Exhaust Port Challenge
AIM: Give a brief description of a Conjugate Heat transfer analysis.
Theoritical Background:
The term conjugate heat transfer (CHT) describes the processes which involve 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 study of Heat Transfer, the rate of transferred heat is directly proportional to the temperature difference between the bodies.
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 high heat transfer rate. In some applications, the performances are further improved by combining convection with 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.
Example: A typical example is the heating or cooling of a solid object by the flow of air in which it is immersed and some other example includes conduction through solids, free and forced convection in the gases/fluids and thermal radiation.
Geometry of Exhaust Manifold
Solid Region Fluid Region
Meshing
Element order: Linear
Element size: 0.15m
Number of nodes: 27359
Number of elements: 137126
Mesh metric
Fluent Setup
Solver: Steady state
Type: Pressure based
Turbulance model: K-epsilon standard wall functions
Material: Fluid - Air, Solid - Alluminium
Boundary conditions:
INLET: Type - Velocity inlet, velocity = 5m/s, Temperature = 700K
OUTLET: Type - Pressure Outlet, Pressure = 0Pa(gauge Pressure), Temperature = 300K
OUTER WALL CONVECTION: Type - Wall, Heat Transfer Coefficient = 20W/m2K, Free Stream Temperature = 300K
INITIALIZATION METHOD: Hybrid initialization, Number of iterations: 450
Residual plots
Temperature Contours
Post Processing
Temperature Contour
In steady state simulation the air coming through outlet have higher velocity, because of higher velocity we have higher Reynolds number, which means there is higher heat transfer coefficient, which means there is more heat transfer form fluid to solid , hence solid temperature in that location is higher.
Velocity Contour
Wall Heat Transfer Coefficient
Wall heat Transfer Coefficient is the quantity that is calculated at the walls that are adjacent to the fluid. The fluid is hot. We will have maximum amount of heat transfer from fluid to the solid which results in higher temperature of solid at that particular location. It was found that the maximum wall heat transfer coefficient was found to be 104.18 W/m2K.
REFINED SETUP:
The above mesh is refined by decreasing the mesh size and by adding inflation layers . Heat transfer Coefficient is available only at the first cell attached to the wall. The reason we added inflation layers is it creates a body fitted mesh which follows geometry which in turn follow curvature.
Solver: Steady state
Type: Pressure based
Turbulance model: K-epsilon standard wall functions
Material: Fluid - Air, Solid - Alluminium
Boundary conditions:
INLET: Type - Velocity inlet, velocity = 5m/s, Temperature = 700K
OUTLET: Type - Pressure Outlet, Pressure = 0Pa(gauge Pressure), Temperature = 300K
OUTER WALL CONVECTION: Type - Wall, Heat Transfer Coefficient = 20W/m2K, Free Stream Temperature = 300K
INITIALIZATION METHOD: Hybrid initialization, Number of iterations: 450
INFLATION: Number of Inflation Layers - 5, Growth rate = 1.2, Maximum thickness = 0.005m Location = On Inner Pipe
BODY SIZING: element size = 0.05m, Location = On Outer Pipe
Meshing:
Element order: Linear
Element size: 0.10m
Number of nodes: 98780
Number of elements: 281573
Mesh Metric
Inflation Layers
Simulation Output
Residuals plot
Temperature Contour
Post Processing
Temperature Contour
Velocity Contour
Wall Heat Transfer Coefficient
Mesh lines at the bend near the Outlet
TABULATION:
The results of 2 cases are tabulated below
Observations:
There is increase in the Wall Heat transfer coefficient value due to refinement of the mesh. The wall heat transfer coefficient is higher at the pipe bend near the outlet due to increase in Reynold's number.
Y + value
The y+ value is a non-dimensional distance (based on local cell fluid velocity) from the wall to the first mesh node. To use a wall function approach for a particular turbulence model with confidence, we need to ensure that our y+ values are within a certain range. The Y+ plot at the inlet for the refined setup is shown below.
Heat Transfer Coefficient(h)
The heat transfer coefficient is the heat transferred per unit area per kelvin. Thus area is included in the equation as it represents the area over which the transfer of heat takes place.
Nusselt Number(Nu)
The Nusselt number is the ratio of convective to conductive heat transfer across a boundary. The convection and conduction heat flows are parallel to each other and to the surface normal of the boundary surface, and are all perpendicular to the mean fluid flow.
h ----->Convective Heat Transfer Coefficient of the flow, L---->Characterstic Length, K---->Thermal conductivity of the fluid.
Factors on which accuracy of Heat Transfer Coefficient depends
1. The Geometry of the model should be accurate to get accurate results
2. Mesh size should be accurate to generate correct results
3. The selection of the solver and the boundary conditions should be done as per the problem
4. Grid Dependency Test should be conducted to check the correctness of the results