Performing CFD Analysis On A 3 Dimensional T-Junction To Observe Thermal Mixing For Two Distinct Models Using ANSYS Fluent.

Abstract:- The experiment is focused on studying the flow characteristics inside a T-junction. Temperature fluctuations occur due to the thermal mixing of hot and cold streams in the T-junctions. If this temperature gradient inside the T-junction is not monitored properly can lead to thermal fatigue of the piping. In the present work, thermal mixing experiments are carried out on two distinct geometry of the T-junction with Newtonian fluid, air. The simulations have been carried out using a pressure-based steady-state solver for both the geometries to predict the velocity and temperature flow fields inside the T-junction. CFD software Ansys Fluent was used to conduct the experiment. The workflow pattern involved in successfully completing the experiment is as follows.

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      1. Introduction 

                  A mixing tee or a T-junction is a temperature control device, typically it has two inlet branches and only one outlet. Of the two inlets, chilled air enters the duct through one of them while hot air enters through the other as shown in Fig 1.1. The air flowing out of the system is a controlled temperature. Thermal mixing characterizes the phenomenon where hot and cold flow streams join, mix, and result in temperature fluctuations. The temperature fluctuations cause cyclic thermal stresses and subsequent fatigue cracking of the pipe wall. Thus the prediction of the thermal field in the piping system is an important aspect. In order to assess the structural strength, stability, and life of such T-junctions, it is essential to know the following: (i) magnitude of the temperature fluctuations, (ii) characteristic frequencies of temperature fluctuations, (iii) regions of pipe wall that experience the temperature fluctuations, (iv) attenuation of the temperature fluctuations in the boundary layer near the pipe wall. Through this experiment, we will investigate flow visualization, temperature measurements, and velocity measurements through contours & animations. Thermal mixing was originally modeled using large eddy simulation (LES) and direct numerical simulation (DNS), which required extensive computational capacity and time. Hence, we will be using RANS based model for our simulation. 

                                                                                                                                      Fig 1.1:- T-junction experimental setup

      2. Geometry Editing

We start by importing the pre-modeled geometry to Spaceclaim, where we will be editing our geometry according to our simulation requirements. Our geometry is made of solid thickness which is the upper layer & the fluid volume i.e. the inner volume of the pipe through which air will be flowing. To extract this fluid volume region we use the "Volume extraction" feature offered by Spaceclaim, as shown in Fig 2.1. We perform this operation on both the geometries i.e. the small & large T-junction geometry.

                                                                                                                        Fig 2.1:- Extracting the Fluid volume (small T-junction)

                                                                                                                        Fig 2.2:- Extracting the Fluid volume (long T-junction)

      3.  Setting up the 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. In our case setup, we used a mesh with an element size of 0.003m for both our geometry. For the smaller T-junction pipe, we observe a total cell of 39879 & 8369 nodes & for the large T-junction pipe, we observe a lesser number of cells & nodes with a total cell count of 56556 & nodes of 11715. Mesh generation around the body for the small & large T-junction pipe can be observed in Fig 3.1 & 3.2. 

                                                                                                                       Fig 3.1:- Mesh generated for the small T-junction pipe.

                                                                                                                      Fig 3.2:- Mesh generated for the Long T-junction pipe

After creating the mesh, we also need to define our boundaries in the mesh module. For both our cases, we will have two inlets (one along  X-axis the other perpendicular to it i.e. in the Y-axis), one outlet & wall boundaries as shown in Fig 3.3. In the following image, the red zone indicates the outlet boundary & the inlet boundaries are represented by blue color.

                                                                                                                                          Fig 3.3:- Boundaries 

      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 inlet from the two inlets is extremely small. Along with the standard PDEs, we will also be solving the Energy equation. 

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 Realizable 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. In the flow physics parameters itself, we will be defining the materials, our choice of fluid for the experiment is "air". We then navigate to the boundary zone, these are user-defined parameters where we assign the inlet velocity & temperature for both the inlets & we define the pressure near the outlet area. The walls of the pipe are stationary walls with a "no-slip" condition. These parameters will vary for all 3 cases as shown below. The final step includes performing a hybrid initialization & running the simulation for 500 iterations till the solutions converge.

      5. Results & Observations 

                                                                                                                                                          A. Case 1                                                                          

From the above Residual, Standard deviation & Area-averaged temperature plots at the outlet, we can observe that for case 1 our solutions have reached convergence after 200-250 iterations. We can conclude our solutions have converged since there is no change on all the convergence criteria, after 250 iterations or timesteps, we can consider that the solution has reached a steady-state, i.e. converged. Even if we run the simulation further long, we will not be able to see any change in the case. The Residuals plots are a function of the error in the model, the higher the residuals the less accurate the solution. From these graphs, we can compute the temperature at the outlet of the (small) T-junction after air gets diffused with the hot & cold air entering the domain. The temperature at the outlet for case 1 is approximately 294.3K or 21.15°C. This indicates that there has been a significant decrease in the temperature after mixing of the fluids inside the domain. Momentum ratio is given by velocity magnitude in the Y_axis (cold)`divide`velocity magnitude in the X_axis (warm) =>  `6 divide 3`  => 2. The diffusion section inside the duct has been captured accurately in the contour plots shown below. 

                                                                                                                                                          B. Case 2

From the above Residual, Standard deviation & Area-averaged temperature plots at the outlet, we can observe that for case 2 our solutions have reached convergence after 150-200 iterations. We can conclude our solutions have converged since there is no change in all the convergence criteria, after 200 iterations or timesteps, we can consider that the solution has reached a steady-state, i.e. converged. Even if we run the simulation further long, we will not be able to see any change in the case. The Residuals plots are a function of the error in the model, the higher the residuals the less accurate the solution. From these graphs, we can compute the temperature at the outlet of the (large) T-junction after air gets diffused with the hot & cold air entering the domain. The temperature at the outlet for case 2 is approximately 291K or 17.85°C. This indicates that there has been a significant decrease in the temperature after mixing of the fluids inside the domain by increasing the size of the T-junction. Momentum ratio is given by velocity magnitude in the Y_axis (cold)`divide`velocity magnitude in the X_axis (warm) =>  `6 divide 3`  => 2. The diffusion section inside the duct has been captured accurately in the contour plots shown below.

                                                                                                                                                          C. Case 3  

From the above Residual, Standard deviation & Area-averaged temperature plots at the outlet, we can observe that for case 3 our solutions have reached convergence after 150-200 iterations. We can conclude our solutions have converged since there is no change in all the convergence criteria, after 200 iterations or timesteps, we can consider that the solution has reached a steady-state, i.e. converged. Even if we run the simulation further long, we will not be able to see any change in the case. The Residuals plots are a function of the error in the model, the higher the residuals the less accurate the solution. From these graphs, we can compute the temperature at the outlet of the (large) T-junction after air gets diffused with the hot & cold air entering the domain. The temperature at the outlet for case 3 is approximately 291K or 17.85°C. This indicates that there has been a significant decrease in the temperature after mixing of the fluids inside the domain by increasing the size of the T-junction. In fact, the results obtained for case 3 is very similar to case 2. It can be concluded from the 3 simulations that to obtain a lowered temperature by keeping the inlet velocities constant at the outlet we can either increase the size of the T-joint or increase the velocity of the cold air entering the domain. Momentum ratio is given by velocity magnitude in the Y_axis (cold) `divide` velocity magnitude in the X_axis (warm) =>  `12 divide 3`  => 4. The diffusion section inside the duct has been captured accurately in the contour plots shown below.

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