Mixing Efficiency of fluids in T-Pipe

Aim: To perform steady state simulations for analysing the mixing effectiveness of fluilds in a T-joint.

Theory: The solid model we will be using for the simulation is a T-joint. It consist of 2 inlets and 1 outlet. The inlet is perpendicular to each other at a certain distance. These kind of pipes are usually used to mix the fluids with different temepratures (hot and cold) to obtain a desired temperature of the fluid at the outlet of the pipe. A model of the solid part of the T-joint can be seen below.

We will be doing the simulation for 2 different length of the T-joint along with different momentum ratio. Momentum ratio is noting but the ratio of velocity of the cold inlet to velocity of the hot inlet. For the Case 1 we will be using a solid model of shorter length T-joint with a momentum ratio of 2. For the Case 2 we will be using a solid model of longer length T-joint with a momentum ratio of 2. For the Case 3 we will be using a solid model of shorter length T-joint with a momentum ratio of 4.

Normally for simulations in Ansys Fluent we follow a set of procedures:

• Geometry.
• Meshing.
• Setup.
• Solving.
• Results/Post Processing.

We will be looking through in detail the above mentioned steps for the above mentioned 3 cases.

Geometry :

We will be loading the geometry in Ansys spaceclaim. Since we are interested in fluid flow inside a pipe we would like to use only the fluid volume for the simulations. From the above geometry we can see the pipe has extra details such as thickness which is not required for this particular case as we wont be doing any solid simulation. A fluid volume is a where there is a particular interaction of the fluid in some parts of the body. In order to extract the fluid volume from the solid we use a command in the Prepare Tab known as Volume Extract. Hence we select the inner walls of the pipe which would be our fluid volume in our case.

Case 1 and Case 3: We would be using a shorter length of the T-pipe.

Case 2:We would be using a longer length of the T-pipe.

This would prepare our Geometry models for the next stage which is Meshing.

Meshing:

We would be using Ansys Meshing to create a mesh for the mesh geometry. Before proceeding to create a mesh we would define the different parts in the pipe such as the inlets, outlet and walls. The different sections of the pipe are as follows:

• inlet-x: It is the inlet of the pipe along x direction.
• inlet-y: It is the inlet of the pipe which is perpendicular to x-axis along y direction.
• outlet.
• Walls.

Inlet-x is the location where the hot fluid enter the pipe at certain velocity and inlet-y is the location where the cold fluid enters the pipe.

In all the 3 cases we have varied the Mesh size and a mesh quality graph is plotted for each of case.

Case 1:

Element Size: 0.003

Number of Elements: 39774

Case 2:

Element Size: 0.002

Number of Elements: 140023

Case 3:

Element Size: 0.019

Number of Elements: 119960

For the all the 3 cases we obtained Mesh quality graph whose x-axis is element metrics and y-axis is the number of elements. X-axis indicates a percentage value between 0 to 1. If the elements mesh quality is less than 5% then the mesh is not suitable for solving. In the above 3 cases the maximum elements has a mesh quality between 80-90% and the least is around 25%. Hence we can proceed with the next step which would be the setting up of physics and the boundary conditions.

Setup :

In fluent user interface we would setup the solver and boundary condition to solve the above required problem. In this case we will be running a steady state simulation using Pressure-based Solver for all the 3 cases. Since the mach number in this case is low a pressure-based solver is selected. The velocity formulation was selected to be Absolute. Under the models column we would also click on the energy tab as we would be solving for the temperature profile as well. Since the flow would have some turbulence due to mixing we will also choose a simple turbulence model which is k-epsilon (2-eqn) Model. A realizable k-epsilon model is choosed with standard Wall Functions for all the 3 cases. The default values were used for the above parameters. Also we use air as fluid material and the default values were used for all the 3 cases.

Under the zones tab we have option for the boundaries where we can define our initial and boundary conditions.

Case 1:

The boundary condition for case 1 is as follows:

• inlet-x :

The type is set to velocity inlet whose magnitude is Normal to the boundary.The velocity Magnitude is set for 3 m/s. Specific method for turbulence is Intensity and Viscosity ratio whose Turbulent Intensity is 5% and Turbulent Viscosity Ratio is 10. For the thermal part we set the temperature to `25 ^o C`.

• inlet-y :

The type is set to velocity inlet whose magnitude is Normal to the boundary.The velocity Magnitude is set for 6 m/s. Specific method for turbulence is Intensity and Viscosity ratio whose Turbulent Intensity is 5% and Turbulent Viscosity Ratio is 10. For the thermal part we set the temperature to `10 ^o C`.

The outlet type is set to pressure outlet and all the other parameters are set to be default. The walls type is set to be wall and all the other parameters are set to be default.

Case 2:

Almost all the boundary conditions is same as above except the geometry used in this case would be a long T-pipe. The boundary condition for case 2 is as follows:

• inlet-x :

The type is set to velocity inlet whose magnitude is Normal to the boundary.The velocity Magnitude is set for 3 m/s. Specific method for turbulence is Intensity and Viscosity ratio whose Turbulent Intensity is 5% and Turbulent Viscosity Ratio is 10. For the thermal part we set the temperature to `25 ^o C`.

• inlet-y :

The type is set to velocity inlet whose magnitude is Normal to the boundary.The velocity Magnitude is set for 6 m/s. Specific method for turbulence is Intensity and Viscosity ratio whose Turbulent Intensity is 5% and Turbulent Viscosity Ratio is 10. For the thermal part we set the temperature to `10 ^o C`.

The outlet type is set to pressure outlet and all the other parameters are set to be default. The walls type is set to be wall and all the other parameters are set to be default.

Case 3:

The boundary condition for case 3 is as follows:

• inlet-x :

The type is set to velocity inlet whose magnitude is Normal to the boundary.The velocity Magnitude is set for 3 m/s. Specific method for turbulence is Intensity and Viscosity ratio whose Turbulent Intensity is 5% and Turbulent Viscosity Ratio is 10. For the thermal part we set the temperature to `25 ^o C`.

• inlet-y :

The type is set to velocity inlet whose magnitude is Normal to the boundary.The velocity Magnitude is set for 12 m/s. Specific method for turbulence is Intensity and Viscosity ratio whose Turbulent Intensity is 5% and Turbulent Viscosity Ratio is 10. For the thermal part we set the temperature to `10 ^o C`.

The outlet type is set to pressure outlet and all the other parameters are set to be default. The walls type is set to be wall and all the other parameters are set to be default.

Solution :

For solving the governing equation we need to go to solution tab.Firstly we check with the residuals and set the absolute criteria value. In all the 3 cases used here we use a criteria value of 1e-06. Also we will be creating the requried plots in our case we will be creating Area-Weighted Average and Standard Deviation for the temperature at the outlet.

Then we will be initializing the solution using Hybrid Method. Hybrid initialization is the collection of recipies and boundary interpolation methods.Once the solution is initialized we proceed to run the calculations. For all the 3 cases we set the No. of Iterations to be 1000. Below we can find the converged residual plots, Area-Weighted Average and Standard deviation plots for various cases.

Case 1:

Residual Plot:

Area-Weighted Average Temperature Plot:

Standard Deviation Temperature Plot:

Case 2:

Residual Plot:

Area-Weighted Average Temperature Plot:

Standard Deviation Temperature Plot:

Case 3:

Residual Plot:

Area-Weighted Average Temperature Plot:

Standard Deviation Temperature Plot:

Once the Solution is converged we will be moving on to the final steps Post-Processing/Results.

Results :

Case 1:

Temperature Contour at symmetric Plane:

Velocity Contour at symmetric Plane:

From the temperature contour we can see that the inlet temperature at inlet-x is 298.15 K (`25^oC`) and along inlet-y is 283.15 K (`10^oC`). We can clearly obaserve, at the outlet near the bottom wall the temperature of the fluid is still 298.15 K. This is because the cold fluid is not well mixed or homogenously mixed with the hot fluid. Also the inlet velocity of the cold fluid is low which results in less mixing of the fluids.

The area weighted average temperature at the outlet is around 19.9 degree and the standard Deviation of temeprature at the outlet is 1.65 degree

From the velocity contour we can see that the inlet velocity at inlet-x is 3 m/s and along inlet-y is 6m/s. Also No-slip condition is applied to the walls as we can see the velocity near the wall boundaries is 0 m/s. Also from the both the contours we can see that the solution is bit diffused. This is because of the element size is larger at that particular region.

Case 2:

Temperature Contour at symmetric Plane:

Velocity Contour at symmetric Plane:

From the temperature contour we can see that the inlet temperature at inlet-x is 298.15 K (`25^oC`) and along inlet-y is 283.15 K (`10^oC`). We can clearly obaserve, at the outlet near the bottom wall the temperature of the fluid is decreased when compared to case 1. Therefore we can say that by increasing the length of the pipe, it leads to further mixing of the fluids.

The area weighted average temperature at the outlet is around 20.05 degree and the standard Deviation of temeprature at the outlet is 1.23 degree.

From the velocity contour we can see that the inlet velocity at inlet-x is 3 m/s and along inlet-y is 6m/s. Also No-slip condition is applied to the walls as we can see the velocity near the wall boundaries is 0 m/s. Also from the both the contours we can see that the solution is less diffused compared to case 1. This is because we reduced the element size to 0.002 from 0.003.

Case 3:

Temperature Contour at symmetric Plane:

Velocity Contour at symmetric Plane:

From the temperature contour we can see that the inlet temperature at inlet-x is 298.15 K (`25^oC`) and along inlet-y is 283.15 K (`10^oC`). We can clearly observe, at the outlet near the bottom wall, the temperature of the fluid is very much decreased when compared to case 1 and case 2. This is because we have increased the velocity at the inlet-y from 6 m/s to 12 m/s. Increasing the velocity helps in effective mixing of the fluids.

The area weighted average temperature at the outlet is around 17.5 degree and the standard Deviation of temeprature at the outlet is 1.11 degree.

From the velocity contour we can see that the inlet velocity at inlet-x is 3 m/s and along inlet-y is 12m/s. Also No-slip condition is applied to the walls as we can see the velocity near the wall boundaries is 0 m/s. Also from the both the contours we can see that the solution is less diffused compared to case 1. This is because we reduced the element size to 0.019.

Conclusions :

Comparing Results for all the 3 cases.

• For all the 3 cases hot inlet temperature is at 25 degree and cold inlet temperatureis at 10 degree.
• The momentum ratio for case1 and case2 is 2 and for case 3 is 4.
• By comparing case 1 and case 2, we can say that by increasing the length of pipe mixing of fluids is better which may be due to diffusion.
• By comparing case 1 and case 3 by increasing the velocity of the cold air, we obtain a homogenous mixing of the fluids resulting in lesser area weighted average temperature and lesser standard deviation temperature at the outlet.

For all the Simulation files and for the simulation files with inlet velocity 4 & 8 m/s, please check the link below.

https://drive.google.com/drive/folders/1xBkuBFJsFvb4U8O1upGlMzxserN3PSXH?usp=sharing