Week 4 - CHT Analysis on Exhaust port

Aim: To develop a numerical set-up for conjugate heat transfer analysis on exhaust port.

Objectives:

1. Investigate wall adjacent and surface heat transfer coefficients.

2. Understand flow and thermal characteristics.

3. To perform mesh independent study.

4. Set-up a rough surface model to understand the effect on thermal and flow properties.

Introduction:

Conjugate Heat Transfer (CHT):

• It is a combination of heat transfer between solid and fluid domain by exchanging thermal energy at their interfaces. In solids conduction is responsible for heat exchange whereas in fluids convection accounts for heat transfer.
• In CHT analysis, thermal radiation also accounts for a equal share as engineering problems does not limit to conduction and convection.
• The principle of conduction is governed by Fourier's law of heat conduction, whereas convection is influenced by Newton's law of cooling.
• In enginnering applications, heat transfer problems are complex to solve due to such combination of modes of heat transfer.
• These problems are tedious to solve through conventional (analytical) means and therefore creates a need for a numerical model which can approximate the physical process.
• CHT analysis is beneficial in accurately predicting solid temperature and heat transfer capabilties in engineering devices.
• Thermal engineers in industries are responsible for controlling heat transfer capabilities for their product to ensure efficient working as per standards.

Applications of CHT:

Heat exchangers, HVAC (Heating Ventilation and Air Conditioning), Air-cooled and liquid-cooled engines, turbochargers, cooling of nuclear reactors, cooling towers, and many more.

Software used: ANSYS Workbench

Module: Fluent

Pressure-velocity coupling method: SIMPLE (Semi-Implicit Method for Pressure Linked Equations)

Project Methodology:

Initially CHT analysis and chronology of the problem set-up is well understood. The geometry clean-up is executed in SpaceClaim and meshing in Fluent meshing set-up. The turbulence model and pressure-velocity coupling method is predertermined. A baseline numerical set-up is created to ensure consistency. Accordingly, the case studies with different turbulence models and mesh refinement are simulated to improvize the accuracy of the numerical approximation. The obtained solutions are post-processed in CFD Post. A similar set-up is produced by assigning roughness grade to understand the effect on thermal and flow characteristics.

Cases:

Steady-state CHT analysis is performed to investigate the thermal distribution as a function of space co-ordinates.

Cases	Y+ value	Turbulence model	Mesh
CASE 1 (Baseline)	NA	K-epsilon (Standard) with Standard wall functions	Coarse
CASE 2	50	K-epsilon (Standard) with Standard wall functions	Refined
CASE 3	5	K-omega-SST	Refined

Similarly CASE 4 is set-up for rough surface modeling in which surface roughness of 3mm is provided to understand the effect of thermal characteristics over a rough surface.

Modeling Approach:

Pre-Processing:

Geometry:

• Initially the exhaust port geometry is imported in SpaceClaim and then fluid volume (wet volume) is extracted from the domain.
• Consequently, solid and fluid volume are combined together as a single geometry by "moving to a new component" function. This will consider the fluid-solid volume as singular.
• Similarly under "Workbench" select "share co-incident topology" because of which a component in SpaceClaim becomes a multi-body part in Ansys.
• In properties "topology" is selected as "share" because fluid and solid volumes will be interacting with each other and must share information (heat exchange information) at the interface as a part of the problem.
• This will prevent "Non-Conformal Mesh" to get generated in Fluent Meshing.

Meshing:

Named Selections:

The faces colored in red define their respective physical purpose. This is done to assign the physical significance to the geometry which consequently will get assigned for boundary conditions.

Till now the modeling approach is similar for all the cases but further it will vary according to mesh characteristics and selection of turbulence models.

CASE 1:

Turbulence model	K-epsilon (Standard)
Wall functions	Standard wall functions

A] Pre-processing:

1.1 Mesh Details:

Element Size	150 mm	---
Total number of cells	1,37,963	Coarse

1.2. Mesh:

1.3. Enlarged view:

A] Post-Processing Results:

1. Residuals:

2.1. Temperature:

2.2. Temperature:

3.1. Wall Adjacent Heat Transfer Coefficient:

3.2. Wall Adjacent Heat Transfer Coefficient (Enlarged View):

4. Surface Heat Transfer Coefficient:

5. Surface Nusselt Number:

6. Pressure:

7. Velocity:

8. Turbulence Kinetic Energy:

C] Animation:

Note: Play-back speed of 0.25X is recommended.

D] Post-Processing Reports:

CASE 2:

Y+	50
Turbulence model	K-epsilon (Standard)
Wall functions	Standard wall functions

A] Pre-Processing:

1.1 Mesh Details:

Element size	16 mm	--
Number of inflation layers	5	--
Growth rate	1.2	--
Inflation type	Total thickness	20 mm
Total number of cells	4,65,751	Refined

1.2 Mesh:

1.3. Inflation layers in between fluid-solid interaction:

B] Post-Processing Results:

1. Residuals:

2.1. Temperature:

2.2. Temperature:

3.1. Wall Adjacent Heat Transfer Coefficient:

3.2. Wall Adjacent Heat Transfer Coefficient (Enlarged view):

4.1. Surface Heat Transfer Coefficient:

4.2. Surface Heat Transfer Coefficient (Enlarged View):

5.1. Surface Nusselt Number:

5.2. Surface Nusselt Number (Enlarged View):

6. Pressure:

7. Velocity:

8. Turbulence Kinetic Energy:

C] Post-Processing Reports:

CASE 3:

Y+	5
Turbulence model	K-omega (SST)

A] Pre-Processing:

1.1. Mesh Details:

Element size	20 mm	--
Number of inflation layers	10	--
Growth rate	1.2	--
Inflation type	Total thickness	8 mm
Total number of cells	5,06,859	Refined

1.2 Mesh:

1.3. Inflation layer in between fluid-solid interaction:

B] Post-Processing Results:

1. Residuals:

2.1. Temperature:

2.2. Temperature:

3.1. Wall Adjacent Heat Transfer Coefficient:

3.2. Wall Adjacent Heat Transfer Coefficient (Enlarged View):

4.1. Surface Heat Transfer Coefficient:

4.2. Surface Heat Transfer Coefficient (Enlarged View):

5.1. Surface Nusselt Number:

5.1. Surface Nusselt Number (Enlarged View):

6. Pressure:

7. Velocity:

8. Turbulence Kinetic Energy:

C] Animation:

Note: Play-back speed of 0.25X is recommended.

D] Post-Processing Reports:

Observation Table:

CASES	Number of Cells	Turbulence model	Average wall heat transfer coefficient (W/m^2 K)	Average surface heat transfer coefficient (W/m^2 K)	Total heat transfer rate (W)	Average surface nusselt number
CASE 1	1,37,963	K-epsilon Standard	31.10	-18.86	-10873.14	-779.70
CASE 2	4,65,741	K-epsilon Standard	32.08	-18.83	-10469.37	-778.33
CASE 3	5,06,859	K-omega SST	33.06	-18.88	-11010.072	-780.37

Note:

• Wall adjacent heat transfer coefficient uses difference of wall temperature and temperature of cell adjacent to the wall.

Wall adjacent heat transfer coefficient = wall heat flux/ (wall temperature - wall adjacent temperature)

• Surface heat transfer coefficient uses difference of wall temperature and reference fluid temperature (bulk fluid temperature).

Surface heat transfer coefficient = wall heat flux / (wall temperature - bulk fluid temperature)

Signifiance of negative sign:

In this case the hot fluid is exchanging heat with the surface which is at normal temperature. The direction of heat flux is pointing towards the solid surface which is opposite to the normal vector of the surface control volume. This results in negative convention of the thermal quantities.

Technical Discussion:

The conjugate heat transfer in this case is in between the solid volume of the exhaust port and heated fluid volume which is flowing through the manifold. The heated fluid (exhaust gases) is exchanging heat with the exhaust manifold via convection. The heat conducted by exhaust manifold is distributed throughout the thickness of the manifold via conduction. As a function of fluid flow through the manifold (spatial function), fluid looses its thermal energy and transfers it to internal manifold walls. The rate of heat transfer due to convection is dependent on the velocity of the exhaust gases. Due to high Reynolds number intense turbulence ensures efficient heat transfer. As it can be observed from the temperature and velocity contour. The manifold wall attains maximum temperature where the velocity of the fluid flow is highest.

The velocity of the fluid is maximum at the bent section of the outlet region. This is because of the continuity (mass conservation) principle, which the domain exhibits. Through four inlets the mass of fluid is entering into the manifold and it has a single way out at the outlet section. Fluid is rushed or more precisely accelerated due to pressure difference i.e. 1 atm at the outet. Due to mass conservation, pressure has to compensate for the acceleration of the fluid. It is clearly observed in the pressure contour.

The maximum velocity region contributes to the maximum heat transfer coefficient. As discussed earlier, the rate of heat transfer is a function of velocity of the fluid. Heat flux in this region is maximum and results in high heat transfer coefficient. Accordingly, the surface Nusselt number is decreased at the solid-fluid volume interface (due to diffusion dominance) and increases away from the interface because of convection.

As per the results, Case 3 (K-omega) tends to be inherently more consistent because of the efficacy of capturing near-wall effects. A lesser Y+ (More finer mesh at the interface) will produce more approximate results. Similarly, Case 2 (K-epsilon) which uses wall functions also produced good results comparatively with neglible variation. However, there is urge to verify these results as they lack in experimental solution datum.

Verification of Heat Transfer Coefficient (HTC):

• The heat transfer coefficient should be verified with experimental results with the respective flow and thermal conditions.
• Analytically heat transfer coefficient can be calculated with the help of Dittus-Boelter equation,

`Nu = 0.023 Re^0.8Pr^0.4` (when fluid is heated along with the flow)

And `Nu = 0.023 Re^0.8Pr^0.3` (When fluid is cooled along with the flow)

• In this case, heated fluid is loosing heat (thermal energy) to the walls of the manifold.
• So, `Nu = 0.023 Re^0.8Pr^0.3` is used to calculate the Nusselt number of the respective case.
• Finally the heat transfer coefficient is calculated using `Nu = (hD_h)/k`

Where,

h = Heat transfer coefficient `(W/(m^2 K))`

D_h = hydraulic diameter (m)

K = Thermal conductivity of the fluid`(W/(m K))`

Note: The heat transfer coefficient obtained using analytical means is calculated using the bulk fluid temperature and not with the local wall adjacent temperatures. For numerical validation it is required to take surface heat transfer coefficient in place of wall adjacent heat transfer coeffcient / wall function heat transfer coefficient.

The accuracy of the predicted heat transfer coefficient is dependent on following factors,

a) Mesh refinement

b) Selection of appropriate turbulence model

c) Selection of pressure-velocity coupling

d) Element quality in the inflation region

e) Use of appropriate reference values

CASE4 : Rough surface modeling

A] Post-Processing:

1. Residuals:

2.1. Temperature:

2.2. Temperature:

3.1. Wall Adjacent Heat Transfer Coefficient:

3.2. Wall Adjacent Heat Transfer Coefficient (Enlarged View):

4.1. Surface Heat Transfer Coefficient:

4.2. Surface Heat Transfer Coefficient (Enlarged View):

5.1. Surface Nusselt Number:

5.2. Surface Nusselt Number (Enlarged View):

6. Pressure:

7. Velocity:

8. Turbulence Kinetic Energy:

C] Animation:

Note: Play-back speed of 0.25X is recommended.

D] Post-Processing Reports:

Observation table:

Cases	Roughness	Number of cells	Turbulence model	Maximum temperature (K)	Average wall heat transfer coefficient (W/m^2 K)	Average surface heat transfer coefficient (W/m^2 K)	Total heat transfer (W)
CASE 1	Smooth surface	4,65,741	K-epsilon (Standard)	642.42	32.08	-18.83	-10469.37
CASE 4	Rough surface	4,65,741	K-epsilon (Standard)	651.48	56.13	-19.04	-12843.8

Technical Discussion:

In this analysis, the impact of surface roughness is taken into consideration. Both the cases are simulated with same input conditions just varying the surface roughness for consistency. The temperature and wall heat transfer coefficient vary significantly as roughness grade is produced. However, surface heat transfer coeffcient is not varying drastically because it takes bulk fluid temperature as the reference temperature which is same for both the cases.

The surface irregularities produces direct effect on thermal and flow characteristics. The irregularities present in rough geometries initiates more intense turbulence. Because of this the exchange of thermal energy is intense and chaotic. The total heat transfer due to convection is also comparatively more in rough surface exhaust manifold. At some instances, it is favourable to have such irregularities to enhance heat dissipation. But generally in internal flows it is not preferred due to increase in pressure drop. As it affects the flow conditions and stability of the system.

In some applications rough surfaces leads to over-heating of the system components which can cause thermal fatigue or thermal stresses.

Conclusion:

The CHT analysis produced consistent results with different mesh refinements. Experimental results are crucial to approve the accuracy of the numerical results. The geometrical characteristics of exhaust port are bit complex which hinder analytical calculations by using Dittus-Boelter formulation. It can be clearly asserted that finer mesh refinement will definitely approximate more accurate results. The thermal and flow characteristics such as heat transfer coefficient, Nusselt number, heat flux, pressure and velocity of the fluid gives an insight about the physical experience in the exhaust manifold. Also the added case of roughness modeling explicitly defines the cause on thermal and flow characteristics. The simulated CHT analysis is useful in determining thermally affected regions and optimization of the cooling capabilities.

References:

1. https://www.comsol.com/blogs/conjugate-heat-transfer/

2. https://www.afs.enea.it/project/neptunius/docs/fluent/html/ug/node469.htm

3. ANSYS Fluent user's guide