Week 4 - CHT Analysis on Exhaust port

AIM:

The aim of this assignment is to perform a Conjugate Heat Transfer analysis and simulate flow inside an Exhaust port.

OBJECTIVE:

The objectives of this assignment are:

• To give a brief description about Conjugate Heat Transfer (CHT) analysis and where and why it is used.
• To perform CHT analysis on Exhaust Port.
• To select a proper turbulence model and maintain the correct Y plus value.
• To compute the Velocity, Temperature, Heat transfer coefficient contours and Y plus plots and other required contours and plots to show the results of the CHT analysis on the Exhaust Port.
• To validate the result and verify if the HTC predictions from the simulations are right or not.
• To state on what factors does the accuracy of the prediction depend on.

INTRODUCTION

In this challenge we perform a CHT analysis on a model of an exhaust manifold and compare the solutions for 2 sizes of meshes. The first one is the baseline mesh and the second one is a finer mesh. Also two different Flow model are used to compare the final results and come to a conclusion. So there will be a total of 4 cases in our challenge. Animations are created to visualize the temperature distribution.

THEORY

CONJUGATE HEAT TRANSFER

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.

The fluid usually plays the role of energy carrier on large distances. 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 vapour phase change).

Even so, solids are also needed, in particular, to separate fluids in a heat exchanger so that fluids exchange energy without being mixed.

The contemporary conjugate convective heat transfer model was developed after computers came into wide use in order to substitute the empirical relations 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 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 with the body flow interface, eliminating the need for a heat transfer coefficient.

Why CHT analysis is used:

• CFD and more specifically CHT analysis can accurately predict heat transfer by simultaneously solving all the relevant solid and flow field heat transfer processes, for e.g, conduction through solids, free and forced convection in the gases/fluids, and thermal radiation.
• 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 these applications where heat transfer is either non-uniform or difficult to calculate empirically.

Where is CHT analysis used:

Starting from simple examples in the 1960s, the CHT method has become a more powerful tool for modelling and investigating natural phenomenon and engineering systems in different areas ranging from aerospace and nuclear reactions to thermal goods treatment and food processing, from the complex procedure in medicine to atmosphere/ocean thermal interaction in metrology, and from relatively simple units to multistage, nonlinear processes.

Applications:

• Internal Combustion Engines
• Electromobility
• Pumps and Compressor
• After-treatment Systems

APPLICATIONS:

• Computational Fluid Dynamics (CFD) and more specifically conjugate heat transfer (CHT) analysis can accurately predict heat transfer by simultaneous 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 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.
• The heat transfer projects have covered a wide range of aerodynamic and hydrodynamic industrial applications but projects typically had objectives such as:
1. Temperature distribution analysis.
2. Heat flux rate analysis – calculation of wall heat flux rates or heat transfer coefficients.
3. Visualization of heat transfer features for improved understanding of system flow phenomena.
4. Identification of localized ‘hot spots or heat sinks in checking against specified requirements.
5. Evaluating variation in temperature peaks for different operating conditions/ failure modes.
6. Assessing insulation or heat shield effectiveness and optimizing of material selections.
7. Coupling CHT with FE analysis to evaluate thermally induced stresses, expansion or fatigue.
8. Temperature field analysis
9. CFD thermal analysis
10. Heat transfer coefficient analysis
11. Heat transfer rate analysis

Maintaining Y+ :

• It is an non-dimensional distance.
• It can be used to determine the first layer distance from the wall which is measured in terms of viscous length.
• Here, we have to maintain Y+ with respect to turbulence model.
• Since the turbulence model for this analysis is taken as K-omega SST, the Y+ value should be between 0 and 10.
• Here, we take the Y+ value of 10 to calculate the first layer thickness.

Reynolds number :

It is a dimensionless number which is defined as the ratio of inertial force to the viscous force of the fluid.

Where

• ρ=Density of the fluid(kg/m³)
• V=Velocity of the fluid(m/s)
• μ=Dynamic viscosity of the fluid(kg/m.s)
• D=Diameter of the fluid(m)

Prandtl number :

It is a dimensionless number which is defined as the ratio of momentum diffusivity to the thermal diffusivity of the fluid.

Where,

• ν=kinematic viscosity of the fluid(m²/s)
• α=Thermal diffusivity (m²/s)

Nusselt number :

It is a dimensionless number which is defined as the ratio of convective heat transfer to conductive heat transfer within the fluid region. It ranges between '0' and '1'. The value closer to '0' mean the heat transfer is mostly due to conduction ( due to direct molecular interactions ) and if the value is closer to '1', the heat transfer is mostly due to convection ( due to fluid bulk motion ).

Nusselt number (Nu) = Convective heat transfer / Conductive heat transfer

Where,

• h=Heat transfer coefficient(W/m²⋅K)
• k = Thermal conductivity of the fluid/material"(W/m.K)

Dittus-Boelter equation:

The Dittus-Boelter equation (for turbulent flow) is an Explicit function for calculating the Nusselt number. It is easy to solve but is less accurate when there is a large temperature difference across the fluid. It is tailored to smooth tubes, so use for rough tubes (most commercial applications) is cautioned.

substitute the friction factor in the Nusselt number equation, we get the governed equation of Dittus-Boelter which is given by;

`Nu=0.023Re^0.8 (Pr)^n`

SOLVING AND MODELLING APPROACH

1. Solid and Fluid volume is defined for the exhaust port and topology is shared between the volumes..
2. Mesh independence study is carried out for two sizes. One for coarse mesh (150mm) and the other for finer mesh (10mm)
3. Turbulent steady state with K-Ω SST & K-ε Std are used
4. The simulation is calculated for convective heat transfer.
5. Animations are created to analyse the flow patterns

PRE-PROCESSOR AND SOLVER SETTING

In our challenge we will create a flow simulation of exhaust port. In general I will be explaining only one case and posting the screenshots of the other cases.

Case 1

Mesh size - 150mm

Fluid - Air 5m/s

Flow Model - Turbulent K-Ω SST

Step 1 : Open the geometry Space Claim and import the exhaust port model. Fluid and solid domain is defined using volume extract tool. Once this is done the topology is shared so the meshing will be smooth.

Once this process is done. We will close the space claim and open the mesh module.

Step 2 : Open the mesh module and under the mesh details give CFD Fluent as preference and Element size of 150mm. But since we are going to go for mesh independence study uniform meshing size is maintained throughout the volume. Note the number of nodes and elements for the study.

After the meshing is done check for the quality criterion. Check whether the mesh quality is above 5%. Once this is done name the faces and volumes. Inlet, Outlet, Fluid domain, Solid Domain.

Step 3 : After the meshing and face naming are done move on to Fluent Solver. In the fluent launcher select double precision, display mesh after reading and give the appropriate solver processors and GPUs.

In the ANSYS CFD we need to give all the conditions, parameters and models. To start with go to physics menu and click general settings. In that select Pressure based type solver, Absolute velocity formulation and steady state flow. Next we need to give the model. For this case Laminar is selected.

After the physics part is done move to the solution part. Initialise the simulation first. click Initialize to initialize the boundary conditions. Hybrid method is selected before initialization. Click on Autosave to obtain a animation of the flow in the post results.

Then run the calculation for a given number of iterations till the convergence is obtained. Depending upon the number of elements and model selected the time required for convergence varies. In the CFD module itself we can compute, measure, plot, animate, etc., if needed.

Step 4 : After the solutions and calculations move to the result module to get different graphs, plots, contours, animations etc.,. Sectional views can be created if required.

RESULTS

Case 1

Mesh size - 150mm

Fluid - Air 5m/s

Flow Model - Turbulent K-Ω SST

Residual

Heat Transfer Coefficient

Average temperature of Pipe wall

Temperature Contour

Temperature contour

Temperature contour

Heat Transfer Coefficient Inside Pipe wall

Animation

Case 2

Mesh size - 150mm

Fluid - Air 5m/s

Flow Model - Turbulent K- ε SST

Residual

Heat Transfer Coefficient

Average temperature of Pipe wall

Temperature Contour

Temperature contour

Temperature contour

Heat Transfer Coefficient Inside Pipe wall

Case 3

Mesh size - 100mm

Fluid - Air 5m/s

Flow Model - Turbulent K- Ω SST

Residual

Heat Transfer Coefficient

Average temperature of Pipe wall

Temperature Contour

Temperature contour

Temperature contour

Heat Transfer Coefficient Inside Pipe wall

Case 4

Mesh size - 100mm

Fluid - Air 5m/s

Flow Model - Turbulent K- ε SST

Residual

Heat Transfer Coefficient

Average temperature of Pipe wall

Temperature Contour

Temperature contour

Temperature contour

Heat Transfer Coefficient Inside Pipe wall

Total of 4 cases are simulated for the exhaust port with two mesh refinements and two turbulence models. In all these cases the heat transfer coefficient of the pipe wall was found nearer to 21.2.K Epsilon gives a faster convergence result. Average temperature of the pipe wall was approximately found to be 504K.

ANALYTICAL CALCULATION for verifying and validating HTC :

Here the properties of air is taken for the calculation purpose since the fluid which is flowing through the exhaust port is air,

Density `ρ=1.225((kg)/m^3 )`

Specific heat capacity, `C_p=1006.43(J/(kg.K))`

Thermal conductivity, `k=0.0242(W/(m.K))`

Dynamic viscosity, `μ=1.7894⋅10^(-5) ((kg)/(m.s))`

We know that Reynolds number,

`Re=ρ⋅V⋅D/μ`

Where,
Velocity, `V=5 (m/s)`

Diameter, `D=0.1661m`

Substituting the values in the above equation, we get, `Re=56854.95`

Prandtl number is given by,

`Pr=ν/α`

`Pr=ν/(k/(ρ⋅C_p ))`

`Pr=ρ⋅ν⋅C_p/k`

`Pr=μ⋅C_p/k`

Where,`μ=ρ⋅ν`

Now, substituting the values in the above equation, we get, `Pr=0.744`

The relationship between the Nusselt number and Reynolds number for a circular pipe with diameter D with a turbulent flow throughout the pipe for heating,

According to The Dittus-Boelter equation,

`Nu=0.023⋅(Re^(4/5) )⋅(Pr^0.3 )`

Substituting the values in the above equation, we get, `Nu=133.97`

We know that the Nusselt number is given by,

`Nu=h⋅D/k`

`h=Nu⋅k/D`

`h=19.52 (W/(m^2⋅K))`

How would you verify if the HTC predictions from the simulations are right? On what factors does the accuracy of the prediction depend on?

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, Q₄ respectively, and Q₅ be the flow rate from the exhaust manifold.

As mass is neither created nor destroyed, mass flow rates are also balanced as below;

Q₁+Q₂+Q₃+Q₄=Q₅ ...........(1)

we have Q= ρ⋅A⋅V ...........(2)

Now equation 1 becomes

A₁V₁+A₂V₂+A₃V₃+A₄V₄=A₅*V₅

As it is an incompressible flow to compensate for 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=f(Re,Pr) for forced convection application.

Nu= hD/k

from above formula Nu ∝ Re. Hence Nu ∝ h, therefore, Re ∝ h.

From our simulation, we have observed velocities are high at bend section of outlet manifold hence higher Reynolds number which was at high heat transfer coefficient. Therefore predictions from our simulations can be considered correct.

Factors that influence accuracy of predictions:

• Mesh quality greatly impacts the accuracy of prediction value in our simulations which can be observed from above contours and maximum values of related parameters like velocity and heat transfer coefficient.
• An appropriate turbulence model has to be used in accordance with the y+ value which is very important.
• Appropriate y+ value helps in calculating total layer thickness from the wall for the better capturing of effects near wall, which is Heat transfer coefficient in our case.

Factors affecting accuracy:

1. Mesh:

The mesh must be coarse enough with additional features such as inflation layers, this helps the software to approximate better values neat the boundaries and the walls. The mesh need not be too coarse because it will be computationally expensive without any significant change in the results.

2. y+ value:

The y+ values are very important when it comes to capturing the fluid interaction and it's effect on the boundaries. Large values of y+ produce less accurate results when compared to lower y+ values. A particular value of y+ requires a certain turbulence model for calculations.

3. Turbulence model:

Appropriate turbulence model which satisfy the y+ value must be chosen.

Y+ : 0 to 30 : K-Omega model.

Y+ : 30 to 300 : K-epsilon model.

CONCLUSION:

• From the simulation of exhaust manifold it was evident that the calculated value of heat transfer coefficient are in range of less than 15% error with CFD results. But the simulation has been carried out without considering any friction factor which would have provided better results for cfd simulation.

• The simulation was carried with two different turbulence model and with different velocities. From the results of residual plot we can say that K-epsilon model converge faster as compared to Standard K-omega model also later one required more iteration for stabilization. From the average temperature plot on the convection wall it was seen that K-epsilon model took lower iteration to get stabilize as compared to standard K-omega model. Whereas, from the table we can say that the percent error is lower in Standard K-omega model as compared to K-epsilon model. In the end it is beneficial to use K-epsilon model for the simulation as it was providing results faster and with great convergence ratio.

• The analytical value of the heat transfer coefficient is h=19.52 (W/(m^2⋅K))

• Velocity tends to increase from inlet to outlet due to mass conservation and mixing of air.

• Transfer of heat from fluid to solid is high and leads to formation high velocity at the junction resulting in HTC capturing.
• The internal flow velocity and its characteristics are affected by initial velocity, pressure and physical features of geometry. Thus, CHT analysis is essential prior experimental process for better prediction product life of design component.
• As shown in the plots, the exhaust gases passing through the manifold transfers some of the heat via convection. The amount of heat transfer can be related directly with the velocity of exhaust.
• The temperature is lower where flow stagnates or is moving at the velocity. As the velocity increases, so does the Reynold’s number and the amount of heat transfer.
• As seen the numerical computed value overpredicts the heat transfer coefficient by 10% when compared with analytical solution obtained from Dittus-boelter heat transfer coefficient correlation. It should be however noted that the numerical computed value is an average value while the analytical solution of heat transfer coefficient holds good for a straight sectioned pipe with fully developed flow profile throughout the pipe. There are other correlation available to compute heat transfer coefficient which can be used. But better approach would be to perform an experiment or interpolate the value of heat transfer coefficient from previously conducted experiments