Performing Conjugate Heat Transfer (CHT) Analysis On A Hypothetical Graphics Card Using Ansys Fluent.

Abstract:- The work is focused on performing a steady-state, pressure-based conjugate heat transfer analysis on a hypothetical graphics card with appropriate user-defined materials. The term conjugate heat transfer (CHT) is used to describe a process that involves variations of temperature within solids and fluids, due to thermal interaction between the solids and fluids. The exchange of thermal energy between the two physical bodies is called the study of Heat Transfer, the rate of transferred heat is directly proportional to the temperature difference between the bodies. A typical example is the heating or cooling of a solid object by the flow of air in which it is immersed. For our study, we will be performing a cooling technique on a graphics card that was pre-modeled in CATIA, by creating a wind tunnel structure around it & allowing fluid (air) to flow past the geometry at variable velocities & studying the effects on the graphics card. We will also be performing a "grid dependency" test & visualize the effect of mesh element size on the velocity & pressure contour & animation plots. We will carry out the entire workflow using ANSYS software.

Theory_________________________________________________________________________

Conjugate heat transfer corresponds with the combination of heat transfer in solids and heat transfer in fluids. In solids, conduction often dominates whereas, in fluids, convection usually dominates. Efficiently combining heat transfer in fluids and solids is the key to designing effective coolers, heaters, or heat exchangers. 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 vapor phase change). Heat transfer in solids and heat transfer in fluids are combined in the majority of applications. This is because fluids flow around solids or between solid walls and because solids are usually immersed in a fluid.

Modes of heat transfer

• Conduction: diffusion of heat due to temperature gradients. A measure of the amount of conduction for a given gradient is heat conductivity.

• Convection: when the heat is carried away by moving fluid. The flow can either be caused by external influences, forced convection; or by buoyancy forces, natural convection. Convective heat transfer is tightly coupled to the fluid flow solution.

• Radiation: transfer of energy by electromagnetic waves between surfaces with different temperatures, separated by a medium that is at least partially transparent to the (infrared) radiation. Radiation is especially important at high temperatures, e.g. during combustion processes, but can also have a measurable effect at room temperatures.

Typical design problems involve the determination of:

• Overall heat transfer coefficient, e.g. for a car radiator.
• Highest (or lowest) temperature in a system, e.g. in a gas turbine, chemical reaction vessels, food ovens.
• Temperature distribution (related to thermal stress), e.g. in the walls of a spacecraft.
• Temperature response in time-dependent heating/cooling problems, e.g. engine cooling, or how fast does a car heat up in the sun and how is it affected by the shape of the windshield?

The fluid flow and heat transfer problems can be tightly coupled through the convection term in the energy equation and when physical properties are temperature-dependent. While analytical solutions exist for some simple problems, we must rely on computational methods to solve most industrially relevant applications.

CHT can be performed to improve the cooling performance of the water jacket and increase engine life. Advancements in cooling for applications such as gas turbines components require improved understanding of the complex heat transfer mechanisms and the interactions between those mechanisms, which our engineers can perform without hassle.

Heat Transfer by Solids and Fluids

Heat Transfer in a Solid

In most cases, heat transfer in solids, if only due to conduction, is described by Fourier’s law defining the conductive heat flux, q, proportional to the temperature gradient: .

For a time-dependent problem, the temperature field in an immobile solid verifies the following form of the heat equation:

Heat Transfer in a Fluid

Due to the fluid motion, three contributions to the heat equation are included:

1. The transport of fluid implies energy transport too, which appears in the heat equation as the convective contribution. Depending on the thermal properties on the fluid and on the flow regime, either the convective or the conductive heat transfer can dominate.
2. The viscous effects of the fluid flow produce fluid heating. This term is often neglected, nevertheless, its contribution is noticeable for fast flow in viscous fluids.
3. As soon as a fluid density is temperature-dependent, a pressure work term contributes to the heat equation. This accounts for the well-known effect that, for example, compressing air produces heat.

Accounting for these contributions, in addition to conduction, results in the following transient heat equation for the temperature field in a fluid:

 

Fluid and Solid Interactions [Fluid/Solid Interface]

The temperature field and the heat flux are continuous at the fluid/solid interface. However, the temperature field can rapidly vary in a fluid in motion: close to the solid, the fluid temperature is close to the solid temperature, and far from the interface, the fluid temperature is close to the inlet or ambient fluid temperature. The distance where the fluid temperature varies from the solid temperature to the fluid bulk temperature is called the thermal boundary layer. The thermal boundary layer size and the momentum boundary layer relative size is reflected by the Prandtl number  for the Prandtl number to equal 1, thermal and momentum boundary layer thicknesses need to be the same. A thicker momentum layer would result in a Prandtl number larger than 1. Conversely, a Prandtl number smaller than 1 would indicate that the momentum boundary layer is thinner than the thermal boundary layer. The Prandtl number for air at atmospheric pressure and at 20°C is 0.7. 

Natural Convection

The natural convection regime corresponds to configurations where the flow is driven by buoyancy effects. Depending on the expected thermal performance, the natural convection can be beneficial (e.g. cooling application) or negative (e.g. natural convection in insulation layer).

The Rayleigh number, noted as , is used to characterize the flow regime induced by the natural convection and the resulting heat transfer. The Rayleigh number is defined from fluid material properties, a typical cavity size, , and the temperature difference,, usually set by the solids surrounding the fluid:

The Grashof number is another flow regime indicator giving the ratio of buoyant to viscous forces:

The Rayleigh number can be expressed in terms of the Prandtl and the Grashof numbers through the relation .

When the Rayleigh number is small (typically <10³), the convection is negligible and most of the heat transfer occurs by conduction in the fluid.

For a larger Rayleigh number, heat transfer by convection has to be considered. When buoyancy forces are large compared to viscous forces, the regime is turbulent, otherwise, it is laminar. The transition between these two regimes is indicated by the critical order of the Grashof number, which is 10⁹. The thermal boundary layer, giving the typical distance for temperature transition between the solid wall and the fluid bulk, can be approximated by  when  is of order 1 or greater.

Forced Convection

The forced convection regime corresponds to configurations where the flow is driven by external phenomena (e.g. wind) or devices (e.g. fans, pumps) that dominate buoyancy effects.

In this case the flow regime can be characterized, similarly to isothermal flow, using the Reynolds number as an indicator,. The Reynolds number represents the ratio of inertial to viscous forces. At low Reynolds numbers, viscous forces dominate, and laminar flow is observed. At high Reynolds numbers, the damping in the system is very low, giving small disturbances. If the Reynolds number is high enough, the flow field eventually ends up in a turbulent regime.

The momentum boundary layer thickness can be evaluated, using the Reynolds number, by .

 

Geometry_______________________________________________________________________

We start by converting the unit system to "m" & then import the pre-modeled wind tunnel with a Graphics card geometry to Spaceclaim, where we will be editing our geometry according to our simulation requirements. Our geometry is made up of two volumes, the solid volume (Graphics Card) where heat will be generated & will be transferred from the processor to the fins & the base, while the fluid volume (WindTunnel) will allow continuous fluid (air) flow from the inlet to the outlet. We create 2 new components & group the solid & fluid volumes separately, this would allow Ansys to apply the fluid conditions to the right zones. Next, we need to assign "share topology" to "share", this is done in order to capture the heat transfer phenomenon from the processors to the fins (solid volume) and then to the fluid volume, we need to mesh both these volumes in such a way that the information is able to transfer the information from one volume to another. Hence, we need to use a conformal meshing strategy, it's a strategy where both fluid & solid volume shares the same vertices at an intersection & are always aligned as shown in Fig 1.3. For this intersection to occur we need to use the "Share topology" feature in SpaceClaim, if not done then we would end up getting a non-conformal mesh as shown in Fig 1.2 this would result in inaccurate values of heat transfer. This Concludes the Geometry editing module, the next step involves the meshing module.

                                                                                         Fig 1.1:- Computational Domain With Graphics Card Inside A Wind Tunnel

                                                                                             Fig 1.2:- Base Line Mesh With Non-conformal Mesh [Share Topology = None]

                                                                                             Fig 1.3:- Refined Mesh With Conformal Meshing [Share Topology = share]

Meshing Module_________________________________________________________

The process of discretizing our domain of interest i.e. the geometry into smaller pieces is called meshing. Ansys Fluent uses a technique called the "bounding box" method to generate a body-fitted mesh. This is done by creating the smallest size hypothetical box possible that can be used to fit the entire geometry into it. We will be running a total of 4 case setup & for case1 & cases 2 to 4 will have varying mesh refinement, therefore each case will have to vary "total number of cells" & "total number of nodes". This is done to perform a Grid independence test & compare the simulation results. In the meshing module interface, we start by assigning names to our geometry. For our case, we have an inlet, an outlet, 3 wall boundaries & the rest of the unmarked walls will automatically be assigned as adiabatic walls by Ansys fluent. The next part of the meshing module involves the meshing strategies used for both cases.

                                                                                                                                           Fig 2.1:- Name selection 

We will be running the simulation for 4 cases with varying mesh sizes. Case 1 will have a baseline mesh of 3 mm equally distributed throughout the geometry with no additional refinements, the results obtained from this simulation will be used as a reference value. For Case 2, 3 & 4, we will be adding "body sizing" on the 3 components of the graphics card to better capture the flow physics. We can expect that this mesh refinement will lead to a high cell count which would allow us to obtain accurate results.

                                                                                             Fig 2.2:- Tetrahedral Mesh With Element Size of 2mm for Case 1 

                                                                                                     Fig 2.3:- Tetra & Hexa Mesh With Element Size of 4mm & 0.6mm for Case 2, 3 & 4 

Setting Up The Flow Physics________________________________________________

In Ansys Fluent after creating the mesh & assigning the boundaries, the next stage of the process is to set up the simulation parameters. This step involves specifying certain properties to capture the physics of the problem perfectly, such as materials used, simulation time parameters, solver parameters, initial & boundary conditions to solve the Navier Stokes equations which are PDEs, defining body forces, type of fluid flow & species involved.

We start by setting up the Domain, here we will be using a pressure-based steady-state solver with absolute velocity formation. We can justify using a pressure-based solver since the velocity or Mach number at the inlets is very low (V= 1 m/s, 5 m/s, 10 m/s). Along with the standard PDEs, we will also be solving the Energy equation. For materials, our choice of fluid (gas) will be air and our solid material for the components are as follows, Base = steel, Fins = aluminum, Processor = copper. 

We also need to add a user-defined value for the heat source i.e. for our case the Processor. We do that by navigating to the Cell-Zone condition & set the Processor/core as the source term as heat will generate in the graphic card. Assuming the power dissipation of the processor to be 10 Watts (W) and the volume of the processor obtained by dimensions of the design model to be 64 m³ (64*10^-8 mm³). The Heat generated (Q) in the processor is calculated to be Q = 15,62,50,000 W/m³.

The next parameter that we need to set up is the Flow Physics, here we will be navigating to the viscous feature & use an upgraded version of the original K-omega (k-`omega`) turbulence model i.e. the k-omega(k-`omega`) SST turbulence model with standard wall function in which the magnitudes of two turbulence quantities, the turbulence kinetic energy ‘k’ and its dissipation rate `omega`, is calculated from transport equations solved simultaneously with those governing equations for capturing better flow physics. 

Results & Observations____________________________________________________

Case 1: Inlet Velocity of 1 m/s for Base (Coarse) mesh 

Case 2: Inlet Velocity of 1 m/s for Refined mesh 

Case 3: Inlet Velocity of 5 m/s for Refined mesh 

Case 4: Inlet Velocity of 10 m/s for Refined mesh 

Conclusion_________________________________________________________

We successfully completed 4 simulations each having variable velocity or mesh refinement & each of the cases has reached convergence. It was observed that the refined mesh gives more accurate results than that of the coarse mesh for the same velocity profile of V=1m/s. We can observe that the highest temperature is observed where the velocity is 1 m/s and the lowest at 10 m/s, i.e. as we increase the velocity the cooling effect is relatively more effective. Therefore, we can conclude that increasing the inlet velocity yields better cooling of the processor.