CHT analysis of a four cylinder exhaust manifold using ANSYS Fluent

1. Introduction

Conjugate heat transfer (CHT) analysis is the term used for studying the heat transfer in solids and fluids where the convective heat transfer takes place at the interface of the solid and fluid flow. The heat transfer is dependent on the temperature difference of the two mediums. CHT analysis can be extended to various applications in which the interacting bodies in the flow consist of solids and fluids. A simple example of this would be air flow over a solid body in heat exchanger. Applications can be found in automotive domain such as car radiators, engine casings; aerospace sector such propulsion systems and various other fields of thermodynamics.

One such application where conjugate heat transfer can be witnessed is the exhaust manifold of an engine. The function of the exhaust manifold is to suck the high temperature exhaust gases from the various cylinders when the exhaust valves are opened, allow flow inside the boundary and exit through a common outlet. This outlet of gases may be used to run the turbochargers. The high temperature of exhaust gases results in convective heat transfer at the interface of the inner walls of the manifold. In a conventional exhaust manifold consisting of two or more inlets, it is observed that the rate of heat transfer measured using the wall heat transfer coefficient is highest at the region of intermixing of the gases. Due to the high velocity imparted to the fluid flow, the convective heat transfer increases. Exhaust manifold play a significant role in engine efficiency as the temperature and flow characteristics of the output fluid determines the work done by the turbocharger.

1.1 Importance of CHT analysis

To understand the importance of CHT analysis, we need to look into the various types heat transfers present in the geometry. Due to the temperature gradients present in solid body, there is conduction of heat within the solid. Due to flow of fluid, there is convection of heat at the interface. And the third type of heat transfer is radiation of heat from the geometry.

Selection of the appropriate material is a crucial parameter in the design phase of the geometry. To effective select the material, we need to understand the temperature characteristics, distribution, Highest (or lowest) temperature in the system and the overall heat transfer coefficient. An effective CHT analysis would enable in accurate estimation of these properties and help determine the material for the geometry.

2. Objective

The current study perform CHT analysis on a conventional design of exhaust manifold to study the velocity, temperature, and heat transfer coefficients for a subjected air flow of 5m/s at inlet. Furthermore, the study is extended to perform grid independence test and compares the solution obtained for two turbulence models- K-Ɛ and K-ω SST.

3. Geometry

The geometry is a conventional exhaust manifold with four inlets and single outlet. Based on the solid model imported, it is cleaned for removing extra edges using Preparation tools.

We use the volume extract command to extract the fluid volume inside the solid outer walls as shown in Figure 1. To ensure conformal meshing at the interface of the solid volume and fluid volume, we merge the two volumes into a single component and enable share topology

Fig 1 Geometry and volume extraction of exhaust manifold

4. Baseline mesh

The named selections are created and the baseline mesh is generated.

Fig 2 Named selections

Fig 3 Baseline mesh

Element size = 0.15 m

The mesh metrics are displayed below

Fig 4 – Mesh metrics

5. Setup

The given case is solved using pressure based, steady state solver. The viscous model used is K-Ɛ turbulence model.

Material for solid wall= Aluminium

Fluid material = Air

5.1 Boundary conditions

Inlet velocity = 5 m/s

Inlet air temperature = 700 K

Outlet= Pressure type (Gauge pressure= 0)

Outer wall, Convective Thermal coefficient = 20 W/m²K

6. Results

6.1 Convergence

Fig 5- Plot of residuals over iterations

6.2 Average velocity, temperature and heat coefficient at walls

Fig 6- Temperature distribution on outerwall

Fig 7- Velocity streamlines in fluid volume

Fig 8- Temperature distribution at U-bend cross-section

Fig 9- Velocity profile and streamlines at U-bend cross-section

Fig 10- Wall heat transfer coefficient contour plot

Area Average of Velocity on outlet = 25 m/s

Area Average of Temperature on outlet= 680.867 K

Area Average of Wall Heat Transfer Coefficient on interface = 28.7796 W /m² K

Refined mesh- 2 cases

The mesh is refined by reducing element size to 0.05 m and adding inflation layer at the interface and introducing body sizing at solid body.

Fig 11- Mesh metrics

7.1 Inflation on volume extract

Fig 12- Inflation layer

Inflation type- Smooth transition

Number of inflation layers- 5 nos

7.2 Solid body sizing

Element size = 0.02 m

Fig 13- Body sizing mesh method

7.3 Results

7.3.1 Convergence

From the residuals plot, it can be seen that the convergence of the solution occurs at iteration = 1100. This is almost twice the iterations taken to attain convergence using a baseline mesh. Thus, to improve accuracy of the solution, more processing time and resources are the drawbacks.

Fig 14- Plot of residuals against iterations

7.3.2 Characteristics

Fig 15- Temperature profile on outerwall

Fig 16- Velocity streamlines

Fig 17- Wall heat transfer coefficient

A brief comparison of the results with baseline mesh and refined mesh is tabulated below. It shows variation in velocity and temperature characteristics within errors of approximation. However, the variation observed in wall heat transfer coefficient is very high. Thus, the given problem needs to be preprocessed effectively to arrive at a grid independent solution.

Table 1- Comparison of results of baseline and refined mesh

Case	Unit	Baseline mesh	Refined mesh
Element size	m	0.15	0.05
Outerwall body sizing	m	Nil	0.02
Inflation on interface	Type	Nil	Smooth transition
Inflation total wall thickness	mm	Nil	-
Number of inflation layers	Nos	Nil	-
Nodes	Nos	30606	116545
Elements	Nos	154830	317862
Avg. outlet velocity	m/s	25.34	25.20
Avg. outlet temperature	K	680.867	678.30
Max. wall heat transfer coefficient	W/m^2K	102.95	188.74
Avg. wall heat transfer coefficient	W/m^2K	28.76	51.32

8. Grid independency test

The mesh is refined for three cases by reducing the thickness of the inflation layer. The results are tabulated below:

Table-2 Comparison of results of refined mesh

Case	Unit	Refined-1	Refined-2	Refined-3	Refined-4
Element size	m	0.05	0.05	0.05	0.05
Outerwall body sizing	m	0.02	0.02	0.02	0.02
Inflation on interface	Type	Smooth transition	Total wall thickness	Total wall thickness	Total wall thickness
Inflation total wall thickness	mm	-	5	1	0.25
Number of inflation layers	Nos	-	5	5	5
Nodes	Nos	116545	121413	125390	125564
Elements	Nos	317862	345765	368412	371270
Avg outlet velocity	m/s	25.20	25.2077	25.199	25.2356
Avg outlet temperature	K	678.30	678.221	677.28	683.402
Max. wall heat transfer coefficient	W/m^2K	188.74	221.03	393.01	1644.85
Avg. wall heat transfer coefficient	W/m^2K	51.32	83.61	361.099	1443.98

Note that further refinement of the inflation layer results in divergence of the residuals. A possible explanation for this would be a very low y+ value resulting in capture of laminar sub-layer in the viscous flow near the walls.

Fig 18- Divergence of residuals for inflation layer thickness 0.125 mm

Hence, considering the limits of turbulence models, the results for refined mesh case-4 can be considered as the best possible solution for the given case.

9. Comparison of results of different turbulence models

The best possible mesh is solved using K-Ɛ and K-ω SST turbulence models and the results are compared.

9.1 Residuals

Fig 19- Residuals plot for both turbulence models

It can be noted that the convergence for K-Ɛ turbulence model occurs at iteration= 500 whereas for K-ω SST model, the solution converges after 800 iterations.

Fig 20- Temperature profile

Fig 21- Velocity streamlines

Fig 22- Temperature at U-bend cross-section

Fig 23- Velocity profile at U-bend cross-section

Fig 24- Wall heat transfer coefficient at U-bend cross-section

Table-3 Comparison of results of turbulence models

Case	Unit	K-Ɛ	K-ω SST
Avg outlet velocity	m/s	25.2356	25.285
Avg outlet temperature	K	683.402	682.685
Max. wall heat transfer coefficient	W/m^2K	1644.85	1644.86
Avg. wall heat transfer coefficient	W/m^2K	1443.98	1444.35

On comparing the results obtained from the two turbulence models, we can conclude that similar results are observed for the two models. However, in terms of simulation time, K-Ɛ model is superior as compared to K-ω SST turbulence model.

10. Verification and validation of results

The results obtained by performing CHT analysis using CAE software such as ANSYS Fluent, STAR CCM+ etc lack confidence when applying to real life applications. Hence, these results need to be validated using experimental methods and analytical solutions. Experimental methods use sensors to determine wall heat flux and monitor temperatures at the nodes of the solid-fluid interface. Using these data, the wall heat transfer coefficient can be calculated analytically.

The accuracy of the solution parameters such as heat transfer coefficient is largely dependent on the mesh generated. Accuracy can be improved by refining the inflation layer at the interface of solid and liquid volume.

11. Conclusion

The study successfully simulates the flow of air inside an exhaust manifold and determines the velocity, temperature and wall heat transfer coefficients. It further studies mesh dependency and arrives at the best possible mesh using mesh refinement. The study concludes by comparing the results obtained for refined mesh using two different turbulence models.