to temperature difference with heat transfer coefficient which was the only tool in theoretical heat convection since the times of Newton. This model, based on a strictly mathematically stated problem, describes the heat transfer between a body and a fluid flowing over or inside it as a result of the interaction of two objects. The physical processes and solutions of the governing equations are considered separately for each object in two subdomains. Matching conditions for these solutions at the interface provide the distributions of temperature and heat flux along the body–flow interface, eliminating the need for a heat transfer coefficient.

2. Why CHT analysis is used:

Computational Fluid Dynamics (CFD) 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, 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.

3. Where is CHT analysis used:

Starting from simple examples in the 1960s, the conjugate heat transfer methods have become a more powerful tool for modeling and investigating natural phenomena and engineering systems in different areas ranging from aerospace and nuclear reactors to thermal goods treatment and food processing, from complex procedures in medicine to atmosphere/ocean thermal interaction in meteorology, and from relatively simple units to multistage, nonlinear processes. A detailed review of more than 100 examples of conjugate modeling selected from a list of 200 early and modern publications shows that conjugate methods are now used extensively in a wide range of applications. That also is confirmed by numerous results published after this book appearance (2009) that one may see, for example, at the Web of Science. The applications in specific areas of conjugate heat transfer at periodic boundary conditions and in exchanger ducts are considered in two recent books.

Applications:

• Effective heat transfer:

Efficiently combining heat transfer in fluids and solids is the key to designing effective coolers, heaters, or heat exchangers.

The fluid usually plays the role of energy carrier on large distances. Forced convection is the most common way to achieve a high heat transfer rate. In some applications, the performances are further improved by combining convection with phase change (for example liquid water to vapor phase change).

Even so, solids are also needed, in particular, to separate fluids in a heat exchanger so that fluids exchange energy without being mixed.

• Energy savings:

Heat transfer in fluids and solids can also be combined to minimize heat losses in various devices. Because most gases (especially at low pressure) have small thermal conductivities, they can be used as thermal insulators… provided they are not in motion. In many situations, gas is preferred to other materials due to its low weight. In any case, it is important to limit the heat transfer by convection, in particular by reducing the natural convection effects. Judicious positioning of walls and the use of small cavities helps to control the natural convection. Applied at the micro-scale, the principle leads to the insulation foam concept where tiny cavities of air (bubbles) are trapped in the materials (e.g. polyurethane), which combines high insulation performances with lightweight.

Geometry setup:-

• Load the model into the SpaceClaim and change the units to meters
• Remove the duplicate edges in the model
• Then extract the volume in the model and name the inner volume as fluid  and outer volume as solid volume and remove the empty components

•  Enable Share topology of the main component so that the mesh and physics information can be shared and conformal mesh can be achieved.

• Lastly, to achieve conjugate heat transfer between the fluid and wall we have to choose share prep under the workbench tool so that the heat transfer is captured throughout the wall from inlet to outlet.

Mesh setup:-

• After the geometry setup is done in the SpaceClaim open the mesh 
• select the faces and name them accordingly
• Create a name selection for fluid volume so that the inflation layer can be achieved on that body since the conjugate heat transfer is between the fluid volume to the solid wall.
• Create a body sizing on the outer wall convection region to achieve mesh refinement and accurate results can be captured at such regions.

Fluent setup:

•  After updating the mesh open fluent setup, select a pressure-based solver using the steady-state time simulation and absolute velocity formulation under the general settings.
• Under physics choose the energy option since we are dealing with temperature properties.  
• Input the Boundary values at the inlet, 5 m/s as inlet velocity at 700k temperature. Set the outer wall convection boundary to convection type and input a constant value for heat transfer coefficient as 20
•  Under materials, properties choose air as the fluid material and aluminum as the solid material
•  Enter the reference values as per the geometry and inlet boundary conditions accordingly.
• Initialize by using the hybrid initialization, and the simulations for 400 iterations as it is optimum to achieve a converged solution.

Temparature distribution:-

Residual plot:-

surface heat transfer co-efficient:-

Temperature and velocity contours:-

Case 2 Refined mesh

Residual plot

Temperature and velocity contours:-

cases	viscous model	no. of elements	surface HT coefficient in(W/m^2-K)	wall HT coefficient in(W/m^2-K)
1	k-epsilon	247571	31.674	211
2	k-epsilon(refined)	336493	28.58	191.9

How would you verify if the HTC predictions from the simulations are right? On what factors does the accuracy of the prediction depend on?

According to Bernoulli's mass conservation principle mass is conserved in our model which is clearly explained below.

Let us assume the flow rate from each inlet as Q1, Q2, Q3, Q4 respectively, and Q5 be the flow rate(outflow) from the exhaust manifold.

As mass is neither created nor destroyed, mass flow rates are also balanced as below

Q1+Q2+Q3+Q4=Q5Q1+Q2+Q3+Q4=Q5 -------(1)

we have Q=ρ.A.VQ=ρ.A.V -------(2)

now the equation 1 becomes

A1.V1+A2.V2+A3.V3+A4.V4==A5.V5

as it is an incompressible flow to compensate for the mass flow, velocity is increased, and the overall mass flow rate is conserved.

As velocities are high, the Reynolds number at the outlet manifold will be high.

Nu=f(Re, pr) for forced convection applications,

Nu=hD/k

from the above equations

Nu∝Re,

Nu∝h,

hence, Re∝h

From our simulations, we have observed velocities are high at bend section of outlet manifold hence higher Reynolds number which has high Heat transfer coefficients.

Therefore predictions from our simulations can be considered correct.

Factors influence accuracy of prediction:

Mesh quality greatly impacts the accuracy of predicted value from our simulations which can be observed from the above contours and maximum values of related parameters like velocity and heat transfer coefficient.
Appropriate y+ value helps in calculating total layer thickness from the wall for the better capturing of effects near walls, which is HTC in our case.
An appropriate turbulence model has to be used in accordance with the y+ value which is very important
Appropriate solvers are one of the most important factors which lead all the calculations in solving the equations
Inflation layers and boundary conditions.