Week 6 - CHT Analysis on a Graphics card

Objective: To perform Conjugate Heat Transfer (CHT) analysis on the exhaust port.

Introduction:

Experiments performed to study the physics of certain phenomenon are costly and time-consuming. Numerical simulation is developed and used to reduce the time needed to study the nature and physics involved in the system of interest. This method indeed provides results very fast compared to experiments but they lack a bit in terms of accuracy. If the experiments take a month to produce results, simulation might take a day and give us results 90% accurate. In the fast-paced world, where developing various solutions require faster results, engineers make a delicate balance between the accuracy and time taken as necessary.

All fluid flows are governed by three equations -Continuity, momentum and energy equations. We need to solve these equations for the given conditions to understand the fluid behavior. Computers are incapable of solving these equations in their integral and differential forms. So, we can divide our geometry into many tiny elements (called mesh) and modify the governing equations into difference equations that can be solved by the computer. We apply these difference equations for all the elements in the geometry and generate an approximate solution. It is hence necessary to validate these results against the experimental data.

The number of difference equations, for a given problem varies with the nature of physics involved. We typically solve a finite number of equations at all the elements. These equations are grouped together, called a turbulence model. A lot of work has been put into developing and improving the turbulence models and the work still goes on today. Examples of turbulence models are S-A, k-epsilon, k-omega etc.

Theory:

Conjugate Heat Transfer (CHT):

The CHT analysis allows us to simulate heat transfer between solid and fluid domains by exchanging thermal energy at the interfaces between them.

This concept was first formulated by Theodore L. Perelman in 1961 and further enhanced in association with A.V. Luikov.

Applications of CHT analysis includes study of flow in IC Engines, Battery Thermal Management Systems, pumps and compressors.

Modelling Approach:

The work flow in Ansys Fluent would follow four steps:

1. Geometry creation.
2. Mesh generation.
3. Pre-processing settings and simulation.
4. Extracting results.

Geometry creation:

We drag and drop the Fluent module to create the standalone system. We open the geometry editing section- Space claim. We import the given geometry to Space claim.

Mesh generation:

It is a good practice to generate a baseline mesh and perform the simulation to understand the physics and then proceed to the mesh refinement as required. So, we generate the mesh with the default value of mesh length as 10 mm.

We assign appropriate named selections to make it easier to work in the simulation section later. Here, we assigned the flow inlet, outlet, PCB, processor, fins and wall. We close the window and the changes are updated in the system.

Grid Independence Test:

For the given engineering problem; continuity, momentum and energy equations need to be solved. But these equations in integral or differential forms make it difficult for the computer to solve them. Hence, we divide the entire computational domain into many small divisions and solve these equations after converting them to difference equations. This division of domain is called discretization.

Based on the number of pieces the domain is split into, the solution for the equations might change. Adequate care needs to be taken that this discretization is done properly and the results obtained do not rely on the size of the mesh elements, but only on the physics and related parameters. The method to ensure this is called Grid Independence test.

We have discretized our computational domain in four different meshes as follows:

Mesh type	Coarse	Medium	Fine	Ultra-fine
No. of elements	83,740	2,00,074	4,07,181	5,84,849

We will now proceed to apply the boundary conditions for all these meshes and finalize the best mesh for further analysis.

Pre-processing settings and Simulation:

We would proceed to Setup the conditions of the model. The process flow would be as follows:

1. Check the mesh in the solver.
2. Choose the turbulence model and enable energy equation.
3. Specify boundary conditions and cell zone conditions.
4. Mention the heat source at the processor.
5. Create necessary surface plots that we need to investigate.
6. We initialize and run the simulation for given number of iterations.

Extracting results:

We open the results section where we can use various visualizing tools like transparency and colouring the created surfaces with the instantaneous variables like temperature, velocity and obtain contours, charts and plots. We need to run the simulation until the residual values are either reach the convergence criteria or display a periodic pattern.

Settings used for current simulation:

We used Pressure-based solver, absolute velocity formulation, steady state simulation.

We used standard k-epsilon turbulence model with standard wall functions. We use air as the working media.

We would use fluid velocity as 3 m/s and use three materials for the geometry with properties as shown:

S. No	Material name	Used for	Density (kg/m3)	Specific heat (J/kg.K)	Thermal conductivity (W/m.K)
1	Silicon	Processor	2330	703	153
2	Aluminum	Fins	2719	871	202.4
3	PCB	PCB	55	1210	0.027

We have to provide heat source term at the processor in Cell zone conditions for processor.

From space claim, we get the size of the processor as 8mm x 8mm x 1mm.

Volume of the processor = 64 x 10^-9 m³

We choose the processor capacity as 2W.

Heat generated q = 2/64 x 10^-9 = 31250000 W/m³

Grid Dependency test:

We have to ensure that the solution does not depend on the number of elements in the model. So, we run few simulations with different number of mesh elements. This is called Grid dependency test, where we decide the minimum number of elements required to make sure the solution is acceptable.

For the given geometry, we would run grid dependency test till we reach a point where we get solutions with acceptable error range (<5%). We will use the average value of temperature and heat transfer coefficient at interface between processor and fins as the parameter to obtain the ideal computational grid.

Case 1- Coarse mesh:

In this case, we used the default mesh size as 10mm for the entire geometry. Ansys would tend to use this value as baseline mesh and adjust the mesh size accordingly at places of curvature or small size as appropriately required. We get the analysis results as follows.

Scaled residuals:

Heat transfer coefficient residuals:

Temperature residuals:

Case 2- Medium mesh:

In this case, we used the default mesh size as 10mm for the entire geometry. We use sizing for fins, PCB and processor as 1mm. We get the analysis results as follows.

Scaled residuals:

Heat transfer coefficient residuals:

Temperature residuals:

Case 3- Fine mesh:

In this case, we used the default mesh size as 10mm for the entire geometry. We use sizing for fins, PCB and processor as 0.5, 1 and 0.5mm respectively. We get the analysis results as follows.

Scaled residuals:

Heat transfer coefficient residuals:

Temperature residuals:

Case 4- Ultra fine mesh:

In this case, we used the default mesh size as 10mm for the entire geometry. We use sizing for fins, PCB and processor as 0.5mm. We get the analysis results as follows.

Scaled residuals:

Heat transfer coefficient residuals:

Temperature residuals:

We extract the surface integral for the average temperature and heat transfer coefficient at the fins and processor interface and the values are tabulated.

We observe that the error in the values of temperature and heat transfer coefficient for fine and ultra-fine configuration are less than 5%. Hence, we can go with the fine mesh with 4,07,181 elements as the suitable discretization of domain and proceed with our analysis.

Analysis using air velocity as parameter:

Using the finalized mesh, we will run simulation for three different air velocities as 1, 3 and 5 m/s and observe the temperature and heat transfer coefficient at the fin and processor interface.

Case 1: Air velocity – 1 m/s:

Scaled Residuals:

Temperature residuals:

Temperature contour:

Heat transfer coefficient residuals:

Heat transfer coefficient contour:

Case 2: Air velocity – 3 m/s:

Scaled Residuals:

Temperature residuals:

Temperature contour:

Heat transfer coefficient residuals:

Heat transfer coefficient contour:

Case 3: Air velocity – 5 m/s:

Scaled Residuals:

Temperature residuals:

Temperature contour:

Heat transfer coefficient residuals:

Heat transfer coefficient contour:

We extract the values of temperature and heat transfer coefficient for the above three cases and tabulate them as follows:

Inference:

It is observed that with increase in the air velocity the temperature of the fin-processor interface decreases and the heat transfer coefficient increases. The negative value obtained for the heat transfer coefficient is due to the loss of heat by the processor. This is the intended result where the processor is cooled using fins and hence the negative value is accepted. Th prediction made by the analysis is in line with the actual physics.

In the temperature contour, we can see a hotspot at the place where the processor is present. This is due to continuous heat generation by the processor. The distinct visibility of the hotspot would imply good effectiveness of the fins. We can clearly see the hotspot in 5 m/s case when compared to 1 m/s case. This means the heat transfer is more pronounced in the former than the later.

Conclusion:

We have performed conjugate heat transfer analysis on the given graphics card and obtained the best results for higher velocity of air.