Conjugate heat transfer analysis of exhaust Port

Aim:-> Conjugate heat transfer (CHT) analysis of exhaust port.

Theory:-

As we know heat is transferred by 3 modes i.e. Conduction, convection & radiation.

1. Conduction:- is an exchange of energy by direct interaction between molecules of a substance containing temperature differences.
2. Convection:- is the transfer of internal energy into or out of an object by the physical movement of a surrounding fluid that transfers the internal energy along with its mass. Although the heat is initially transferred between the object and the fluid by conduction, the bulk transfer of energy comes from the motion of the fluid. Convection can arise spontaneously (or naturally or freely) through the creation of convection cells or can be forced by propelling the fluid across the object or by the object through the fluid.
3. Radiation:- is a transfer of thermal energy in the form of electromagnetic waves emitted by atomic and subatomic agitation at the surface of a body. Like all electromagnetic waves (light, X-rays, microwaves), thermal radiation travels at the speed of light, passing most easily through a vacuum or a nearly "transparent" gas such as oxygen or nitrogen. Liquids, "participating" gases such as carbon dioxide and water vapor, and glasses transmit only a portion of incident radiation. Most other solids are essentially opaque to radiation. The analysis of thermal radiation has a strong theoretical basis in physics, beginning with the work of Maxwell and of Planck.

Fig: Modes of Heat transfer

Conjugate heat transfer (CHT) is a type of simulation where it allows heat transfer between fluid and solid domain by exchanging thermal energy at contact surface. Here heat is exchanged at interfaces and transported by conduction process in solid and additionally by convection process within liquid. The CHT approach has an advantage over Finite element thermal analysis 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.

Heat transfer in solids and heat transfer in fluids are combined in the majority of applications. This is because fluids flow around solids or between solid walls and because solids are usually immersed in a fluid. 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). Efficiently combining heat transfer in fluids and solids is the key to designing effective coolers, heaters, or heat exchangers.

Results obtained by CHT analysis:-

1. Temperature distribution (contour).
2. Wall heat transfer coefficient
3. Heat fluxes
4. Heat transfer rate analysis
5. Realistic visualization of heat transfer
6. Identification of localized ‘hot spots’ or heat sinks in checking against specified requirements
7. Coupling CHT with FE analysis to evaluate thermally induced stresses, expansion or fatigue
8. Assessing insulation or heat shield effectiveness and optimizing of material selections

Fig: Conjugate heat transfer analysis example

Applications of CHT analysis:-

1. HVAC
2. Heat exchanger
3. IC engines
4. Heat sink
5. Boiler
6. Turbocharger

CHT analysis of exhaust manifold:-

Geometry preparation:-

Above figure shows prepared geometry in ANSYS Space-claim for simulation. The green color shows solid wall, and pink color shows fluid volume. Here fluid material is considered as air with air density `rho=1.225(kg)/m^3` and kinematic viscosity `nu=1.7894e^-5`. The material for solid exhaust system wall is considered as Aluminum.

Above geometry figure shows inlet and outlet ports for exhaust manifold. The fluid i.e. air with initial velocity 5m/s and with initial temperature of 700K is delivered through inlet port. The blue color shows inlet ports and red color shows outlet port.

Y+ Calculations:-

We have used `k-epsilon` solver for project. y+ value range for this type of solver is 30 to 300.

Reynolds number, `Re=(rhoxxvxxD)/nu`

`Re=(1.225xx5xx0.16)/(1.7894e^-5) =54766.961`

`Cf=0.0576/(Re)^(1/5) =0.0064971`

`tau_w=(Cfxxrhoxxv^2)/2`

`:.tau_w=(0.0064971xx1.225xx5^2)/2`

`:.tau_w=0.0994867N/m^2`

`u_f=sqrt(tau_w/rho)`

`:.u_f=sqrt(0.0994867/1.225)=0.28498m/s`

As we considered y+ value 30,

hence first layer thickness,

`y_1=(nuy^+)/(rhou_f)`

`y_1=(1.7894xx10^(-5)xx30)/(1.225xx0.28498)`

`y_1=1.5377235 mm`

Meshing:-

Above figure shows geometry after meshing. For capturing better result we have provided inflation layers. Here we have considered 4 cases of meshes to capture result. In first case we consider baseline mesh without inflation layer. And in last condition we have considered most refined mesh and provided inflation layer. As we know range of y+ value for `k-epsilon` solver is 30 to 300. So refining mesh at inflation layer we have also vary y+ value, which successively results change in inflation layer thickness.

~Case A (Baseline mesh):

Number of nodes = 33578

Number of elements = 137590

Temperature at outlet = 680.99069 K

Fig: Residual plot

Fig: Outlet temperature

Fig: Velocity streamlines

Fig: Temperature contour

Fig a: Velocity distribution Fig b: Wall heat transfer coefficient

~Case B:

Number of nodes = 55987

Number of elements = 150326

y+ value = 100

Temperature at outlet = 677.92577 K

Fig: Residual plot

Fig: Outlet temperature

Fig: Velocity streamlines

Fig: Temperature contour

Fig a: Velocity distribution Fig b: Wall heat transfer coefficient

~Case C:

Number of nodes = 81410

Number of elements = 227403

y+ value = 50

Temperature at outlet = 678.26986 K

Fig: Residual plot

Fig: Outlet temperature

Fig: Velocity streamlines

Fig: Temperature contour

Fig a: Velocity distribution Fig b: Wall heat transfer coefficient

~Case D:

Number of nodes = 155416

Number of elements = 498830

y+ value = 30

Temperature at outlet = 677.7963 K

Fig: Residual plot

Fig: Outlet temperature

Fig: Velocity streamlines

Fig: Temperature contour

Fig a: Velocity distribution Fig b: Wall heat transfer coefficient

Temperature distribution animation:-

Fig: Wall temperature distribution animation

As we know, Nusselt number is ratio of heat transfer due to convection to heat transfer due to conduction.

`Nu=(hl)/k`

From all of the above streamline figures and velocity contour its visible that velocity at bend is maximum. It is correct as law of conservation of mass is present. The maximum velocity is presented at corner due to bend i.e. suddenly change in direction of fluid.

So as velocity is maximum, the Reynolds number at that place is also maximum cause Reynolds number is directly proportional to velocity.

Reynolds number is also directly proportional to the Nusselt number which results high convection rate.

Points to confirm the simulation results are accurate:-

• Calculated value of HTC (heat transfer coefficient) by simulation can be confirmed from experimental data.
• HTC value can be verified by theoretical authentic data.
• By comparing Nusselt number we can verify HTC.

Factors which increases accuracy of simulation result:-

• Accurate modeling of physics.
• Mesh should be enough refined to capture smooth shedding.
• By performing mesh independent test.
• Mesh should capture geometry (curved faces) precisely.
• Inflation layers.
• Selection of y+ value in range.
• Selection of viscous solver model.
• Material selection.
• Accurate property of material should mentioned in problem.

Conclusion:- From above obtained result data and postprocessed plots we can conclude that-

1. For refined mesh the result obtained are more accurate.
2. y+ value is an important factor to obtained precise results.
3. HTC can be calculated at first cell near to wall surface only.