Week 1- Mixing Tee

AIM

For this challenge, we have created two versions of the mixing tee. One of them is longer than the other.

To set up steady-state simulations to compare the mixing effectiveness when the hot inlet temperature is 360C & the Cold inlet is 190C.

OBJECTIVE

Use the k-epsilon and k-omega SST model for the first case and based on your judgment use the more suitable model for further cases. Giving the reason for choosing a suitable model is compulsory.

Case 1

Short mixing tee with a hot inlet velocity of 3m/s.

Momentum ratio of 2, 4.

Case 2

Long mixing tee with a hot inlet velocity of 3m/s.

Momentum ratio of 2, 4.

Momentum ratio = velocity at cold inlet / velocity at hot inlet

In a table, compare the following values from the 2 cases.

Cell count

Average outlet temperature

Number of iterations for convergence

INTRODUCTION

In industrial process engineering, mixing is a unit operation that involves the manipulation of a heterogeneous physical system with the intent to make it more homogeneous. Mixing is performed to allow heat and/or mass transfer to occur between one or more streams, components, or phases. Modern industrial processing almost always involves some form of mixing

A mixing tee, also known as a T-mixer or Y-mixer, is an essential component used in fluid systems to connect and distribute flows from two or more pipes into a single pipe or vice versa. The design of the mixing shirt resembles the letter "T" with three holes: one at the top (input) and two on the sides (outputs). This configuration allows the fluid to flow into the top of the tee and split into two separate streams through the side holes.

Mixing tees serve a variety of purposes in a variety of applications, including:

• Mixing Fluids: One of the primary applications of mixing tees is to combine two different fluids to create a homogeneous mixture. It is commonly used in chemical processes and water treatment systems.
• Flow Distribution: In many industrial systems, it is essential to distribute the fluid flow evenly between two or more pipes. Mixing tees help achieve this by splitting the flow from the main pipe into multiple branches.
• Process Control: Mixing tees are used in a variety of process control systems to control the flow, pressure, or temperature of fluids in the system.
• Instrumentation and Sampling: In some cases, mixing tees are used to provide a means of collecting representative samples or measuring certain properties of the fluid.
• Diversion: In certain applications, mixing tees can be used to divert flow from a primary pipe to two or more secondary pipes.

It is important to note that mixing tees do not always result in an even distribution of flow between the outlet pipes. The flow distribution depends on factors such as tee design, fluid properties, and the pressure or velocity of the fluid supplied.

When designing or selecting a mixing tee, engineers must consider factors such as pressure drop, fluid compatibility, and flow rates to ensure proper system performance.

. Mixing Tees utilizes a specifically engineered internal geometry to efficiently mix two fluid streams into one combined stream. Mixing tees are widely used in the petrochemical, HVAC industry, etc. in which two fluid streams with different physical and/or chemical properties mix together

Turbulent mixing of fluid of different temperature in T-junction geometries became of significant importance in the field of nuclear reactor safety, since it can lead to highly transient temperature fluctuations at the adjacent pipe walls, cyclic thermal stresses in the pipe walls and consequently to thermal fatigue and failure of the pipeline. Thermal striping and mixing, in general, is however challenging to predict by using common CFD simulation and turbulence modeling approaches. For this, we have created two versions of the mixing tee. One of them is longer than the other.

It is set up as steady-state simulations to compare the mixing effectiveness when hot inlet temperature is 36⁰C & Cold inlet is 19⁰C.

1. Case 1
• Short mixing tee with a hot inlet velocity of 3m/s.
• Momentum ratio of 2, 4.
2. Case 2
• Long mixing tee with a hot inlet velocity of 3m/s.
• Momentum ratio of 2, 4.

The momentum ratio is defined as the ratio of velocity at the cold inlet to the velocity at the hot inlet.

THEORY

When dealing with a mixing tee, several equations can be used to describe the fluid flow and properties at different points within the system. Here are some of the essential equations:

1. Mass Conservation Equation (Continuity Equation):
   The continuity equation states that the mass flow rate at the inlet of the tee is equal to the sum of the mass flow rates at the outlets. Mathematically, it can be represented as:

`ρ1 * A1 * V1 = ρ2 * A2 * V2 + ρ3 * A3 * V3`

Where:
ρ1, ρ2, ρ3: Density of the fluid at the inlet and outlets, respectively.
A1, A2, A3: Cross-sectional area of the inlet and outlets, respectively.
V1, V2, V3: Velocity of the fluid at the inlet and outlets, respectively.

2. Bernoulli's Equation:
   Bernoulli's equation describes the relationship between pressure, velocity, and height for an incompressible fluid flowing through a streamline. It can be written as:

`P1 + 0.5 * ρ1 * V1^2 + ρ1 * g * h1 = P3 + 0.5 * ρ3 * V3^2 + ρ3 * g * h3`

`P1 + 0.5 * ρ1 * V1^2 + ρ1 * g * h1 = P3 + 0.5 * ρ3 * V3^2 + ρ3 * g * h3`

Where:
P1, P2, P3: Pressure at the inlet and outlets, respectively.
V1, V2, V3: Velocity at the inlet and outlets, respectively.
ρ1, ρ2, ρ3: Density of the fluid at the inlet and outlets, respectively.
g: Acceleration due to gravity.
h1, h2, h3: Height above a reference plane at the inlet and outlets, respectively.

3. Flow Split Equations:
   In some cases, the flow through each outlet of the mixing tee may be expressed as a function of the inlet flow and some other variables. The flow split equations can be specific to the design and characteristics of the tee and may involve empirical coefficients.

For example, for a simple Y-mixer, the flow through each outlet may be represented as:
`Q2 = C2 * Q1`

`Q3 = C3 * Q1`

Where:
Q1: Flow rate at the inlet.
Q2: Flow rate at one of the outlets.
Q3: Flow rate at the other outlet.
C2, C3: Flow split coefficients for the respective outlets.

Keep in mind that the exact equations and their complexity will depend on the specific characteristics of the mixing tee, the fluid properties, and the assumptions made in the analysis. In some cases, computational fluid dynamics (CFD) simulations may be required for a more accurate representation of the flow behavior within the mixing tee.

CASE setup-

CAD cleanup/Pre-processing- SpaceClaim.

The CAD model is imported into SpaceClaim to extract the flow volume field from the model. The extracted volume is shown below:

Mesh

The boundary names are applied in this section and a mesh is generated.

Setup

In this section, we apply different boundary conditions like inlet, and outlet boundary conditions. Turbulence models are set up like K-epsilon or K-omega for solving the turbulent mixing of air. The number of iterations is set in this section.

CFD-Post

Post-processing is carried out in this section in which different contours are set up to visualize the properties (such as Temperature, velocity etc.) for which simulation is run.

[For Moment ratio 2 and velocity is 3m/s^2 and using k-Omega)

MESH

For inlet velocity of 3m/s and momentum ratio of 2

Mesh size- 3mm

A mesh element metric that identifies the quality of mesh was employed and it can be seen that the elements of the lowest quality are minimal. Most of the elements have quality in the range of 0.6-1. Hence, the mesh is of acceptable quality.

CFD-Post

Post-processing is carried out in this section in which different contours are set up to visualize the properties (such as Temperature, velocity etc.) for which simulation is run. In this stage, we see the post results of the mixing tee simulation using the k-omegaa turbulence model and to make a plane along the XY axis to see the contour plots clearly.

The momentum ratio is 2.

Inlet velocity(x)=3m/s

Inlet velocity(y)=6m/s

Inlet temp(x)=

RESULTS:

Solution converged at 206

PLOTS:

RESIDUAL

STANDARD DEVIATION

TEMPERATURE

CONTOURS:

TEMPERATURE

VELOCITY

CASE 1- SHORT TEE

1. a) For inlet velocity of 3m/s and momentum ratio of 2

Mesh size- 3mm

A mesh element metric that identifies the quality of mesh was employed and it can be seen that the elements of the lowest quality are minimal. Most of the elements have quality in the range of 0.6-1. Hence, the mesh is of acceptable quality.

MESH

Cfd post:-

In this stage, we see the post results of the mixing tee simulation using the k-epsilon turbulence model and to make a plane along the XY axis to see the contour plots clearly.

The momentum ratio is 2.

Inlet velocity(x)=3m/s

Inlet velocity(y)=6m/s

Inlet temp(x)=

Inlet temp(y)=

PLOTS:

RESIDUAL

STANDARD DEVIATION

TEMPERATURE PLOT

CONTOURS:

TEMPERATURE:

VELOCITY:

[For Moment ratio 2 and velocity is 3m/s^2 and using k-omega)

MESH

Cfd post:-

In this stage, we see the post results of the mixing tee simulation using the k-epsilon turbulence model and to make a plane along the XY axis to see the contour plots clearly.

The momentum ratio is 4.

Inlet velocity(x)=3m/s

Inlet velocity(y)=12m/s

Inlet temp(x)=

Inlet temp(y)=

PLOTS:

RESIDUAL

STANDARD DEVIATION

TEMPERATURE PLOT

CONTOURS:

VELOCITY

TEMPERATURE:

RESULTS

The above contour plots are showing the diffusion of temperature and velocity with respect to the mesh size and momentum ratio value. A number of elements in the 104716, solution is converged at the 150th iteration. Area weighted average=33.6659 & Standard deviation=1.445488

CASE 2:

Long mixing tee with a hot inlet velocity of 3m/s.

Momentum ratio of 2, 4.

Momentum ratio = velocity at cold inlet / velocity at hot inlet

MESH: MESH SIZE OF 3mm

Cfd post:-

In this stage, we see the post results of the mixing tee simulation using the k-epsilon turbulence model and to make a plane along the XY axis to see the contour plots clearly.

The momentum ratio is 2.

Inlet velocity(x)=3m/s

Inlet velocity(y)=6m/s

Inlet temp(x)=

Inlet temp(y)=

PLOTS:

RESIDUAL

STANDARD DEVIATION

TEMPERATURE

CONTOURS:

TEMPERATURE

VELOCITY

Cfd post:-

In this stage, we see the post results of the mixing tee simulation using the k-epsilon turbulence model and to make a plane along the XY axis to see the contour plots clearly.

The momentum ratio is 4.

Inlet velocity(x)=3m/s

Inlet velocity(y)=12m/s

Inlet temp(x)=

Inlet temp(y)=

PLOTS:
RESIDUAL

STANDARD DEVIATION

TEMPERATURE

CONTOURS:

TEMPERATURE

VELOCITY

For the above simulation of long. tee with momentum ratio 4, using the k-epsilon turbulence model.

total cell count is 140990

mesh size is default- 3 and 4 mm

Area weighted average temperature- 28.09085degC

Standard deviation temperature- 0.8410328degC

Comparing all the results the long tee with momentum ratio 4 has a low standard deviation temperature.

CONCLUSION:

1. The resultant average temperature for both turbulence models Realizable K -Epsilon & K omega SST looks similar, but computing K omega SST takes more time and more number of iterations for convergence.
2. For both cases momentum ratios of 4, the outlet temperature drops significantly this occurs because of very high cold velocity air. So this clearly shows higher the momentum ratio greater the efficiency of the mixing.
3. We are getting an almost similar result for short tee & long tee for the momentum ratio of 4 from this we can get to know that the length of the pipe doesn't affect the efficiency of the pipe.
4. When it comes to standard deviation, the long tee gives a very lower value compared to the short tee. Indeed, we can increase high inlet cold air velocity for the application so we can get pretty good mixing in nature for a short pipe instead of using the long pipe.
5. If we increase velocity will get better turbulent mixing. majority of the mixing is because of higher velocity and as we go along the length of the pipe there is additional mixing that occurs because of diffusion.
6. And there is not much difference in the analytical outlet temperature and numerical outlet temperature
7. Overall, the short tee pipe gives a pretty good result, and also it saves material costs. Increasing the pipe length doesn't create any difference in the outlet temperature.