Performing Conjugate Heat Transfer (CHT) Analysis On A Hypothetical Exhaust Manifold For A 4 Cylinder Engine Using Ansys Fluent.

ABSTRACT:- The purpose of this experiment is to perform Conjugate Heat Transfer (CHT) analysis on a hypothetical exhaust manifold of an IC engine using a pressure-based steady-state solver in ANSYS Fluent. The Exhaust manifold in the engines is an important component which has a considerable effect on the performance of the IC engine. The manifold was pre-modeled in CATIA, the present work focuses on mesh refinement and CFD analysis of the exhaust port using ANSYS Fluent software.  Exhaust Manifolds play an important role in the performance of an engine and are affected by thermal stresses and deformations due to the temperature distribution, heat accumulation or dissipation, and other related thermal characteristics. The simulation was run for 2 cases to plot the velocity & temperature contours.

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                                                                      Keywords: Exhaust Manifold, Conjugate Heat Transfer (CHT), Finite Volume Method (FVM), Mesh Refinement

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     1. Theory

        An exhaust manifold is a key component in a 4-stroke IC engine. The exhaust manifold is mounted on the cylinder head of an engine that collects exhaust gases from multiple cylinders into one pipe & plays an important role in the performance of an engine system. Particularly, the efficiencies of emission and fuel consumption are closely related to the performance of the exhaust manifold. The temperature of these hot gases is near about 800 and pressures are varying about 100 to 500 kpa, this temperature and pressure gradient is experiencing during the exhaust stroke. Exhaust Manifolds are affected by thermal stresses and deformations due to temperature distribution, heat accumulation or dissipation, and other related thermal characteristics. Backpressure is an undesired effect because as the backpressure increases so does the number of residuals left in the head. The increase in weight of residuals will decrease the volume of the fresh charge, in turn, increases the temperature at the beginning of compression as well. 

      The term Conjugate Heat Transfer (CHT) is used to describe a process that involves simultaneous energy exchange between solid and fluid domains due to such interaction between them it is frequently encountered in a variety of engineering applications such as internal combustion engines, turbomachinery, heat exchangers.

 The finite volume method (FVM) is a method for representing and evaluating partial differential equations in the form of algebraic equations. In the finite volume method, volume integrals in a partial differential equation that contain a divergence term are converted to the surface integrals, using the divergence theorem. These terms are then evaluated as fluxes at the surfaces of each finite volume. Because the flux entering a given volume is identical to that leaving the adjacent volume, these methods are conservative. Another advantage of the finite volume method is that it is easily formulated to allow for unstructured meshes. The method is used in many computational fluid dynamics (CFD) packages. "Finite volume" refers to the small volume surrounding each node point on a mesh.

     2. Geometry

We start by converting the unit system to "m" & then import the pre-modeled Exhaust Port 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 where heat will be transferred & the fluid volume though which fluid flow will occur. We use the "Volume Extraction" tool to create two separate regions (solid & volume region) as shown in Fig 2.1. The hot exhaust gas entering through the inlets will interact with the fluid volume & the heat from the fluid volume will be transferred to the solid volume. In order the capture both this phenomenon, 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 2.4 & 2.5. 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 2.2 & 2.3 this would result in inaccurate values of heat transfer. This Concludes the Geometry editing module, the next step involves the meshing module.

                                                                                                                      Fig 2.1:- Fluid Volume Extraction by "Volume Extraction" tool

                Fig 2.3:- Solid & Fluid Volume Mesh misaligned (Non-conformal Mesh)                 Fig 2.4:-  Solid & Fluid Volume Mesh aligned (Conformal Mesh)   

     3. Mesh

The process of discretizing our domain of interest i.e. the geometry into smaller pieces is called mesh generation. 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 2 case setup & each of the cases will have varying mesh refinement, therefore each case will have varying "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 4 inlets, 1 outlet, 1 wall boundary & 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 3.1:- Named Selection

We will be running the simulation for 2 cases with varying mesh sizes. Case 1 will have a baseline mesh of 100 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, we will be adding 7 layers of "inflation layers" near the solid & volume interface to better capture the physics. We will also reduce the base mesh to 70 mm & add an additional layer of mesh with an element size of 15 mm on the solid body. We can expect that these several layers of mesh refinement will lead to a high cell count which would allow us to obtain accurate results.

                                                                                                           Fig 3.2:- Mesh interface for case 1 with baseline mesh

                                                                                                  Fig 3.3:- Mesh interface for case 2 with inflation layers & refined mesh

Note:- The grid scaling or the base grid size was calculated near the wall boundaries by taking the desired Y+ value, with inputs of the free-stream velocity, density characteristic length, dynamic viscosity in the pointwise Y+ calculator (https://www.pointwise.com/yplus/). The standard values of density & dynamics viscosity are based on the flat-plate boundary layer theory. The following equations are needed to be solved to obtain the wall spacing `triangle S`.

Reynolds Number => `Re = ( rho V L)/ mu` ; Skin Friction coefficient => `Cf = 0.0026/ (Re)^0.142` , non-dimensional number indicating the friction between the FSAE body & air ; Wall Shear Stress => `tauw= (Cf rho V^2)/2`; Friction Velocity => `Uf = ((tauw)/rho)^ 0.2`; Wall Spacing => `((Y^+) mu)/(Uf rho)`

Based on these calculations the wall spacing `triangle S` comes out to be 0.00006m or 0.06mm, which is incredibly fine & would require a huge amount of computing power. Since the experiment has been carried out with a laptop such a fine grid will lead to the simulation running indefinitely. Hence, the base grid was increased to a value such that it is compatible with the ANSYS Student license limitations.

         4. Setting up the Flow Physics for the Computational Model

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 equation 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= 5 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 will be aluminum. 

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-epsilon (k-ε) turbulence model i.e. the Standard k-epsilon (k-ε) turbulence with standard wall function in which the magnitudes of two turbulence quantities, the turbulence kinetic energy ‘k’ and its dissipation rate ‘ϵ’, is calculated from transport equations solved simultaneously with those governing equations for capturing better flow physics. 

We then navigate to the boundary zone, these are user-defined parameters where we assign the inlet velocity & temperature for our case all the 4 inlets will have a velocity magnitude of 5m/s with a thermal value of 700K & we define the pressure near the outlet area to be 1pa or gauge pressure of 0pa. The walls of the exhaust port are walls with a heat transfer coeff of `20 (w/(m^2K))`. The final step includes performing a hybrid initialization & running the simulation for 400-500 iterations until the solutions converge.

         5. Results & Conclusion

                    A. Case 1

For Case 1, we used a baseline mesh with a mesh size of 100 mm throughout the geometry which resulted in a total cell count of 147577 or 0.14 million cells. This can be referred to as a coarse mesh. From the temperature contours, we can observe that the temperature is maximum near the outlet, this is the region where hight temperature gas from the 4 inlets meets & stagnates before exiting from the domain, thus the results can be justified. As for the velocity contours, we observe that the velocity is higher near the outlet region around the curve of the outlet duct, due to mass conservation, it is expected to obtain a higher Heat Transfer coeff at a region where the velocity is high. 

                    B. Case 2

For Case 2, we used a baseline mesh with a mesh size of 70mm throughout the geometry, 15mm on the solid volume & added 7 inflation layers between the solid & fluid volume interface which resulted in a total cell count of 467577 or 0.46 million cells. This can be referred to as a fine mesh. From the temperature & velocity contours, we can observe that our results are identical to the case 1 observation except that the resolution near the high velocity & temperature regions is more prominent due to finer mesh size. We can conclude that the results obtained from case1 with no mesh refinement technique were fairly reliable but to obtain the best results we can add the first mesh layer according to the `triangle S` value. This would require high computational power & run time will increase significantly.

Verification of Heat Transfer Coefficient (HTC) predictions from simulations & factors affecting accuracy

The heat transfer coefficient or film coefficient, or film effectiveness, in thermodynamics and in mechanics is the proportionality constant between the heat flux and the thermodynamic driving force for the flow of heat (i.e., the temperature difference, ΔT). It is given by:-

 

where:

q: heat flux, W/m²; 

h: heat transfer coefficient, W/(m²•K)

ΔT: difference in temperature between the solid surface and surrounding fluid area, (K)

HTC is often calculated from the Nusselt Number. Nusselt number (Nu) is the ratio of convective to conductive heat transfer at a boundary in a fluid. 

where h is the convective heat transfer coeff of the flow, L is the characteristic length, k is the thermal conductivity of the fluid.

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