Conjugate Heat Transfer Analysis on Exhaust Port and Validation on the Assumption made over outer wall boundary condition

INTRODUCTION:

Exhaust port in an IC engine is a conduit which acts as a passage for the exhaust gases from IC engines at the engine running time. The gas which passes through the port is the undesirable but unavoidable gas at the end of the combustion i.e., at the end of the chemical reaction which converts chemical energy in to thermal energy inside the combustion chamber. These gas includes CO₂, H₂O (water vapour), CO, unburned HC, Particulate emissions, NO₂ etc., at very high temperature would go maximum up to 1000^oC.

These hot gases will dissipate its heat wherever it passes due to existence of temperature difference between its stream and its surroundings. While it passes through the exhaust port it transfers its heat content to the surroundings via the material of the exhaust port. Here the transfer of heat takes convection mode (between hot exhaust gas stream and inner surface of the solid exhaust port) followed by conduction mode (through solid material of the exhaust port) and finally again by convection mode (between outer surface of exhaust port and surrounding atmospheric air). This type of heat transfer is known as conjugate heat transfer.

In this study we are going to analyze the conjugate heat transfer in the exhaust port using CFD technique in ANSYS. To perform this analysis certain assumptions were made on boundary conditions such as inlet gas velocity & temperature as 5 m/s & 700K and another one important assumption made is that the conjugate heat transfer between hot gas stream and solid exhaust port only, the external surface is assumed to have a convective boundary having heat transfer coefficient, h = 20W/m².K.

Justification for Assuming h = 20W/m2.K:

h =

_Where,

_{h – Heat transfer Coefficient,} W/m².K.

Nu – Nusselt Number external flow,

K – Thermal conductivity of exhaust gas, W/m.K = 0.05298 W/m.K (from data book based on hot air temperature)

D – Diameter of the cylinder, m = 0.15m

On referring to Heat and Mass Transfer data book by C.P.Kothandaraman, the Nusselt number for flow over cylinder is formulated as

Nu = C.Re_D^m.Pr^0.333

Where,

Pr – Prandtl number = 0.6965 (from data book based on hot air temperature)

Re_D = Reynolds number = uD/u

C = Constant

m = Coefficient

Where,

u – Flow velocity m/s = 5.8 m/s (assuming 30% of vehicle velocity 70 Km/hr)

u - Kinematic viscosity, m²/s = 6.997x10^-5 m²/s (from data book based on hot air temperature)

Re_D = = 12,433

From the Re_D value on referring to HMT data book

C = 0.193

m = 0.618

Therefore

Nu = 0.193 x 12433^0.618 x 0.6965^0.333 = 58.036

h = = 20.498W/m².K (which we can take a round off value of h = 20W/m².K).

Exhaust port

Fig 1:Model of exhaust port

Fig 2: Model of exhaust port – fluid volume generated

The above Fig 1 shows the 3D model of an exhaust port which we are going to do the conjugate heat transfer analysis which having 4 inlets and one converged outlet. Let us consider the port material as aluminium. Fig 2 shows the model of the exhaust port after fluid volume extraction using space claim module by generating the fluid volume inside the exhaust port.

Base line

Fig 3: Meshed model of exhaust port - base line.

Trial 1

Fig 4: Meshed model of exhaust port – Trial 1

The above shown Fig 3 is the mesh model of baseline setup which is a coarsely meshed model, where the results out of this model is not appreciated because of its degree of error. The Fig 4 shows the meshed model of Trial 1 setup which finer than base line setup and also inflation layers were developed from inner surface of port in fluid volume to capture the surface interaction while convective heat transfer taking place. As we have mesh count limitation we could not make further finer mesh. Both models will be analyzed with same set of boundary conditions. In both case the connectivity between meshes of solid and fluid volume is fixed by making conformal meshing between them with the help share topology option in space claim.

Table 1: Details of mesh in Base line and Trial 1 setup.

Setup	Base Line		Trial 1
Domain	Nodes	Elements	Nodes	Elements
fluid	17185	82965	116602	329304
solid	16483	55526	48384	179150
All Domains	33668	138491	164986	508454

Base line

Fig 5: Mesh metrics plot showing mesh quality in base line setup

Trial 1

Fig 6: Mesh metrics plot showing mesh quality in Trial 1 setup

The above Table 1 contains the details of mesh generated in Base line and Trial 1 setup. The above Fig 5 & 6 shows the mesh metrics plot on mesh quality of Base line and Trial 1 setup respectively. In that we could see that the number of Tetrahedral elements having good mesh quality is quite higher in Trial 1 model when compared to Base line setup but the wedges present in Trial 1 model is of poor quality and that could not be refined further due to the mesh count constraint. This wedges only present in Trial 1 because of having inflation layers in that model. This wedges quality can be refined by gradually reducing the size meshes at inner surface of port using face sizing option.

The model is analyzed with above said boundary condition, steady state, K-ε turbulent model and pressure based solver starting the iterations with hybrid initialization. Both the cases were allowed to iterate the solution for several iterations until it gets converged. The convergence of the solution is not achieved by the solver but it can be converged based on the scaled residual plot which is bearing a steady uniform pattern of variation. After the convergence the solution by this method the solution is examined using several contour plots which are shown below.

Base line

Fig 7: Temperature contour of outer wall of exhaust port in base line setup

Trial 1

Fig 8: Temperature contour of outer wall of exhaust port in Trial 1 setup

The above Fig 7& 8 shows the temperature contour of outer wall surface of the exhaust port. Due to the mesh refinement we could see the improvement of the results from base line setup to Trial 1 setup. The maximum and minimum temperature in base line setup is 574.418 K and 463.691 K respectively but when we look on to Trial 1 setup it is 601.45 K and 490.63 K respectively. This increase in temperature values is because of development of required mesh types in the model to capture the physics, the mesh count in Trial 1 also responsible for the improvement of values. The development of face sizing in intermediate surface i.e., inner surface of exhaust port and inflation layers in the fluid region from the intermediate surface helps in the analysis of conjugate heat transfer. From the Fig 7 & 8 we could also evidence that the surface of exhaust port near port outlet experiences the highest temperature than any other place in the exhaust port outer surface, which indicates that the converging portion of the port increases the kinetic energy of the flow which increases the heat transfer coefficient at the inner surface of the port and transfers the heat from exhaust gases to solid metal Walls of exhaust port. Also accumulation of high temperature exhaust gases from four independent combustion chambers will increases the heat content of the exhaust gas stream at converging portion of the exhaust port which is the outlet of it.

Base line

Fig 9: Temperature contour of inner wall of exhaust port in base line setup

Trial 1

Fig 10: Temperature contour of inner wall of exhaust port in Trial 1 setup

From the Fig 9 & 10we could evidence that the inner surface of the exhaust port experiences the highest temperature in the whole solid body of the port. Also it again proves the increased heat transfer coefficient and heat accumulation in converging portion of the exhaust port by having a clear temperature contour plot showing the increased temperature over the surface near flow outlet of exhaust port. The maximum temperature in both cases base line and Trial 1 are 634 K and 630 K respectively which makes deviation in our understanding but the thing is, as per the contour plot major surface near outlet of base line is approximately between 558 K to 577 K rather in Trial 1 setup it is between 592 K to 604 K which makes our understanding more stronger. The highest temperature on both cases exists at the sharp corners at the exits and this is due to the discontinuity in the boundary and also that sharp corner has poor heat dissipation probability.

Base line

Fig 11: Temperature contour at Ref-plane of exhaust port in base line setup

Trial 1

Fig 12: Temperature contour at Ref-plane of exhaust port in Trial 1 setup

The Fig 11 & 12 shows the temperature contour of the reference plane which is placed at the mid portion of the conduit which is acting as an outlet of the exhaust port. When we look on the Fig 11 the contour which we get is distended due to the coarse meshing in base line setup and the temperature distribution we get is not in an acceptable way due to the poor mesh generated. But on examining the Fig 12 the distribution is well defined and we can figure out the formation of thermal boundary layer near the exit portion of the port. The thermal boundary layer formed in Trial 1 setup can be seen with the smooth transition as like the in the real case. The variation in the temperature range between base line and Trial 1 setup says that the dissipation of heat in base line setup is poorly captured rather in Trial 1 it is well captured. Due to poor dissipation only the peak temperature in Base line setup is little higher than Trial 1. It means heat is not dissipated properly in all the directions.

Base line

Fig 13: Velocity contour at Ref-plane of exhaust port in base line setup

Trial 1

Fig 14: Velocity contour at Ref-plane of exhaust port in Trial 1 setup

Velocity contour plot of reference plane of Base line and Trial 1 setup is shown in above Fig 13 &14. From the above two figure we can come to a conclusion that flow gets accelerated and at the inner bend region and reaches the maximum velocity there. Maximum velocity of Base line and Trial 1 setup is 36.73 m/s and 41.23 m/s respectively. In Trial 1 setup the formation of hydrodynamic boundary layer and flow separation is well captured here which we can see evidently in Fig 14.

Base line

Fig 15: Wall Heat transfer coefficient at IW of exhaust port in base line setup

Trial 1

Fig 16: Wall Heat transfer coefficient at IW of exhaust port in Trial 1 setup

The Heat transfer coefficient existing in the inner surface of the both the Base line and Trial 1 model is shown in the Fig 15 & 16. By examining both the cases the peak heat transfer coefficient exists at the region where the fluid velocity is maximum, because of the high velocity only the heat dissipation rate is higher in that region. The high heat transfer coefficient makes large amount of heat to heat transferred from the fluid stream to solid port. This is one of the reason to make the temperature of the region near fluid exit to be higher. The heat transfer coefficient of the inner surface of the base line setup ranges from 8.588 to 102.468 W/m².K and for Trial 1 setup it is from 26.59 to 191.53 W/m².K.

Modified:

To capture the exact physics existing in this exhaust port case, we have to model the problem without any huge assumptions for exhaust port boundary conditions. Hence we are attaching a volume around the exhaust port which is the atmospheric air flowing over it in actual scenario. This makes the problem much more complicated than the previous case by having two fluid, one is flowing at a higher temperature inside port and another one flowing over the port at atmospheric temperature. For justification of heat transfer coefficient on the outer wall, we have assumed that the flow over the exhaust port will have only 30% of kinetic energy from average velocity of the vehicle (70Km/hr) which would be 5.8 m/s is taken in to consideration for applying boundary condition for the inlet of the external flow fluid in this modified model. The initial inlet temperature would be 300K for the outer fluid.

3D Model

Fig 17: Modified 3D model of exhaust port having external flow

Mesh model

Fig 18: Mesh of Modified model of exhaust port having external flow

The above two Fig 17 & 18 shows the 3D and Mesh model respectively of the exhaust port modified model. Both the surface of the port should have conformal meshing for mesh connectivity. In this case fine meshing is not appreciated because of mesh count constraint.

Mesh Metrics

Fig 19: Mesh metrics of element quality – Modified.

Table 2: Details of mesh in Modified setup.

Domain	Nodes	Elements
fluid	17140	82448
solid	16487	55394
wind	46653	247160
All Domains	80280	385002

The above Fig 19 shows the statistics over mesh quality in the modified model of exhaust port. The quality of mesh is quite convincing but the mesh count is poor which is unavoidable due to coarse meshing. The number of elements and nodes which we create for this model is mentioned the in the Table 2. In terms of numbers this count was higher than the Base line setup but difference is, we have created an additional volume around the port. That consumes the mesh count and the resulting mesh we got is a coarse mesh which is an undesirable thing and this would deviate the solutions to some extent.

Outer wall – Modified Model

Fig 20: Outer wall Heat transfer Coefficient Contour on Modified Model

Inner wall – Modified Model

Fig 21: Inner wall Heat transfer Coefficient Contour on Modified Model

The wall heat transfer coefficient of outer and inner wall is shown in above Fig 20 & 21 respectively. The value of HTC which we measured in previous cases on inner wall is much higher than the value which we got in this model that can be seen in Fig 20. This may be due to the influence of boundary conditions in this setup and the poor mesh refinement. When we look on Fig 21 one thing we could convince on our assumption of boundary condition over outer surface of the port in previous two setup, that the HTC is more or less nearby 20 20 W/m².Kin this modified. Because the most area in outer surface is in a range between 3420 W/m².Kto 18 20 W/m².K.This range is not enough for us to come for a conclusion that boundary condition for this type of problem can be given as a convective boundary with 20 W/m².K HTC. So we should have an average value of HTC over this range of values which is distributed over the surface.

Output

Fig 22: Output of Area weighted average Heat Transfer Coefficient at outer wall on Modified Model

The area weighted average of wall heat transfer coefficient is taken over the outer surface of the port for modified model, which gives a value of 20.089 20 W/m².K. This value exactly matches with our assumption, thus this modified model analysis also validates our assumption.

Reference plane - Velocity

Fig 23: Velocity contour at Ref-plane on Modified Model

Reference plane - Temperature

Fig 24: Temperature contour at Ref-plane on Modified Model

The velocity contour and temperature contour in the reference plane of the modified setup is given in above Fig 23 & 24. Due to poor mesh size the similar distorted contour plot of velocity can be seen in Fig 23 having maximum velocity of 37.0844 m/s which matches the base line setup. In the temperature plot also distorted at its boundary but temperature range is similar.

Cut Plane 1

Fig 25: Velocity vector at a cut plane - 1 on Modified Model

Cut Plane 2

Fig 26: Velocity vector at a cut plane - 2 on Modified Model

The above two Fig 25 & 26 shows the velocity vector plot of the external flow over the exhaust port and that coins the maximum velocity region and the recirculation region formed on the flow domain.

Outer wall – Modified Model

Fig 27: Outer wall Temperature Contour on Modified Model

Inner wall – Modified Model

Fig 28: Inner wall Temperature Contour on Modified Model

The above two Fig 27 & 28 shows the temperature contour plot of the Outer & inner wall of the exhaust port and that coins the maximum Temperature region over its surfaces the values which we get from the plot lower than the Base line setup. The important thing here is that the temperature contour plot of the outer wall of Modified setup is different from the Base line and Trail 1 setup, which proves the influence of the boundary condition over the problem.

CONCLUSION:

• The Conjugate heat transfer analysis in Exhaust port is successfully performed and the maximum HTC region is coined out near the bend area in inner surface of converged conduit.
• The outer wall boundary condition assumption is validated analytically and also numerically.