Analyzing the heat transfer for flow through a mixing tee joint using ANSYS Fluent

INTRODUCTION:

In this project, we will be simulating flow through a tee joint to analyze the mixing and the heat transfer. A tee joint is formed when two members are connected perpendicularly to each other. The tee joint has a variety of applications. In plumbing applications, it is used to direct the flow in one direction or the other. Household and commercial indoor plumbing, outdoor irrigation systems make use of the tee joints heavily. It is also used in HVAC systems where secondary gases or liquids are conveyed through the tee joint for required ventilation or air conditioning. We will be using two geometries for this project, where one of the primary pipes is short and the other is longer. We will be analyzing three cases for the purpose of this project:

• Case 1: Short tee joint with cold inlet/hot inlet velocity ratio `2`
• Case 2: Short tee joint with cold inlet/hot inlet velocity ratio `4`
• Case 3: Long tee joint with cold inlet/hot inlet velocity ratio `2`

The steps involved in the analysis are as follows:

• Creating the flow domain
• Meshing the computational domain
• Setting up the flow physics and solver settings
• Post-processing the results

CREATING THE FLOW DOMAIN:

For the flow simulation, we need to create a fluid domain from the solid domain. This can be done in ANSYS DesignModeler using the "Fill" tool, which creates a volume based on the chosen faces. The fluid domain is created for both the short and the long configuration of the tee joint and assigned a Fluid body condition.

MESHING:

The meshing is done using the ANSYS Workbench interface. First named selections are created for different faces of the fluid domain. These named selections are useful when setting up the boundary conditions as well.

The mesh near the outlet and inlet-y is a relatively coarser mesh with elements of size `4` `mm`. Near the mixing area, a finer mesh is used for which a cuboidal "Body of Influence" is created as shown below.

This body of influence is used to mesh the mixing area with a finer mesh of `2.5` `mm`. The finer mesh is tried with different sizes for mesh convergence study which will be discussed in later sections. `5` inflation layers with a growth rate of `1.4` are implemented near the walls of the tee joint to capture the boundary layer of the flow. The meshed computational domain for the short and long configurations are shown below.

The mesh quality metric is shown below which shows the quality of most of the elements is close to `1`.

SETUP OF THE SOLVER:

The setup of the flow and physics is done in the Fluent interface. The analysis is an incompressible steady-state analysis. The governing equations used are the energy equation along with the Reynolds' Averaged Navier Stokes (RANS) equation with the `k`-`epsilon` turbulence formulation. The fluid used in this analysis is air with the following properties:

Density: `rho = 1.225` `kg"/"m^3`

Specific Heat: `c_p = 1006.43` `J"/"kg-K`

Thermal Conductivity: `k = 0.0242` `W"/"m-K`

Dynamic Viscosity: `mu = 1.7894 times 10^{-5}` `kg"/"m-s`

The boundary conditions are assigned based on the named selections assigned in the previous section:

• inlet-x: Velocity inlet with normal velocity in the x-direction of `3` `m"/"s` and temperature of `25^0C`.
• inlet-y: Velocity inlet with normal velocity in the y-direction of `6` `m"/"s` (for cases 1 and 3) and `12` `m"/"s` (for case 2) and temperature of `10^0C`.
• outlet: Pressure outlet with a gauge pressure of `0` `Pa`.
• walls: No-slip boundary condition.

A coupled pressure-velocity solver is implemented with second-order spatial discretization for pressure and momentum. The convergence criteria for the momentum, velocity, and turbulence residuals is `1e"-"03` and for energy is `1e"-"06`. Custom reports are set up for the average and standard deviation of the temperature on the outlet face to monitor the convergence. The solution is initialized with the values computed from the inlet-x. The solution is set up to run for a maximum of `300` iterations, but the solution converges well before that.

MESH CONVERGENCE STUDY:

In order to assure that the mesh generated provides a precise solution, we need to perform the mesh convergence study, which involves performing the simulation for different meshes and monitoring an output variable. For this project, the mesh is altered in "Body of Influence" element sizing - Coarse (`3` `mm`), Fine (`2.5` `mm`) and Very Fine (`2` `mm`). The variable that is monitored is the average outlet temperature. The following table summarizes the results for the three different meshes and their solution and the number of iterations it takes to converge.

`{:(ul{text{Mesh size}},ul{text{No. of elements}},ul{text{Mean outlet temperature}},ul{text{Iterations to converge}}),(text{Coarse},58890,20.158 ^0C,104),(text{Fine},89424,20.136^0C,107),(text{Very Fine},154298,20.149^0C,111):}`

From the above table, we can see that the average temperature stays consistent with the mesh size. So, ideally, we can use any of the three mesh sizes for our final simulation. The "Fine" mesh is used for this simulation as it can provide accurate results as well as capture the flow profile.

RESULTS AND DISCUSSION:

Case 1 - Short Tee Joint with Momentum Ratio `2`

Residuals and convergence

Contours and streamlines

Case 2 - Short Tee Joint with Momentum Ratio `4`

Residuals and convergence

Contours and streamlines

Case 3 - Long Tee Joint with Momentum Ratio `2`

Residuals and convergence

Contours and streamlines

The streamlines show the mixing of the flow from the two inlets which is slightly more turbulent for the higher cold inlet velocity. For the longer tee joint, it also becomes more uniform than the shorter one. The following table compares the results from all the three cases:

`{:(ul{text{Case}},ul{text{No. of elements}},ul{text{Average Outlet Temperature}},ul{text{Standard Deviation}},ul{text{Iterations to converge}}),(1,89424,20.136^0C,1.315,107),(2,89424,17.627^0C,1.076,118),(3,131553,20.158^0C,0.738,113):}`

The number of iteration required for convergence is almost similar for all the three cases. From the table, we can see that as we increase the cold inlet velocity, the heat transfer and the cooling increase as well. Also, as the length of the section increases, the mixing becomes more uniform, hence the lower standard deviation for the longer length and same flow parameters.