Week 4 - CHT Analysis on Exhaust port

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.

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 coefficient 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.

Where 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.

Simulation setup:

Geometry:

• Load the model into the SpaceClaim
• Extract the volume in the model and name the inner volume as fluid volume 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:

Initially, click on generate mesh and check for proper meshing. Here, the mesh is correct.

Now, remove the generated mesh and name the faces.

Generate the mesh accordingly.

Fluent:

Hybrid initialize and run for 500 iterations.

Simulation:

No. of elements = 247571

Viscous model = k-epsilon

Inlet velocity = 5m/s

Inlet temperature = 700k

HT co-efficient = 20W/m^2-k

Results:

Temperature distribution:

Residual plot:

Surface HT co-eff:

The surface HT co-eff is 28.5972

Contours:

Temperature:

Velocity:

Velocity streamline:

4. How to verify HTC predictions are correct?

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, and 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)

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 (Nusselt number) = f(Re, pr) for forced convection applications,

Nu = hD/k

from the above equations,

Nu ∝ Re,

Nu ∝ h,

Therefore, Re∝h

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

Therefore predictions from our simulations can be considered correct.